diff --git a/.github/workflows/make_docs.yaml b/.github/workflows/make_docs.yaml index 5afd21344..7e213ba2d 100644 --- a/.github/workflows/make_docs.yaml +++ b/.github/workflows/make_docs.yaml @@ -4,7 +4,7 @@ on: push: branches: - main - tags: + tags: - '*' pull_request: @@ -31,26 +31,23 @@ jobs: with: version: '1.11' - - name: Restore Julia cache + - name: Restore Julia cache (packages, artifacts, compiled, registries) uses: actions/cache@v4 with: - path: ~/.julia - key: ${{ runner.os }}-julia-${{ hashFiles('**/Project.toml') }} + path: | + ~/.julia/packages + ~/.julia/artifacts + ~/.julia/compiled + ~/.julia/registries + # include Manifest.toml so cache invalidates when resolved versions change + key: ${{ runner.os }}-julia-${{ hashFiles('**/Project.toml','**/Manifest.toml') }} restore-keys: | - ${{ runner.os }}-julia-${{ hashFiles('**/Project.toml') }} - - name: Download BLAS - run: sudo apt install -y libopenblas-dev - - name: Instantiate Julia environment - run: julia --project=. -e 'using Pkg; Pkg.instantiate()' + ${{ runner.os }}-julia-${{ hashFiles('**/Project.toml','**/Manifest.toml') }} + - name: Install system dependencies + run: sudo apt-get update && sudo apt-get install -y libopenblas-dev - - name: Build package - run: julia --project=. -e 'using Pkg; Pkg.build(); Pkg.precompile()' - - - name: Instantiate docs environment - run: julia --project=docs -e 'using Pkg; Pkg.instantiate()' - - - name: Add local package to docs environment - run: julia --project=docs -e 'using Pkg; Pkg.develop(PackageSpec(path="."))' + - name: Prepare docs environment (develop local package, then instantiate) + run: julia --project=docs -e 'using Pkg; Pkg.activate("docs"); Pkg.develop(PackageSpec(path=".")); Pkg.instantiate(update_registry=false)' - name: Build and deploy documentation env: diff --git a/.github/workflows/test.yaml b/.github/workflows/test.yaml index 7bb26b0bf..dbd6c0b3f 100644 --- a/.github/workflows/test.yaml +++ b/.github/workflows/test.yaml @@ -2,6 +2,8 @@ name: Build and Test Julia Package on: pull_request: + branches: + - main push: branches: - main @@ -19,19 +21,19 @@ jobs: with: version: '1.11' - - name: Restore Julia cache + - name: Restore Julia cache (packages, artifacts, compiled, registries) uses: actions/cache@v4 with: - path: ~/.julia - key: ${{ runner.os }}-julia-${{ hashFiles('**/Project.toml') }} + path: | + ~/.julia/packages + ~/.julia/artifacts + ~/.julia/compiled + ~/.julia/registries + # include Manifest.toml so cache invalidates when resolved versions change + key: ${{ runner.os }}-julia-${{ hashFiles('**/Project.toml','**/Manifest.toml') }} restore-keys: | - ${{ runner.os }}-julia-${{ hashFiles('**/Project.toml') }} - - name: Download BLAS - run: sudo apt install -y libopenblas-dev - - name: Instantiate Julia environment - run: julia --project=. -e 'using Pkg; Pkg.instantiate()' - - - name: Build package - run: julia --project=. -e 'using Pkg; Pkg.build(); Pkg.precompile()' - - name: Run tests - run: julia --project=. -e 'using Pkg; Pkg.test("JPEC")' \ No newline at end of file + ${{ runner.os }}-julia-${{ hashFiles('**/Project.toml','**/Manifest.toml') }} + - name: Install system dependencies + run: sudo apt-get update && sudo apt-get install -y libopenblas-dev + - name: Run tests (instantiate without registry update + test) + run: julia --project=. -e 'using Pkg; Pkg.activate("."); Pkg.instantiate(update_registry=false); include("test/runtests.jl")' diff --git a/.gitignore b/.gitignore index e3d11d7f2..d7a15741f 100644 --- a/.gitignore +++ b/.gitignore @@ -1,11 +1,15 @@ *.mod *.dylib -.vscode +*.dll +*.so *.o *.i -*.so +*.out +*.h5 +.vscode *.DS_Store -notebooks/*.in +.gitattributes Manifest.toml build.log -docs/build/ \ No newline at end of file +docs/build/ +anaconda_projects/ \ No newline at end of file diff --git a/Project.toml b/Project.toml index 10d982367..18d0108e0 100644 --- a/Project.toml +++ b/Project.toml @@ -1,17 +1,31 @@ name = "JPEC" uuid = "462872dd-e066-4d2e-b993-6468b5239634" -authors = ["Matthew Pharr ", "Rithik Banerjee ", "Jaebeom Cho "] +authors = ["Matthew Pharr ", "Rithik Banerjee ", "Jaebeom Cho ", "Jacob Halpern "] version = "0.1.0" license = 'MIT' [deps] +DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" +FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341" +HDF5 = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" +TOML = "fa267f1f-6049-4f14-aa54-33bafae1ed76" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [compat] +DiffEqCallbacks = "4.9.0" Documenter = "1.14.1" +FFTW = "1.9.0" +HDF5 = "0.17.2" +LinearAlgebra = "1.11.0" +OrdinaryDiffEq = "6.102.0" Pkg = "1.11.0" Plots = "1.40.15" -Test = "1.11.0" +Printf = "1.11.0" +TOML = "1.0.3" +Test = "1.11.0" \ No newline at end of file diff --git a/README.md b/README.md index f3d68aa5a..3565bf03a 100644 --- a/README.md +++ b/README.md @@ -1,28 +1,49 @@ -# JPEC +# Perturbed Equilibrium This is a work in progress juliafication of the Generalized Perturbed Equilibrium Code suite https://github.com/PrincetonUniversity/GPEC. -## Documentation +## Documentation Pages The WIP documentation can be found [here](https://openfusiontoolkit.github.io/JPEC/dev/). + + ## Developer Notes -### Commit messages +### GIT Workflow + +All developers need to use Vincent Driessen's [GitFlow](http://nvie.com/posts/a-successful-git-branching-model) workflow when editing the GPEC package. PLEASE READ THE ENTIRE POST. It is short, very thorough, and good for both experienced and new git users. + +The highlights are, + - There are two permanent branches: master and develop + - The master branch is only updated for at release ready stages + - New features should be developed in short-lived (days) branches coming off of and merging back to the development branch. + +Specific instructions are given in the link above as to exactly how to branch and merge these various branches. For example, the --no-ff option should be used when merging in order to keep branch histories. Just follow the examples and you wont go wrong! + +#### Using github + +Please see [this link](https://docs.google.com/document/d/1XAOTz1IV8ErZAAk-iSuEuddNOLB5XcoVZsAbPKRUUuA/edit?usp=sharing) for a guide on how to discuss your code development using github. + +#### Commit messages To assist with the process of compiling release notes, please confirm to the commit message format: ``` CODE - TAG - Detailed message ``` -where CODE is EQUIL, DCON, VAC, etc. and TAGs are short descriptors of the type of commit. Example tags might be WIP (work in progress), MINOR, IMPROVEMENT, BUG FIX, NEW FEATURE, etc. Look through old commits for examples of what tags are commonly used. +where CODE is EQUIL, DCON, VAC, etc. and TAGs are short descriptors of the type of commit. Example tags might be WIP (work in progress), MINOR, IMPROVEMENT, BUG FIX, NEW FEATURE, etc. Look through old commits for examples of what tags are commonly used. Again, this is currently used for the by-hand compilation of release notes. The tags thus need to be human readable but are not strictly inforced to be within some limited set. The objective is to allow a lead developer to skim through commits and pick out only the key new features / bug fixes / improvements to note in the release while not having to read all the work-in-progress or minor changes. -### Code Formatting +### Julia Tips + +#### Revise -To retain consistency in code formatting, we request that all PRs include code formatting cleanup before merging. We will make use of [JuliaFormatter.jl](https://domluna.github.io/JuliaFormatter.jl/stable/), which can be used in both Vim and VSCode. For Vim installation, follow the instructions [here](https://github.com/kdheepak/JuliaFormatter.vim). In VSCode, the [Julia](https://www.julia-vscode.org/docs/dev/userguide/formatter/) extension has built-in capabiltiies for JuliaFormatter.jl. The [folder formatter](https://marketplace.visualstudio.com/items?itemName=MichaKaleta.folderformatter&ssr=false#overview) extension allows formatting of all files within a given folder, which can be useful for larger commits. +When developing and recompiling code often, use Revise.jl to speed up the compile times by only recompiling what is impacted by the changed code. Integrate Revise.jl into your default Julia environment for use across projects, do not directly add it to the Project.toml of this particular project. To install Revise.jl in your global environment, open the Julia REPL using the `julia` command, enter the package manager by pressing `]`, and then `add Revise`: -The JuliaFormatter.toml file contains the default settings we will use; this should not be changed unless reformatting the entire repository. +Code -### Using github + $ julia + julia> ] + pkg> add Revise -Please see [this link](https://docs.google.com/document/d/1XAOTz1IV8ErZAAk-iSuEuddNOLB5XcoVZsAbPKRUUuA/edit?usp=sharing) for a guide on how to discuss your code development using github. +Now, in the top of each Jupyter notebook, you can call `using Revise` at the top of any Jupyter notebook to speed up compile times as you develop and test. Better yet, set up your environement to [use Revise by default](https://timholy.github.io/Revise.jl/stable/config/#Using-Revise-by-default) \ No newline at end of file diff --git a/build_docs_local.jl b/build_docs_local.jl index 805509f90..ffab6ab21 100644 --- a/build_docs_local.jl +++ b/build_docs_local.jl @@ -8,7 +8,7 @@ Pkg.instantiate() # Build the package Pkg.build() -# Activate and instantiate the docs environment +# Activate and instantiate the docs environment Pkg.activate("docs") Pkg.instantiate() diff --git a/deps/build.jl b/deps/build.jl index bf60a9b6e..2c5f6ed21 100644 --- a/deps/build.jl +++ b/deps/build.jl @@ -6,82 +6,9 @@ const parent_dir = joinpath(@__DIR__, "..", "src") +include(joinpath(@__DIR__, "build_helpers.jl")) + export build_fortran export build_spline_fortran, build_vacuum_fortran -function build_fortran() - ENV["FC"] = get(ENV, "FC", "gfortran") - # Set OS-dependent flags - if Sys.isapple() - ENV["LIBS"] = "-framework Accelerate" - ENV["LIBSUFFIX"] = ".dylib" - elseif Sys.islinux() - ENV["LIBS"] = "-lopenblas" - ENV["LIBSUFFIX"] = ".so" - elseif Sys.iswindows() - ENV["LIBS"] = "-lopenblas" - ENV["LIBSUFFIX"] = ".dll" - else - error("Unsupported OS for Fortran build") - end - ENV["RECURSFLAG"] = "-frecursive" - ENV["LEGACYFLAG"] = "-std=legacy" - ENV["ZEROFLAG"] = "-finit-local-zero" - ENV["FFLAGS"] = "-fPIC" - ENV["LDFLAGS"] = "-shared" - - results = [ - # build_jpec_fortran() add here - build_spline_fortran(), - build_vacuum_fortran() - ] - - if all(results) - @info "All Fortran builds succeeded!" - else - @error "Some Fortran builds failed." - end - -end - -function build_spline_fortran() - dir = joinpath(parent_dir, "Splines", "fortran") - try - run(pipeline(`make -C $dir`)) - @info "Splines-fortran compiled well" - return true - catch e - @error "Failed to build Splines-fortran: $e" - return false - end -end - -function build_vacuum_fortran() - dir = joinpath(parent_dir, "Vacuum", "fortran") - try - run(pipeline(`make -C $dir`)) - @info "Vacuum-fortran compiled well" - return true - catch e - @error "Failed to build Vacuum-fortran: $e" - return false - end - -end - -# Example for including more fortran: -# -# function build_jpec_fortran() -# dir = joinpath(parent_dir, "Gpec", "fortran") -# try -# run(pipeline(`make -C $dir`, stdout=DevNull, stderr=DevNull)) -# println("Gpec-fortran compiled well") -# return true -# catch e -# println("Failed to build Gpec-fortran: $e") -# return false -# end -# end - - build_fortran() # Call the build function to execute the builds \ No newline at end of file diff --git a/deps/build_helpers.jl b/deps/build_helpers.jl new file mode 100644 index 000000000..215cfa2bb --- /dev/null +++ b/deps/build_helpers.jl @@ -0,0 +1,85 @@ +# How to modify build_helpers.jl: +# 1) Declare build functions for each Fortran codes as 'build_*_fortran()' +# 2) Add these functions to the results array in build_fortran() +# 3) Export the functions you want to be accessible from outside + + +const parent_dir = joinpath(@__DIR__, "..", "src") + +export build_spline_fortran, build_vacuum_fortran + +function build_fortran() + ENV["FC"] = get(ENV, "FC", "gfortran") + # Set OS-dependent flags + println("Setting up environment for ", Sys.KERNEL) + if Sys.isapple() + ENV["LIBS"] = "-framework Accelerate" + ENV["LIBSUFFIX"] = ".dylib" + elseif Sys.islinux() + ENV["LIBS"] = "-lopenblas" + ENV["LIBSUFFIX"] = ".so" + elseif Sys.iswindows() + ENV["LIBS"] = "-lopenblas" + ENV["LIBSUFFIX"] = ".dll" + else + error("Unsupported OS for Fortran build") + end + ENV["RECURSFLAG"] = "-frecursive" + ENV["LEGACYFLAG"] = "-std=legacy" + ENV["ZEROFLAG"] = "-finit-local-zero" + ENV["FFLAGS"] = "-fPIC" + ENV["LDFLAGS"] = "-shared" + + results = [ + # build_jpec_fortran() add here + build_spline_fortran(), + build_vacuum_fortran(), + ] + + if all(results) + @info "All Fortran builds succeeded!" + else + @error "Some Fortran builds failed." + end + +end + +function build_spline_fortran() + dir = joinpath(parent_dir, "Splines", "fortran") + try + run(pipeline(`make -C $dir`)) + @info "Splines-fortran compiled well" + return true + catch e + @error "Failed to build Splines-fortran: $e" + return false + end +end + +function build_vacuum_fortran() + dir = joinpath(parent_dir, "Vacuum", "fortran") + try + run(pipeline(`make -C $dir`)) + @info "Vacuum-fortran compiled well" + return true + catch e + @error "Failed to build Vacuum-fortran: $e" + return false + end + +end + +# Example for including more fortran: +# +# function build_jpec_fortran() +# dir = joinpath(parent_dir, "Gpec", "fortran") +# try +# run(pipeline(`make -C $dir`, stdout=DevNull, stderr=DevNull)) +# println("Gpec-fortran compiled well") +# return true +# catch e +# println("Failed to build Gpec-fortran: $e") +# return false +# end +# end + diff --git a/docs/Project.toml b/docs/Project.toml index e2d55ee0e..a0026afa7 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -1,5 +1,6 @@ [deps] Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" +JPEC = "462872dd-e066-4d2e-b993-6468b5239634" [compat] Documenter = "1.0" diff --git a/docs/make.jl b/docs/make.jl index f7e40eeef..556d7f21c 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -24,7 +24,8 @@ makedocs(; "Home" => "index.md", "API Reference" => [ "Splines" => "splines.md", - "Vacuum" => "vacuum.md" + "Vacuum" => "vacuum.md", + "Equilibrium" => "equilibrium.md" ], "Examples" => [ "Spline Examples" => "examples/splines.md", diff --git a/docs/src/equilibrium.md b/docs/src/equilibrium.md new file mode 100644 index 000000000..ab4b486ce --- /dev/null +++ b/docs/src/equilibrium.md @@ -0,0 +1,116 @@ +# Equilibrium Module + +The Equilibrium module provides tools to read, construct, and analyze +magnetohydrodynamic (MHD) plasma equilibria. It wraps a variety of +equilibrium file formats (EFIT, CHEASE, SOL, LAR, and others), runs the +appropriate direct or inverse solver, and returns a processed +`PlasmaEquilibrium` object ready for downstream calculations. + +## Overview + +Key responsibilities of the module: + +- Read equilibrium input files and TOML configuration (see `EquilibriumConfig`). +- Provide convenient constructors for analytic / model equilibria (Large + Aspect Ratio, Solev'ev). +- Build spline representations used throughout the code (1D cubic and + 2D bicubic splines). +- Run the direct or inverse equilibrium solver and post-process results + (global parameters, q-profile finding, separatrix finding, GSE checks). + +The module exposes a small public API that covers setup, configuration, +and common analyses used by other JPEC components (e.g. `DCON`, vacuum +interfaces). + +## API Reference + +```@autodocs +Modules = [JPEC.Equilibrium] +``` + +## Important types + +- `EquilibriumConfig` — top-level configuration container parsed from a + TOML file (outer constructor `EquilibriumConfig(path::String)` is + provided). +- `EquilibriumControl` — low-level control parameters (grid, jacobian + type, tolerances, etc.). +- `EquilibriumOutput` — options controlling what output is written. +- `PlasmaEquilibrium` — the runtime structure containing spline fields, + geometry, profiles, and computed diagnostics (q-profile, separatrix, + etc.). +- `LargeAspectRatioConfig`, `SolevevConfig` — convenience structs to + construct analytic/model equilibria when using `eq_type = "lar"` or + `eq_type = "sol"`. + +## Key functions + +- `setup_equilibrium(path::String = "equil.toml")` + — main entry point that reads configuration, builds the equilibrium, + runs the solver, and returns a `PlasmaEquilibrium` instance. +- `equilibrium_separatrix_find!(pe::PlasmaEquilibrium)` — locate + separatrix and related boundary geometry in-place. +- `equilibrium_global_parameters!(pe::PlasmaEquilibrium)` — populate + common global parameters (major radius, magnetic axis, volumes, etc.). +- `equilibrium_qfind!(pe::PlasmaEquilibrium)` — compute safety factor + (q) information across the grid. +- `equilibrium_gse!(pe::PlasmaEquilibrium)` — diagnostics on the + Grad–Shafranov solution. + +## Example usage + +Basic example: read a TOML config and build an equilibrium + +```julia +using JPEC + +# Build from a TOML file (searches relative paths if needed) +pe = JPEC.Equilibrium.setup_equilibrium("docs/examples/dcon.toml") + +println("Magnetic axis: ", pe.params.r0, ", ", pe.params.z0) +println("q(0) = ", pe.params.q0) + +# Find separatrix (in-place) and inspect results +JPEC.Equilibrium.equilibrium_separatrix_find!(pe) +println("rsep = ", pe.params.rsep) +``` + +Analytic / testing example: construct a large-aspect-ratio model + +```julia +using JPEC + +# Create a LAR config from a small TOML fragment or file +larcfg = JPEC.Equilibrium.LargeAspectRatioConfig(lar_r0=10.0, lar_a=1.0, beta0=1e-3) +pe = JPEC.Equilibrium.setup_equilibrium(JPEC.Equilibrium.EquilibriumConfig(control=Dict("eq_filename"=>"unused","eq_type"=>"lar")), larcfg) + +println("Built LAR equilibrium with a = ", lorcfg.lar_a) +``` + +Notes: + +- The `EquilibriumConfig(path::String)` constructor parses TOML and + expects `[EQUIL_CONTROL]` to contain at minimum `eq_filename` and + `eq_type` fields. Paths that are not absolute are resolved relative + to the TOML file location. +- When `eq_type == "inverse_testing"` a small example inverse run is + constructed (useful in tests and examples). + +## Notes and Caveats + +- Many routines rely on spline representations; the `Splines` module is + used heavily and should be initialized where appropriate. +- The Equilibrium module contains several reader routines for external + formats (EFIT/CHEASE) and also interfaces to older Fortran helpers — + ensure required data files are present for those backends. +- For programmatic usage, prefer constructing `EquilibriumConfig` from a + TOML file to ensure all path resolution and defaults are handled. + +## See also + +- `docs/src/splines.md` — spline helpers used by equilibrium routines +- `docs/src/vacuum.md` — coupling between equilibrium and vacuum solvers + +``` + + diff --git a/docs/src/examples/splines.md b/docs/src/examples/splines.md index 6be5da3d5..7401039da 100644 --- a/docs/src/examples/splines.md +++ b/docs/src/examples/splines.md @@ -18,7 +18,7 @@ fc = cos.(xs) fs_matrix = hcat(fs, fc) # Set up spline for 2 quantities -spline = JPEC.SplinesMod.spline_setup(xs, fs_matrix, 2) +spline = JPEC.SplinesMod.CubicSpline(xs, fs_matrix, 2) # Evaluate on fine grid xs_fine = collect(range(0.0, stop=2π, length=100)) @@ -43,7 +43,7 @@ fp = exp.(im .* xs) # e^(ix) fs_matrix = hcat(fm, fp) # Set up complex spline -spline = JPEC.SplinesMod.spline_setup(xs, fs_matrix, 2) +spline = JPEC.SplinesMod.CubicSpline(xs, fs_matrix, 2) # Evaluate xs_fine = collect(range(0.0, stop=2π, length=100)) @@ -83,7 +83,7 @@ ys_fine = collect(range(0.0, stop=2π, length=100)) fs_fine = JPEC.SplinesMod.bicube_eval(bcspline, xs_fine, ys_fine) # Create contour plot -contourf(xs_fine, ys_fine, fs_fine[:, :, 1]', +contourf(xs_fine, ys_fine, fs_fine[:, :, 1]', title="Bicubic Spline: sin(x)cos(y) + 1") ``` @@ -108,7 +108,7 @@ This example shows spline usage with the Solov'ev equilibrium: ```julia # Create equilibrium parameters kappa = 1.8 # elongation -a = 1.0 # minor radius +a = 1.0 # minor radius r0 = 3.5 # major radius q0 = 1.25 # safety factor @@ -140,8 +140,8 @@ zs_fine = collect(range(zmin, stop=zmax, length=100)) psi_fine = JPEC.SplinesMod.bicube_eval(psi_spline, rs_fine, zs_fine) # Create contour plot -contourf(rs_fine, zs_fine, psi_fine[:, :, 1]', - title="Ψ: Solov'ev Equilibrium", +contourf(rs_fine, zs_fine, psi_fine[:, :, 1]', + title="Ψ: Solov'ev Equilibrium", xlabel="R", ylabel="Z", aspect_ratio=:equal) ``` diff --git a/docs/src/examples/vacuum.md b/docs/src/examples/vacuum.md index 4f857ad35..0ed3babb1 100644 --- a/docs/src/examples/vacuum.md +++ b/docs/src/examples/vacuum.md @@ -21,7 +21,7 @@ qa1in = 1.23 # Safety factor parameter # Create geometry arrays n_modes = lmax - lmin + 1 xin = rand(Float64, n_modes) # Radial coordinates -zin = rand(Float64, n_modes) # Vertical coordinates +zin = rand(Float64, n_modes) # Vertical coordinates deltain = rand(Float64, n_modes) # Displacement data # Initialize DCON interface @@ -41,7 +41,7 @@ wv = zeros(ComplexF64, mpert, mpert) # Calculation flags complex_flag = true # Use complex arithmetic -kernelsignin = -1.0 # Kernel sign +kernelsignin = -1.0 # Kernel sign wall_flag = false # Include wall effects farwal_flag = true # Far wall approximation @@ -67,17 +67,17 @@ println("Result matrix dimensions: ", size(wv)) using Plots # Plot magnitude of vacuum matrix elements -heatmap(abs.(wv), +heatmap(abs.(wv), title="Vacuum Matrix |W| Elements", - xlabel="Mode j", + xlabel="Mode j", ylabel="Mode i", color=:plasma) # Plot phase information -heatmap(angle.(wv), +heatmap(angle.(wv), title="Vacuum Matrix Phase", xlabel="Mode j", - ylabel="Mode i", + ylabel="Mode i", color=:phase) ``` @@ -158,7 +158,7 @@ println("Most unstable eigenvalue: ", eigenvals[max_growth_idx]) ```julia # For large problems, consider: # - Reducing mtheta/mthvac if possible -# - Using real arithmetic (complex_flag=false) when appropriate +# - Using real arithmetic (complex_flag=false) when appropriate # - Parallelization (if available in Fortran backend) # Monitor memory usage @@ -166,7 +166,7 @@ using Pkg Pkg.add("BenchmarkTools") using BenchmarkTools -@time JPEC.VacuumMod.mscvac(wv, mpert, mtheta, mthvac, +@time JPEC.VacuumMod.mscvac(wv, mpert, mtheta, mthvac, complex_flag, kernelsignin, wall_flag, farwal_flag, grrio, xzptso) diff --git a/docs/src/index.md b/docs/src/index.md index a572bf5c7..4cbd24e7b 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -28,7 +28,7 @@ using JPEC ## Modules ```@contents -Pages = ["splines.md", "vacuum.md"] +Pages = ["splines.md", "vacuum.md", "equilibrium.md"] Depth = 1 ``` diff --git a/docs/src/splines.md b/docs/src/splines.md index 287043fd3..e1aaf73ad 100644 --- a/docs/src/splines.md +++ b/docs/src/splines.md @@ -30,9 +30,9 @@ Represents a Fourier spline interpolation object for decomposed data. ## Functions -### spline_setup +### CubicSpline ```@docs -JPEC.SplinesMod.spline_setup +JPEC.SplinesMod.CubicSpline ``` ### spline_eval @@ -40,9 +40,9 @@ JPEC.SplinesMod.spline_setup JPEC.SplinesMod.spline_eval ``` -### bicube_setup +### BicubicSpline ```@docs -JPEC.SplinesMod.bicube_setup +JPEC.SplinesMod.BicubicSpline ``` ### bicube_eval @@ -50,6 +50,16 @@ JPEC.SplinesMod.bicube_setup JPEC.SplinesMod.bicube_eval ``` +### FourierSpline +```@docs +JPEC.SplinesMod.FourierSpline +``` + +### fspline_eval +```@docs +JPEC.SplinesMod.fspline_eval +``` + ## Example Usage ### 1D Cubic Spline @@ -61,7 +71,7 @@ xs = collect(range(0.0, stop=2π, length=21)) fs = sin.(xs) # Set up spline (1 quantity) -spline = JPEC.SplinesMod.spline_setup(xs, hcat(fs), 1) +spline = JPEC.SplinesMod.CubicSpline(xs, hcat(fs), 1) # Evaluate at new points xs_fine = collect(range(0.0, stop=2π, length=100)) @@ -81,7 +91,7 @@ for i in 1:20, j in 1:20 end # Set up bicubic spline -bcspline = JPEC.SplinesMod.bicube_setup(xs, ys, fs, 1, 1) +bcspline = JPEC.SplinesMod.BicubicSpline(xs, ys, fs, 1, 1) # Evaluate with derivatives x_eval, y_eval = π/2, π/4 diff --git a/docs/src/vacuum.md b/docs/src/vacuum.md index 801beb16c..7adcb4cb7 100644 --- a/docs/src/vacuum.md +++ b/docs/src/vacuum.md @@ -36,7 +36,7 @@ using JPEC mthin, lmin, lmax, nnin = Int32(4), Int32(1), Int32(4), Int32(2) qa1in = 1.23 xin = rand(Float64, lmax - lmin + 1) -zin = rand(Float64, lmax - lmin + 1) +zin = rand(Float64, lmax - lmin + 1) deltain = rand(Float64, lmax - lmin + 1) # Initialize DCON interface diff --git a/notebooks/Chease_Binary_example/INP1 b/notebooks/Chease_Binary_example/INP1 new file mode 100644 index 000000000..7a39ceeab Binary files /dev/null and b/notebooks/Chease_Binary_example/INP1 differ diff --git a/notebooks/Chease_Binary_example/equil.toml b/notebooks/Chease_Binary_example/equil.toml new file mode 100644 index 000000000..e75c90ec2 --- /dev/null +++ b/notebooks/Chease_Binary_example/equil.toml @@ -0,0 +1,30 @@ +[EQUIL_CONTROL] +eq_type = "chease" # Type of the input 2D equilibrium file +eq_filename = "INP1" # path to equilibrium file + +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) +power_bp = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r +power_b = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r +power_r = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r + +grid_type = "ldp" # Radial grid packing +psilow = 1e-4 # Min psi (normalized) +psihigh = 0.993 # Max psi (normalized) +mpsi = 128 # Radial grid intervals +mtheta = 256 # Poloidal grid intervals + +newq0 = 0 # Override q(0) +etol = 1e-7 # Reconstruction tolerance +use_classic_splines = false # Use classical spline (vs. tri-diagonal) + +input_only = false # Quit after input read + +[EQUIL_OUTPUT] +gse_flag = false # Output G-S equation accuracy diagnostics +out_eq_1d = false # ASCII output of 1D eq data +bin_eq_1d = false # Binary output of 1D eq data +out_eq_2d = false # ASCII output of 2D eq data +bin_eq_2d = true # Binary output of 2D eq data (used by GPEC) +out_2d = false # ASCII output of processed 2D data +bin_2d = false # Binary output of processed 2D data +dump_flag = false # Binary dump of equilibrium data diff --git a/notebooks/DIIID_example/dcon.toml b/notebooks/DIIID_example/dcon.toml new file mode 100644 index 000000000..a0a93c8bf --- /dev/null +++ b/notebooks/DIIID_example/dcon.toml @@ -0,0 +1,62 @@ +[DCON_CONTROL] +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +mat_flag = true # Construct coefficient matrices for diagnostic purposes +ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +vac_flag = true # Compute plasma, vacuum, and total energies for free-boundary modes +mer_flag = true # Evaluate the Mercier criterian + +sas_flag = true # Safety factor (q) limit determined as q_ir+dmlim... +dmlim = 0.2 # See sas_flag +psiedge = 1.00 # If less then psilim, calculates dW(psi)... +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) + +nn = 1 # Toroidal mode number +delta_mlow = 8 # Expands lower bound of Fourier harmonics +delta_mhigh = 8 # Expands upper bound of Fourier harmonics +delta_mband = 0 # Integration keeps only this wide a band... +mthvac = 512 # Number of points used in splines over poloidal angle at plasma-vacuum interface. +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds + +kin_flag = false # Kinetic EL equation (default: false) +con_flag = false # Continue integration through layers (default: false) +kinfac1 = 1.0 # Scale factor for energy contribution (default: 1.0) +kinfac2 = 1.0 # Scale factor for torque contribution (default: 1.0) +kingridtype = 0 # Regular grid method (default: 0) +passing_flag = true # Includes passing particle effects (default: false) +ktanh_flag = true # Ignore kinetic effects in the core smoothly (default: false) +ktc = 0.1 # Parameter for ktanh_flag (default: 0.1) +ktw = 50.0 # Parameter for ktanh_flag (default: 50.0) +ion_flag = true # Include ion dW_k when kin_flag is true +electron_flag = false # Include electron dW_k when kin_flag is true + +tol_nr = 1e-6 # Relative tolerance of dynamic integration steps away from rationals +tol_r = 1e-7 # Relative tolerance of dynamic integration steps near rationals +crossover = 1e-2 # Fractional distance from rational q at which tol switches +singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced +ucrit = 1e4 # Maximum fraction of solutions allowed before re-normalized + +numunorms_init = 30 # Storage size for unorming data + +termbycross_flag = false # Terminate ODE solver in the event of a zero crossing + +use_classic_splines = false # Use a classical cubic spline instead of tri-diagonal solution + +[DCON_OUTPUT] +out_ahg2msc = false # Output deprecated ahg2msc.out files +crit_break = true # Color of the crit curve changes when crossing a singular surface +ahb_flag = false # Output normal magnetic field eigenvalues... +msol_ahb = 1 # Number of eigenfunctions output by ahb_flag = true? +mthsurf0 = 1 # Linear multiplier on number of boundary points for ahgb_flag = true + +bin_euler = true # Output M psi-by-M euler-lagrange solutions to binary file euler.bin +bin_vac = false # Output deprecated binary vacuum.bin +euler_stride = 1 # Output only every euler_stride'th psi step + +out_bal1 = false # Ascii output for bal_flag poloidal functions +bin_bal1 = false # Binary output for bal_flag poloidal functions +out_bal2 = false # Ascii output for bal_flag functions +bin_bal2 = false # Binary output for bal_flag functions + +netcdf_out = true # Replicate ascii dcon.out information in a netcdf file \ No newline at end of file diff --git a/notebooks/DIIID_example/equil.toml b/notebooks/DIIID_example/equil.toml new file mode 100644 index 000000000..0b230bdd5 --- /dev/null +++ b/notebooks/DIIID_example/equil.toml @@ -0,0 +1,30 @@ +[EQUIL_CONTROL] +eq_type = "efit" # Type of the input 2D equilibrium file +eq_filename = "g147131.02300_DIIID_KEFIT" # path to equilibrium file + +jac_type = "hamada" # Coordinate system (hamada, pest, boozer, equal_arc) +power_bp = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r +power_b = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r +power_r = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r + +grid_type = "ldp" # Radial grid packing +psilow = 1e-4 # Min psi (normalized) +psihigh = 0.993 # Max psi (normalized) +mpsi = 128 # Radial grid intervals +mtheta = 256 # Poloidal grid intervals + +newq0 = 0 # Override q(0) +etol = 1e-7 # Reconstruction tolerance +use_classic_splines = false # Use classical spline (vs. tri-diagonal) + +input_only = false # Quit after input read + +[EQUIL_OUTPUT] +gse_flag = false # Output G-S equation accuracy diagnostics +out_eq_1d = false # ASCII output of 1D eq data +bin_eq_1d = false # Binary output of 1D eq data +out_eq_2d = false # ASCII output of 2D eq data +bin_eq_2d = true # Binary output of 2D eq data (used by GPEC) +out_2d = false # ASCII output of processed 2D data +bin_2d = false # Binary output of processed 2D data +dump_flag = false # Binary dump of equilibrium data diff --git a/notebooks/DIIID_example/g147131.02300_DIIID_KEFIT b/notebooks/DIIID_example/g147131.02300_DIIID_KEFIT new file mode 100644 index 000000000..15da8c793 --- /dev/null +++ b/notebooks/DIIID_example/g147131.02300_DIIID_KEFIT @@ -0,0 +1,6668 @@ + EFITD 03/13/2012 #147131 2300ms 3 129 129 + 0.170000000E+01 0.320000000E+01 0.169550002E+01 0.840000000E+00 0.000000000E+00 + 0.175888032E+01 0.244191348E-01-0.299591296E+00-0.373057194E-01-0.172279610E+01 + 0.118663454E+07-0.299591296E+00 0.000000000E+00 0.175888032E+01 0.000000000E+00 + 0.244191348E-01 0.000000000E+00-0.373057194E-01 0.000000000E+00 0.000000000E+00 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0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + FFTENS = 2.000000000000000 , + KWWFNC = 0, + KWWKNT = 0, + WWKNT = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + WWTENS = 0.000000000000000 , + PPBDRY = 620844.4103959909 , + 158313.5777226928 , + 141414.5129313806 , + 315668.7249493082 , + 448281.5092263866 , + 664288.9511872320 , + 407224.0308621362 , + 179728.4116576705 , + 108641.8366059566 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + PP2BDRY = 22932171.22922356 , + 5868728.220783956 , + -3474615.074536501 , + 167982639.2419721 , + 1151513694.066376 , + -2048012171.209169 , + -110552274.9895208 , + 1442826158.424312 , + -3600231013.000693 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + KPPBDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + KPP2BDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + FFBDRY = 0.9114307588631456 , + 0.5211455287937966 , + 0.2368879341631518 , + -0.1298418203475191 , + -0.3325109793088990 , + -0.6697285434882476 , + -0.5566780385014780 , + -0.3060984383688860 , + -0.2002143303358702 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + FF2BDRY = -99.07288472601269 , + 0.1704819144219263 , + 3.385019078475219 , + -232.5891067997149 , + -1623.631644131465 , + 2326.759872403892 , + 324.3915798601789 , + -148.7293255361868 , + -1365.687572250405 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + KFFBDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + KFF2BDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + WWBDRY = 753378.4125525327 , + 1254.750893700115 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + WW2BDRY = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + KWWBDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + KWW2BDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + KEEFNC = 0, + KEEKNT = 0, + EEKNT = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + EETENS = 5.000000000000000 , + EEBDRY = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + EE2BDRY = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + KEEBDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + KEE2BDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + / + &MSEOUT + RRRGAM = 1.519000053405762 , + 1.570000052452087 , + 1.620000004768372 , + 1.669999957084656 , + 1.718999981880188 , + 1.768000006675720 , + 1.819000005722046 , + 1.871000051498413 , + 1.919999957084656 , + 1.973000049591064 , + 2.022000074386597 , + 1.980999946594238 , + 2.030999898910522 , + 2.075000047683716 , + 2.119999885559082 , + 2.157999992370605 , + 2.196000099182129 , + 2.240000009536743 , + 2.243000030517578 , + 2.246000051498413 , + 2.250000000000000 , + 2.253000020980835 , + 2.256000041961670 , + 2.259999990463257 , + 2.263000011444092 , + 2.266000032424927 , + 1.689000010490417 , + 1.733000040054321 , + 1.779999971389771 , + 1.822999954223633 , + 1.868000030517578 , + 1.912999987602234 , + 1.955999970436096 , + 2.000999927520752 , + 2.046999931335449 , + 2.095000028610229 , + 1.583999991416931 , + 1.628999948501587 , + 1.679000020027161 , + 1.730000019073486 , + 2.069000005722046 , + 2.117000102996826 , + 2.176000118255615 , + 2.243999958038330 , + 2.328000068664551 , + 1.697000026702881 , + 1.741999983787537 , + 1.786999940872192 , + 1.832000017166138 , + 1.876000046730042 , + 1.919000029563904 , + 1.963000059127808 , + 2.007999897003174 , + 2.029000043869019 , + 2.069999933242798 , + 2.109999895095825 , + 2.148000001907349 , + 2.184999942779541 , + 2.217999935150146 , + 2.236000061035156 , + 2.242000102996826 , + 2.247999906539917 , + 2.253999948501587 , + 2.259000062942505 , + 2.265000104904175 , + 2.269999980926514 , + 2.276999950408936 , + 2.282999992370605 , + 2.288000106811523 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + ZZZGAM = -2.5000000372529030E-002, + -2.3000000044703484E-002, + -1.7000000923871994E-002, + -1.3000000268220901E-002, + -1.2000000104308128E-002, + -9.9999997764825821E-003, + -7.0000002160668373E-003, + -2.0000000949949026E-003, + -2.0000000949949026E-003, + 3.0000000260770321E-003, + -4.9999998882412910E-003, + 1.0999999940395355E-002, + 1.2000000104308128E-002, + 6.0000000521540642E-003, + 6.0000000521540642E-003, + 6.0000000521540642E-003, + 4.9999998882412910E-003, + 6.0000000521540642E-003, + 8.0000003799796104E-003, + 8.9999996125698090E-003, + 7.0000002160668373E-003, + 4.9999998882412910E-003, + 8.0000003799796104E-003, + 6.0000000521540642E-003, + 6.0000000521540642E-003, + 7.0000002160668373E-003, + -7.0000002160668373E-003, + -1.2000000104308128E-002, + -8.9999996125698090E-003, + -8.0000003799796104E-003, + -6.0000000521540642E-003, + -8.9999996125698090E-003, + -2.0000000949949026E-003, + 0.000000000000000 , + 2.0000000949949026E-003, + 2.0000000949949026E-003, + -1.2000000104308128E-002, + -9.9999997764825821E-003, + -8.9999996125698090E-003, + -4.9999998882412910E-003, + -3.0000000260770321E-003, + 2.0000000949949026E-003, + 4.0000001899898052E-003, + 1.0000000474974513E-003, + 0.000000000000000 , + -5.0999999046325684E-002, + -4.6999998390674591E-002, + -4.3000001460313797E-002, + -3.9000000804662704E-002, + -3.4000001847743988E-002, + -3.9999999105930328E-002, + -3.9999999105930328E-002, + -4.1000001132488251E-002, + 3.2000001519918442E-002, + 3.5999998450279236E-002, + 3.9999999105930328E-002, + 4.3999999761581421E-002, + 4.8000000417232513E-002, + 5.4000001400709152E-002, + 4.6999998390674591E-002, + 4.6999998390674591E-002, + 4.3000001460313797E-002, + 4.3000001460313797E-002, + 4.6999998390674591E-002, + 4.8000000417232513E-002, + 4.6999998390674591E-002, + 4.6999998390674591E-002, + 4.6999998390674591E-002, + 4.6999998390674591E-002, + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + AA1GAM = -0.6313996900000000 , + -0.6530994800000000 , + -0.6723998799999999 , + -0.6893998400000000 , + -0.7052001400000000 , + -0.7192996699999999 , + -0.7327996500000000 , + -0.7457004800000000 , + -0.7569004300000000 , + -0.7678999300000000 , + -0.7775996300000000 , + 0.7204002100000000 , + 0.6924998200000000 , + 0.6648001100000001 , + 0.6345999200000000 , + 0.6058998700000000 , + 0.5760001500000000 , + 0.5373997700000001 , + 0.5349999100000000 , + 0.5319002900000001 , + 0.5279999399999999 , + 0.5256003100000000 , + 0.5223999600000000 , + 0.5191001300000000 , + 0.5158997800000000 , + 0.5133996600000000 , + 0.8473002300000000 , + 0.8274996900000000 , + 0.8026999800000000 , + 0.7761001000000000 , + 0.7433001400000000 , + 0.7047997700000000 , + 0.6615998700000000 , + 0.6096000100000000 , + 0.5471997300000000 , + 0.4711996600000000 , + -0.6588998400000000 , + -0.6755997500000001 , + -0.6926001899999999 , + -0.7084003700000000 , + -0.7863999000000000 , + -0.7946000700000000 , + -0.8041995800000000 , + -0.8143997800000000 , + -0.8256999300000000 , + 0.8306999800000000 , + 0.8165002500000000 , + 0.8007000700000000 , + 0.7835999100000000 , + 0.7653003900000001 , + 0.7456001600000000 , + 0.7234000600000000 , + 0.6991998000000000 , + 0.6865001900000000 , + 0.6609997200000000 , + 0.6334000200000000 , + 0.6053004300000000 , + 0.5753001599999999 , + 0.5466996400000000 , + 0.5303997400000000 , + 0.5249003200000000 , + 0.5193003400000000 , + 0.5135998100000000 , + 0.5086001800000000 , + 0.5027999900000000 , + 0.4986000100000000 , + 0.4918001900000000 , + 0.4857998200000000 , + 0.4806002100000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + AA2GAM = 0.6500999927520752 , + 0.6779000163078308 , + 0.7016999721527100 , + 0.7221999764442444 , + 0.7408000230789185 , + 0.7570999860763550 , + 0.7723000049591064 , + 0.7864000201225281 , + 0.7986000180244446 , + 0.8101999759674072 , + 0.8203999996185303 , + 0.8127999901771545 , + 0.8227999806404114 , + 0.8312000036239624 , + 0.8388000130653381 , + 0.8450999855995178 , + 0.8507000207901001 , + 0.8569999933242798 , + 0.8572999835014343 , + 0.8578000068664551 , + 0.8583999872207642 , + 0.8587999939918518 , + 0.8592000007629395 , + 0.8597000241279602 , + 0.8600999712944031 , + 0.8604999780654907 , + 0.7304000258445740 , + 0.7458999752998352 , + 0.7610999941825867 , + 0.7738000154495239 , + 0.7860000133514404 , + 0.7969999909400940 , + 0.8072000145912170 , + 0.8166999816894531 , + 0.8256999850273132 , + 0.8342999815940857 , + 0.6848999857902527 , + 0.7053999900817871 , + 0.7260000109672546 , + 0.7444000244140625 , + 0.8294000029563904 , + 0.8375999927520752 , + 0.8470000028610229 , + 0.8569999933242798 , + 0.8677999973297119 , + 0.7358999848365784 , + 0.7512000203132629 , + 0.7652999758720398 , + 0.7778000235557556 , + 0.7889999747276306 , + 0.7994999885559082 , + 0.8091999888420105 , + 0.8180999755859375 , + 0.8216000199317932 , + 0.8291000127792358 , + 0.8360999822616577 , + 0.8424000144004822 , + 0.8482000231742859 , + 0.8532999753952026 , + 0.8551999926567078 , + 0.8558999896049500 , + 0.8562999963760376 , + 0.8571000099182129 , + 0.8582000136375427 , + 0.8590999841690063 , + 0.8593999743461609 , + 0.8604000210762024 , + 0.8610000014305115 , + 0.8616999983787537 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + 1.000000000000000 , + AA3GAM = 0.7579997200000000 , + 0.7332996100000000 , + 0.7103997500000000 , + 0.6895001500000000 , + 0.6694999900000000 , + 0.6511001000000000 , + 0.6329997800000000 , + 0.6151999800000000 , + 0.5995002400000000 , + 0.5834999700000000 , + 0.5695000300000000 , + 0.5818003400000000 , + 0.5674996400000000 , + 0.5552998200000000 , + 0.5436997400000000 , + 0.5338997800000000 , + 0.5247997599999999 , + 0.5144003600000000 , + 0.5137997900000000 , + 0.5130003700000000 , + 0.5119996700000000 , + 0.5114998200000000 , + 0.5107001700000000 , + 0.5098996800000000 , + 0.5091000200000000 , + 0.5084996800000000 , + 0.6819996200000000 , + 0.6646996700000000 , + 0.6471999300000000 , + 0.6319003700000000 , + 0.6165999800000000 , + 0.6019000400000000 , + 0.5886997600000000 , + 0.5755997899999999 , + 0.5627001500000000 , + 0.5496998400000001 , + 0.7263999600000000 , + 0.7064998100000000 , + 0.6854002500000000 , + 0.6653000700000000 , + 0.5564001800000000 , + 0.5438002300000000 , + 0.5291003000000000 , + 0.5130003700000000 , + 0.4946999000000000 , + -0.6749000000000001 , + -0.6573998900000000 , + -0.6403999900000000 , + -0.6245001600000000 , + -0.6095004100000000 , + -0.5960002500000000 , + -0.5823997900000000 , + -0.5695000300000000 , + -0.5631003400000000 , + -0.5520997000000000 , + -0.5415997500000000 , + -0.5321002600000000 , + -0.5230999600000000 , + -0.5154996500000000 , + -0.5109003800000000 , + -0.5095003800000000 , + -0.5079001800000000 , + -0.5065998400000000 , + -0.5055999799999999 , + -0.5042997000000000 , + -0.5032998300000000 , + -0.5018001200000000 , + -0.5004001300000001 , + -0.4992002500000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + AA4GAM = -4.0899996000000001E-002, + -3.9700024000000000E-002, + -3.9999984000000002E-002, + -3.9600007000000000E-002, + -3.8300015000000000E-002, + -3.7400004000000001E-002, + -3.6700007000000000E-002, + -3.6599997000000002E-002, + -3.5200000000000002E-002, + -3.5099990999999997E-002, + -3.1900014999999997E-002, + 2.0099999000000000E-002, + 2.2099984999999999E-002, + 2.0099999000000000E-002, + 2.1499995000000001E-002, + 2.2800006000000001E-002, + 2.3199997999999999E-002, + 2.5599991999999998E-002, + 2.7099999000000000E-002, + 2.7699985999999999E-002, + 2.6900014000000000E-002, + 2.5099995000000000E-002, + 2.7600013000000000E-002, + 2.6299993000000001E-002, + 2.6399980999999999E-002, + 2.6999990000000001E-002, + 1.8800007000000001E-002, + 2.4299989000000001E-002, + 2.5500014000000001E-002, + 2.7300000000000001E-002, + 2.9399992999999999E-002, + 3.5599976999999998E-002, + 3.2299999000000003E-002, + 3.2799984999999997E-002, + 3.2999995999999997E-002, + 3.7500015999999997E-002, + -4.3099985000000000E-002, + -4.2099979000000003E-002, + -4.0600035000000000E-002, + -4.0099996999999998E-002, + -3.1200016000000001E-002, + -3.1299981999999997E-002, + -3.0500019000000000E-002, + -2.8399982000000001E-002, + -2.6600001000000002E-002, + -3.0699994000000001E-002, + -3.4199983000000003E-002, + -3.9199978000000003E-002, + -4.3900008999999997E-002, + -4.9999975000000002E-002, + -4.9900033000000003E-002, + -5.3499999999999999E-002, + -5.6699995000000003E-002, + 6.4800017000000001E-002, + 6.6100053000000006E-002, + 6.7199960000000003E-002, + 6.7399985999999995E-002, + 6.7800029999999997E-002, + 6.6100053000000006E-002, + 7.4100009999999994E-002, + 7.5200029000000002E-002, + 7.9600029000000003E-002, + 8.0199993999999997E-002, + 7.6499953999999995E-002, + 7.5599968000000003E-002, + 7.8000024000000001E-002, + 7.7699958999999999E-002, + 7.9299970999999997E-002, + 7.9799958000000004E-002, + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + TGAMMA = 0.1303013400000000 , + 0.1143766900000000 , + 8.2041472000000004E-002, + 5.4787508999999998E-002, + 2.6905693000000001E-002, + -5.0727487999999996E-003, + -4.3465170999999997E-002, + -7.7258646000000000E-002, + -0.1154772300000000 , + -0.1558073800000000 , + -0.1796950700000000 , + 0.1393254500000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.1560978100000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.1666563300000000 , + 0.1627760200000000 , + 0.1566226800000000 , + -9.5734119000000006E-002, + 0.1618352200000000 , + 0.1681328700000000 , + 0.1695525300000000 , + 0.1744692600000000 , + 0.1790687400000000 , + -8.0011873999999997E-002, + -3.6637045000000000E-002, + -1.2452187000000000E-003, + 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0.000000000000000 , + 0.000000000000000 , + AA5GAM = -3.5300019000000000E-007, + -3.5700015000000000E-007, + -3.5800007999999998E-007, + -3.5899995999999999E-007, + -3.5899995999999999E-007, + -3.5700015000000000E-007, + -3.5599990000000002E-007, + -3.5300019000000000E-007, + -3.5100003999999999E-007, + -3.4799999000000001E-007, + -3.4500024999999999E-007, + 3.5300019000000000E-007, + 3.5400008999999998E-007, + 3.5599990000000002E-007, + 3.5700015000000000E-007, + 3.5800007999999998E-007, + 3.5800007999999998E-007, + 3.5899995999999999E-007, + 3.5899995999999999E-007, + 3.5899995999999999E-007, + 3.5899995999999999E-007, + 3.5899995999999999E-007, + 3.5899995999999999E-007, + 3.5899995999999999E-007, + 3.5899995999999999E-007, + 3.5899995999999999E-007, + 6.8200037999999994E-008, + 4.7099999000000001E-008, + 2.3600013000000000E-008, + 8.6500024000000005E-010, + -2.4299995000000001E-008, + -5.0700005999999999E-008, + -7.7500026000000001E-008, + -1.0699992000000001E-007, + 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0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 + / + &ECCD + KKSTARK = 101, + CHIGAMT = 6.288350332173052 , + CHIGAM = 6.8718846858426309E-003, + 0.8642208357382712 , + 4.5772342066763942E-002, + 0.1441107743782717 , + 5.8704275788020442E-004, + 0.1330170177436550 , + 0.1100136407777549 , + 0.4974061584921390 , + 5.8007832743605867E-002, + 1.337812503053351 , + 2.0986415934678100E-008, + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 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1.8482801924204526E-002, + 0.1815426499039182 , + 8.3429880135030242E-003, + 0.000000000000000 , + 8.7386235165995835E-002, + 2.5813930068840717E-004, + 9.9474461019504728E-003, + 8.2844412786942684E-002, + 7.5933865885683099E-002, + 0.2627442485853556 , + 0.3509357812678711 , + 9.6033841666670933E-007, + 2.2118508979707265E-002, + 0.4808962475029976 , + 1.3046329959515745E-002, + 1.1359027072828433E-002, + 2.7870960784433643E-002, + 9.5976807321789658E-003, + 3.0660773224850475E-005, + 3.0227180285408595E-002, + 2.0979367874545563E-002, + 3.1562805991269456E-003, + 0.1760459999290185 , + 0.2574616611965144 , + 0.1816740584544634 , + 8.7708270642808228E-002, + 3.4209550823340429E-002, + 0.000000000000000 , + 3.1158381237082113E-003, + 0.3400561762082721 , + 0.1627616238474943 , + 3.5272957564644949E-003, + 0.6931974499377125 , + 0.2565074263891799 , + 9.8884503548996496E-003, + 3.3764510207446585E-003, + 0.1131026446293127 , + 5.9048635948197412E-002, + 0.000000000000000 , + 2.1441786665032077E-003, + 0.5329646325769650 , + SAIMPI = 0.1664956734408607 , + 0.000000000000000 , + 0.2069890581742621 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.9625388096277667 , + 0.000000000000000 , + 0.000000000000000 , + 0.9395681019411204 , + 0.000000000000000 , + 0.2531281336482902 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.7743150177662679 , + 0.000000000000000 , + 0.000000000000000 , + 5.7097149963797229E-003, + 7.2591824784642919E-002, + 4.3550977956466367E-003, + 3.0373203503747406E-002, + 0.1262520950513119 , + 5.4597015166318152E-002, + 0.3675616781690489 , + 0.2450045031423853 , + 0.4875873432697144 , + 1.638041225492166 , + 1.595691424778917 , + 0.000000000000000 , + 7.2013596293274640E-002, + 8.5872038220408970E-003, + 4.3225384258836722E-002, + 1.7508110800918040E-004, + 0.1025167665000940 , + 9.9402418869484806E-003, + 0.5657908661525793 , + 6.9254557685246063E-002, + 8.8465863142351622E-003, + 0.2427614440886205 , + 7.5902565528919372E-002, + 6.2268607119479957E-002, + 0.000000000000000 , + 0.4591730294678171 , + 0.1164963608783690 , + 2.3716235575672658E-002, + 9.7360485808618197E-002, + 2.0547716593933629E-002, + 0.1635269758339434 , + 0.3562749054621027 , + 1.230396761661656 , + 1.4742685234513338E-002, + 0.000000000000000 , + 0.3974465226608165 , + 0.2434253110628695 , + 0.2976340978930932 , + 4.9916901857596084E-002, + 0.1537242396472875 , + 0.000000000000000 , + 5.8825006947044048E-003, + 5.4957901438118474E-003, + 0.000000000000000 , + 2.0276489206899072E-002, + 3.5533777446743110E-002, + 1.8582184560361222E-004, + SAIPR = 0.000000000000000 , + SAIIP = 4.5405653514677624E-002 + / + KIM diff --git a/notebooks/DIIID_example/vac.in b/notebooks/DIIID_example/vac.in new file mode 100644 index 000000000..68e91e03e --- /dev/null +++ b/notebooks/DIIID_example/vac.in @@ -0,0 +1,99 @@ +! **** Running DCON's input *** +&MODES + mth = 480 + xiin(1:9) = 0 0 0 0 0 0 0 1 0 + lsymz = .TRUE. + leqarcw = 1 + lzio = 0 + lgato = 0 + lrgato = 0 +/ +&DEBUGS + checkd = .FALSE. + check1 = .FALSE. + check2 = .FALSE. + checke = .FALSE. + checks = .FALSE. + wall = .FALSE. + lkplt = 0 + verbose_timer_output = f +/ +&VACDAT + ishape = 6 + aw = 0.05 + bw = 1.5 + cw = 0 + dw = 0.5 + tw = 0.05 + nsing = 500 + epsq = 1e-05 + noutv = 37 + idgt = 6 + idot = 0 + idsk = 0 + delg = 15.01 + delfac = 0.001 + cn0 = 1 +/ +&SHAPE + ipshp = 0 + xpl = 100 + apl = 1 + a = 20 + b = 170 + bpl = 1 + dpl = 0 + r = 1 + abulg = 0.932 + bbulg = 17.0 + tbulg = 0.02 + qain = 2.5 +/ +&DIAGNS + lkdis = .FALSE. + ieig = 0 + iloop = 0 + lpsub = 1 + nloop = 128 + nloopr = 0 + nphil = 3 + nphse = 1 + xofsl = 0 + ntloop = 32 + aloop = 0.01 + bloop = 1.6 + dloop = 0.5 + rloop = 1.0 + deloop = 0.001 + mx = 21 + mz = 21 + nph = 0 + nxlpin = 6 + nzlpin = 11 + epslp = 0.02 + xlpmin = 0.7 + xlpmax = 2.7 + zlpmin = -1.5 + zlpmax = 1.5 + linterior = 2 +/ +&SPRK + nminus = 0 + nplus = 0 + mphi = 16 + lwrt11 = 0 + civ = 0.0 + sp2sgn1 = 1 + sp2sgn2 = 1 + sp2sgn3 = 1 + sp2sgn4 = 1 + sp2sgn5 = 1 + sp3sgn1 = -1 + sp3sgn2 = -1 + sp3sgn3 = -1 + sp3sgn4 = 1 + sp3sgn5 = 1 + lff = 0 + ff = 1.6 + fv = 1.6 1.6 1.6 1.6 1.6 1.0 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 +/ diff --git a/notebooks/beta_1.00 b/notebooks/beta_1.00 new file mode 100644 index 000000000..957a82384 --- /dev/null +++ b/notebooks/beta_1.00 @@ -0,0 +1,3596 @@ + FROM CHEASE BUT COCOS=02 ,SI UNITS20250525 3 129 128 + 3.299530345E+00 5.355011898E+00 3.000000000E+00 1.350300118E+00-2.997821744E-06 + 3.117635059E+00-2.997821744E-06-1.367210836E+00 0.000000000E+00 1.000000000E+00 + 3.670648220E+06-1.367210836E+00 0.000000000E+00 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4.457207284E+00-4.058867547E-01 4.463088084E+00-3.769907056E-01 4.468536806E+00 +-3.480759119E-01 4.473552828E+00-3.191429453E-01 4.478135440E+00-2.901925612E-01 + 4.482284088E+00-2.612257380E-01 4.485998084E+00-2.322435926E-01 4.489276773E+00 +-2.032474064E-01 4.492119692E+00-1.742386255E-01 4.494526218E+00-1.452187922E-01 + 4.496495959E+00-1.161895814E-01 4.498028669E+00-8.715275983E-02 4.499123931E+00 +-5.811014675E-02 4.499781143E+00-2.906362128E-02 4.499999497E+00-1.513208407E-05 + 1.350313621E+00-2.677482172E+00 4.649797468E+00-2.677482172E+00 4.649797468E+00 + 2.677476176E+00 1.350313621E+00 2.677476176E+00 1.350313621E+00-2.677482172E+00 + + 1.51912315E-01 abs(PSI-AXIS) --> [T M**2] -1.36721084E+00 + 1.03921169E+00 R OF MAGAXE --> [M] 3.11763506E+00 + -9.99273915E-07 Z OF MAGAXE --> [M] -2.99782174E-06 + -5.04402802E-06 Z0 --> [M] -1.51320841E-05 + 3.00000000E+00 R0 [M] USED FOR CONVERTING TO MKSA + 1.00000000E+00 B0 [T] USED FOR CONVERTING TO MKSA + 1.00000000E+00 SIGN OF B0 IN EXPERIMENT (CHEASE ASSUMES 1.0) + 1.53755753E+00 TOTAL CURRENT --> [A] 3.67064822E+06 + 1.00000000E+00 SIGN OF IP IN EXPERIMENT (CHEASE ASSUMES 1.0) + 1.69999553E+00 b/a + 1.05000000E+00 Q_ZERO, USING SIGNS OF IP AND B0, WOULD GIVE: 1.05000000E+00 + 4.43373475E+00 Q_EDGE, USING SIGNS OF IP AND B0, WOULD GIVE: 4.43373475E+00 + 1.51426490E-01 POLOIDAL BETA + 2.34029713E-02 BETA_EXP=

*2*MU0/B0**2 + 7.25523874E-01 LI + 3.46308209E-02 PRESSURE ON AXIS --> [Pa] 2.75583316E+04 --> [10**19 M**-3 KEV]: 1.72024542E+01 + 1.63188124E-02 BETA + 2.18184292E-02 BETA* (SQRT()) + 5.58550793E-02 BETA-AXIS=2p0/(T0/Rmag)^2; with Rmag->Rgeo(LCFS): 5.17194368E-02 + -1.51912315E-01 PSI-AXIS --> [T M**2] -1.36721084E+00 + -9.54493226E-01 2*PI*PSI-AXIS --> -8.59043904E+00 + -1.51912315E-01 IP_SIGN*PSI-AXIS --> [T M**2] -1.36721084E+00 + -9.54493226E-01 IP_SIGN*2*PI*PSI-AXIS --> -8.59043904E+00 + 1.99999525E+00 ASPECT RATIO ; a/R= 5.00001188E-01 + 7.64779790E+00 VOLUME -> 2.06490543E+02 + 1.29389993E+00 AREA -> 1.16450994E+01 + 2.53018281E+01 SURFACE -> 2.27716453E+02 + 4.34432012E+00 LENGTH -> 1.30329604E+01 + 5.00003104E-01 RMIN -> RMIN [m] 1.50000931E+00 + 1.49999983E+00 RMAX -> RMAX [m] 4.49999950E+00 + -8.49976057E-01 ZMIN -> ZMIN [m] -2.54992817E+00 + 8.49976009E-01 ZMAX -> ZMAX [m] 2.54992803E+00 + 1.00000147E+00 RGEOM -> RGEOM [m] 3.00000440E+00 + 4.99998364E-01 MINOR RADIUS -> A [m] 1.49999509E+00 diff --git a/notebooks/dcon_test.ipynb b/notebooks/dcon_test.ipynb new file mode 100644 index 000000000..dc21f3ac8 --- /dev/null +++ b/notebooks/dcon_test.ipynb @@ -0,0 +1,57 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b792c57b", + "metadata": {}, + "source": [ + "### This notebook can be used as a basic example to show how to run the main DCON program" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "710e987d", + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"..\")\n", + "using JPEC" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d8bcf5be", + "metadata": {}, + "outputs": [], + "source": [ + "JPEC.DCON.Main(\"DIIID_example\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "18cbc50a", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/equil_chease_binary_test.ipynb b/notebooks/equil_chease_binary_test.ipynb new file mode 100644 index 000000000..03c4088be --- /dev/null +++ b/notebooks/equil_chease_binary_test.ipynb @@ -0,0 +1,250 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "1b50e9cb", + "metadata": {}, + "outputs": [], + "source": [ + "# Test inverse.jl using the chease binary file IN1\n", + "\n", + "using Revise\n", + "using Pkg\n", + "#Pkg.update()\n", + "Pkg.activate(\"..\")\n", + "Pkg.instantiate()\n", + "using JPEC, Plots\n", + "gr()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "94c3d4e9", + "metadata": {}, + "outputs": [], + "source": [ + "println(\"Starting equilibrium reconstruction...\")\n", + "plasma_eq = JPEC.Equilibrium.setup_equilibrium(\"Chease_Binary_example/equil.toml\")\n", + "println(\"Equilibrium reconstruction complete.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c0c6ffc5", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n", + "println(\"\\n--- Generating data for 2D color plots ---\")\n", + "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n", + "# This part is identical to the previous steps.\n", + "equil_control = plasma_eq.config.control\n", + "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n", + "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n", + "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n", + "println(\"Evaluating the 'rzphi' mapping spline...\")\n", + "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n", + "println(\"Evaluation complete.\")\n", + "# 3. Transform the spline output to physical (R, Z) coordinates.\n", + "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n", + "rfac_sq = fs_grid[:, :, 1]\n", + "eta_term = fs_grid[:, :, 2]\n", + "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n", + "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n", + "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n", + "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n", + "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n", + "println(\"Calculated R and Z grids.\")\n", + "# 4. Create the 2D color plot for R(ψ,θ)\n", + "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n", + "p_r_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " R_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Major Radius R(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"R [m]\"\n", + ")\n", + "display(p_r_heatmap)\n", + "# 5. Create the 2D color plot for Z(ψ,θ)\n", + "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n", + "p_z_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " Z_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Vertical Position Z(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"Z [m]\"\n", + ")\n", + "display(p_z_heatmap)\n", + "println(\"\\n2D color plots for R and Z have been saved.\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9859d659", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n", + "# This code block goes at the end of your existing script.\n", + "\n", + "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n", + "\n", + "# 1. Select a number of contours to display for clarity\n", + "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n", + "num_theta_contours = 13 # e.g., every 30 degrees\n", + "\n", + "# 2. Initialize the plot\n", + "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n", + "p_flux_surfaces = plot(\n", + " title=\"Flux Coordinate System Contours in (R, Z)\",\n", + " xlabel=\"R [m]\",\n", + " ylabel=\"Z [m]\",\n", + " aspect_ratio=:equal,\n", + " legend=:outertopright\n", + ")\n", + "\n", + "# 3. Plot contours of constant ψ (flux surfaces) in blue\n", + "# We loop through the ROWS of the R_grid and Z_grid matrices.\n", + "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n", + "\n", + "for i in psi_indices\n", + " # Each row corresponds to a single psi value\n", + " # We must add the last point to the start to close the loop for a smooth plot\n", + " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n", + " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n", + " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n", + "end\n", + "\n", + "# 4. Plot contours of constant θ (angle contours) in red\n", + "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n", + "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n", + "\n", + "for j in theta_indices\n", + " # Each column corresponds to a single theta value\n", + " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n", + "end\n", + "\n", + "# 5. Add a legend manually (a common trick in Plots.jl)\n", + "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n", + "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n", + "\n", + "# 6. Display and save the final plot\n", + "display(p_flux_surfaces)\n", + "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2c625a4a", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n", + "# This code block goes at the end of your existing script.\n", + "\n", + "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n", + "\n", + "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n", + "# not just on its internal knot points.\n", + "psi_eval_grid = range(0.0, 1.0, length=200)\n", + "\n", + "# 2. Evaluate the 'sq' spline across this dense grid.\n", + "# Calling spline_eval with a vector input is efficient and returns a matrix\n", + "# where each column corresponds to one of the splined quantities.\n", + "println(\"Evaluating 'sq' spline on a dense grid...\")\n", + "evaluated_profiles = JPEC.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n", + "println(\"Evaluation complete.\")\n", + "\n", + "# 3. Extract each profile into its own variable for clarity.\n", + "# Based on the direct_run implementation:\n", + "# Column 1: F = R*Bt (Toroidal Field Function)\n", + "# Column 2: P*μ₀ (Scaled Pressure)\n", + "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n", + "# Column 4: q (Safety Factor)\n", + "F_profile = evaluated_profiles[:, 1]\n", + "P_profile = evaluated_profiles[:, 2]\n", + "Flux_profile = evaluated_profiles[:, 3]\n", + "q_profile = evaluated_profiles[:, 4]\n", + "\n", + "# 4. Create and display the plots\n", + "\n", + "# Plot 1: Safety Factor (q)\n", + "p_q = plot(\n", + " psi_eval_grid,\n", + " q_profile,\n", + " title=\"Safety Factor Profile\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"q\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_q)\n", + "\n", + "# Plot 2: Scaled Pressure (P*μ₀)\n", + "p_p = plot(\n", + " psi_eval_grid,\n", + " P_profile,\n", + " title=\"Pressure Profile\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"P * μ₀ [T²]\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_p)\n", + "\n", + "\n", + "# Plot 3: Toroidal Field Function (F)\n", + "p_f = plot(\n", + " psi_eval_grid,\n", + " F_profile,\n", + " title=\"Toroidal Field Function\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"F = R * B_t [T*m]\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_f)\n", + "\n", + "# Plot 4: Combined plot for comparison\n", + "p_all_profiles = plot(\n", + " title=\"1D Equilibrium Profiles\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " legend=:best\n", + ")\n", + "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n", + "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n", + "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n", + "# We can also plot the 3rd quantity, though it's less commonly viewed.\n", + "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n", + "display(p_all_profiles)\n", + "\n", + "\n", + "println(\"1D profile plots saved successfully.\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/equil_gfile_example.ipynb b/notebooks/equil_gfile_example.ipynb new file mode 100644 index 000000000..08f17052d --- /dev/null +++ b/notebooks/equil_gfile_example.ipynb @@ -0,0 +1,267 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "814db625", + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"..\")\n", + "Pkg.resolve()\n", + "Pkg.instantiate()\n", + "using JPEC, Plots\n", + "gr() " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "94c3d4e9", + "metadata": {}, + "outputs": [], + "source": [ + "# 1. Define the input parameters for the equilibrium solver.\n", + "# - eq_filename: The name of the g-file we just created.\n", + "# - eq_type: \"efit\" for a standard g-file.\n", + "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n", + "# - mpsi, mtheta: Resolution of the output grid.\n", + "\n", + " equil_control = JPEC.Equilibrium.EquilibriumControl(;\n", + " eq_filename=\"beta_1.00\", # eq_filename\n", + " eq_type=\"efit\", # eq_type\n", + " jac_type=\"boozer\", # jac_type\n", + " grid_type=\"ldp\",\n", + " psilow=0.01, # psilow\n", + " psihigh=0.994) # psihigh\n", + "\n", + "equil_config = JPEC.Equilibrium.EquilibriumConfig(equil_control,JPEC.Equilibrium.EquilibriumOutput())\n", + "# 2. Run the main equilibrium setup function.\n", + "# This will read the file, solve the direct problem, and return the final object.\n", + "println(\"Starting equilibrium reconstruction...\")\n", + "\n", + "\n", + "plasma_eq = JPEC.Equilibrium.setup_equilibrium(equil_config)\n", + "#plasma_eq = JPEC.Equilibrium.setup_equilibrium(\"./DIIID_example/equil.toml\")\n", + "println(\"Equilibrium reconstruction complete.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f61a9987", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n", + "println(\"\\n--- Generating data for 2D color plots ---\")\n", + "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n", + "# This part is identical to the previous steps.\n", + "equil_control = plasma_eq.config.control\n", + "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n", + "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n", + "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n", + "println(\"Evaluating the 'rzphi' mapping spline...\")\n", + "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n", + "println(\"Evaluation complete.\")\n", + "# 3. Transform the spline output to physical (R, Z) coordinates.\n", + "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n", + "rfac_sq = fs_grid[:, :, 1]\n", + "eta_term = fs_grid[:, :, 2]\n", + "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n", + "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n", + "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n", + "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n", + "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n", + "println(\"Calculated R and Z grids.\")\n", + "# 4. Create the 2D color plot for R(ψ,θ)\n", + "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n", + "p_r_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " R_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Major Radius R(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"R [m]\"\n", + ")\n", + "display(p_r_heatmap)\n", + "# 5. Create the 2D color plot for Z(ψ,θ)\n", + "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n", + "p_z_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " Z_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Vertical Position Z(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"Z [m]\"\n", + ")\n", + "display(p_z_heatmap)\n", + "println(\"\\n2D color plots for R and Z have been saved.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9cf8a3c1", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n", + "# This code block goes at the end of your existing script.\n", + "\n", + "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n", + "\n", + "# 1. Select a number of contours to display for clarity\n", + "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n", + "num_theta_contours = 13 # e.g., every 30 degrees\n", + "\n", + "# 2. Initialize the plot\n", + "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n", + "p_flux_surfaces = plot(\n", + " title=\"Flux Coordinate System Contours in (R, Z)\",\n", + " xlabel=\"R [m]\",\n", + " ylabel=\"Z [m]\",\n", + " aspect_ratio=:equal,\n", + " legend=:outertopright\n", + ")\n", + "\n", + "# 3. Plot contours of constant ψ (flux surfaces) in blue\n", + "# We loop through the ROWS of the R_grid and Z_grid matrices.\n", + "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n", + "\n", + "for i in psi_indices\n", + " # Each row corresponds to a single psi value\n", + " # We must add the last point to the start to close the loop for a smooth plot\n", + " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n", + " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n", + " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n", + "end\n", + "\n", + "# 4. Plot contours of constant θ (angle contours) in red\n", + "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n", + "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n", + "\n", + "for j in theta_indices\n", + " # Each column corresponds to a single theta value\n", + " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n", + "end\n", + "\n", + "# 5. Add a legend manually (a common trick in Plots.jl)\n", + "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n", + "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n", + "\n", + "# 6. Display and save the final plot\n", + "display(p_flux_surfaces)\n", + "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "97a529f4", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n", + "# This code block goes at the end of your existing script.\n", + "\n", + "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n", + "\n", + "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n", + "# not just on its internal knot points.\n", + "psi_eval_grid = range(0.0, 1.0, length=200)\n", + "\n", + "# 2. Evaluate the 'sq' spline across this dense grid.\n", + "# Calling spline_eval with a vector input is efficient and returns a matrix\n", + "# where each column corresponds to one of the splined quantities.\n", + "println(\"Evaluating 'sq' spline on a dense grid...\")\n", + "evaluated_profiles = JPEC.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n", + "println(\"Evaluation complete.\")\n", + "\n", + "# 3. Extract each profile into its own variable for clarity.\n", + "# Based on the direct_run implementation:\n", + "# Column 1: F = R*Bt (Toroidal Field Function)\n", + "# Column 2: P*μ₀ (Scaled Pressure)\n", + "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n", + "# Column 4: q (Safety Factor)\n", + "F_profile = evaluated_profiles[:, 1]\n", + "P_profile = evaluated_profiles[:, 2]\n", + "Flux_profile = evaluated_profiles[:, 3]\n", + "q_profile = evaluated_profiles[:, 4]\n", + "\n", + "# 4. Create and display the plots\n", + "\n", + "# Plot 1: Safety Factor (q)\n", + "p_q = plot(\n", + " psi_eval_grid,\n", + " q_profile,\n", + " title=\"Safety Factor Profile\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"q\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_q)\n", + "\n", + "# Plot 2: Scaled Pressure (P*μ₀)\n", + "p_p = plot(\n", + " psi_eval_grid,\n", + " P_profile,\n", + " title=\"Pressure Profile\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"P * μ₀ [T²]\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_p)\n", + "\n", + "\n", + "# Plot 3: Toroidal Field Function (F)\n", + "p_f = plot(\n", + " psi_eval_grid,\n", + " F_profile,\n", + " title=\"Toroidal Field Function\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"F = R * B_t [T*m]\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_f)\n", + "\n", + "# Plot 4: Combined plot for comparison\n", + "p_all_profiles = plot(\n", + " title=\"1D Equilibrium Profiles\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " legend=:best\n", + ")\n", + "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n", + "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n", + "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n", + "# We can also plot the 3rd quantity, though it's less commonly viewed.\n", + "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n", + "display(p_all_profiles)\n", + "\n", + "\n", + "println(\"1D profile plots saved successfully.\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/equil_inverse_test.ipynb b/notebooks/equil_inverse_test.ipynb new file mode 100644 index 000000000..9049207d8 --- /dev/null +++ b/notebooks/equil_inverse_test.ipynb @@ -0,0 +1,276 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "1b50e9cb", + "metadata": {}, + "outputs": [], + "source": [ + "# Test inverse.jl using the file inverse.inverse_chease4_run\n", + "\n", + "using Revise\n", + "using Pkg\n", + "Pkg.activate(\"..\") \n", + "Pkg.instantiate()\n", + "using JPEC, Plots\n", + "gr() " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "94c3d4e9", + "metadata": {}, + "outputs": [], + "source": [ + "# 1. Define the input parameters for the equilibrium solver.\n", + "# - eq_filename: The name of the g-file we just created.\n", + "# - eq_type: \"efit\" for a standard g-file.\n", + "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n", + "# - mpsi, mtheta: Resolution of the output grid.\n", + "equil_input = JPEC.Equilibrium.EquilibriumConfig(control=JPEC.Equilibrium.EquilibriumControl(;eq_filename=\"inverse.chease.10\",\n", + " eq_type=\"chease2\", jac_type=\"hamada\", mpsi=128, mtheta=256),\n", + " output=JPEC.Equilibrium.EquilibriumOutput())\n", + "\n", + "# 2. Run the main equilibrium setup function.\n", + "# This will read the file, solve the direct problem, and return the final object.\n", + "println(\"Starting equilibrium reconstruction...\")\n", + "plasma_eq = JPEC.Equilibrium.setup_equilibrium(\"/Users/bursche/Documents/GitHub/JPEC/notebooks/Inverse_Text_Example/equil.toml\")\n", + "println(\"Equilibrium reconstruction complete.\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c0c6ffc5", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n", + "println(\"\\n--- Generating data for 2D color plots ---\")\n", + "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n", + "# This part is identical to the previous steps.\n", + "equil_control = plasma_eq.config.control\n", + "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n", + "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n", + "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n", + "println(\"Evaluating the 'rzphi' mapping spline...\")\n", + "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n", + "println(\"Evaluation complete.\")\n", + "# 3. Transform the spline output to physical (R, Z) coordinates.\n", + "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n", + "rfac_sq = fs_grid[:, :, 1]\n", + "eta_term = fs_grid[:, :, 2]\n", + "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n", + "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n", + "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n", + "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n", + "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n", + "println(\"Calculated R and Z grids.\")\n", + "# 4. Create the 2D color plot for R(ψ,θ)\n", + "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n", + "p_r_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " R_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Major Radius R(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"R [m]\"\n", + ")\n", + "display(p_r_heatmap)\n", + "# 5. Create the 2D color plot for Z(ψ,θ)\n", + "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n", + "p_z_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " Z_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Vertical Position Z(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"Z [m]\"\n", + ")\n", + "display(p_z_heatmap)\n", + "println(\"\\n2D color plots for R and Z have been saved.\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9859d659", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n", + "# This code block goes at the end of your existing script.\n", + "\n", + "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n", + "\n", + "# 1. Select a number of contours to display for clarity\n", + "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n", + "num_theta_contours = 13 # e.g., every 30 degrees\n", + "\n", + "# 2. Initialize the plot\n", + "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n", + "p_flux_surfaces = plot(\n", + " title=\"Flux Coordinate System Contours in (R, Z)\",\n", + " xlabel=\"R [m]\",\n", + " ylabel=\"Z [m]\",\n", + " aspect_ratio=:equal,\n", + " legend=:outertopright\n", + ")\n", + "\n", + "# 3. Plot contours of constant ψ (flux surfaces) in blue\n", + "# We loop through the ROWS of the R_grid and Z_grid matrices.\n", + "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n", + "\n", + "for i in psi_indices\n", + " # Each row corresponds to a single psi value\n", + " # We must add the last point to the start to close the loop for a smooth plot\n", + " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n", + " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n", + " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n", + "end\n", + "\n", + "# 4. Plot contours of constant θ (angle contours) in red\n", + "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n", + "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n", + "\n", + "for j in theta_indices\n", + " # Each column corresponds to a single theta value\n", + " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n", + "end\n", + "\n", + "# 5. Add a legend manually (a common trick in Plots.jl)\n", + "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n", + "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n", + "\n", + "# 6. Display and save the final plot\n", + "display(p_flux_surfaces)\n", + "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2c625a4a", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n", + "# This code block goes at the end of your existing script.\n", + "\n", + "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n", + "\n", + "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n", + "# not just on its internal knot points.\n", + "psi_eval_grid = range(0.0, 1.0, length=200)\n", + "\n", + "# 2. Evaluate the 'sq' spline across this dense grid.\n", + "# Calling spline_eval with a vector input is efficient and returns a matrix\n", + "# where each column corresponds to one of the splined quantities.\n", + "println(\"Evaluating 'sq' spline on a dense grid...\")\n", + "evaluated_profiles = JPEC.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n", + "println(\"Evaluation complete.\")\n", + "\n", + "# 3. Extract each profile into its own variable for clarity.\n", + "# Based on the direct_run implementation:\n", + "# Column 1: F = R*Bt (Toroidal Field Function)\n", + "# Column 2: P*μ₀ (Scaled Pressure)\n", + "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n", + "# Column 4: q (Safety Factor)\n", + "F_profile = evaluated_profiles[:, 1]\n", + "P_profile = evaluated_profiles[:, 2]\n", + "Flux_profile = evaluated_profiles[:, 3]\n", + "q_profile = evaluated_profiles[:, 4]\n", + "\n", + "# 4. Create and display the plots\n", + "\n", + "# Plot 1: Safety Factor (q)\n", + "p_q = plot(\n", + " psi_eval_grid,\n", + " q_profile,\n", + " title=\"Safety Factor Profile\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"q\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_q)\n", + "\n", + "# Plot 2: Scaled Pressure (P*μ₀)\n", + "p_p = plot(\n", + " psi_eval_grid,\n", + " P_profile,\n", + " title=\"Pressure Profile\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"P * μ₀ [T²]\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_p)\n", + "\n", + "\n", + "# Plot 3: Toroidal Field Function (F)\n", + "p_f = plot(\n", + " psi_eval_grid,\n", + " F_profile,\n", + " title=\"Toroidal Field Function\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"F = R * B_t [T*m]\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_f)\n", + "\n", + "# Plot 4: Combined plot for comparison\n", + "p_all_profiles = plot(\n", + " title=\"1D Equilibrium Profiles\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " legend=:best\n", + ")\n", + "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n", + "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n", + "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n", + "# We can also plot the 3rd quantity, though it's less commonly viewed.\n", + "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n", + "display(p_all_profiles)\n", + "\n", + "\n", + "println(\"1D profile plots saved successfully.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b359ecb", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d8ba8174", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/equil_lar_example.ipynb b/notebooks/equil_lar_example.ipynb new file mode 100644 index 000000000..4d73d548e --- /dev/null +++ b/notebooks/equil_lar_example.ipynb @@ -0,0 +1,263 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "bc77cb03", + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"..\")\n", + "Pkg.resolve() \n", + "Pkg.instantiate()\n", + "using DifferentialEquations,JPEC, Plots, DelimitedFiles" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8fb8cfd4", + "metadata": {}, + "outputs": [], + "source": [ + "equil_input = JPEC.Equilibrium.EquilibriumConfig(; control=JPEC.Equilibrium.EquilibriumControl(eq_type=\"lar\", eq_filename=\"lar.toml\"), output=JPEC.Equilibrium.EquilibriumOutput())\n", + "lar_input = JPEC.Equilibrium.LargeAspectRatioConfig(; lar_r0=10, lar_a=1, beta0=0.001, q0=1.5, p_pres=2, p_sig=1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d7836d02", + "metadata": {}, + "outputs": [], + "source": [ + "plasma_eq= JPEC.Equilibrium.setup_equilibrium(equil_input, lar_input)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "88a7f2d7", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n", + "println(\"\\n--- Generating data for 2D color plots ---\")\n", + "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n", + "# This part is identical to the previous steps.\n", + "equil_control = plasma_eq.config.control\n", + "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n", + "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n", + "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n", + "println(\"Evaluating the 'rzphi' mapping spline...\")\n", + "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n", + "println(\"Evaluation complete.\")\n", + "# 3. Transform the spline output to physical (R, Z) coordinates.\n", + "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n", + "rfac_sq = fs_grid[:, :, 1]\n", + "eta_term = fs_grid[:, :, 2]\n", + "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n", + "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n", + "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n", + "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n", + "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n", + "println(\"Calculated R and Z grids.\")\n", + "# 4. Create the 2D color plot for R(ψ,θ)\n", + "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n", + "p_r_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " R_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Major Radius R(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"R [m]\"\n", + ")\n", + "display(p_r_heatmap)\n", + "# 5. Create the 2D color plot for Z(ψ,θ)\n", + "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n", + "p_z_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " Z_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Vertical Position Z(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"Z [m]\"\n", + ")\n", + "display(p_z_heatmap)\n", + "println(\"\\n2D color plots for R and Z have been saved.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "22c45ff5", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n", + "# This code block goes at the end of your existing script.\n", + "\n", + "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n", + "\n", + "# 1. Select a number of contours to display for clarity\n", + "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n", + "num_theta_contours = 13 # e.g., every 30 degrees\n", + "\n", + "# 2. Initialize the plot\n", + "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n", + "p_flux_surfaces = plot(\n", + " title=\"Flux Coordinate System Contours in (R, Z)\",\n", + " xlabel=\"R [m]\",\n", + " ylabel=\"Z [m]\",\n", + " aspect_ratio=:equal,\n", + " legend=:outertopright\n", + ")\n", + "\n", + "# 3. Plot contours of constant ψ (flux surfaces) in blue\n", + "# We loop through the ROWS of the R_grid and Z_grid matrices.\n", + "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n", + "\n", + "for i in psi_indices\n", + " # Each row corresponds to a single psi value\n", + " # We must add the last point to the start to close the loop for a smooth plot\n", + " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n", + " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n", + " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n", + "end\n", + "\n", + "# 4. Plot contours of constant θ (angle contours) in red\n", + "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n", + "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n", + "\n", + "for j in theta_indices\n", + " # Each column corresponds to a single theta value\n", + " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n", + "end\n", + "\n", + "# 5. Add a legend manually (a common trick in Plots.jl)\n", + "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n", + "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n", + "\n", + "# 6. Display and save the final plot\n", + "display(p_flux_surfaces)\n", + "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "87de5490", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n", + "# This code block goes at the end of your existing script.\n", + "\n", + "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n", + "\n", + "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n", + "# not just on its internal knot points.\n", + "psi_eval_grid = range(0.0, 1.0, length=200)\n", + "\n", + "# 2. Evaluate the 'sq' spline across this dense grid.\n", + "# Calling spline_eval with a vector input is efficient and returns a matrix\n", + "# where each column corresponds to one of the splined quantities.\n", + "println(\"Evaluating 'sq' spline on a dense grid...\")\n", + "evaluated_profiles = JPEC.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n", + "println(\"Evaluation complete.\")\n", + "\n", + "# 3. Extract each profile into its own variable for clarity.\n", + "# Based on the direct_run implementation:\n", + "# Column 1: F = R*Bt (Toroidal Field Function)\n", + "# Column 2: P*μ₀ (Scaled Pressure)\n", + "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n", + "# Column 4: q (Safety Factor)\n", + "F_profile = evaluated_profiles[:, 1]\n", + "P_profile = evaluated_profiles[:, 2]\n", + "Flux_profile = evaluated_profiles[:, 3]\n", + "q_profile = evaluated_profiles[:, 4]\n", + "\n", + "# 4. Create and display the plots\n", + "\n", + "# Plot 1: Safety Factor (q)\n", + "p_q = plot(\n", + " psi_eval_grid,\n", + " q_profile,\n", + " title=\"Safety Factor Profile\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"q\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_q)\n", + "\n", + "# Plot 2: Scaled Pressure (P*μ₀)\n", + "p_p = plot(\n", + " psi_eval_grid,\n", + " P_profile,\n", + " title=\"Pressure Profile\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"P * μ₀ [T²]\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_p)\n", + "\n", + "\n", + "# Plot 3: Toroidal Field Function (F)\n", + "p_f = plot(\n", + " psi_eval_grid,\n", + " F_profile,\n", + " title=\"Toroidal Field Function\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"F = R * B_t [T*m]\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_f)\n", + "\n", + "# Plot 4: Combined plot for comparison\n", + "p_all_profiles = plot(\n", + " title=\"1D Equilibrium Profiles\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " legend=:best\n", + ")\n", + "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n", + "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n", + "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n", + "# We can also plot the 3rd quantity, though it's less commonly viewed.\n", + "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n", + "display(p_all_profiles)\n", + "\n", + "\n", + "println(\"1D profile plots saved successfully.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0735e75a", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/equil_soloviev_example.ipynb b/notebooks/equil_soloviev_example.ipynb new file mode 100644 index 000000000..086dcddec --- /dev/null +++ b/notebooks/equil_soloviev_example.ipynb @@ -0,0 +1,316 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "710e987d", + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"..\")\n", + "Pkg.resolve()\n", + "Pkg.instantiate()\n", + "using JPEC, Plots\n", + "# test" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cb106129", + "metadata": {}, + "outputs": [], + "source": [ + "### Set equil input parameters\n", + "equil_in = JPEC.Equilibrium.EquilibriumConfig(control=JPEC.Equilibrium.EquilibriumControl(\n", + " eq_filename=\"sol_test\", # eq_filename\n", + " eq_type=\"sol\", # eq_type\n", + " jac_type=\"hamada\", # jac_type\n", + " mpsi=100, # mpsi (number of radial grid points)\n", + " mtheta=128), # mtheta (number of poloidal grid points)\n", + " output=JPEC.Equilibrium.EquilibriumOutput()) \n", + "\n", + "### Set Soloviev input parameters\n", + "sol_inputs = JPEC.Equilibrium.SolevevConfig(;\n", + " mr=65, # number of radial grid zones\n", + " mz=65, # number of axial grid zones\n", + " ma=64, # number of flux grid zones\n", + " e=1.0, # elongation\n", + " a=1.0, # minor radius\n", + " r0=3.0, # major radius\n", + " q0=1.26, # safety factor at the o-point\n", + " p0fac=1.0, # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant)\n", + " b0fac=1.0, # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant)\n", + " f0fac=1.0 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant)\n", + " )\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9843a0d1", + "metadata": {}, + "outputs": [], + "source": [ + "### Set up Soloviev equilibrium and generate input splines\n", + "\n", + "directrun_inputs = JPEC.Equilibrium.sol_run(\n", + " equil_in,\n", + " sol_inputs\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b37e0a5c", + "metadata": {}, + "outputs": [], + "source": [ + "plot(\n", + " directrun_inputs.sq_in.xs,\n", + " directrun_inputs.sq_in.fs[:,2],\n", + " label=raw\"pfac * (p0fac - $\\psi_N$)\",\n", + " xlabel=raw\"$\\psi_N$\"\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6488baff", + "metadata": {}, + "outputs": [], + "source": [ + "### Execute direct_run() and solve equilibrium\n", + "\n", + "plasma_eq = JPEC.Equilibrium.equilibrium_solver(directrun_inputs)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "179089da", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n", + "println(\"\\n--- Generating data for 2D color plots ---\")\n", + "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n", + "# This part is identical to the previous steps.\n", + "equil_control = plasma_eq.config.control\n", + "psi_norm_grid = collect(range(equil_control.psilow, equil_control.psihigh, length=equil_control.mpsi + 1))\n", + "theta_new_grid = collect(range(0.0, 1.0, length=equil_control.mtheta + 1))\n", + "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n", + "println(\"Evaluating the 'rzphi' mapping spline...\")\n", + "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n", + "println(\"Evaluation complete.\")\n", + "# 3. Transform the spline output to physical (R, Z) coordinates.\n", + "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n", + "rfac_sq = fs_grid[:, :, 1]\n", + "eta_term = fs_grid[:, :, 2]\n", + "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n", + "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n", + "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n", + "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n", + "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n", + "println(\"Calculated R and Z grids.\")\n", + "# 4. Create the 2D color plot for R(ψ,θ)\n", + "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n", + "p_r_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " R_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Major Radius R(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"R [m]\"\n", + ")\n", + "display(p_r_heatmap)\n", + "# 5. Create the 2D color plot for Z(ψ,θ)\n", + "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n", + "p_z_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " Z_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Vertical Position Z(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"Z [m]\"\n", + ")\n", + "display(p_z_heatmap)\n", + "println(\"\\n2D color plots for R and Z have been saved.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b5f09972", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Code to Plot Psi and Theta Contours in R-Z Space ---\n", + "# This code block goes at the end of your existing script.\n", + "\n", + "println(\"\\n--- Plotting Psi and Theta Contours in R-Z Space ---\")\n", + "\n", + "# 1. Select a number of contours to display for clarity\n", + "num_psi_contours = 11 # e.g., from ψ_norm = 0.0 to 1.0 in steps of 0.1\n", + "num_theta_contours = 13 # e.g., every 30 degrees\n", + "\n", + "# 2. Initialize the plot\n", + "# aspect_ratio=:equal is crucial for tokamak plots to look physically correct.\n", + "p_flux_surfaces = plot(\n", + " title=\"Flux Coordinate System Contours in (R, Z)\",\n", + " xlabel=\"R [m]\",\n", + " ylabel=\"Z [m]\",\n", + " aspect_ratio=:equal,\n", + " legend=:outertopright\n", + ")\n", + "\n", + "# 3. Plot contours of constant ψ (flux surfaces) in blue\n", + "# We loop through the ROWS of the R_grid and Z_grid matrices.\n", + "psi_indices = round.(Int, range(1, stop=size(R_grid, 1), length=num_psi_contours))\n", + "\n", + "for i in psi_indices\n", + " # Each row corresponds to a single psi value\n", + " # We must add the last point to the start to close the loop for a smooth plot\n", + " R_surface = [R_grid[i, :]; R_grid[i, 1]]\n", + " Z_surface = [Z_grid[i, :]; Z_grid[i, 1]]\n", + " plot!(p_flux_surfaces, R_surface, Z_surface, label=\"\", color=:blue, linewidth=1.5)\n", + "end\n", + "\n", + "# 4. Plot contours of constant θ (angle contours) in red\n", + "# We loop through the COLUMNS of the R_grid and Z_grid matrices.\n", + "theta_indices = round.(Int, range(1, stop=size(R_grid, 2), length=num_theta_contours))\n", + "\n", + "for j in theta_indices\n", + " # Each column corresponds to a single theta value\n", + " plot!(p_flux_surfaces, R_grid[:, j], Z_grid[:, j], label=\"\", color=:red, linewidth=1)\n", + "end\n", + "\n", + "# 5. Add a legend manually (a common trick in Plots.jl)\n", + "plot!(p_flux_surfaces, [], [], color=:blue, label=\"Constant ψ\")\n", + "plot!(p_flux_surfaces, [], [], color=:red, label=\"Constant θ\")\n", + "\n", + "# 6. Display and save the final plot\n", + "display(p_flux_surfaces)\n", + "println(\"Flux surface contour plot saved as 'flux_surfaces_RZ.png'\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f07cd2f9", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Code to Plot 1D Profiles from the 'sq' Spline ---\n", + "# This code block goes at the end of your existing script.\n", + "\n", + "println(\"\\n--- Plotting 1D Profiles from 'sq' Spline ---\")\n", + "\n", + "# 1. To get smooth curves, we'll evaluate the spline on a dense grid,\n", + "# not just on its internal knot points.\n", + "psi_eval_grid = range(0.0, 1.0, length=200)\n", + "\n", + "# 2. Evaluate the 'sq' spline across this dense grid.\n", + "# Calling spline_eval with a vector input is efficient and returns a matrix\n", + "# where each column corresponds to one of the splined quantities.\n", + "println(\"Evaluating 'sq' spline on a dense grid...\")\n", + "evaluated_profiles = JPEC.Spl.spline_eval(plasma_eq.sq, collect(psi_eval_grid), 0)\n", + "println(\"Evaluation complete.\")\n", + "\n", + "# 3. Extract each profile into its own variable for clarity.\n", + "# Based on the direct_run implementation:\n", + "# Column 1: F = R*Bt (Toroidal Field Function)\n", + "# Column 2: P*μ₀ (Scaled Pressure)\n", + "# Column 3: Toroidal Flux function (related to dV/dψ_pol)\n", + "# Column 4: q (Safety Factor)\n", + "F_profile = evaluated_profiles[:, 1]\n", + "P_profile = evaluated_profiles[:, 2]\n", + "Flux_profile = evaluated_profiles[:, 3]\n", + "q_profile = evaluated_profiles[:, 4]\n", + "\n", + "# 4. Create and display the plots\n", + "\n", + "# Plot 1: Safety Factor (q)\n", + "p_q = plot(\n", + " psi_eval_grid,\n", + " q_profile,\n", + " title=\"Safety Factor Profile\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"q\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_q)\n", + "\n", + "# Plot 2: Scaled Pressure (P*μ₀)\n", + "p_p = plot(\n", + " psi_eval_grid,\n", + " P_profile,\n", + " title=\"Pressure Profile\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"P * μ₀ [T²]\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_p)\n", + "\n", + "\n", + "# Plot 3: Toroidal Field Function (F)\n", + "p_f = plot(\n", + " psi_eval_grid,\n", + " F_profile,\n", + " title=\"Toroidal Field Function\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"F = R * B_t [T*m]\",\n", + " legend=false,\n", + " linewidth=2\n", + ")\n", + "display(p_f)\n", + "\n", + "# Plot 4: Combined plot for comparison\n", + "p_all_profiles = plot(\n", + " title=\"1D Equilibrium Profiles\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " legend=:best\n", + ")\n", + "plot!(p_all_profiles, psi_eval_grid, q_profile, label=\"q (Safety Factor)\", linewidth=2)\n", + "plot!(p_all_profiles, psi_eval_grid, P_profile, label=\"P*μ₀ (Pressure)\", linewidth=2)\n", + "plot!(p_all_profiles, psi_eval_grid, F_profile, label=\"F (Toroidal Field Fn.)\", linewidth=2)\n", + "# We can also plot the 3rd quantity, though it's less commonly viewed.\n", + "# plot!(p_all_profiles, psi_eval_grid, Flux_profile, label=\"Toroidal Flux Fn.\", linewidth=2)\n", + "display(p_all_profiles)\n", + "\n", + "\n", + "println(\"1D profile plots saved successfully.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "42602d76", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/equil_test_bu.ipynb b/notebooks/equil_test_bu.ipynb new file mode 100644 index 000000000..a32f278a7 --- /dev/null +++ b/notebooks/equil_test_bu.ipynb @@ -0,0 +1,350 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "814db625", + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"..\") \n", + "Pkg.instantiate()\n", + "using JPEC, Plots\n", + "gr() " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "94c3d4e9", + "metadata": {}, + "outputs": [], + "source": [ + "# 1. Define the input parameters for the equilibrium solver.\n", + "# - eq_filename: The name of the g-file we just created.\n", + "# - eq_type: \"efit\" for a standard g-file.\n", + "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n", + "# - mpsi, mtheta: Resolution of the output grid.\n", + "equil_input = JPEC.Equilibrium.EquilInput(\n", + " \"beta_1.00\", # eq_filename\n", + " \"efit\", # eq_type\n", + " \"boozer\", # jac_type\n", + " 0.01, # psilow\n", + " 1.0, # psihigh\n", + " 100, # mpsi (number of radial grid points)\n", + " 128 # mtheta (number of poloidal grid points)\n", + ")\n", + "\n", + "# 2. Run the main equilibrium setup function.\n", + "# This will read the file, solve the direct problem, and return the final object.\n", + "println(\"Starting equilibrium reconstruction...\")\n", + "plasma_eq = JPEC.Equilibrium.setup_equilibrium(equil_input)\n", + "println(\"Equilibrium reconstruction complete.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "82c831fb", + "metadata": {}, + "outputs": [], + "source": [ + "# 새 셀: JPEC 스플라인 직접 테스트\n", + "println(\"🔍 Direct JPEC Spline Testing\")\n", + "println(\"=\"^40)\n", + "\n", + "# 1D 프로파일 스플라인 테스트\n", + "println(\"\\n📈 Testing 1D profile splines...\")\n", + "try\n", + " psi_test = [0.0, 0.25, 0.5, 0.75, 1.0]\n", + " \n", + " for psi in psi_test\n", + " result = JPEC.SplinesMod.spline_eval(plasma_eq.sq, psi)\n", + " println(\" ψ=$(psi): F=$(round(result[1], digits=3)), P=$(round(result[2], digits=3)), q=$(round(result[4], digits=3))\")\n", + " end\n", + " \n", + " println(\" ✅ 1D spline evaluation successful\")\n", + " \n", + "catch e\n", + " println(\" ❌ 1D spline evaluation failed: $e\")\n", + "end\n", + "\n", + "# 2D 기하학적 스플라인 테스트\n", + "println(\"\\n🗺️ Testing 2D geometry splines...\")\n", + "try\n", + " psi_test = 0.5\n", + " theta_test = [0.0, 0.25, 0.5, 0.75]\n", + " \n", + " for theta in theta_test\n", + " f, fx, fy = JPEC.SplinesMod.bicube_eval(plasma_eq.rzphi, psi_test, theta, 1)\n", + " println(\" (ψ=$(psi_test), θ=$(theta)): r²=$(round(f[1], digits=3)), shift=$(round(f[2], digits=3))\")\n", + " end\n", + " \n", + " println(\" ✅ 2D spline evaluation successful\")\n", + " \n", + "catch e\n", + " println(\" ❌ 2D spline evaluation failed: $e\")\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "23bbd6ba", + "metadata": {}, + "outputs": [], + "source": [ + "# Fourfit v4 테스트 (v3 대신 v4 사용)\n", + "println(\"🚀 Testing Fourfit v4 with Real JPEC Equilibrium Data\")\n", + "println(\"=\"^60)\n", + "\n", + "# plasma_eq 존재 확인\n", + "if !@isdefined(plasma_eq)\n", + " println(\"❌ plasma_eq is not defined - please run equilibrium setup first!\")\n", + " return\n", + "end\n", + "\n", + "# 1. Fourfit v4 모듈 로드\n", + "include(\"/Users/seoda-eun/JPEC/fourfit_old_v4.jl\")\n", + "using .FourfitOldV4\n", + "\n", + "# 2. 실제 JPEC 평형으로 Fourfit 실행\n", + "println(\"\\n📊 JPEC Equilibrium Info:\")\n", + "println(\" Type: $(typeof(plasma_eq))\")\n", + "println(\" Magnetic axis: R₀=$(round(plasma_eq.ro, digits=3)), Z₀=$(round(plasma_eq.zo, digits=6))\")\n", + "println(\" Flux normalization: ψ₀=$(round(plasma_eq.psio, digits=3))\")\n", + "println(\" Splines available:\")\n", + "println(\" - sq (1D profiles): $(plasma_eq.sq !== nothing ? \"✅\" : \"❌\")\")\n", + "println(\" - rzphi (2D geometry): $(plasma_eq.rzphi !== nothing ? \"✅\" : \"❌\")\")\n", + "println(\" - eq_quantities: $(plasma_eq.eq_quantities !== nothing ? \"✅\" : \"❌\")\")\n", + "\n", + "# 3. Fourfit 실행\n", + "println(\"\\n🧪 Running Fourfit v4 with real JPEC data...\")\n", + "global success, fourfit_data, eq_data = test_fourfit_with_jpec_equilibrium(plasma_eq)\n", + "\n", + "if success\n", + " println(\"\\n🎉 Fourfit execution successful!\")\n", + " \n", + " # 결과 분석\n", + " println(\"\\n📈 Results Analysis:\")\n", + " println(\" Grid size: $(fourfit_data.mpsi+1) × $(fourfit_data.mtheta+1)\")\n", + " println(\" Mode range: $(fourfit_data.mlow):$(fourfit_data.mhigh)\")\n", + " println(\" Toroidal mode: n = $(fourfit_data.nn)\")\n", + " \n", + " # 데이터 소스 확인\n", + " println(\"\\n🔍 Data Sources:\")\n", + " println(\" 1D Profiles: $(get(eq_data, \"has_real_jpec\", false) ? \"Real JPEC splines\" : \"Mock data\")\")\n", + " println(\" 2D Geometry: $(get(eq_data, \"has_real_geometry\", false) ? \"Real JPEC bicubic\" : \"Simplified\")\")\n", + " \n", + " # 프로파일 정보\n", + " println(\"\\n📊 Equilibrium Profiles:\")\n", + " F_prof = eq_data[\"F_profile\"]\n", + " P_prof = eq_data[\"P_profile\"] \n", + " q_prof = eq_data[\"q_profile\"]\n", + " \n", + " println(\" F profile range: [$(round(minimum(F_prof), digits=3)), $(round(maximum(F_prof), digits=3))] T⋅m\")\n", + " println(\" P profile range: [$(round(minimum(P_prof), digits=3)), $(round(maximum(P_prof), digits=3))] T²\")\n", + " println(\" q profile range: [$(round(minimum(q_prof), digits=3)), $(round(maximum(q_prof), digits=3))]\")\n", + " \n", + " # MHD 행렬 정보\n", + " if haskey(fourfit_data.cache, \"mhd_matrix\")\n", + " matrix = fourfit_data.cache[\"mhd_matrix\"]\n", + " println(\"\\n🔢 MHD Matrix Properties:\")\n", + " println(\" Matrix size: $(size(matrix[\"A_matrix\"]))\")\n", + " \n", + " # 고유값 분석\n", + " try\n", + " eigenvals = eigvals(matrix[\"A_matrix\"])\n", + " real_eigs = real(eigenvals)\n", + " println(\" Eigenvalues:\")\n", + " println(\" Range: [$(round(minimum(real_eigs), digits=3)), $(round(maximum(real_eigs), digits=3))]\")\n", + " println(\" All positive: $(all(real_eigs .> 0) ? \"✅\" : \"❌\")\")\n", + " println(\" Smallest eigenvalue: $(round(minimum(real_eigs), digits=6))\")\n", + " \n", + " # 조건수\n", + " cond_num = cond(matrix[\"A_matrix\"])\n", + " println(\" Condition number: $(round(cond_num, digits=2))\")\n", + " \n", + " catch e\n", + " println(\" Eigenvalue analysis failed: $e\")\n", + " end\n", + " end\n", + " \n", + "else\n", + " println(\"\\n❌ Fourfit execution failed!\")\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "97a529f4", + "metadata": {}, + "outputs": [], + "source": [ + "# The plasma_eq object contains the final 1D profile spline, `sq`.\n", + "# We will evaluate it on a fine grid to get smooth plot lines.\n", + "psi_norm_grid = range(0.0, 1.0, length=200)\n", + "\n", + "# spline_eval returns the function values (and derivatives if requested).\n", + "# For sq, the quantities are: 1:F, 2:P*mu0, 3:Toroidal Flux, 4:q\n", + "f_profiles = JPEC.spline_eval(plasma_eq.sq, collect(psi_norm_grid))\n", + "\n", + "# Extract each profile into its own variable for clarity\n", + "F_profile = f_profiles[:, 1]\n", + "P_profile = f_profiles[:, 2]\n", + "tor_flux_prof = f_profiles[:, 3]\n", + "q_profile = f_profiles[:, 4]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "131e2883", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "p = plot(layout=(2, 2), size=(900, 700), margin=5Plots.mm)\n", + "\n", + "# Plot 1: F = R*B_phi\n", + "plot!(p[1], psi_norm_grid, F_profile,\n", + " xlabel=\"Normalized Poloidal Flux (ψ_norm)\",\n", + " ylabel=\"F [T⋅m]\",\n", + " title=\"Toroidal Field Function (F)\",\n", + " legend=false,\n", + " lw=2\n", + ")\n", + "\n", + "# Plot 2: Pressure\n", + "plot!(p[2], psi_norm_grid, P_profile,\n", + " xlabel=\"Normalized Poloidal Flux (ψ_norm)\",\n", + " ylabel=\"μ₀P [T²]\",\n", + " title=\"Pressure Profile\",\n", + " legend=false,\n", + " lw=2\n", + ")\n", + "\n", + "# Plot 3: Safety Factor (q)\n", + "plot!(p[3], psi_norm_grid, q_profile,\n", + " xlabel=\"Normalized Poloidal Flux (ψ_norm)\",\n", + " ylabel=\"q\",\n", + " title=\"Safety Factor (q) Profile\",\n", + " legend=false,\n", + " lw=2\n", + ")\n", + "\n", + "# Plot 4: Toroidal Flux\n", + "plot!(p[4], psi_norm_grid, tor_flux_prof,\n", + " xlabel=\"Normalized Poloidal Flux (ψ_norm)\",\n", + " ylabel=\"Φ / (2π)² [Wb]\",\n", + " title=\"Toroidal Flux Profile\",\n", + " legend=false,\n", + " lw=2\n", + ")\n", + "\n", + "# Display the final plot\n", + "p" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d74a45e4", + "metadata": {}, + "outputs": [], + "source": [ + "# block 6\n", + "# --- Plot Straight-Field-Line Angle (θ) Contours ---\n", + "\n", + "p_theta = contour(\n", + " R_grid, \n", + " Z_grid, \n", + " THETA_values_on_grid,\n", + " title=\"Straight-Field-Line Angle (θ) Contours\",\n", + " xlabel=\"R [m]\",\n", + " ylabel=\"Z [m]\",\n", + " levels=20,\n", + " c=:hsv,\n", + " colorbar_title=\"Normalized θ\",\n", + " aspect_ratio=:equal,\n", + " linewidth=1.5\n", + ")\n", + "\n", + "# Mark the magnetic axis\n", + "scatter!(p_theta, [plasma_eq.ro], [plasma_eq.zo], label=\"Magnetic Axis\", mc=:black, ms=5)\n", + "\n", + "display(p_theta)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a79bf309", + "metadata": {}, + "outputs": [], + "source": [ + "# 노트북 셀 1: JPEC 로드\n", + "using Pkg\n", + "Pkg.activate(\"/Users/seoda-eun/JPEC/JPEC\")\n", + "using JPEC\n", + "\n", + "# 노트북 셀 2: Fourfit 포함\n", + "include(\"/Users/seoda-eun/JPEC/fourfit_old_v4.jl\")\n", + "using .FourfitOldV4\n", + "\n", + "# 노트북 셀 3: 실제 JPEC 평형 사용\n", + "# plasma_eq는 실제 JPEC 평형 객체라고 가정\n", + "success, fourfit_data, eq_data = test_fourfit_with_jpec_equilibrium(plasma_eq)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9859d659", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2c625a4a", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b359ecb", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d8ba8174", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/equildev.ipynb b/notebooks/equildev.ipynb deleted file mode 100644 index cc12a4745..000000000 --- a/notebooks/equildev.ipynb +++ /dev/null @@ -1,199 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "710e987d", - "metadata": {}, - "outputs": [], - "source": [ - "using JPEC, Plots" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "95f32fa1", - "metadata": {}, - "outputs": [], - "source": [ - "struct equil_settings\n", - " grid_type::String\n", - " mpsi::Int\n", - " psilow::Float64\n", - " psihigh::Float64\n", - "end\n", - "\n", - "mutable struct equil_bdata\n", - " psi::Float64\n", - " psir::Float64\n", - " psiz::Float64\n", - " psirz::Float64\n", - " psirr::Float64\n", - " psizz::Float64\n", - " f::Float64\n", - " f1::Float64\n", - " p::Float64\n", - " p1::Float64\n", - " br::Float64\n", - " bz::Float64\n", - " brr::Float64\n", - " brz::Float64\n", - " bzr::Float64\n", - " bzz::Float64\n", - "end\n", - "\n", - "function bfield_eval(bdata::equil_bdata, psi_in::JPEC.SplinesMod.BicubicSplineType, sq_in::JPEC.SplinesMod.CubicSplineType, r::Float64, z::Float64, psio::Float64)\n", - " # Equivalent of direct_mod.direct_get_bfield from fortran version\n", - " f, fr, fz, frr, frz, fzz = JPEC.SplinesMod.bicube_eval(psi_in, r, z, 2)\n", - " bdata.psi = f[1]\n", - " fq, fq1 = JPEC.SplinesMod.cube_eval(sq_in, 1-bdata.psi / psio, 1)\n", - " bdata.f, bdata.f1 = fq[1], fq1[1]\n", - " bdata.p, bdata.p1 = fq[2], fq1[2]\n", - " bdata.psir, bdata.psiz = fr[1], fz[1]\n", - " bdata.br, bdata.bz = bdata.psiz/r, -bdata.psir/r\n", - " bdata.psirr, bdata.psizz = frr[1], fzz[1]\n", - " bdata.psirz = frz[1]\n", - " bdata.brr = (bdata.psirz - bdata.br) / r\n", - " bdata.brz = bdata.psizz / r\n", - " bdata.bzr = -(bdata.psirr + bdata.bz) / r\n", - " bdata.bzz = -bdata.psirz / r\n", - " return bdata\n", - "end\n", - "\n", - "function equil_setup(eqsett::equil_settings, sq_in:: JPEC.SplinesMod.CubicSplineType, psi_in::JPEC.SplinesMod.BicubicSplineType)\n", - " # WIP direct_mod.direct_run\n", - " if eqsett.grid_type == \"ldp\"\n", - " psixs = collect(range(0, 1, eqsett.mpsi))\n", - " psi = eqsett.psilow .+ (eqsett.psihigh - eqsett.psilow) .* sin.(psixs .* π / 2).^2\n", - " end\n", - " return psi\n", - "end" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "788c2e66", - "metadata": {}, - "outputs": [], - "source": [ - "kappa = 1.8 # elongation\n", - "a = 1.0 # minor radius\n", - "r0 = 3.5 # major radius\n", - "q0 = 1.25 # safety factor at r0\n", - "p0fac = 1.0 # >= 1\n", - "b0fac = 1.0\n", - "f0fac = 1.0\n", - "\n", - "mr = 40\n", - "mz = 43\n", - "ma = 50\n", - "\n", - "r = zeros(mr)\n", - "z = zeros(mz)\n", - "rg = zeros(mr,mz)\n", - "zg = zeros(mr,mz)\n", - "\n", - "# psi_in = bicube(mr, mz, 1)\n", - "# sq_in = spline(ma,4)\n", - "\n", - "println(\"equilibrium of shape: \", mr, \"x\", mz, \" and radially resolved: \", ma)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6fcf34f4", - "metadata": {}, - "outputs": [], - "source": [ - "ro, zo = 0., 0.\n", - "f0 = r0*b0fac\n", - "psio = kappa * f0 * a^2 / (2 * q0 * r0)\n", - "psifac = psio / (a*r0)^2\n", - "efac = 1/kappa^2\n", - "pfac = 2*psio^2*(kappa^2+1)/(a*r0*kappa)^2\n", - "rmin = r0-1.5*a\n", - "rmax = r0+1.5*a\n", - "zmin = -1.5*kappa*a\n", - "zmax = -zmin" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "513f2c97", - "metadata": {}, - "outputs": [], - "source": [ - "#linspace(0,1,mr)\n", - "rhos = collect(range(0, stop=1, length=ma))\n", - "psis = rhos .^2\n", - "sqfs = zeros(ma, 4)\n", - "sqfs[:, 1] .= f0*f0fac\n", - "sqfs[:, 2] .= pfac * (p0fac .- rhos)\n", - "sqfs[:, 3] .= 0\n", - "sqfs[:, 4] .= rhos\n", - "\n", - "psifs = zeros(mr, mz, 1)\n", - "\n", - "sq_in = GPECsplines.spline_setup(psis, sqfs, 3)\n", - "rs = collect(range(rmin, stop=rmax, length=mr))\n", - "zs = collect(range(zmin, stop=zmax, length=mz))\n", - "for i in 1:mr\n", - " for j in 1:mz\n", - " psifs[i, j, 1] = psio - psifac * (efac * (rs[i] * zs[j])^2 + (rs[i]^2-r0^2)^2/4)\n", - " end\n", - "end\n", - "\n", - "psi_in = GPECsplines.bicube_setup(rs, zs, psifs, 3, 3)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "e86e3f7f", - "metadata": {}, - "outputs": [], - "source": [ - "# Make a contour plot of the bicubic spline\n", - "xs_fine = collect(range(rmin, stop=rmax, length=110))\n", - "ys_fine = collect(range(zmin, stop=zmax, length=100))\n", - "fs_fine = GPECsplines.bicube_eval(psi_in, xs_fine, ys_fine)\n", - "# plot the bicubic spline\n", - "p1 = contourf(xs_fine, ys_fine, fs_fine[:, :, 1]', label=\"psi\", legend=:topright)\n", - "title!(\"Psi, solov'ev equilibrium\")\n", - "xlabel!(\"R\")\n", - "ylabel!(\"Z\")\n", - "# equal axis scales\n", - "plot(p1, aspect_ratio=:equal)\n", - "xlims!(rmin, rmax)\n", - "ylims!(zmin, zmax)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "f8b12103", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Julia 1.11.4", - "language": "julia", - "name": "julia-1.11" - }, - "language_info": { - "file_extension": ".jl", - "mimetype": "application/julia", - "name": "julia", - "version": "1.11.4" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/eulerbinread.ipynb b/notebooks/eulerbinread.ipynb new file mode 100644 index 000000000..288a468ae --- /dev/null +++ b/notebooks/eulerbinread.ipynb @@ -0,0 +1,301 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "db314816", + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg; Pkg.add(\"FortranFiles\"); Pkg.add(\"LinearAlgebra\")\n", + "using FortranFiles\n", + "using LinearAlgebra" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7fec1fab", + "metadata": {}, + "outputs": [], + "source": [ + "# Create solution, sing structs\n", + "struct solution_type\n", + " msol :: Int32\n", + " u :: Array{ComplexF64,3}\n", + "end\n", + "\n", + "struct resist_type\n", + " e :: Float64\n", + " f :: Float64\n", + " h :: Float64\n", + " m :: Float64\n", + " g :: Float64\n", + " k :: Float64\n", + " eta :: Float64\n", + " rho :: Float64\n", + " taua :: Float64\n", + " taur :: Float64\n", + " di :: Float64\n", + " dr :: Float64\n", + " sfac :: Float64\n", + " deltac :: Float64\n", + " eigenvalue :: ComplexF64\n", + "end\n", + "\n", + "struct sing_type\n", + " msol_l :: Int32\n", + " msol_r :: Int32\n", + " jfix :: Int32\n", + " jpert :: Int32\n", + " psifac :: Float64\n", + " q :: Float64\n", + " q1 :: Float64\n", + " ca_l :: Array{ComplexF64,3}\n", + " ca_r :: Array{ComplexF64,3}\n", + " restype :: resist_type\n", + "end\n", + "\n", + "mutable struct fixfac_type\n", + " msol :: Int32\n", + " index :: Vector{Int32}\n", + " fixfac :: Array{ComplexF64,2}\n", + " transform :: Array{ComplexF64,2}\n", + " gauss :: Array{ComplexF64,2}\n", + " function fixfac_type(msol::Int32, index::Vector{Int32},fixfac::Array{ComplexF64,2})\n", + " transform = Matrix{ComplexF64}(I,msol,msol)\n", + " gauss = Matrix{ComplexF64}(I,msol,msol)\n", + " new(msol,index,fixfac,transform,gauss)\n", + " end\n", + "end\n", + "\n", + "function idcon_transform(fixtype, sing_flag)\n", + " \n", + " msol = length(fixtype[2].index)\n", + " mfix = length(fixtype)-1\n", + " identity = Matrix{ComplexF64}(I,msol,msol)\n", + "\n", + " # Construct gaussian reduction matrix\n", + " for ifix in 2:1:mfix+1\n", + " fixtype[ifix].gauss = copy(identity)\n", + " mask = zeros(Bool, msol)\n", + " mask .= true\n", + " for isol in 1:msol\n", + " ksol = fixtype[ifix].index[isol]\n", + " mask[ksol] = false\n", + " temp = copy(identity)\n", + " for jsol in 1:msol\n", + " if mask[jsol]\n", + " temp[ksol,jsol] = fixtype[ifix].fixfac[ksol,jsol]\n", + " end\n", + " end\n", + " # Matrix multiplication gauss = gauss * temp\n", + " fixtype[ifix].gauss = fixtype[ifix].gauss * temp\n", + " end\n", + " if sing_flag[ifix-1]\n", + " fixtype[ifix].gauss[:,fixtype[ifix].index[1]] .= 0.0\n", + " end\n", + " end\n", + " \n", + " # Concatenate gaussian reduction matrix\n", + " fixtype[mfix+1].transform = copy(identity)\n", + " for ifix in mfix:-1:1\n", + " fixtype[ifix].transform = fixtype[ifix+1].gauss * fixtype[ifix+1].transform\n", + " end\n", + " return fixtype\n", + "end\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "59f1ad09", + "metadata": {}, + "outputs": [], + "source": [ + "fstream = FortranFile(\"euler.bin\", \"r\")\n", + "\n", + "# --- Read header ---\n", + "mlow, mhigh, nn, mpsi, mtheta, ro, zo = read(fstream, Int32, Int32, Int32, Int32, Int32, Float64, Float64)\n", + "mband, mthsurf0, mthvac, psio, psilow, psilim, qlim, singfac_min = read(fstream, Int32, Int32, Int32, Float64, Float64, Float64, Float64, Float64)\n", + "power_b, power_r, power_bp = read(fstream, Int32, Int32, Int32)\n", + "kin_flag, con_flag = read(fstream, Int32, Int32)\n", + "\n", + "amean, rmean, aratio, kappa, delta1, delta2, \n", + " li1, li2, li3, betap1, betap2, betap3, betat, betan, bt0, \n", + " q0, qmin, qmax, qa, crnt, q95, shotnum, shottime = read(fstream, \n", + " Float64, Float64, Float64, Float64, Float64, Float64,\n", + " Float64, Float64, Float64, Float64, Float64, Float64,\n", + " Float64, Float64, Float64, Float64, Float64, Float64,\n", + " Float64, Float64, Float64, Float64, Float64)\n", + "\n", + "# --- Read equilibrium on flux coordinates ---\n", + "# sq%xs is size mpsi, sq%fs is size mpsi x 4, sq%fs1 is size mpsi x 4, sq%xpower is size 2 x 4\n", + "sq_xs, sq_fs, sq_fs1, sq_xpower = read(fstream, (Float64, mpsi), (Float64, (mpsi,4)), (Float64, (mpsi,4)), (Float64, (2,4)))\n", + "# rzphi%xs is size mpsi, rzphi%ys is size mtheta, rzphi%fs is size mpsi x mtheta, etc.\n", + "rzphi_xs, rzphi_ys, \n", + " rzphi_fs, rzphi_fsx, rzphi_fsy, rzphi_fsxy, \n", + " rzphi_x0, rzphi_y0, rzphi_xpower, rzphi_ypower = read(fstream, \n", + " (Float64, mpsi), (Float64, mtheta), \n", + " (Float64, (mpsi,mtheta,4)), (Float64, (mpsi,mtheta,4)), (Float64, (mpsi,mtheta,4)), (Float64, (mpsi,mtheta,4)),\n", + " (Float64, 2), (Float64, 2), (Float64, (2,4)), (Float64, (2,4)))\n", + "\n", + "# misc derived quantities\n", + "chi1=2*pi*psio\n", + "mpert=mhigh-mlow+1\n", + "\n", + "# --- Count solutions in file (first pass) ---\n", + "mstep = -1\n", + "mfix = 0\n", + "msing = 0\n", + "\n", + "while !eof(fstream)\n", + " data_type = read(fstream, Int32)\n", + " if data_type == 1\n", + " mstep += 1\n", + " read(fstream) # skip\n", + " read(fstream)\n", + " read(fstream)\n", + " elseif data_type == 2\n", + " mfix += 1\n", + " read(fstream)\n", + " read(fstream)\n", + " elseif data_type == 3\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " elseif data_type == 4\n", + " msing += 1\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " elseif data_type == 5\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " read(fstream)\n", + " else\n", + " error(\"Cannot recognize data_type = $data_type\")\n", + " end\n", + "end\n", + "\n", + "close(fstream)\n", + "\n", + "psifac = zeros(Float64, mstep+1)\n", + "rhofac = zeros(Float64, mstep+1)\n", + "qfac = zeros(Float64, mstep+1)\n", + "\n", + "soltype = Vector{solution_type}(undef, mstep+1)\n", + "singtype = Vector{sing_type}(undef, msing)\n", + "fixstep = zeros(Float64, mfix+2)\n", + "fixtype = Vector{fixfac_type}(undef, mfix+1)\n", + "sing_flag = zeros(Bool, mfix)\n", + "\n", + "fixtype[1] = fixfac_type(Int32(0), zeros(Int32, 0), zeros(ComplexF64, 0, 0))\n", + "\n", + "et = zeros(ComplexF64, mpert)\n", + "ep = zeros(ComplexF64, mpert)\n", + "ee = zeros(ComplexF64, mpert)\n", + "\n", + "wt = zeros(ComplexF64, (mpert,mpert))\n", + "wt0 = zeros(ComplexF64, (mpert,mpert))\n", + "\n", + "wft = zeros(ComplexF64, (mpert,mpert))\n", + "eft = zeros(ComplexF64, mpert)\n", + "efp = zeros(ComplexF64, mpert)\n", + "wtraw = zeros(ComplexF64, (mpert,mpert))\n", + "\n", + "eft = -1\n", + "wft = 0\n", + "fixstep[1] = 0\n", + "fixstep[mfix+2] = mstep\n", + "\n", + "fstream = FortranFile(\"euler.bin\", \"r\")\n", + "# --- Read header again ---\n", + "mlow, mhigh, nn, mpsi, mtheta, ro, zo = read(fstream, Int32, Int32, Int32, Int32, Int32, Float64, Float64)\n", + "mband, mthsurf0, mthvac, psio, psilow, psilim, qlim, singfac_min = read(fstream, Int32, Int32, Int32, Float64, Float64, Float64, Float64, Float64)\n", + "power_b, power_r, power_bp = read(fstream, Int32, Int32, Int32)\n", + "kin_flag, con_flag = read(fstream, Int32, Int32)\n", + "istep = -1\n", + "ifix = 0\n", + "ising = 0\n", + "\n", + "println(\"mfix = \", mfix)\n", + "\n", + "while !eof(fstream)\n", + " data_type = read(fstream, Int32)\n", + " if data_type == 1\n", + " istep += 1\n", + " psifac[istep+1], qfac[istep+1], msoli = read(fstream, Float64, Float64, Int32)\n", + " u = Array{ComplexF64}(undef,(mpert,msoli,4))\n", + " u[:,:,1:2] = read(fstream, (ComplexF64,(mpert,msoli,2)))\n", + " u[:,:,3:4] = read(fstream, (ComplexF64,(mpert,msoli,2)))\n", + " soltype[istep+1] = solution_type(msoli,u)\n", + " elseif data_type == 2\n", + " ifix += 1\n", + " println(\"Writing to fixtype[\", ifix+1, \"]\")\n", + " fixstep[ifix+1] = istep\n", + " sing_flag[ifix], msoli = read(fstream, Int32, Int32)\n", + " fixfac, index = read(fstream, (ComplexF64,(msoli,msoli)),(Int32,msoli))\n", + " fixtype[ifix+1] = fixfac_type(msoli,index,fixfac)\n", + " elseif data_type == 3\n", + " ep = read(fstream,(ComplexF64,mpert))\n", + " et = read(fstream,(ComplexF64,mpert))\n", + " wt = read(fstream,(ComplexF64,(mpert,mpert)))\n", + " wt0 = read(fstream,(ComplexF64,(mpert,mpert)))\n", + " wv_farwall_flag = read(fstream, Int32)\n", + " elseif data_type == 4\n", + " ising += 1\n", + " jfixi = ifix\n", + " jperti = round(Int32, nn*qfac[istep+1] + 0.5)\n", + " psifaci, qi, q1i = read(fstream, Float64, Float64, Float64)\n", + " msol_l = read(fstream, Int32)\n", + " ca_l = read(fstream, (ComplexF64,(mpert,msol_l,2)))\n", + " msol_r = read(fstream, Int32)\n", + " ca_r = read(fstream, (ComplexF64,(mpert,msol_r,2)))\n", + " e, f, h, m, g, k, eta, rho, taua, taur = read(fstream, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64, Float64)\n", + " elseif data_type == 5\n", + " ep = read(fstream,(ComplexF64,mpert))\n", + " et = read(fstream,(ComplexF64,mpert))\n", + " wt = read(fstream,(ComplexF64,(mpert,mpert)))\n", + " efp = read(fstream,(Float64,mpert))\n", + " eft = read(fstream,(Float64,mpert))\n", + " wft = read(fstream,(ComplexF64,(mpert,mpert)))\n", + " wtraw = read(fstream,(ComplexF64,(mpert,mpert)))\n", + " else\n", + " # for all the reads we skipped in the second pass\n", + " print()\n", + " end\n", + "end\n", + "\n", + "close(fstream)\n", + "\n", + "idcon_transform(fixtype, sing_flag)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/sing_find_example.ipynb b/notebooks/sing_find_example.ipynb new file mode 100644 index 000000000..ea4f3de05 --- /dev/null +++ b/notebooks/sing_find_example.ipynb @@ -0,0 +1,493 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "3162f30d", + "metadata": {}, + "outputs": [], + "source": [ + "# using Pkg\n", + "# Pkg.activate(\"..\") \n", + "# Pkg.instantiate()\n", + "using JPEC, Plots\n", + "gr() " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cbcbbf1a", + "metadata": {}, + "outputs": [], + "source": [ + "using LinearAlgebra\n", + "using Printf\n", + "using Plots" + ] + }, + { + "cell_type": "markdown", + "id": "1a4b93da", + "metadata": {}, + "source": [ + "### read Equil" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "91adefe3", + "metadata": {}, + "outputs": [], + "source": [ + "# 1. Define the input parameters for the equilibrium solver.\n", + "# - eq_filename: The name of the g-file we just created.\n", + "# - eq_type: \"efit\" for a standard g-file.\n", + "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n", + "# - mpsi, mtheta: Resolution of the output grid.\n", + "equil_input = JPEC.Equilibrium.EquilInput(\n", + " \"beta_1.00\", # eq_filename\n", + " \"efit\", # eq_type\n", + " \"boozer\", # jac_type\n", + " 0.01, # psilow\n", + " 1.0, # psihigh\n", + " 100, # mpsi (number of radial grid points)\n", + " 128 # mtheta (number of poloidal grid points)\n", + ")\n", + "\n", + "# 2. Run the main equilibrium setup function.\n", + "# This will read the file, solve the direct problem, and return the final object.\n", + "println(\"Starting equilibrium reconstruction...\")\n", + "plasma_eq = JPEC.Equilibrium.setup_equilibrium(equil_input)\n", + "println(\"Equilibrium reconstruction complete.\")" + ] + }, + { + "cell_type": "markdown", + "id": "c34090af", + "metadata": {}, + "source": [ + "### Use spline_eval \n", + "sq!!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9fc11a8e", + "metadata": {}, + "outputs": [], + "source": [ + "# The plasma_eq object contains the final 1D profile spline, `sq`.\n", + "# We will evaluate it on a fine grid to get smooth plot lines.\n", + "psi_norm_grid = range(0.0, 1.0, length=200)\n", + "\n", + "# spline_eval returns the function values (and derivatives if requested).\n", + "# For sq, the quantities are: 1:F, 2:P*mu0, 3:Toroidal Flux, 4:q\n", + "f_profiles = JPEC.SplinesMod.spline_eval(plasma_eq.sq, collect(psi_norm_grid))\n", + "\n", + "# Extract each profile into its own variable for clarity\n", + "F_profile = f_profiles[:, 1]\n", + "P_profile = f_profiles[:, 2]\n", + "tor_flux_prof = f_profiles[:, 3]\n", + "q_profile = f_profiles[:, 4];" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "24c68c15", + "metadata": {}, + "outputs": [], + "source": [ + "plot(psi_norm_grid, q_profile, \n", + " xlabel=\"Normalized Flux\", ylabel=\"Safety Factor q\", \n", + " title=\"Safety Factor Profile\",\n", + " legend=:topright, label=\"q(ψ)\", lw=2, color=:blue)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4ca48f63", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + " sing_find!(sing_surf_data, plasma_eq; mex=2, nn=1, itmax=200)\n", + "\n", + "Finds and appends rational (singular) surfaces in a plasma equilibrium profile,\n", + "where `m = nn*q` within each interval between extrema of the safety factor profile `q(ψ)`.\n", + "\n", + "The results are stored as `NamedTuple`s in the supplied vector `sing_surf_data`, \n", + "with keys: `m`, `ψfac`, `ρ`, `q`, and `q1`.\n", + "\n", + "# Arguments\n", + "- `sing_surf_data::Vector`: Container for output; will be emptied and updated in-place.\n", + "- `plasma_eq`: Plasma equilibrium object with a field `.sq` suitable for spline evaluation.\n", + "- `mex::Int`: Number of `q` profile extrema. Defaults to 2 (monotonic `q`).\n", + "- `nn::Int`: Toroidal mode number `n`.\n", + "- `itmax::Int`: Maximum allowed bisection iterations per root.\n", + "\n", + "# Details\n", + "Searches each interval between adjacent `q`-profile extrema for all integer poloidal mode numbers `m`\n", + "that satisfy the rational surface condition `m = n*q(ψ)`, using bisection to find the roots.\n", + "Assumes a monotonic `q` profile, unless a generalized interface is implemented\n", + "(TODO: support for non-monotonic profiles).\n", + "\n", + "# Output\n", + "For each rational surface found, a `NamedTuple` with:\n", + "- `m`: Poloidal mode number at this surface\n", + "- `ψfac`: Normalized flux label at the surface\n", + "- `ρ`: Square root of `ψfac`\n", + "- `q`: `q` value at the surface (`m/nn`)\n", + "- `q1`: Derivative of `q` at the surface\n", + "\n", + "is pushed to `sing_surf_data`.\n", + "\"\"\"\n", + "function sing_find!(sing_surf_data, plasma_eq; nn=1, itmax=200)\n", + " \n", + " # Ensure sing_surf_data is empty before starting\n", + " empty!(sing_surf_data)\n", + "\n", + " # Define functions to evaluate q and its first derivative\n", + " qval(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 0)[4]\n", + " q1val(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 1)[2][4] \n", + "\n", + " # TODO: I assume monotonic here for checking, will need to provide some interface\n", + " # for the actual values fo (mex, qex) determined from the equil code\n", + " qex = [qval(0.0), qval(1.0)]\n", + " ψex = [0.0, 1.0]\n", + " mex = 2\n", + "\n", + " # Loop over extrema of q, find all rational values in between\n", + " for iex in 2:mex\n", + " dq = qex[iex] - qex[iex-1]\n", + " m = floor(Int, nn * qex[iex-1])\n", + " if dq > 0\n", + " m += 1\n", + " end\n", + " dm = Int(sign(dq * nn))\n", + "\n", + " # Loop over possible m's in interval\n", + " while (m - nn * qex[iex-1]) * (m - nn * qex[iex]) <= 0\n", + " it = 0\n", + " ψ0 = ψex[iex-1]\n", + " ψ1 = ψex[iex]\n", + " ψfac = 0.0\n", + "\n", + " # Bisection method to find singular surface\n", + " while it < itmax\n", + " it += 1\n", + " ψfac = (ψ0 + ψ1)/2\n", + " singfac = (m - nn * qval(ψfac)) * dm\n", + " if abs(singfac) <= 1e-12\n", + " break\n", + " elseif singfac > 0\n", + " ψ0 = ψfac\n", + " else\n", + " ψ1 = ψfac\n", + " end\n", + " end\n", + " if it == itmax\n", + " @warn \"Bisection did not converge for m = $m\"\n", + " # You may want to continue, break, or error here\n", + " else\n", + " push!(sing_surf_data, (\n", + " m = m,\n", + " ψfac = ψfac,\n", + " ρ = sqrt(ψfac),\n", + " q = m / nn,\n", + " q1 = q1val(ψfac),\n", + " ))\n", + " end\n", + " m += dm\n", + " end\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3899bb00", + "metadata": {}, + "outputs": [], + "source": [ + "sing_surf_data = []\n", + "sing_find!(sing_surf_data, plasma_eq)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fea33c45", + "metadata": {}, + "outputs": [], + "source": [ + "sing_surf_data[1].ψfac" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4a23c2ce", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + " bubble!(key::AbstractVector, index::AbstractVector{Int}, mmin::Int, mmax::Int)\n", + "\n", + "Sorts the indices in `index` in place such that `key[index[i]]` are in decreasing order\n", + "from `mmin` to `mmax` (inclusive).\n", + "\"\"\"\n", + "function bubble!(key::AbstractVector, index::AbstractVector{Int}, mmin::Int, mmax::Int)\n", + " switched = true\n", + " while switched\n", + " switched = false\n", + " for i in mmin:(mmax-1)\n", + " if key[index[i]] < key[index[i+1]]\n", + " index[i], index[i+1] = index[i+1], index[i]\n", + " switched = true\n", + " end\n", + " end\n", + " end\n", + " return nothing\n", + "end\n", + "\n", + "\"\"\"\n", + " ode_axis_init(sing_surf_data, sq; nn = 1, ψlim = 0.9936, ψlow = 0.01, mlow = -12, mhigh = 20, singfac_min = 1e-5, qlow = 0.0, sort_type = \"absm\")\n", + "\n", + "Initializes the ODE system near the magnetic axis for MHD or kinetic-MHD stability\n", + "analysis. This routine prepares solution vectors and sorting indices, locates\n", + "the relevant singular surfaces in the plasma equilibrium based on input data,\n", + "and sets integration boundaries and normalization factors for subsequent ODE integration\n", + "through singularities.\n", + "\n", + "# Arguments\n", + "- `sing_surf_data`: Array of structures, each containing information about singular surfaces,\n", + " including fields like `.ψfac`, `.q`, and `.q1`. Filled from sing_find function\n", + "- `sq`: Spline object controlling the equilibrium safety factor profile (typically contains equilibrium profile splines).\n", + "\n", + "# Keyword Arguments (these are likely to be replaced by the user input file structure)\n", + "- `nn`: Integer. Toroidal mode number.\n", + "- `ψlim`: Float. Upper bound for normalized flux coordinate ψ.\n", + "- `ψlow`: Float. Lower bound for normalized flux coordinate ψ.\n", + "- `mlow`: Integer. Lowest poloidal mode number to consider.\n", + "- `mhigh`: Integer. Highest poloidal mode number to consider.\n", + "- `singfac_min`: Float. Minimum separation from a singular surface.\n", + "- `qlow`: Float. Lower bound for safety factor q. (Currently not implemented if > 0.)\n", + "- `sort_type`: String. Sorting criteria for mode numbers (`\"absm\"` for |m|, or\n", + " `\"sing\"` for proximity to the first singular surface's m).\n", + "\n", + "# Details\n", + "This function does the following:\n", + "- Determines relevant singular surfaces from the provided equilibrium/singularity data.\n", + "- Sets up arrays for the ODE solution and related workspaces for all poloidal harmonics in the range [`mlow`, `mhigh`].\n", + "- Sorts the initial harmonics according to the specified `sort_type`.\n", + "- Initializes normalization factors and solution arrays for use in the ODE integrator.\n", + "- Computes the initial offset (`singfac`) from the next singular surface.\n", + "\n", + "Several features for kinetic MHD (indicated by `kin_flag`) or for `qlow > 0` are noted but not yet implemented.\n", + "\n", + "\"\"\"\n", + "\n", + "function ode_axis_init(sing_surf_data, plasma_eq; nn = 1, ψlim=0.9936, ψlow = 0.01, mlow = -12, mhigh = 20, singfac_min = 1e-5, qlow = 0.0, sort_type = \"absm\")\n", + " # JMH - I think all default values here will be supplied by inputs\n", + " # Right now, there are a lot of globals - not sure how we want to handle these\n", + " # But at least the major outputs here match fortran dcon\n", + "\n", + " # maybe change how this is passed in?\n", + " qval(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 0)[4]\n", + " q1val(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 1)[2][4] \n", + "\n", + " # Preliminary computations\n", + " new = true\n", + " ix = 0\n", + " psiout = 1.0\n", + " ψfac = 0.0 # TODO: this was Fortran sq%xs(0)?\n", + " msing = size(sing_surf_data)[1]\n", + " \n", + " # TODO: defined elsewhere\n", + " mpert = mhigh - mlow + 1\n", + "\n", + " # Use Newton iteration to find starting psi if qlow is above q0\n", + " # TODO: add this. For now, assume qlow = 0.0 and start at the first singular surface\n", + " if qlow > 0.0\n", + " @warn \"qlow > 0.0 is not implemented in ode_axis_init\"\n", + " end\n", + "\n", + " # Find inner singular surface\n", + " global ising = 0\n", + " if false #(TODO: kin_flag)\n", + " # for ising = 1:kmsing\n", + " # if kinsing[ising].psifac > psifac\n", + " # break\n", + " # end\n", + " # end\n", + " else\n", + " for ising in 1:msing\n", + " if sing_surf_data[ising].ψfac > ψfac\n", + " break\n", + " end\n", + " end\n", + " end\n", + " ising = max(0, ising - 1)\n", + "\n", + " # Find next singular surface\n", + " if false # TODO: (kin_flag)\n", + " # while true\n", + " # ising += 1\n", + " # if ising > kmsing\n", + " # break\n", + " # end\n", + " # if psilim < kinsing[ising].psifac\n", + " # break\n", + " # end\n", + " # q = kinsing[ising].q\n", + " # if mlow <= nn * q && mhigh >= nn * q\n", + " # break\n", + " # end\n", + " # end\n", + " # if ising > kmsing || singfac_min == 0\n", + " # psimax = psilim * (1 - eps)\n", + " # next = \"finish\"\n", + " # elseif psilim < kinsing[ising].psifac\n", + " # psimax = psilim * (1 - eps)\n", + " # next = \"finish\"\n", + " # else\n", + " # psimax = kinsing[ising].psifac - singfac_min / abs(nn * kinsing[ising].q1)\n", + " # next = \"cross\"\n", + " # end\n", + " else\n", + " while true\n", + " ising += 1\n", + " if ising > msing || ψlim < sing_surf_data[min(ising, msing)].ψfac\n", + " break\n", + " end\n", + " q = sing_surf_data[ising].q\n", + " if mlow <= nn * q && mhigh >= nn * q\n", + " break\n", + " end\n", + " end\n", + " if ising > msing || ψlim < sing_surf_data[min(ising, msing)].ψfac || singfac_min == 0\n", + " ψmax = ψlim * (1 - eps)\n", + " next = \"finish\"\n", + " else\n", + " ψmax = sing_surf_data[ising].ψfac - singfac_min / abs(nn * sing_surf_data[ising].q1)\n", + " next = \"cross\"\n", + " end\n", + " end\n", + "\n", + " # Allocate and sort solutions by increasing value of |m-ms1|\n", + " global u = zeros(ComplexF64, mpert, mpert, 2)\n", + " global du = zeros(ComplexF64, mpert, mpert, 2)\n", + " global u_save = zeros(ComplexF64, mpert, mpert, 2)\n", + " global unorm0 = zeros(Float64, 2 * mpert)\n", + " global unorm = zeros(Float64, 2 * mpert)\n", + " global index = collect(1:mpert)\n", + " m = mlow - 1 .+ index\n", + " if sort_type == \"absm\"\n", + " key = abs.(m)\n", + " elseif sort_type == \"sing\"\n", + " key = m\n", + " if msing > 0\n", + " key = key .- sing[1].m\n", + " end\n", + " key = -abs.(key)\n", + " else\n", + " error(\"Cannot recognize sort_type = $sort_type\")\n", + " end\n", + " bubble!(key, index, 1, mpert) # in original Fortran: bubble(key, index, 1, mpert)\n", + " println(key)\n", + " println(index)\n", + "\n", + " # Initialize solutions\n", + " u .= 0\n", + " for ipert = 1:mpert\n", + " u[index[ipert], ipert, 2] = 1\n", + " end\n", + " global msol = mpert\n", + " global neq = 4 * mpert * msol\n", + " u_save .= u\n", + " global psi_save = ψfac\n", + "\n", + " # Initialize integrator parameters (JMH - not sure if these are needed in Julia)\n", + " # global istep = 0\n", + " # global iopt = 1\n", + " # global itask = 5\n", + " # global itol = 2\n", + " # global mf = 10\n", + " # global istate = 1\n", + "\n", + " # Compute conditions at next singular surface\n", + " q = qval(ψlow) # Fortran: q=sq%fs(0,4)\n", + " println(q)\n", + " if false #TODO: (kin_flag)\n", + " # if kmsing > 0\n", + " # m1 = round(Int, nn * kinsing[ising].q)\n", + " # else\n", + " # m1 = round(Int, nn * qlim) + sign(one, nn * sq.fs1[mpsi, 5])\n", + " # end\n", + " else\n", + " if msing > 0\n", + " m1 = round(Int, nn * sing_surf_data[ising].q)\n", + " else\n", + " m1 = round(Int, nn * qlim) + sign(nn * q1val[end])\n", + " end\n", + " end\n", + " global singfac = abs(m1 - nn * q)\n", + "\n", + " println(m1)\n", + " println(singfac)\n", + "\n", + " # Set up work arrays (JMH - not sure if these are needed in Julia)\n", + " # global liw = length(iwork)\n", + " # global lrw = 22 + 64 * mpert * msol\n", + " # global rwork = zeros(Float64, lrw)\n", + " # global atol = zeros(ComplexF64, mpert, msol, 2)\n", + " # global fixfac = zeros(ComplexF64, msol, msol)\n", + " # iwork = 0\n", + " # rwork = 0\n", + " # rwork[1] = psimax\n", + " # rwork[5] = psifac * 1e-3\n", + " # rwork[11] = rwork[5]\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b414bf00", + "metadata": {}, + "outputs": [], + "source": [ + "ode_axis_init(sing_surf_data, plasma_eq)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2e6fc625", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.5", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/soloviev_ideal/dcon.toml b/notebooks/soloviev_ideal/dcon.toml new file mode 100644 index 000000000..b8e08dc0a --- /dev/null +++ b/notebooks/soloviev_ideal/dcon.toml @@ -0,0 +1,59 @@ +[DCON_CONTROL] +bal_flag = false # Ideal MHD ballooning criterion for short wavelengths +mat_flag = true # Construct coefficient matrices for diagnostic purposes +ode_flag = true # Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) +vac_flag = false # Compute plasma, vacuum, and total energies for free-boundary modes +mer_flag = true # Evaluate the Mercier criterian + +sas_flag = false # Safety factor (q) limit determined as q_ir+dmlim... +dmlim = 0.2 # See sas_flag +qlow = 1.02 # Integration initiated at q determined by min(q0, qlow)... +qhigh = 1e3 # Integration terminated at q limit determined by min(qa, qhigh)... +sing_start = 0 # Start integration at the sing_start'th rational from the axis (psilow) + +nn = 1 # Toroidal mode number +delta_mlow = 8 # Expands lower bound of Fourier harmonics +delta_mhigh = 8 # Expands upper bound of Fourier harmonics +delta_mband = 0 # Integration keeps only this wide a band... +mthvac = 960 # Number of points used in splines over poloidal angle at plasma-vacuum interface. +thmax0 = 1 # Linear multiplier on the automatic choice of theta integration bounds + +kin_flag = false # Kinetic EL equation (default: false) +con_flag = false # Continue integration through layers (default: false) +kinfac1 = 1.0 # Scale factor for energy contribution (default: 1.0) +kinfac2 = 1.0 # Scale factor for torque contribution (default: 1.0) +kingridtype = 0 # Regular grid method (default: 0) +passing_flag = true # Includes passing particle effects (default: false) +ktanh_flag = true # Ignore kinetic effects in the core smoothly (default: false) +ktc = 0.1 # Parameter for ktanh_flag (default: 0.1) +ktw = 50.0 # Parameter for ktanh_flag (default: 50.0) +ion_flag = true # Include ion dW_k when kin_flag is true +electron_flag = false # Include electron dW_k when kin_flag is true + +tol_nr = 1e-6 # Relative tolerance of dynamic integration steps away from rationals +tol_r = 1e-7 # Relative tolerance of dynamic integration steps near rationals +crossover = 1e-2 # Fractional distance from rational q at which tol switches +singfac_min = 1e-4 # Fractional distance from rational q at which ideal jump enforced +ucrit = 1e3 # Maximum fraction of solutions allowed before re-normalized + +termbycross_flag = false # Terminate ODE solver in the event of a zero crossing + +use_classic_splines = false # Use a classical cubic spline instead of tri-diagonal solution + +[DCON_OUTPUT] +out_ahg2msc = false # Output deprecated ahg2msc.out files +crit_break = true # Color of the crit curve changes when crossing a singular surface +ahb_flag = false # Output normal magnetic field eigenvalues... +msol_ahb = 1 # Number of eigenfunctions output by ahb_flag = true? +mthsurf0 = 1 # Linear multiplier on number of boundary points for ahgb_flag = true + +bin_euler = true # Output M psi-by-M euler-lagrange solutions to binary file euler.bin +bin_vac = false # Output deprecated binary vacuum.bin +euler_stride = 1 # Output only every euler_stride'th psi step + +out_bal1 = false # Ascii output for bal_flag poloidal functions +bin_bal1 = false # Binary output for bal_flag poloidal functions +out_bal2 = false # Ascii output for bal_flag functions +bin_bal2 = false # Binary output for bal_flag functions + +netcdf_out = true # Replicate ascii dcon.out information in a netcdf file \ No newline at end of file diff --git a/notebooks/soloviev_ideal/equil.toml b/notebooks/soloviev_ideal/equil.toml new file mode 100644 index 000000000..7abe0a9d0 --- /dev/null +++ b/notebooks/soloviev_ideal/equil.toml @@ -0,0 +1,30 @@ +[EQUIL_CONTROL] +eq_type = "sol" # Type of the input 2D equilibrium file +eq_filename = "sol.toml" # path to equilibrium file + +jac_type = "pest" # Coordinate system (hamada, pest, boozer, equal_arc) +power_bp = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r +power_b = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r +power_r = 0 # del.B ~ B_p^power_bp * B^power_b / R^power_r + +grid_type = "ldp" # Radial grid packing +psilow = 1e-4 # Min psi (normalized) +psihigh = 0.99999 # Max psi (normalized) +mpsi = 128 # Radial grid intervals +mtheta = 256 # Poloidal grid intervals + +newq0 = 0 # Override q(0) +etol = 1e-7 # Reconstruction tolerance +use_classic_splines = false # Use classical spline (vs. tri-diagonal) + +input_only = false # Quit after input read + +[EQUIL_OUTPUT] +gse_flag = false # Output G-S equation accuracy diagnostics +out_eq_1d = false # ASCII output of 1D eq data +bin_eq_1d = false # Binary output of 1D eq data +out_eq_2d = false # ASCII output of 2D eq data +bin_eq_2d = true # Binary output of 2D eq data (used by GPEC) +out_2d = false # ASCII output of processed 2D data +bin_2d = false # Binary output of processed 2D data +dump_flag = false # Binary dump of equilibrium data diff --git 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100644 index 000000000..cb8418b12 --- /dev/null +++ b/notebooks/soloviev_ideal/sol.toml @@ -0,0 +1,11 @@ +[SOL_INPUT] +mr = 128 # number of radial grid zones +mz = 128 # number of axial grid zones +ma = 128 # number of flux grid zones +e = 1.6 # elongation +a = 0.33 # minor radius +r0 = 1.0 # major radius +q0 = 1.9 # safety factor at the o-point +p0fac=1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) +b0fac=1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) +f0fac=1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) \ No newline at end of file diff --git a/notebooks/spline_bug_solovev_ideal.ipynb b/notebooks/spline_bug_solovev_ideal.ipynb new file mode 100644 index 000000000..28aefde81 --- /dev/null +++ b/notebooks/spline_bug_solovev_ideal.ipynb @@ -0,0 +1,302 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "710e987d", + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"..\")\n", + "using JPEC\n", + "using Plots" + ] + }, + { + "cell_type": "markdown", + "id": "30c317c5", + "metadata": {}, + "source": [ + "## Overview\n", + "In this notebook, I attempt to show where I am seeing bugs in the equilibrium knots/splines when running the Solovev ideal example. I noticed in the fourfit functions, I was seeing discrepancies for the metric tensor computation, and traced them down to the following function calls giving sufficiently different values from the same values when I dumped the same values from the Fortran code run with the same input files (above what is to be expected due to machine precision/floating point errors). I have put the Fortran data from this dump in the soloviev_ideal example, but could also be obtained by adding the relevant write statements for `fourfit_make_metric` and `fourfit_make_matrix` within `fourfit.F`. \n", + "\n", + "I **think** this is an issue with equil and not splines, since I have verified that if I use the Fortran knot values, I get the correct matrices, which involves a creating a Fourier spline for the metric tensor, but I am not 100% sure.\n", + "\n", + "The relevant data for these calculations is:\n", + "\n", + "fortran_rzphi_knots.dat: rzphi%f(1:4), fx(1:4), fy(1:4) at each psi and theta\n", + "\n", + "fortran_sq_knots.dat: sq%fs1(2), sq%fs(4), sq%fs1(4), -sq%fs1(1) (p1, q, q1, and jtheta, respectively) at each psi" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cb106129", + "metadata": {}, + "outputs": [], + "source": [ + "### Set up the equilibrium data for the solovev ideal example\n", + "equil = Equilibrium.setup_equilibrium(\"soloviev_ideal/equil.toml\")" + ] + }, + { + "cell_type": "markdown", + "id": "f85da686", + "metadata": {}, + "source": [ + "## 1D Profiles\n", + "\n", + "First, I will show the errors I was finding with the 1D profiles from sq" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f7ab5918", + "metadata": {}, + "outputs": [], + "source": [ + "# Extract knots from the sq data that we will compare to the Fortran values\n", + "psi = equil.sq.xs\n", + "p1 = equil.sq.fs1[:, 2]\n", + "q = equil.sq.fs[:, 4]\n", + "q1 = equil.sq.fs1[:, 4]\n", + "jtheta = -equil.sq.fs1[:, 1]\n", + "\n", + "# Read the Fortran data into equivalent arrays\n", + "lines = readlines(\"soloviev_ideal/fortran_sq_knots.dat\")\n", + "data = [parse.(Float64, split(l)) for l in lines[2:end]]\n", + "ipsi_f = zeros(size(psi))\n", + "psi_f = zeros(size(psi))\n", + "p1_f = zeros(size(psi))\n", + "q_f = zeros(size(psi))\n", + "q1_f = zeros(size(psi))\n", + "jtheta_f = zeros(size(psi))\n", + "for row in data\n", + " ipsi_f[Int(row[1])+1] = row[1] # shift to Julia indexing\n", + " psi_f[Int(row[1])+1] = row[2]\n", + " p1_f[Int(row[1])+1] = row[3]\n", + " q_f[Int(row[1])+1] = row[4]\n", + " q1_f[Int(row[1])+1] = row[5]\n", + " jtheta_f[Int(row[1])+1] = row[6]\n", + "end\n", + "\n", + "# Plot q profile comparison (log scale)\n", + "plot(psi, abs.((q - q_f) ./ q_f), label=\"rel error\", xlabel=\"psi\", ylabel=\"|q(Julia) - q(Fortran)| / |q(Fortran)|\", title=\"q profile comparison\", yscale=:log10)\n", + "display(current())\n", + "\n", + "# Plot p1 profile comparison (log scale)\n", + "plot(psi, abs.((p1 - p1_f) ./ p1_f), label=\"rel error\", xlabel=\"psi\", ylabel=\"|p1(Julia) - p1(Fortran)| / |p1(Fortran)|\", title=\"p1 profile comparison\", yscale=:log10)\n", + "display(current())\n", + "\n", + "# Plot q1 profile comparison (log scale)\n", + "plot(psi, abs.((q1 - q1_f) ./ q1_f), label=\"rel error\", xlabel=\"psi\", ylabel=\"|q1(Julia) - q1(Fortran)| / |q1(Fortran)|\", title=\"q1 profile comparison\", yscale=:log10)\n", + "display(current())\n", + "\n", + "# Plot jtheta profile comparison (log scale)\n", + "plot(psi, abs.((jtheta - jtheta_f) ./ jtheta_f), label=\"rel error\", xlabel=\"psi\", ylabel=\"|jtheta(Julia) - jtheta(Fortran)| / |jtheta(Fortran)|\", title=\"jtheta profile comparison\", yscale=:log10)\n", + "display(current())" + ] + }, + { + "cell_type": "markdown", + "id": "343b6c96", + "metadata": {}, + "source": [ + "We can see that the q and p1 profiles look good in terms of error, but the q1 profile has a large spike at the magnetic axis and jtheta has large relative errors throughout. These values are needed for assembling the matrices in fourfit_make_matrix, and this was propagating to cause large errors in those values as well" + ] + }, + { + "cell_type": "markdown", + "id": "49cf819a", + "metadata": {}, + "source": [ + "## 2D Profiles\n", + "\n", + "Now, we will look at the relative and absolute errors resulting from the rzphi values used to assemble the metric tensor in fourfit_make_metric" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0ea19718", + "metadata": {}, + "outputs": [], + "source": [ + "# Assemble arrays of Julia equilibrium values. Note that there is a bicube eval here to match the line in Fortran, but the\n", + "# evaluation occurs on the knot values so I don't think this would be a spline issue, but again not 100% sure.\n", + "rzphi = equil.rzphi\n", + "psi = rzphi.xs\n", + "theta = rzphi.ys\n", + "mpsi = length(rzphi.xs) - 1\n", + "mtheta = length(rzphi.ys) - 1\n", + "f_store = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4) \n", + "fx_store = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4)\n", + "fy_store = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4)\n", + "f_store_f = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4) \n", + "fx_store_f = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4)\n", + "fy_store_f = Array{Float64}(undef, mpsi + 1, mtheta + 1, 4)\n", + "for ipsi in 1:(mpsi+1)\n", + " for jtheta in 1:(mtheta+1)\n", + " f, fx, fy = SplinesMod.bicube_eval(rzphi, rzphi.xs[ipsi], rzphi.ys[jtheta], 1)\n", + " f_store[ipsi, jtheta, :] .= f\n", + " fx_store[ipsi, jtheta, :] .= fx\n", + " fy_store[ipsi, jtheta, :] .= fy\n", + " end\n", + "end\n", + "\n", + "# Read in equivalent Fortran data\n", + "lines = readlines(\"soloviev_ideal/fortran_rzphi_knots.dat\")\n", + "data = [parse.(Float64, split(l)) for l in lines[2:end]]\n", + "for row in data\n", + " ipsi = Int(row[1]) + 1 # shift to Julia indexing\n", + " itheta = Int(row[2]) + 1\n", + " f_store_f[ipsi, itheta, :] .= row[3:6]\n", + " fx_store_f[ipsi, itheta, :] .= row[7:10]\n", + " fy_store_f[ipsi, itheta, :] .= row[11:14]\n", + "end\n", + "\n", + "# Plot relative error between Julia and Fortran values\n", + "labels = [\"(1)\", \"(2)\", \"(3)\", \"(4)\"]\n", + "for i in 1:4\n", + " # Relative error for f\n", + " rel_err_f = abs.((f_store[:, :, i] .- f_store_f[:, :, i]) ./ f_store_f[:, :, i])\n", + " contour(\n", + " psi,\n", + " theta,\n", + " rel_err_f',\n", + " title=\"Relative Error: f$(labels[i])\",\n", + " xlabel=\"psi\",\n", + " ylabel=\"theta\",\n", + " colorbar_title=\"rel error\",\n", + " colorbar_scale=:log10\n", + " )\n", + " display(current())\n", + "\n", + " # Relative error for fx\n", + " rel_err_fx = abs.((fx_store[:, :, i] .- fx_store_f[:, :, i]) ./ fx_store_f[:, :, i])\n", + " contour(\n", + " psi,\n", + " theta,\n", + " rel_err_fx',\n", + " title=\"Relative Error: fx$(labels[i])\",\n", + " xlabel=\"psi\",\n", + " ylabel=\"theta\",\n", + " colorbar_title=\"rel error\",\n", + " colorbar_scale=:log10\n", + " )\n", + " display(current())\n", + "\n", + " # Relative error for fy\n", + " rel_err_fy = abs.((fy_store[:, :, i] .- fy_store_f[:, :, i]) ./ fy_store_f[:, :, i])\n", + " contour(\n", + " psi,\n", + " theta,\n", + " rel_err_fy',\n", + " title=\"Relative Error: fy$(labels[i])\",\n", + " xlabel=\"psi\",\n", + " ylabel=\"theta\",\n", + " colorbar_title=\"rel error\",\n", + " colorbar_scale=:log10\n", + " )\n", + " display(current())\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "303654b4", + "metadata": {}, + "outputs": [], + "source": [ + "labels = [\"(1)\", \"(2)\", \"(3)\", \"(4)\"]\n", + "for i in 1:4\n", + " # Absolute error for f\n", + " abs_err_f = abs.(f_store[:, :, i] .- f_store_f[:, :, i])\n", + " contour(\n", + " psi,\n", + " theta,\n", + " abs_err_f',\n", + " title=\"Absolute Error: f$(labels[i])\",\n", + " xlabel=\"psi\",\n", + " ylabel=\"theta\",\n", + " colorbar_title=\"abs error\",\n", + " colorbar_scale=:log10\n", + " )\n", + " display(current())\n", + "\n", + " # Absolute error for fx\n", + " abs_err_fx = abs.(fx_store[:, :, i] .- fx_store_f[:, :, i])\n", + " contour(\n", + " psi,\n", + " theta,\n", + " abs_err_fx',\n", + " title=\"Absolute Error: fx$(labels[i])\",\n", + " xlabel=\"psi\",\n", + " ylabel=\"theta\",\n", + " colorbar_title=\"abs error\",\n", + " colorbar_scale=:log10\n", + "\n", + " )\n", + " display(current())\n", + "\n", + " # Absolute error for fy\n", + " abs_err_fy = abs.(fy_store[:, :, i] .- fy_store_f[:, :, i])\n", + " contour(\n", + " psi,\n", + " theta,\n", + " abs_err_fy',\n", + " title=\"Absolute Error: fy$(labels[i])\",\n", + " xlabel=\"psi\",\n", + " ylabel=\"theta\",\n", + " colorbar_title=\"abs error\",\n", + " colorbar_scale=:log10\n", + " )\n", + " display(current())\n", + "end" + ] + }, + { + "cell_type": "markdown", + "id": "4ef457c7", + "metadata": {}, + "source": [ + "It is a bit difficult to see on the relative error plots since there are a few extremely large spikes (that I think occur when the value is below machine precision and the relative error is inaccurate), but I think the jist here is to look at the absolute error in fx(2:4), where there is an anomalous spike near the axis. This difference was drectly affecting the calculations. I **think** the rest of the values are ok, but we could double check by filtering out errors of values below 10^-10 or something and verifying that all relative errors for values above this limit are small" + ] + }, + { + "cell_type": "markdown", + "id": "67eea7ae", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "Based on these plots, I think the mostly likely source of error is how the first grid point is dealt with between the two codes. Most likely the actual spline evals are ok, and it seems like for most of the rest of the knots (besides jtheta perhaps?) the errors are small" + ] + }, + { + "cell_type": "markdown", + "id": "4e9d9417", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/spline_examples2.ipynb b/notebooks/spline_examples2.ipynb new file mode 100644 index 000000000..21c2769d0 --- /dev/null +++ b/notebooks/spline_examples2.ipynb @@ -0,0 +1,661 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "814db625", + "metadata": {}, + "outputs": [], + "source": [ + "using Pkg\n", + "Pkg.activate(\"..\")\n", + "Pkg.resolve()\n", + "Pkg.instantiate() # Usually only need to run this once\n", + "using Plots, Printf\n", + "using JPEC.SplinesMod" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6892132a", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "#=\n", + "======================================================================\n", + "1. VALIDATION FOR 1D CUBIC SPLINE (Real)\n", + "======================================================================\n", + "=#\n", + "println(\"\\n--- Testing 1D Spline Derivatives and Integration ---\")\n", + "\n", + "# --- 1.1 Data Generation ---\n", + "# Using 20 nodes to create a periodic spline for sin(x) and cos(x)\n", + "xs_nodes = collect(range(0.0, stop=2*pi, length=20))\n", + "y1_nodes = sin.(xs_nodes)\n", + "y2_nodes = cos.(xs_nodes)\n", + "fs_nodes_matrix = hcat(y1_nodes, y2_nodes)\n", + "\n", + "# --- 1.2 Spline Setup (bctype=3 for periodic)---\n", + "spline_real = CubicSpline(xs_nodes, fs_nodes_matrix; bctype=3)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0d38581c", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# --- 1.3 Evaluation on a Fine Grid ---\n", + "xs_fine = collect(range(0.0, stop=2*pi, length=200))\n", + "\n", + "\n", + "# Evaluate the spline and its derivatives up to the 3rd order\n", + "f_s, f1_s, f2_s, f3_s = spline_eval(spline_real, xs_fine, 3)\n", + "\n", + "\n", + "# --- 1.4 Perform Integration ---\n", + "# This modifies the spline_real object in-place, adding the .fsi field\n", + "SplinesMod.spline_integrate!(spline_real)\n", + "\n", + "# The result of integration is stored at the original node points.\n", + "# spline_real.fsi now contains the cumulative integral values.\n", + "integral_s = spline_real.fsi\n", + "\n", + "# --- 1.5 Analytical (True) Values ---\n", + "# True values for the function and its derivatives on the fine grid\n", + "true_f = hcat(sin.(xs_fine), cos.(xs_fine))\n", + "true_f1 = hcat(cos.(xs_fine), -sin.(xs_fine))\n", + "true_f2 = hcat(-sin.(xs_fine), -cos.(xs_fine))\n", + "true_f3 = hcat(-cos.(xs_fine), sin.(xs_fine))\n", + "\n", + "# True values for the integral on the original coarse grid (xs_nodes)\n", + "# Integral of sin(x) from 0 to t is -cos(t) - (-cos(0)) = 1 - cos(t)\n", + "# Integral of cos(x) from 0 to t is sin(t) - sin(0) = sin(t)\n", + "true_integral = hcat(1.0 .- cos.(xs_nodes), sin.(xs_nodes))\n", + "\n", + "print(\"evaluation complete\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a90e8828", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# --- 1.6 Plotting (Focusing on the first function, sin(x)) ---\n", + "\n", + "# Plot for Function Value f(x)\n", + "function generate_spline_plot(\n", + " x_vals, \n", + " spline_data, \n", + " analytic_data;\n", + " title, \n", + " spline_label, \n", + " analytic_label,\n", + " error_scale=1.0,\n", + " legend_pos=:best,\n", + " x_nodes=nothing,\n", + " y_nodes=nothing,\n", + " nodes_label=\"Original Nodes\",\n", + " kwargs...\n", + ")\n", + " \n", + " p = plot(x_vals, spline_data, label=spline_label, title=title, legend=legend_pos; kwargs...)\n", + " \n", + " plot!(p, x_vals, analytic_data, ls=:dash, label=analytic_label)\n", + " scaler_str = isinteger(error_scale) ? string(Int(error_scale)) : string(error_scale)\n", + " error_label = error_scale == 1.0 ? \"Error\" : \"Error x\" * scaler_str\n", + " plot!(p, x_vals, spline_data .- analytic_data, ls=:dot, label=error_label, color=:red)\n", + " \n", + " if x_nodes !== nothing && y_nodes !== nothing\n", + " scatter!(p, x_nodes, y_nodes, label=nodes_label, markersize=3, markerstrokewidth=0)\n", + " end\n", + " \n", + " return p\n", + "end\n", + "\n", + "# --- 1.6 Generate and Display all plots ---\n", + "\n", + "println(\"--- Generating 1D Spline Validation Plots ---\")\n", + "\n", + "plot_configs_real = [\n", + " # f(x) \n", + " (\n", + " spline_data = f_s[:, 1], analytic_data = true_f[:, 1], x_vals = xs_fine,\n", + " title = \"Function: sin(x)\", spline_label = \"Spline f(x)\", analytic_label = \"True f(x)\",\n", + " error_scale = 1000.0, legend_pos = :bottomleft,\n", + " x_nodes = xs_nodes, y_nodes = y1_nodes\n", + " ),\n", + " # f'(x) \n", + " (\n", + " spline_data = f1_s[:, 1], analytic_data = true_f1[:, 1], x_vals = xs_fine,\n", + " title = \"1st Deriv: cos(x)\", spline_label = \"Spline f'(x)\", analytic_label = \"True f'(x)\",\n", + " error_scale = 100.0, legend_pos = :bottomleft\n", + " ),\n", + " # f''(x)\n", + " (\n", + " spline_data = f2_s[:, 1], analytic_data = true_f2[:, 1], x_vals = xs_fine,\n", + " title = \"2nd Deriv: -sin(x)\", spline_label = \"Spline f''(x)\", analytic_label = \"True f''(x)\",\n", + " error_scale = 1.0, legend_pos = :bottomleft\n", + " ),\n", + " # f'''(x)\n", + " (\n", + " spline_data = f3_s[:, 1], analytic_data = true_f3[:, 1], x_vals = xs_fine,\n", + " title = \"3rd Deriv: -cos(x)\", spline_label = \"Spline f'''(x)\", analytic_label = \"True f'''(x)\",\n", + " error_scale = 1.0, legend_pos = :bottomleft\n", + " ),\n", + " # integral \n", + " (\n", + " spline_data = integral_s[:, 1], analytic_data = true_integral[:, 1], x_vals = xs_nodes,\n", + " title = \"Integral: 1-cos(x)\", spline_label = \"Spline Integral\", analytic_label = \"True Integral\",\n", + " error_scale = 1000.0, legend_pos = :topleft,\n", + " style = (markershape=:circle, markersize=3)\n", + " )\n", + "]\n", + "\n", + "\n", + "plot_list_real = []\n", + "println(\"--- Generating 1D Spline Validation Plots ---\")\n", + "\n", + "for config in plot_configs_real\n", + " \n", + " p = generate_spline_plot(\n", + " config.x_vals,\n", + " config.spline_data,\n", + " config.analytic_data;\n", + " title = config.title,\n", + " spline_label = config.spline_label,\n", + " analytic_label = config.analytic_label,\n", + " error_scale = config.error_scale,\n", + " legend_pos = config.legend_pos,\n", + " \n", + " x_nodes = get(config, :x_nodes, nothing),\n", + " y_nodes = get(config, :y_nodes, nothing),\n", + " \n", + " (haskey(config, :style) ? config.style : ())...\n", + " )\n", + " push!(plot_list_real, p)\n", + "end\n", + "\n", + "\n", + "display(plot(plot_list_real..., layout=(3, 2), size=(1200, 1000), margin=5Plots.mm))\n", + "\n", + "\n", + "\n", + "println(\"\\nAll 1D validation plots generated.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "94c3d4e9", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "#=\n", + "======================================================================\n", + "2. VALIDATION FOR 1D CUBIC SPLINE (Complex)\n", + "======================================================================\n", + "=#\n", + "println(\"\\n--- Testing 1D Complex Spline Derivatives and Integration ---\")\n", + "\n", + "# --- 2.1 Data Generation ---\n", + "xs_nodes = collect(range(0.0, stop=2*pi, length=40))\n", + "fs_complex_nodes = exp.(im .* xs_nodes)\n", + "\n", + "# --- 2.2 Spline Setup (bctype=3 for periodic) ---\n", + "spline_complex = CubicSpline(xs_nodes, fs_complex_nodes; bctype = 3)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9178555a", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# --- 2.3 Evaluation on a Fine Grid ---\n", + "xs_fine = collect(range(0.0, stop=2*pi, length=200))\n", + "f_cs, f1_cs, f2_cs, f3_cs = spline_eval(spline_complex, xs_fine, 3)\n", + "\n", + "# --- 2.4 Perform Integration ---\n", + "# This modifies the spline_complex object in-place, adding the .fsi field\n", + "SplinesMod.spline_integrate!(spline_complex)\n", + "integral_cs = spline_complex.fsi\n", + "\n", + "# --- 2.5 Analytical (True) Values ---\n", + "true_f_c = exp.(im .* xs_fine)\n", + "true_f1_c = im .* exp.(im .* xs_fine)\n", + "true_f2_c = -1 .* exp.(im .* xs_fine)\n", + "true_f3_c = -im .* exp.(im .* xs_fine)\n", + "\n", + "# True values for the integral on the original node grid\n", + "# Integral of exp(ix) from 0 to t is i*(1 - exp(ix))\n", + "true_integral_c = im .* (1.0 .- exp.(im .* xs_nodes))\n", + "\n", + "print(\"evaluation complete\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "587b6ed1", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# --- 2.6 Plotting ---\n", + "function generate_complex_spline_plot(\n", + " x_vals, \n", + " spline_c, \n", + " analytic_c; \n", + " part, \n", + " title, \n", + " kwargs...\n", + " )\n", + " func = (part == :real) ? real : imag\n", + " \n", + " spline_data = func(spline_c)\n", + " analytic_data = func(analytic_c)\n", + " error_data = spline_data .- analytic_data\n", + " \n", + " p = plot(x_vals, analytic_data, ls=:dash, label=\"True\", title=title; kwargs...)\n", + " \n", + " plot!(p, x_vals, spline_data, label=\"Spline\")\n", + " \n", + " plot!(p, x_vals, error_data, ls=:dot, label=\"Error\", color=:red)\n", + " \n", + " return p\n", + "end\n", + "\n", + "\n", + "\n", + "plot_configs = [\n", + " (label=\"f(x)\", data_s=f_cs, data_t=true_f_c, formula=\"e^ix\", re_res=\"cos(x)\", im_res=\"sin(x)\", x_vals=xs_fine),\n", + " (label=\"f'(x)\", data_s=f1_cs, data_t=true_f1_c, formula=\"ie^ix\", re_res=\"-sin(x)\", im_res=\"cos(x)\", x_vals=xs_fine),\n", + " (label=\"f''(x)\", data_s=f2_cs, data_t=true_f2_c, formula=\"-e^ix\", re_res=\"-cos(x)\", im_res=\"-sin(x)\", x_vals=xs_fine),\n", + " (label=\"f'''(x)\",data_s=f3_cs, data_t=true_f3_c, formula=\"-ie^ix\", re_res=\"sin(x)\", im_res=\"-cos(x)\", x_vals=xs_fine),\n", + " (label=\"∫f dt\", data_s=integral_cs, data_t=true_integral_c, formula=\"i(1-e^ix)\", re_res=\"sin(x)\", im_res=\"1-cos(x)\", x_vals=xs_nodes, style=(markershape=:circle, markersize=2)),\n", + "]\n", + "\n", + "plot_list = []\n", + "println(\"--- Generating Complex Spline Validation Plots ---\")\n", + "\n", + "\n", + "for config in plot_configs\n", + " for part_info in ((part=:real, name=\"Re\", res=config.re_res), \n", + " (part=:imag, name=\"Im\", res=config.im_res))\n", + " \n", + " title = \"$(config.label) = $(part_info.name)($(config.formula)) = $(part_info.res)\"\n", + " \n", + " plot_style = haskey(config, :style) ? config.style : (legend=:bottomleft,)\n", + "\n", + " p = generate_complex_spline_plot(\n", + " config.x_vals, \n", + " config.data_s, \n", + " config.data_t;\n", + " part=part_info.part,\n", + " title=title,\n", + " plot_style... \n", + " )\n", + " push!(plot_list, p)\n", + " end\n", + "end\n", + "\n", + "display(plot(plot_list..., layout=(5, 2), size=(1000, 1500),\n", + " plot_title=\"Complex Spline: f(x) = e^(ix), Derivatives, and Integral\",\n", + " margin=4Plots.mm))\n", + "\n", + "println(\"\\nAll complex validation plots generated.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "97a529f4", + "metadata": {}, + "outputs": [], + "source": [ + "#=\n", + "======================================================================\n", + "3. VALIDATION FOR 2D BICUBIC SPLINE\n", + "======================================================================\n", + "=#\n", + "println(\"\\n--- Testing 2D Bicubic Spline Derivatives ---\")\n", + "\n", + "# --- 3.1 Data Generation (for fitting) ---\n", + "nx_nodes, ny_nodes = 20, 20\n", + "x_nodes = collect(range(0.0, stop=2*pi, length=nx_nodes))\n", + "y_nodes = collect(range(0.0, stop=2*pi, length=ny_nodes))\n", + "\n", + "f_nodes = zeros(nx_nodes, ny_nodes, 1) # n_qty = 1 for this test\n", + "for j in 1:ny_nodes, i in 1:nx_nodes\n", + " f_nodes[i, j, 1] = sin(x_nodes[i]) * cos(y_nodes[j])\n", + "end\n", + "\n", + "# --- 3.2 Spline Setup (bctype=2 for periodic in both dimensions) ---\n", + "bcspline = BicubicSpline(x_nodes, y_nodes, f_nodes, bctypex=2, bctypey= 2)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1cd773be", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# --- 3.3 Evaluation ---\n", + "nx_fine, ny_fine = 50, 50\n", + "x_fine = collect(range(0.0, stop=2*pi, length=nx_fine))\n", + "y_fine = collect(range(0.0, stop=2*pi, length=ny_fine))\n", + "\n", + "# Get derivatives up to 2nd order\n", + "f_s, fx_s, fy_s, fxx_s, fxy_s, fyy_s = bicube_eval(bcspline, x_fine, y_fine, 2)\n", + "\n", + "\n", + "# --- 3.4 Analytical (True) Functions ---\n", + "f_analytic(x, y) = sin(x) * cos(y)\n", + "fx_analytic(x, y) = cos(x) * cos(y)\n", + "fy_analytic(x, y) = -sin(x) * sin(y)\n", + "fxx_analytic(x, y) = -sin(x) * cos(y)\n", + "fyy_analytic(x, y) = -sin(x) * cos(y)\n", + "fxy_analytic(x, y) = -cos(x) * sin(y)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7c70289a", + "metadata": {}, + "outputs": [], + "source": [ + "# --- 3.5 Plotting Helper Function ---\n", + "function generate_bicube_plots(name, spline_data, analytic_func, x_grid, y_grid)\n", + " \n", + " analytical_data = [analytic_func(x, y) for x in x_grid, y in y_grid]\n", + " spline_slice = spline_data[:, :, 1]\n", + " error_data = spline_slice - analytical_data\n", + " max_abs_error = maximum(abs, error_data)\n", + " \n", + " p1 = heatmap(x_grid, y_grid, spline_slice', title=\"Spline: $name\", c=:viridis)\n", + " p2 = heatmap(x_grid, y_grid, analytical_data', title=\"Analytical: $name\", c=:viridis)\n", + " p3 = heatmap(x_grid, y_grid, error_data', title=\"Error (Max Abs: $(@sprintf(\"%.2e\", max_abs_error)))\", c=:bwr)\n", + "\n", + " return plot(p1, p2, p3, layout=(1, 3), size=(1000, 300), aspect_ratio=:equal)\n", + "end\n", + "\n", + "# --- 3.6 Generate and Display all plots ---\n", + "display(generate_bicube_plots(\"f\", f_s, f_analytic, x_fine, y_fine))\n", + "display(generate_bicube_plots(\"fx\", fx_s, fx_analytic, x_fine, y_fine))\n", + "display(generate_bicube_plots(\"fy\", fy_s, fy_analytic, x_fine, y_fine))\n", + "display(generate_bicube_plots(\"fxx\", fxx_s, fxx_analytic, x_fine, y_fine)) \n", + "display(generate_bicube_plots(\"fyy\", fyy_s, fyy_analytic, x_fine, y_fine)) \n", + "display(generate_bicube_plots(\"fxy\", fxy_s, fxy_analytic, x_fine, y_fine))\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "131e2883", + "metadata": {}, + "outputs": [], + "source": [ + "#=\n", + "======================================================================\n", + "4. VALIDATION FOR 2D FOURIER SPLINE (CUBIC-X, FOURIER-Y)\n", + "======================================================================\n", + "=#\n", + "# Assuming FourierSpline is where the module is located\n", + "# For standalone testing, you might need:\n", + "# include(\"FourierSpline.jl\")\n", + "# using .FourierSpline\n", + "\n", + "println(\"\\n--- Testing 2D Fourier-Spline Derivatives ---\")\n", + "\n", + "\n", + "\n", + "# --- 4.1 Data Generation (for fitting) ---\n", + "# For fit_method=2 (FFT), my_nodes must be a power of 2.\n", + "# We use mx+1 points for x and my+1 points for y.\n", + "# The grid is [0, mx] and [0, my].\n", + "mx_nodes, my_nodes = 32, 32 # my_nodes must be a power of 2 for FFT test\n", + "x_nodes = collect(range(0.0, stop=3.0, length=mx_nodes + 1))\n", + "# y is periodic from 0 to 2pi. The last point y_nodes[my+1] should equal the first y_nodes[1] + 2pi\n", + "y_nodes = collect(range(0.0, stop=2*pi, length=my_nodes + 1))\n", + "\n", + "f_nodes = zeros(mx_nodes + 1, my_nodes + 1, 1) # n_qty = 1\n", + "for j in 1:(my_nodes + 1), i in 1:(mx_nodes + 1)\n", + " f_nodes[i, j, 1] = x_nodes[i]^2 * cos(2 * y_nodes[j])\n", + "end\n", + "\n", + "# --- 4.2 Spline Setup ---\n", + "# Use bctype=1 (natural) for x-direction as it's not periodic.\n", + "# The y-direction is inherently periodic.\n", + "# mband determines how many Fourier modes are used. A higher number gives more accuracy.\n", + "mband_val = 10\n", + "\n", + "# Test both fit methods\n", + "println(\"\\n--- Setting up with fit_method=1 (Integral) ---\")\n", + "fspline_m1 = FourierSpline(x_nodes, y_nodes, f_nodes, mband_val, bctype=4, fit_method=1,fit_flag=true)\n", + "\n", + "println(\"\\n--- Setting up with fit_method=2 (FFT) ---\")\n", + "# This requires my_nodes to be a power of 2.\n", + "fspline_m2 = FourierSpline(x_nodes, y_nodes, f_nodes, mband_val, bctype=2, fit_method=2,fit_flag=true)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "343bbb04", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# --- 4.3 Evaluation ---\n", + "# We will evaluate using the FFT-fitted spline (method 2) as it's generally faster if applicable.\n", + "# You can switch to fspline_m1 to compare.\n", + "chosen_fspline = fspline_m1\n", + "\n", + "nx_fine, ny_fine = 60, 60\n", + "x_fine = collect(range(0.0, stop=3.0, length=nx_fine))\n", + "y_fine = collect(range(0.0, stop=2*pi, length=ny_fine))\n", + "\n", + "# Get derivatives up to 2nd order\n", + "f_s, fx_s, fy_s, fxx_s, fxy_s, fyy_s = fspline_eval(chosen_fspline, x_fine, y_fine, Int(2))\n", + "\n", + "\n", + "# --- 4.4 Analytical (True) Functions (Periodic in y) ---\n", + "f_analytic(x, y) = x^2 * cos(2*y)\n", + "fx_analytic(x, y) = 2*x * cos(2*y)\n", + "fy_analytic(x, y) = -2 * x^2 * sin(2*y)\n", + "fxx_analytic(x, y) = 2 * cos(2*y)\n", + "fyy_analytic(x, y) = -4 * x^2 * cos(2*y)\n", + "fxy_analytic(x, y) = -4 * x * sin(2*y)\n", + "\n", + "print(\"evaluation complete\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "234f912c", + "metadata": {}, + "outputs": [], + "source": [ + "function generate_fspline_plot(name, spline_data, analytic_func, x_grid, y_grid)\n", + "\n", + " \n", + " # 1. Generate the analytical data on the fine grid\n", + " analytical_data = [analytic_func(x, y) for x in x_grid, y in y_grid]\n", + " \n", + " # 2. Extract the 2D slice from the 3D spline output array (n_qty=1)\n", + " spline_slice = spline_data[:, :, 1]\n", + " \n", + " # 3. Calculate the error between the spline and analytical data\n", + " error_data = spline_slice - analytical_data\n", + " max_abs_error = maximum(abs, error_data)\n", + " \n", + " # 4. Create three separate heatmaps for comparison\n", + " # Note: We transpose the data (') because Plots.jl heatmap expects (y, x) data layout\n", + " p1 = heatmap(x_grid, y_grid, spline_slice', \n", + " title=\"Spline: $name\", c=:viridis, aspect_ratio=:equal)\n", + " \n", + " p2 = heatmap(x_grid, y_grid, analytical_data', \n", + " title=\"Analytical: $name\", c=:viridis, aspect_ratio=:equal)\n", + " \n", + " p3 = heatmap(x_grid, y_grid, error_data', \n", + " title=\"Error (Max Abs: $(@sprintf(\"%.2e\", max_abs_error)))\", c=:bwr, aspect_ratio=:equal)\n", + "\n", + " # 5. Combine the three heatmaps into a single plot object with a 1x3 layout\n", + " return plot(p1, p2, p3, layout=(1, 3), size=(800, 400), margin=4Plots.mm)\n", + "end\n", + "\n", + "\n", + "# --- 4.5 Generate all plots ---\n", + "# This section calls the helper function for the main function and each derivative,\n", + "# displaying each result as a separate row of plots.\n", + "\n", + "display(generate_fspline_plot(\"f\", f_s, f_analytic, x_fine, y_fine))\n", + "display(generate_fspline_plot(\"fx\", fx_s, fx_analytic, x_fine, y_fine))\n", + "display(generate_fspline_plot(\"fy\", fy_s, fy_analytic, x_fine, y_fine))\n", + "display(generate_fspline_plot(\"fxx\", fxx_s, fxx_analytic, x_fine, y_fine))\n", + "display(generate_fspline_plot(\"fyy\", fyy_s, fyy_analytic, x_fine, y_fine))\n", + "display(generate_fspline_plot(\"fxy\", fxy_s, fxy_analytic, x_fine, y_fine))\n", + "\n", + "println(\"\\nAll Fourier Spline validation plots generated.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "aee4d93b", + "metadata": {}, + "outputs": [], + "source": [ + "coeffs = chosen_fspline.cs.fs\n", + "num_x, num_modes = size(coeffs)\n", + "for ix in 1:num_x # x 좌표 인덱스 루프\n", + " for m_idx in 1:num_modes # 푸리에 모드 인덱스 루프\n", + " # 모드 인덱스(m_idx)는 1부터 시작하므로, 실제 모드(m)는 m_idx - 1 입니다.\n", + " m = m_idx - 1\n", + " \n", + " # 현재 요소 값 가져오기\n", + " val = coeffs[ix, m_idx]\n", + " \n", + " # 출력\n", + " @printf(\"x_index=%2d, mode=%2d (coeffs[%2d, %2d]): Re = %+.4e, Im = %+.4e\\n\", \n", + " ix, m, ix, m_idx, real(val), imag(val))\n", + " end\n", + " println(\"-\"^20) # 각 x-point 그룹 사이에 구분선 추가\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "85209e3a-6a08-40e8-874e-85258736419b", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Block 5: Validation of Fourier Coefficients ---\n", + "\n", + "println(\"\\n--- Validating Fourier Coefficients c_m(x) ---\")\n", + "\n", + "# Evaluate the spline of coefficients on the fine x-grid\n", + "# The result is a matrix of size (nx_fine, cs_nqty)\n", + "coeffs_spline_fine = spline_eval(chosen_fspline.cs, x_fine)\n", + "\n", + "# Define the analytical functions for the first few coefficients\n", + "c0_analytic(x) = 0.0 + 0.0im\n", + "c1_analytic(x) = 0.0 + 0.0im\n", + "c2_analytic(x) = (x^2 / 2.0) + 0.0im # This is the only non-zero one\n", + "c3_analytic(x) = 0.0 + 0.0im\n", + "c4_analytic(x) = 0.0 + 0.0im\n", + "\n", + "analytic_funcs = [c0_analytic, c1_analytic, c2_analytic, c3_analytic, c4_analytic]\n", + "\n", + "# Create a list to hold the plot objects\n", + "coefficient_plots = []\n", + "\n", + "\n", + "num_modes_to_plot = min(5, chosen_fspline.cs.nqty)\n", + "\n", + "for m_idx in 1:num_modes_to_plot\n", + " m = m_idx - 1 # Current mode number (m=0, 1, 2, ...)\n", + " \n", + " # Extract the data for the m-th mode from the spline evaluation result\n", + " spline_c_m = coeffs_spline_fine[:, m_idx]\n", + " \n", + " # Generate the analytical data for the m-th mode\n", + " analytic_c_m = [analytic_funcs[m_idx](x) for x in x_fine]\n", + " \n", + " # Plot the real part\n", + " p_real = generate_complex_spline_plot(\n", + " x_fine,\n", + " spline_c_m,\n", + " analytic_c_m,\n", + " part=:real,\n", + " title=\"Re(c_$m(x))\"\n", + " )\n", + " \n", + " # Plot the imaginary part\n", + " p_imag = generate_complex_spline_plot(\n", + " x_fine,\n", + " spline_c_m,\n", + " analytic_c_m,\n", + " part=:imag,\n", + " title=\"Im(c_$m(x))\"\n", + " )\n", + " \n", + " # Add the pair of plots to our list\n", + " push!(coefficient_plots, p_real)\n", + " push!(coefficient_plots, p_imag)\n", + "end\n", + "\n", + "# Combine all coefficient plots into a single figure with a readable layout\n", + "# The layout will be (num_modes_to_plot x 2 columns)\n", + "coeff_plot_layout = (num_modes_to_plot, 2)\n", + "final_coeff_plot = plot(coefficient_plots..., layout=coeff_plot_layout, size=(800, 250 * num_modes_to_plot))\n", + "\n", + "# Display the final combined plot\n", + "display(final_coeff_plot)\n", + "\n", + "println(\"\\nFourier coefficient validation plots generated.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3cc65ddf-ddbf-4138-af94-8a69e714b097", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.5", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/src/DCON/DCON.jl b/src/DCON/DCON.jl new file mode 100644 index 000000000..ba28c3ce7 --- /dev/null +++ b/src/DCON/DCON.jl @@ -0,0 +1,26 @@ +module DCON + +# All imports and includes for the DCON module +using LinearAlgebra +using LinearAlgebra.LAPACK #required for banded matrix operations +using TOML +using FFTW +using OrdinaryDiffEq +using HDF5 +import ..Equilibrium +import ..Spl +import ..VacuumMod +using Printf + +# Include all necessary files +include("DconStructs.jl") +include("Main.jl") +include("Mercier.jl") +include("Ode.jl") +include("Sing.jl") +include("Fourfit.jl") +include("OdeOutput.jl") +include("Utils.jl") +include("Free.jl") + +end \ No newline at end of file diff --git a/src/DCON/DconStructs.jl b/src/DCON/DconStructs.jl new file mode 100644 index 000000000..38bd7684e --- /dev/null +++ b/src/DCON/DconStructs.jl @@ -0,0 +1,258 @@ +# TODO: add descriptions of what all variables are and/or explanation of defaults +# TODO: remove all unused variables before first pull request +@kwdef mutable struct ResistType + e::Float64 = 0.0 + f::Float64 = 0.0 + h::Float64 = 0.0 + m::Float64 = 0.0 + g::Float64 = 0.0 + k::Float64 = 0.0 + eta::Float64 = 0.0 + rho::Float64 = 0.0 + taua::Float64 = 0.0 + taur::Float64 = 0.0 +end + +# TODO: ideally, everything is allocated at construction, but mpert is determined after +# since these are allocated in sing_find. What's the best way to handle this? +# For now, leaving as missing, per Brendan's github comment +# Something simple could be not creating sing_types within sing_find, but instead saving the data, +# then creating them all at once after mpert is determined in dcon.jl +# This wouldn't be as clean, but would allow preallocation. Does this greatly impact performance? +@kwdef mutable struct SingType + m::Int = 0 + r1::Vector{Int} = [0] + r2::Vector{Int} = [0, 0] + psifac::Float64 = 0.0 + rho::Float64 = 0.0 + q::Float64 = 0.0 + q1::Float64 = 0.0 + di::Float64 = 0.0 + alpha::ComplexF64 = 0.0 + 0.0im + n1::Vector{Int} = Int[] + n2::Vector{Int} = Int[] + power::Union{Missing, Vector{ComplexF64}} = missing # we know the size of these, but it depends on mpert + vmat::Union{Missing, Array{ComplexF64,4}} = missing + mmat::Union{Missing, Array{ComplexF64,4}} = missing + m0mat::Matrix{ComplexF64} = zeros(ComplexF64, 2, 2) + restype::ResistType = ResistType() +end +# @kwdef mutable struct SingType +# mpert::Int +# order::Int +# m::Int = 0 +# psifac::Float64 = 0.0 +# rho::Float64 = 0.0 +# q::Float64 = 0.0 +# q1::Float64 = 0.0 +# di::Float64 = 0.0 +# alpha::ComplexF64 = 0.0 + 0.0im +# r1::Vector{Int} = [0] +# r2::Vector{Int} = [0, 0] +# n1::Vector{Int} = Vector{Int}(undef, mpert - 1) +# n2::Vector{Int} = Vector{Int}(undef, 2 * mpert - 2) +# power::Vector{ComplexF64} = Vector{ComplexF64}(undef, 2 * mpert) +# vmat::Array{ComplexF64,4} = Array{ComplexF64}(undef, mpert, 2 * mpert, 2, order + 1) +# mmat::Array{ComplexF64,4} = Array{ComplexF64}(undef, mpert, 2 * mpert, 2, order + 3) +# m0mat::Union{Nothing, Matrix{ComplexF64}} = zeros(ComplexF64, 2, 2) +# restype::ResistType = ResistType() +# end +# # Constructor to allocate matrices +# SingType(mpert::Int, order::Int; kwargs...) = SingType(; mpert, order, kwargs...) + +@kwdef mutable struct DconInternal + dir_path::String = "" + mlow::Int = 0 #Copy of delta_mlow, but with limits enforced + mhigh::Int = 0 #Copy of delta_mhigh, but with limits enforced + mpert::Int = 0 #mpert = mhigh-mlow+1 + mband::Int = 0 #mband = mpert-1-delta_mband + vac_memory::Bool = true # TODO: most likely just remove, always true in ahg_flag is deprecated + keq_out::Bool = false + theta_out::Bool = false + xlmda_out::Bool = false + fkg_kmats_flag::Bool = false + sol_base::Int = 50 + msing::Int = 0 + kmsing::Int = 0 + sing::Union{Nothing, Vector{SingType}} = SingType[] + kinsing::Union{Nothing, Vector{SingType}} = SingType[] + psilim::Float64 = 0.0 + qlim::Float64 = 0.0 + q1lim::Float64 = 0.0 + # TODO: how to initialize a spline? This will be a spline of size mpsi x 5 + locstab::Union{Missing, Spl.CubicSpline{Float64}} = missing + size_edge::Int = 0 + pre_edge::Int = 1 + i_edge::Int = 1 + # TODO: what are the lengths of these? can use to initialize + q_edge::Union{Missing, Vector{Float64}} = missing + psi_edge::Union{Missing, Vector{Float64}} = missing + dw_edge::Union{Missing, Vector{ComplexF64}} = missing +end + +@kwdef mutable struct DconControl + verbose::Bool = true + bal_flag::Bool = false + mat_flag::Bool = false + ode_flag::Bool = false + vac_flag::Bool = false + mer_flag::Bool = false + res_flag::Bool = false + fft_flag::Bool = false + node_flag::Bool = false + # saves_per_region::Int = 2 # number of u to save per interrational region, must be >> 0 to run GPEC + # save_spacing::String = "Chebyshev" # method for determining spacing of saved u points + mthvac::Int = 480 + sing_start::Int = 0 + nn::Int = 0 + delta_mlow::Int = 0 + delta_mhigh::Int = 0 + delta_mband::Int = 0 + thmax0::Float64 = 1.0 + nstep::Int = typemax(Int) + ksing::Int = -1 + tol_nr::Float64 = 1e-5 + tol_r::Float64 = 1e-5 + crossover::Float64 = 1e-2 + ucrit::Float64 = 1e4 + numsteps_init::Int = 4000 # used to set initial size of data store in OdeState + numunorms_init::Int = 100 # used to set initial size of saved unorm data in OdeState + singfac_min::Float64 = 0.0 + singfac_max::Float64 = 0.0 + cyl_flag::Bool = false + dmlim::Float64 = 0.5 + lim_flag::Bool = false + sas_flag::Bool = false + sing_order::Int = 2 + sort_type::String = "absm" + termbycross_flag::Bool = false + qhigh::Float64 = 1e3 + kin_flag::Bool = false + con_flag::Bool = false + kinfac1::Float64 = 1.0 + kinfac2::Float64 = 1.0 + kingridtype::Int = 0 + ktanh_flag::Bool = false + passing_flag::Bool = false + trapped_flag::Bool = true + ion_flag::Bool = true + electron_flag::Bool = false + ktc::Float64 = 0.1 + ktw::Float64 = 50.0 + qlow::Float64 = 0.0 + use_classic_splines::Bool = false + reform_eq_with_psilim::Bool = false + psiedge::Float64 = 1.0 + nperq_edge::Int = 20 + wv_farwall_flag::Bool = false + dcon_kin_threads::Int = 1 + parallel_threads::Int = 1 + diagnose::Bool = false + diagnose_ca::Bool = false +end + +# TODO: a lot of these will be deprecated, this will be a general data structure that handles output +# Since file I/O in Julia will be very different than Fortran, this will likely be reworked significantly +@kwdef mutable struct DconOutput + # output switches + write_crit_out::Bool = true + write_dcon_out::Bool = true + write_euler_h5::Bool = true + write_eqdata_h5::Bool = false + + # filenames + fname_crit_out::String = "crit.out" + fname_dcon_out::String = "dcon.out" + fname_euler_h5::String = "euler.h5" + fname_eqdata_h5::String = "eqdata.h5" + + handles::Dict{Symbol,Any} = Dict() + + # Old or unused yet + interp::Bool = false + crit_break::Bool = true + out_bal1::Bool = false + bin_bal1::Bool = false + out_bal2::Bool = false + bin_bal2::Bool = false + out_metric::Bool = false + bin_metric::Bool = false + feval_flag::Bool = false + out_fmat::Bool = false + bin_fmat::Bool = false + out_gmat::Bool = false + bin_gmat::Bool = false + out_kmat::Bool = false + bin_kmat::Bool = false + out_sol::Bool = false + out_sol_min::Int = 0 + out_sol_max::Int = 0 + bin_sol::Bool = false + bin_sol_min::Int = 0 + bin_sol_max::Int = 0 + out_fl::Bool = false + bin_fl::Bool = false + out_evals::Bool = false + bin_evals::Bool = false + bin_euler::Bool = false + euler_stride::Int = 1 + bin_vac::Bool = false # TODO: deprecated + ahb_flag::Bool = false # TODO: deprecated + mthsurf0::Float64 = 1.0 # TODO: deprecated + msol_ahb::Int = 0 # TODO: deprecated + netcdf_out::Bool = true # TODO: might be deprecated + out_fund::Bool = false + out_ahg2msc::Bool = false # TODO: deprecated +end + +# TODO: how can we initialize the splines to not be nothings? +@kwdef mutable struct FourFitVars + mpert::Int + mband::Int + + # Spline matrices + # TODO: how to initialize these splines? + amats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + bmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + cmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + dmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + emats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + hmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + dbats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + ebats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + fbats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + fmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + kmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + gmats::Union{Missing,Spl.CubicSpline{ComplexF64}} = missing + # kaats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # gaats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # f0mats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # pmats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # paats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # kkmats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # kkaats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # r1mats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # r2mats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # r3mats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # akmats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # bkmats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + # ckmats::Union{Nothing,Spl.CubicSpline{ComplexF64}} = nothing + + # k0s::JPEC.Spl.SplineType + + # ipiva::Union{Nothing,Vector{Int}} = nothing + # TODO: these might be deprecated? They're used with a ahb_flag in free + asmat::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, mpert, mpert) + bsmat::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, mpert, mpert) + csmat::Matrix{ComplexF64} = Matrix{ComplexF64}(undef, mpert, mpert) + jmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, 2 * mband + 1) + + parallel_threads::Int = 0 + dcon_kin_threads::Int = 0 + + # kinetic ABCDEH mats for sing_mod + # kwmats::Vector{JPEC.Spl.CubicSpline{ComplexF64}} = [JPEC.Spl.CubicSpline{ComplexF64}() for _ in 1:6] + # ktmats::Vector{JPEC.Spl.CubicSpline{ComplexF64}} = [JPEC.Spl.CubicSpline{ComplexF64}() for _ in 1:6] +end + +FourFitVars(mpert::Int) = FourFitVars(; mpert) diff --git a/src/DCON/Fourfit.jl b/src/DCON/Fourfit.jl new file mode 100644 index 000000000..08b3e496f --- /dev/null +++ b/src/DCON/Fourfit.jl @@ -0,0 +1,343 @@ +""" + MetricData + +A structure to hold the computed metric tensor components and their +Fourier-spline representation. This is the Julia equivalent of the `fspline_type` +named `metric` in the Fortran `fourfit_make_metric` subroutine. + +# Fields +- `mpsi::Int`: Number of radial grid points minus one. +- `mtheta::Int`: Number of poloidal grid points minus one. +- `xs::Vector{Float64}`: Radial coordinates (normalized poloidal flux `ψ_norm`). +- `ys::Vector{Float64}`: Poloidal angle coordinates `θ` in radians (0 to 2π). +- `fs::Array{Float64, 3}`: The raw metric data on the grid, size `(mpsi, mtheta, 8)`. + The 8 quantities are: `g¹¹`, `g²²`, `g³³`, `g²³`, `g³¹`, `g¹²`, `J`, `∂J/∂ψ`. +- `fspline::Spl.FourierSpline`: The fitted Fourier-cubic spline object. +""" +@kwdef mutable struct MetricData + mpsi::Int + mtheta::Int + xs::Vector{Float64} = zeros(mpsi) + ys::Vector{Float64} = zeros(mtheta) + fs::Array{Float64,3} = zeros(mpsi, mtheta, 8) + fspline::Union{Spl.FourierSpline,Nothing} = nothing +end + +MetricData(mpsi::Int, mtheta::Int) = MetricData(; mpsi, mtheta) + +""" + make_metric(equil::Equilibrium.PlasmaEquilibrium; mband::Int=10, fft_flag::Bool=true) -> MetricData + +Constructs the metric tensor data on a (ψ, θ) grid from an input plasma equilibrium. + +# Arguments +- `equil::Equilibrium.PlasmaEquilibrium`: + An equilibrium object containing spline data (`rzphi`) for flux coordinates and geometry. +- `mband::Int=10`: + Number of Fourier modes to retain in the metric representation. +- `fft_flag::Bool=true`: + If `true`, enables use of Fourier fitting for storing metric coefficients. + (Currently reserved for downstream processing.) + +# Returns +- `metric::MetricData`: + A structure containing the metric coefficients, coordinate grids, and Jacobians for the specified equilibrium. + +# Details +- Uses bicubic spline evaluation (`Spl.bicube_eval`) on the equilibrium geometry to compute + contravariant basis vectors ∇ψ, ∇θ, and ∇ζ at each grid point. +- The metric coefficients stored in `metric.fs` include: + 1. g^ψψ · J + 2. g^θθ · J + 3. g^ζζ · J + 4. g^θζ · J + 5. g^ζψ · J + 6. g^ψθ · J + 7. J (Jacobian) + 8. ∂J/∂ψ +- The ψ grid is taken directly from `rzphi.xs`, and θ is scaled from `[0,1]` to `[0, 2π]`. +""" +function make_metric(equil::Equilibrium.PlasmaEquilibrium; mband::Int=10, fft_flag::Bool=true) + + # TODO: add kinetic metric tensor components + + # --- Extract data from the PlasmaEquilibrium object --- + rzphi = equil.rzphi + mpsi = length(rzphi.xs) + mtheta = length(rzphi.ys) + + println(" Equilibrium grid: $mpsi (ψ) × $mtheta (θ)") + println(" Fourier fit modes (mband): $mband") + + metric = MetricData(mpsi, mtheta) + + # Set coordinate grids based on the input equilibrium + # The `rzphi.ys` from EquilibriumAPI is normalized (0 to 1), so scale to radians. + metric.xs .= Vector(rzphi.xs) + metric.ys .= Vector(rzphi.ys .* 2π) + + # Temporary array for contravariant basis vectors + v = zeros(Float64, 3, 3) + + # --- Main computation loop over the (ψ, θ) grid --- + for ipsi in 1:mpsi + psi_norm = rzphi.xs[ipsi] + for jtheta in 1:mtheta + theta_norm = rzphi.ys[jtheta] # θ is from 0 to 1 + + # Evaluate the geometry spline to get (R,Z) and their derivatives + f, fx, fy = Spl.bicube_eval(rzphi, psi_norm, theta_norm, 1) + + # Extract geometric quantities from the spline data + # See EquilibriumAPI.txt for `rzphi` quantities + r_coord_sq = f[1] + eta_offset = f[2] + jac = f[4] + jac1 = fx[4] # ∂J/∂ψ + + rfac = sqrt(r_coord_sq) + eta = 2π * (theta_norm + eta_offset) + r_major = equil.ro + rfac * cos(eta) # This is the R coordinate + + # --- Compute contravariant basis vectors ∇ψ, ∇θ, ∇ζ --- + fx1, fx2, fx3 = fx[1], fx[2], fx[3] + fy1, fy2, fy3 = fy[1], fy[2], fy[3] + + v[1, 1] = fx1 / (2.0 * rfac * jac) + v[1, 2] = fx2 * 2π * rfac / jac + v[1, 3] = fx3 * r_major / jac + v[2, 1] = fy1 / (2.0 * rfac * jac) + v[2, 2] = (1.0 + fy2) * 2π * rfac / jac + v[2, 3] = fy3 * r_major / jac + v[3, 3] = 2π * r_major / jac + + # Store results + metric.fs[ipsi, jtheta, 1] = sum(v[1, :] .^ 2) * jac + metric.fs[ipsi, jtheta, 2] = sum(v[2, :] .^ 2) * jac + metric.fs[ipsi, jtheta, 3] = v[3, 3] * v[3, 3] * jac + metric.fs[ipsi, jtheta, 4] = v[2, 3] * v[3, 3] * jac + metric.fs[ipsi, jtheta, 5] = v[3, 3] * v[1, 3] * jac + metric.fs[ipsi, jtheta, 6] = sum(v[1, :] .* v[2, :]) * jac + metric.fs[ipsi, jtheta, 7] = jac + metric.fs[ipsi, jtheta, 8] = jac1 + + # TODO: kinetic metric tensor here fmodb in Fortran + end + end + + # --- Fit the grid data to a Fourier-cubic spline --- + fit_method = fft_flag ? 2 : 1 + # In Fortran, `bctype` was set for the periodic `y` dimension. Here, the `FourierSpline` + # `bctype` argument applies to the non-periodic `x` dimension. The Fortran + # code used "extrap" for this. + bctype_x = "not-a-knot" + + # The poloidal (y) dimension is handled implicitly as periodic by the Fourier transform. + metric.fspline = Spl.FourierSpline( + metric.xs, + metric.ys, + metric.fs, + mband; + bctype=bctype_x, + fit_method=fit_method + ) + return metric +end + +""" + make_matrix(metric::MetricData, equil::Equilibrium.PlasmaEquilibrium, ctrl::DconControl, intr::DconInternal) -> FourFitVars + +Constructs Fourier–poloidal coupling matrices for a given toroidal mode number and returns them as a new `FourFitVars` object. + +# Arguments +- `metric::MetricData`: + Metric coefficients on the (ψ, θ) grid, including Fourier representations of g^ij and J. +- `equil::Equilibrium.PlasmaEquilibrium`: + Plasma equilibrium object providing 1D flux-surface profiles (`sq`) and normalization constants. +- `ctrl::DconControl`: + Control parameters for the DCON calculation, including mode numbers and flags. +- `intr::DconInternal`: + Internal state for the DCON calculation, including mode number ranges and splines. + +# Returns +- `ffit::FourFitVars`: + A container holding cubic spline fits of the assembled matrices +""" +function make_matrix(metric::MetricData, equil::Equilibrium.PlasmaEquilibrium, ctrl::DconControl, intr::DconInternal) + + # TODO: add banded matrices (if desired), kinetic matrices + + # --- Extract inputs --- + sq = equil.sq + mpsi = metric.mpsi + + if ctrl.verbose + println(" Toroidal mode n=$(ctrl.nn), Poloidal modes m=$(intr.mlow):$(intr.mhigh) ($(intr.mpert) modes)") + println(" Matrix bandwidth: $(intr.mband)") + end + + # Allocations + amats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + bmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + cmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + dmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + emats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + hmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + fmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + gmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + kmats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + dbats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + ebats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + fbats = zeros(ComplexF64, mpsi, intr.mpert, intr.mpert) + g11 = zeros(ComplexF64, 2 * intr.mband + 1) + g22 = zeros(ComplexF64, 2 * intr.mband + 1) + g33 = zeros(ComplexF64, 2 * intr.mband + 1) + g23 = zeros(ComplexF64, 2 * intr.mband + 1) + g31 = zeros(ComplexF64, 2 * intr.mband + 1) + g12 = zeros(ComplexF64, 2 * intr.mband + 1) + jmat = zeros(ComplexF64, 2 * intr.mband + 1) + jmat1 = zeros(ComplexF64, 2 * intr.mband + 1) + + # Instead of using Offset Arrays like in Fortran (-mband:mband), we store everything in + # a single 1:(2*mband+1) array and map the zero index to the middle + mid = intr.mband + 1 # "zero" position in Julia arrays + imat = zeros(ComplexF64, 2 * intr.mband + 1) + imat[mid] = 1 + 0im + + for ipsi in 1:mpsi + # --- Create views for this surface --- + amat = @view amats[ipsi, :, :] + bmat = @view bmats[ipsi, :, :] + cmat = @view cmats[ipsi, :, :] + dmat = @view dmats[ipsi, :, :] + emat = @view emats[ipsi, :, :] + hmat = @view hmats[ipsi, :, :] + fmat = @view fmats[ipsi, :, :] + gmat = @view gmats[ipsi, :, :] + kmat = @view kmats[ipsi, :, :] + dbat = @view dbats[ipsi, :, :] + ebat = @view ebats[ipsi, :, :] + fbat = @view fbats[ipsi, :, :] + + # --- Profiles --- + p1 = sq.fs1[ipsi, 2] + q = sq.fs[ipsi, 4] + q1 = sq.fs1[ipsi, 4] + jtheta = -sq.fs1[ipsi, 1] + chi1 = 2π * equil.psio + nq = ctrl.nn * q + + # Fill lower half (0, -1, …, -mband) + g11[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 1:intr.mband+1] + g22[mid:-1:1] .= metric.fspline.cs.fs[ipsi, intr.mband+2:2*intr.mband+2] + g33[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 2*intr.mband+3:3*intr.mband+3] + g23[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 3*intr.mband+4:4*intr.mband+4] + g31[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 4*intr.mband+5:5*intr.mband+5] + g12[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 5*intr.mband+6:6*intr.mband+6] + jmat[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 6*intr.mband+7:7*intr.mband+7] + jmat1[mid:-1:1] .= metric.fspline.cs.fs[ipsi, 7*intr.mband+8:8*intr.mband+8] + + # Fill upper half (+1:mband) with conjugate symmetry + for k = 1:intr.mband + g11[mid+k] = conj(g11[mid-k]) + g22[mid+k] = conj(g22[mid-k]) + g33[mid+k] = conj(g33[mid-k]) + g23[mid+k] = conj(g23[mid-k]) + g31[mid+k] = conj(g31[mid-k]) + g12[mid+k] = conj(g12[mid-k]) + jmat[mid+k] = conj(jmat[mid-k]) + jmat1[mid+k] = conj(jmat1[mid-k]) + end + + # Construct primitive matrices via m1/dm loops + ipert = 0 + for m1 in intr.mlow:intr.mhigh + ipert += 1 + sing1 = m1 - nq + for dm in max(1 - ipert, -intr.mband):min(intr.mpert - ipert, intr.mband) + m2 = m1 + dm + sing2 = m2 - nq + jpert = ipert + dm + dmidx = dm + mid + + amat[ipert, jpert] = (2π)^2 * (ctrl.nn^2 * g22[dmidx] + ctrl.nn * (m1 + m2) * g23[dmidx] + m1 * m2 * g33[dmidx]) + bmat[ipert, jpert] = -2π * im * chi1 * (ctrl.nn * g22[dmidx] + (m1 + nq) * g23[dmidx] + m1 * q * g33[dmidx]) + cmat[ipert, jpert] = 2π * im * ((2π * im * chi1 * sing2 * (ctrl.nn * g12[dmidx] + m1 * g31[dmidx])) - + (q1 * chi1 * (ctrl.nn * g23[dmidx] + m1 * g33[dmidx]))) - + 2π * im * (jtheta * sing1 * imat[dmidx] + ctrl.nn * p1 / chi1 * jmat[dmidx]) + dmat[ipert, jpert] = 2π * chi1 * (g23[dmidx] + g33[dmidx] * m1 / ctrl.nn) + emat[ipert, jpert] = -chi1 / ctrl.nn * (q1 * chi1 * g33[dmidx] - 2π * im * chi1 * g31[dmidx] * sing2 + jtheta * imat[dmidx]) + hmat[ipert, jpert] = (q1 * chi1)^2 * g33[dmidx] + + (2π * chi1)^2 * sing1 * sing2 * g11[dmidx] - + 2π * im * chi1 * dm * q1 * chi1 * g31[dmidx] + + jtheta * q1 * chi1 * imat[dmidx] + + p1 * jmat1[dmidx] + fmat[ipert, jpert] = (chi1 / ctrl.nn)^2 * g33[dmidx] + kmat[ipert, jpert] = 2π * im * chi1 * (g23[dmidx] + g33[dmidx] * m1 / ctrl.nn) + end + end + dbat .= dmat + ebat .= emat + fbat .= fmat + + # --- Factorize and build composites --- + # TODO: Fortran throws an error if the factorization fails for a/fmat, not sure what this delta_mband comment is referencing. + # I am keeping this here to most closely match the Fortran behavior, but it may be unnecessary if we only use dense matrices. + if isposdef(Hermitian(amat, :L)) + amat_fact = cholesky(Hermitian(amat, :L)) + else + error("cholesky: amat is not positive definite (singular) at ipsi = $ipsi, reduce delta_mband") + end + temp1 = amat_fact \ dmat + temp2 = amat_fact \ cmat + # Use * for matrix multiplication (instead of .* for element-wise) + fmat .-= adjoint(dmat) * temp1 + kmat .= emat .- (adjoint(kmat) * temp2) + gmat .= hmat .- (adjoint(cmat) * temp2) + + # Store factorized F matrix (lower triangular only) since we always will need F⁻¹ later + # and this make computation more efficient via combined forward and back substitution + if isposdef(Hermitian(fmat, :L)) + fmat .= cholesky(Hermitian(fmat)).L + else + error("cholesky: fmat is not positive definite (singular) at ipsi = $ipsi, reduce delta_mband") + end + + # TODO: add kinetic matrices here + + # TODO: banded matrix calculations would also go here if implemented + end + + # --- Fit splines (reshape 3D to 2D: (mpsi) × (mpert^2)) --- + ffit = FourFitVars(mpert=intr.mpert, mband=intr.mband) + ffit.amats = Spl.CubicSpline(metric.xs, reshape(amats, mpsi, :); bctype=3) + ffit.bmats = Spl.CubicSpline(metric.xs, reshape(bmats, mpsi, :); bctype=3) + ffit.cmats = Spl.CubicSpline(metric.xs, reshape(cmats, mpsi, :); bctype=3) + ffit.dmats = Spl.CubicSpline(metric.xs, reshape(dmats, mpsi, :); bctype=3) + ffit.emats = Spl.CubicSpline(metric.xs, reshape(emats, mpsi, :); bctype=3) + ffit.hmats = Spl.CubicSpline(metric.xs, reshape(hmats, mpsi, :); bctype=3) + ffit.fmats = Spl.CubicSpline(metric.xs, reshape(fmats, mpsi, :); bctype=3) + ffit.gmats = Spl.CubicSpline(metric.xs, reshape(gmats, mpsi, :); bctype=3) + ffit.kmats = Spl.CubicSpline(metric.xs, reshape(kmats, mpsi, :); bctype=3) + ffit.dbats = Spl.CubicSpline(metric.xs, reshape(dbats, mpsi, :); bctype=3) + ffit.ebats = Spl.CubicSpline(metric.xs, reshape(ebats, mpsi, :); bctype=3) + ffit.fbats = Spl.CubicSpline(metric.xs, reshape(fbats, mpsi, :); bctype=3) + + # TODO: set powers + # Do we need this yet? Only called if power_flag = true + + if ctrl.sas_flag + # TODO: these seem to only be used for the ahb_flag, which I think is deprecated + ffit.asmat = reshape(Spl.spline_eval(ffit.amats, intr.psilim), intr.mpert, intr.mpert) + ffit.bsmat = reshape(Spl.spline_eval(ffit.bmats, intr.psilim), intr.mpert, intr.mpert) + ffit.csmat = reshape(Spl.spline_eval(ffit.cmats, intr.psilim), intr.mpert, intr.mpert) + # TODO: this is used in free.f vacuum calculations, verify this is correct + # Should we store lower triangular factorization? + ffit.asmat .= cholesky(Hermitian(ffit.asmat)).L + end + + # This is used in free_run + ffit.jmat = jmat + + return ffit +end \ No newline at end of file diff --git a/src/DCON/Free.jl b/src/DCON/Free.jl new file mode 100644 index 000000000..4801bd0e6 --- /dev/null +++ b/src/DCON/Free.jl @@ -0,0 +1,291 @@ +function free_run(odet::OdeState, ctrl::DconControl, intr::DconInternal, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, outp::DconOutput; op_netcdf_out::Bool=false) + + # TODO: it looks like vac_memory is always true - remove all ahg things and just assume true? + vac_memory = true + # TODO: this is always true in fortran - just get rid of it? + normalize = true + # Flags used within VACUUM + complex_flag = true + wall_flag = false + ahg_file = "ahg2msc_dcon.out" # Deprecated + + # Allocations + star = fill(' ', intr.mpert, odet.msol) + ep = zeros(ComplexF64, intr.mpert) + ev = zeros(ComplexF64, intr.mpert) + et = zeros(ComplexF64, intr.mpert) + tt = zeros(ComplexF64, intr.mpert) + wv = zeros(ComplexF64, intr.mpert, intr.mpert) + wt = zeros(ComplexF64, intr.mpert, intr.mpert) + wt0 = zeros(ComplexF64, intr.mpert, intr.mpert) + wp = zeros(ComplexF64, intr.mpert, intr.mpert) + temp = zeros(ComplexF64, intr.mpert, intr.mpert) + wpt = zeros(ComplexF64, intr.mpert, intr.mpert) + wvt = zeros(ComplexF64, intr.mpert, intr.mpert) + + mtheta = length(equil.rzphi.ys) + + # Evaluate dV/dpsi at the plasma edge + v1 = Spl.spline_eval(equil.sq, intr.psilim, 0)[3] + + # Compute plasma response matrix. + if ctrl.ode_flag + temp = adjoint(odet.u[:, 1:intr.mpert, 1]) + wp .= adjoint(odet.u[:, 1:intr.mpert, 2]) + # Compute wp using LU decomposition + temp_fact = lu(temp) + wp .= temp_fact \ wp + wp .= adjoint(wp) / equil.psio^2 + end + + # Write file for mscvac + # TODO: can likely remove last two arguments, ahgstr_op is deprecated + # TODO: actually, can probably remove this function entirely and just call set_dcon_params directly + free_write_msc(intr.psilim, ctrl, intr, equil; inmemory_op = vac_memory, ahgstr_op = ahg_file) + + # TODO: there is some ahb_flag logic here that has a comment "must be false if using GPEC" + # I am assuming this means we don't have to implement any of it + # if ahb_flag + # free_ahb_prep(wp, nmat, smat, asmat, bsmat, csmat, ipiva) + # end + + # Compute vacuum response matrix. + grri = Array{Float64}(undef, 2*(ctrl.mthvac+5), intr.mpert*2) + xzpts = Array{Float64}(undef, ctrl.mthvac+5, 4) + + farwal_flag = true + kernelsignin = -1.0 + # TODO: make this a ! function + VacuumMod.mscvac(wv, intr.mpert, mtheta, ctrl.mthvac, complex_flag, kernelsignin, + wall_flag, farwal_flag, grri, xzpts, ahg_file, intr.dir_path) + + # TODO: assuming bin_vac is deprecated for good, will remove all calls later after checking + # if bin_vac + # @warn "!! WARNING: Use of vacuum.bin is deprecated in GPEC. Set bin_vac = false in dcon.in to reduce file IO." + # bin_open(vac_unit, "vacuum.bin", "UNKNOWN", "REWIND", "none") + # write(vac_unit, grri) + # end + + kernelsignin = 1.0 + VacuumMod.mscvac(wv, intr.mpert, mtheta, ctrl.mthvac, complex_flag, kernelsignin, + wall_flag, farwal_flag, grri, xzpts, ahg_file, intr.dir_path) + # if bin_vac + # write(vac_unit, grri) + # end + if ctrl.wv_farwall_flag + temp .= wv + end + + farwal_flag = false + kernelsignin = -1.0 + VacuumMod.mscvac(wv, intr.mpert, mtheta, ctrl.mthvac, complex_flag, kernelsignin, + wall_flag, farwal_flag, grri, xzpts, ahg_file, intr.dir_path) + # if bin_vac + # write(vac_unit, grri) + # end + + kernelsignin = 1.0 + VacuumMod.mscvac(wv, intr.mpert, mtheta, ctrl.mthvac, complex_flag, kernelsignin, + wall_flag, farwal_flag, grri, xzpts, ahg_file, intr.dir_path) + # if bin_vac + # write(vac_unit, grri) + # write(vac_unit, xzpts) + # bin_close(vac_unit) + # end + + if ctrl.wv_farwall_flag + wv .= temp + end + + # Scale vacuum matrix by singfac = (m - nn*qlim) + singfac = (intr.mlow .- ctrl.nn .* intr.qlim) .+ collect(0:intr.mpert-1) + for ipert in 1:intr.mpert + wv[ipert, :] .*= singfac[ipert] + wv[:, ipert] .*= singfac[ipert] + end + + # Compute complex energy eigenvalues. + wt .= wp .+ wv + wt0 .= wt + + # use Eigen decomposition for general complex matrix (get left & right eigenvectors) + # For general complex: use eigen(wt) which returns eigenvalues and eigenvectors (right) + # For left eigenvectors we can compute eigen(wt') and conj-transpose as needed, + # but Fortran uses zgeev('V','V',...) returning both vl and vr. + Ev = eigen(wt) # Ev.values, Ev.vectors (columns are eigenvectors) + # Ev.vectors are right eigenvectors; we need to reorder by magnitude using bubble on real parts of eigenvalues + et .= Ev.values + eindex = sortperm(real.(et), rev=true) + + tt .= et + # rearrange wt columns to correspond to eigenvector reordering similar to Fortran + for ipert in 1:intr.mpert + wt[:, ipert] .= Ev.vectors[:, eindex[intr.mpert+1-ipert]] + et[ipert] = tt[eindex[intr.mpert+1-ipert]] + end + + # Normalize eigenfunction and energy. + if normalize + for isol in 1:intr.mpert + norm = 0.0 + 0.0im + for ipert in 1:intr.mpert, jpert in 1:intr.mpert + norm += ffit.jmat[jpert - ipert + intr.mband + 1] * wt[ipert, isol] * conj(wt[jpert, isol]) + end + norm /= v1 + wt[:, isol] ./= sqrt(norm) + et[isol] /= norm + end + end + + # Normalize phase and label largest component. + imax = 0 + for isol in 1:intr.mpert + # get index of largest absolute component (first occurrence) + imax = argmax(abs.(wt[:, isol])) + phase = abs(wt[imax, isol]) / wt[imax, isol] + wt[:, isol] .*= phase + # Mark largest component with *, all others initalized to ' ' + star[imax, isol] = '*' + end + + # Compute plasma and vacuum contributions. + # wpt = wt' * wp * wt ; wvt = wt' * wv * wt + wpt .= adjoint(wt) * (wp * wt) + wvt .= adjoint(wt) * (wv * wt) + + for ipert in 1:intr.mpert + ep[ipert] = wpt[ipert, ipert] + ev[ipert] = wvt[ipert, ipert] + end + + plasma1 = ComplexF64(real(ep[1]), 0.0) + vacuum1 = ComplexF64(real(ev[1]), 0.0) + total1 = ComplexF64(real(et[1]), 0.0) + + # Write data for ahb and deallocate. + # if ahb_flag + # free_ahb_write(nmat, smat, wt, et) + # # Fortran did DEALLOCATE(r,z,theta,dphi,thetas,project) - we assume they are module arrays + # # and will be GC'd or freed by dcon_dealloc below + # end + + # Write to euler.h5 + if outp.write_euler_h5 + write_output(outp, :euler_h5, ep; dsetname="vacuum/ep") + write_output(outp, :euler_h5, ev; dsetname="vacuum/ev") + write_output(outp, :euler_h5, et; dsetname="vacuum/et") + write_output(outp, :euler_h5, wt; dsetname="vacuum/wt") + write_output(outp, :euler_h5, wt0; dsetname="vacuum/wt0") + write_output(outp, :euler_h5, ctrl.wv_farwall_flag; dsetname="vacuum/wv_farwall_flag") + end + + # Write to screen and copy to output. + if ctrl.verbose + println("Energies: plasma = ", real(ep[1]), ", vacuum = ", real(ev[1]), + ", real = ", real(et[1]), ", imaginary = ", imag(et[1])) + end + + # Write eigenvalues to file + write_output(outp, :dcon_out, "\nTotal Energy Eigenvalues:") + write_output(outp, :dcon_out, "\n isol plasma vacuum re total im total\n") + for isol in 1:intr.mpert + write_output(outp, :dcon_out, @sprintf("%6d %11.3e %11.3e %11.3e %11.3e", + isol, real(ep[isol]), real(ev[isol]), real(et[isol]), imag(et[isol]))) + end + write_output(outp, :dcon_out, "\n isol plasma vacuum re total im total\n") + + # Write eigenvectors to file + write_output(outp, :dcon_out, "Total Energy Eigenvectors:") + m = intr.mlow .+ collect(0:intr.mpert-1) + for isol in 1:intr.mpert + write_output(outp, :dcon_out, "\n isol imax plasma vacuum re total im total\n") + write_output(outp, :dcon_out, @sprintf("%6d %6d %11.3e %11.3e %11.3e %11.3e", + isol, imax, real(ep[isol]), real(ev[isol]), real(et[isol]), imag(et[isol]))) + write_output(outp, :dcon_out, "\n ipert m re wt im wt abs wt\n") + for ipert in 1:intr.mpert + write_output(outp, :dcon_out, + @sprintf("%6d %6d %11.3e %11.3e %11.3e %s", + ipert, m[ipert], real(wt[ipert, isol]), imag(wt[ipert, isol]), abs(wt[ipert, isol]), star[ipert, isol])) + end + write_output(outp, :dcon_out, "\n ipert m re wt im wt abs wt\n") + end + + # Write the plasma matrix. + write_output(outp, :dcon_out, "Plasma Energy Matrix:\n") + for isol in 1:intr.mpert + write_output(outp, :dcon_out, "isol = $(isol), m = $(m[isol])") + write_output(outp, :dcon_out, "\n i re wp im wp abs wp\n") + for ipert in 1:intr.mpert + write_output(outp, :dcon_out, @sprintf("%3d%13.5e%13.5e%13.5e", + ipert, real(wp[ipert, isol]), imag(wp[ipert, isol]), abs(wp[ipert, isol]))) + end + write_output(outp, :dcon_out, "\n i re wp im wp abs wp\n") + end + + # Compute separate plasma and vacuum eigenvalues. + # Right eigenvalues/vectors of wp + Ev_wp = eigen(wp) + ep .= Ev_wp.values + eindex = sortperm(real.(ep), rev=true) + tt .= ep + for ipert in 1:intr.mpert + wp[:, ipert] .= Ev_wp.vectors[:, eindex[intr.mpert+1-ipert]] + ep[ipert] = tt[eindex[intr.mpert+1-ipert]] + end + # For vacuum (Hermitian) use eigen of Hermitian wv + Ev_wv = eigen(Hermitian(wv, :U)) + ev .= Ev_wv.values + + # Optionally write netcdf file + # TODO: move this to HDF5 or something else later, make it an input flag? + # if op_netcdf_out + # dcon_netcdf_out(wp, wv, wt, wt0, ep, ev, et) + # end + + return plasma1, vacuum1, total1 +end + +function free_write_msc(psifac::Float64, ctrl::DconControl, intr::DconInternal, equil::Equilibrium.PlasmaEquilibrium; inmemory_op::Union{Bool,Nothing}=nothing, + ahgstr_op::Union{String,Nothing}=nothing) + + # Defaults for optional arguments + inmemory = isnothing(inmemory_op) ? false : inmemory_op + ahgstr = isnothing(ahgstr_op) ? "ahg2msc_dcon.out" : ahgstr_op + inmemory = true # TODO: remove the above, and modify the code logic so VACUUM is always in memory + + # Allocations + theta_norm = Vector(equil.rzphi.ys) + mtheta = length(theta_norm) + angle = zeros(Float64, mtheta) + r = zeros(Float64, mtheta) + z = zeros(Float64, mtheta) + delta = zeros(Float64, mtheta) + rfac = zeros(Float64, mtheta) + + # Compute output + qa = Spl.spline_eval(equil.sq, psifac, 0)[4] # TODO: this had a deriv = 1 in Fortran, but not used? + for itheta in 1:mtheta + f = Spl.bicube_eval(equil.rzphi, psifac, theta_norm[itheta], 0) + rfac[itheta] = sqrt(f[1]) + angle[itheta] = 2π * (theta_norm[itheta] + f[2]) + delta[itheta] = -f[3] / qa + end + r .= equil.ro .+ rfac .* cos.(angle) + z .= equil.zo .+ rfac .* sin.(angle) + + # Invert values for nn < 0 + n = ctrl.nn + if ctrl.nn < 0 + qa = -qa + delta .= -delta + n = -n + end + + # Pass all required values to VACUUM + if inmemory + VacuumMod.set_dcon_params(mtheta, intr.mlow, intr.mhigh, n, qa, + reverse(r), reverse(z), reverse(delta)) + else + # TODO: this section contains ahg2msc file writing, which is deprecated, just remove + end +end \ No newline at end of file diff --git a/src/DCON/Main.jl b/src/DCON/Main.jl new file mode 100644 index 000000000..df38d617c --- /dev/null +++ b/src/DCON/Main.jl @@ -0,0 +1,203 @@ +function Main(path::String) + + println("DCON START") + println("----------------------------------") + start_time = time() + + # Read input data and set up data structures + intr = DconInternal(; dir_path=path) + inputs = TOML.parsefile(joinpath(intr.dir_path, "dcon.toml")) + ctrl = DconControl(; (Symbol(k)=>v for (k,v) in inputs["DCON_CONTROL"])...) + outp = DconOutput(; (Symbol(k)=>v for (k,v) in inputs["DCON_OUTPUT"])...) + equil = Equilibrium.setup_equilibrium(joinpath(intr.dir_path, "equil.toml")) + init_files(outp, intr.dir_path) + + # Set up variables + # TODO: dcon_kin_threads logic? + ctrl.delta_mhigh *= 2 # for consistency with Fortran DCON TODO: why is this present in the Fortran? + + # Determine if qhigh is truncating before psihigh and reform equilibrium if needed + sing_lim!(intr, ctrl, equil) + if intr.psilim != equil.config.control.psihigh && ctrl.reform_eq_with_psilim + @warn "psilim != psihigh not implemented yet, skipping reforming equilibrium splines" + # JMH - Nik please put the logic we discussed here + # something like ? + # equil.config.control.psihigh = intr.psilim + # equil = set_up_equilibrium(equil.config) + end + + # TODO: add some data dump to dcon.out from equil here or in setup_equilibrium + + # Compute Mercier and Ballooning stability (if desired) + # This holds di, dr, h (calculated in mercier_scan), ca1, and ca2 (calculated in ballooning scan) + locstab_fs = zeros(Float64, length(equil.sq.xs), 5) + if ctrl.mer_flag + if ctrl.verbose + println("Evaluating Mercier criterion") + end + mercier_scan!(locstab_fs, equil) + end + # TODO: ballooning stability + #IF(bal_flag)THEN + # IF(ctrl.verbose) WRITE(*,*)"Evaluating ballooning criterion" + # CALL bal_scan + #ENDIF + + # Fit stability data to splines and dump to file + intr.locstab = Spl.CubicSpline(Vector(equil.sq.xs), locstab_fs; bctype=3) + + # Dump equilibrium data to files + if outp.write_eqdata_h5 + write_output(outp, :eqdata_h5, Vector(equil.sq.xs); dsetname="psi") + write_output(outp, :eqdata_h5, Vector(equil.sq.fs[:, 1] ./ (2π)); dsetname="f") + write_output(outp, :eqdata_h5, Vector(equil.sq.fs[:, 2]); dsetname="mu0p") + write_output(outp, :eqdata_h5, Vector(equil.sq.fs[:, 3]); dsetname="dV/dpsi") + write_output(outp, :eqdata_h5, Vector(equil.sq.fs[:, 4]); dsetname="q") + write_output(outp, :eqdata_h5, Vector(locstab_fs[:, 1] ./ equil.sq.xs); dsetname="di") + write_output(outp, :eqdata_h5, Vector(locstab_fs[:, 2] ./ equil.sq.xs); dsetname="dr") + write_output(outp, :eqdata_h5, Vector(locstab_fs[:, 4]); dsetname="ca1") + end + + if outp.write_dcon_out + write_output(outp, :dcon_out, @sprintf("%4s %12s %12s %12s %12s %12s %12s %12s %12s", "ipsi","psifac","f","mu0 p","dvdpsi","q","di","dr","ca1")) + for ipsi in 1:length(equil.sq.xs) + write_output(outp, :dcon_out, + @sprintf("%4d %12.4e %12.4e %12.4e %12.4e %12.4e %12.4e %12.4e %12.4e", + ipsi, + equil.sq.xs[ipsi], + equil.sq.fs[ipsi, 1] / (2π), + equil.sq.fs[ipsi, 2], + equil.sq.fs[ipsi, 3], + equil.sq.fs[ipsi, 4], + locstab_fs[ipsi, 1] / equil.sq.xs[ipsi], + locstab_fs[ipsi, 2] / equil.sq.xs[ipsi], + locstab_fs[ipsi, 4] + ) + ) + end + write_output(outp, :dcon_out, @sprintf("%4s %12s %12s %12s %12s %12s %12s %12s %12s", "ipsi","psifac","f","mu0 p","dvdpsi","q","di","dr","ca1")) + end + + # Find all singular surfaces in the equilibrium + sing_find!(ctrl, equil, intr) + + # Determine poloidal mode numbers + if ctrl.cyl_flag + intr.mlow = ctrl.delta_mlow + intr.mhigh = ctrl.delta_mhigh + elseif ctrl.sing_start == 0 + intr.mlow = min(ctrl.nn * equil.params.qmin, 0) - 4 - ctrl.delta_mlow + intr.mhigh = trunc(Int, ctrl.nn * equil.params.qmax) + ctrl.delta_mhigh + else + intr.mmin = Inf # HUGE in Fortran + for ising in Int(ctrl.sing_start):intr.msing + intr.mmin = min(intr.mmin, sing[ising].m) + end + intr.mlow = intr.mmin - ctrl.delta_mlow + intr.mhigh = trunc(Int, intr.nn * equil.qmax) + ctrl.delta_mhigh + end + intr.mpert = intr.mhigh - intr.mlow + 1 + intr.mband = intr.mpert - 1 - ctrl.delta_mband + intr.mband = min(max(intr.mband, 0), intr.mpert - 1) + + # Fit equilibrium quantities to Fourier-spline functions. + if ctrl.mat_flag || ctrl.ode_flag + if ctrl.verbose + println(" q0 = $(equil.params.q0), qmin = $(equil.params.qmin), qmax = $(equil.params.qmax), q95 = $(equil.params.q95)") + println(" sas_flag = $(ctrl.sas_flag), dmlim = $(ctrl.dmlim), qlim = $(intr.qlim), psilim = $(intr.psilim)") + println(" betat = $(equil.params.betat), betan = $(equil.params.betan), betap1 = $(equil.params.betap1)") + println(" nn = $(ctrl.nn), mlow = $(intr.mlow), mhigh = $(intr.mhigh), mpert = $(intr.mpert), mband = $(intr.mband)") + println(" Fourier analysis of metric tensor components") + end + + if outp.write_dcon_out + write_output(outp, :dcon_out, @sprintf("\n mlow mhigh mpert mband nn lim_fl dmlim qlim psilim")) + write_output(outp, :dcon_out, @sprintf("%6d %6d %6d %6d %6d %6s %11.3e %11.3e %11.3e", + intr.mlow, intr.mhigh, intr.mpert, intr.mband, ctrl.nn, + string(ctrl.sas_flag), ctrl.dmlim, intr.qlim, intr.psilim)) + end + + # Compute metric tensor + metric = make_metric(equil, mband=intr.mband, fft_flag=ctrl.fft_flag) + + if ctrl.verbose + println("Computing F, G, and K Matrices") + end + + # Compute matrices and populate FourFitVars struct + ffit = make_matrix(metric, equil, ctrl, intr) + + if ctrl.kin_flag + error("kin_flag not implemented yet") + end + sing_scan!(intr, ctrl, equil, ffit, outp) + # TODO: implement resist_eval at some point, not urgent for initial functionality. + # for ising in 1:msing + # resist_eval(sing[ising]) + # end + if ctrl.kin_flag + # ksing_find() + end + end + + # Integrate Euler-Lagrange Equation + if ctrl.ode_flag + if ctrl.verbose + println("Integrating Euler-Lagrange equation") + end + odet = ode_run(ctrl, equil, intr, ffit, outp) + if intr.size_edge > 0 + # Find peak index in dw_edge[pre_edge:i_edge] + dw_slice = real.(intr.dw_edge[intr.pre_edge:intr.i_edge]) + peak_index = findmax(dw_slice)[2] + (intr.pre_edge - 1) + ctrl.qhigh = intr.q_edge[peak_index] + ctrl.sas_flag = false + ctrl.psiedge = equil.psihigh + sing_lim!(intr, ctrl, equil) + println("Re-Integrating to peak dW @ qlim = $(intr.qlim), psilim = $(intr.psilim)") + # Full re-run because outputs were written to disk each step + # making it hard to backtrack + # if outp.bin_euler + # bin_close(euler_bin_unit) # TODO: Need to decide ho we're handling io + # end + odet = ode_run(ctrl, equil, intr, ffit, outp) + end + end + + # Compute free boundary energies + plasma1 = 0 + vacuum1 = 0 + total1 = 0 + if ctrl.vac_flag && !(ctrl.ksing > 0 && ctrl.ksing <= intr.msing + 1) + if ctrl.verbose + println("Computing free boundary energies") + end + plasma1, vacuum1, total1 = free_run(odet, ctrl, intr, equil, ffit, outp; op_netcdf_out=false) # outp.netcdf_out) + end + + # Output results of fixed-boundary stability calculations + if ctrl.ode_flag && odet.nzero != 0 + if ctrl.verbose + println("Fixed-boundary mode unstable for nn = $(ctrl.nn).") + end + end + + # Output results of free-boundary stability calculations + if ctrl.vac_flag && !(ctrl.ksing > 0 && ctrl.ksing <= intr.msing + 1 && outp.bin_sol) + if real(total1) < 0 + if ctrl.verbose + println("Free-boundary mode unstable for nn = $(ctrl.nn).") + end + else + if ctrl.verbose + println("All free-boundary modes stable for nn = $(ctrl.nn).") + end + end + end + + end_time = time() - start_time + close_files(outp) + println("----------------------------------") + println("Run time: $end_time seconds") + println("Normal termination.") +end \ No newline at end of file diff --git a/src/DCON/Mercier.jl b/src/DCON/Mercier.jl new file mode 100644 index 000000000..b1654b4bd --- /dev/null +++ b/src/DCON/Mercier.jl @@ -0,0 +1,76 @@ +""" + mercier_scan!(locstab_fs::Array{Float64,5}, plasma_eq::PlasmaEquilibrium) + +Evaluates Mercier criterion for local stability and modifies results in place +within the local stability array. + +""" +function mercier_scan!(locstab_fs::Matrix{Float64}, plasma_eq::Equilibrium.PlasmaEquilibrium) + + # Shorthand + sq = plasma_eq.sq + rzphi = plasma_eq.rzphi + + # Allocate splines + ff_fs = zeros(length(rzphi.ys), 5) + + # Compute surface quantities + for ipsi in 1:length(sq.xs) + twopif = sq.fs[ipsi, 1] + p1 = sq.fs1[ipsi, 2] + v1 = sq.fs[ipsi, 3] + v2 = sq.fs1[ipsi, 3] + q = sq.fs[ipsi, 4] + q1 = sq.fs1[ipsi, 4] + chi1 = 2π * plasma_eq.psio + + # Evaluate coordinates and jacobian + for itheta in 1:length(rzphi.ys) + theta = rzphi.ys[itheta] + + # Evaluate bicubic spline at grid point + f, _, fy = Spl.bicube_eval(rzphi, rzphi.xs[ipsi], theta, 1) + + rfac = sqrt(f[1]) + eta = 2π * (theta + f[2]) + r = plasma_eq.ro + rfac * cos(eta) + jac = f[4] # Jacobian + + # Evaluate other local quantities + v21 = fy[1] / (2.0 * rfac * jac) + v22 = (1.0 + fy[2]) * 2π * rfac / jac + v23 = fy[3] * r / jac + v33 = 2π * r / jac + bsq = chi1^2 * (v21^2 + v22^2 + (v23 + q * v33)^2) + dpsisq = (2π * r)^2 * (v21^2 + v22^2) + + # Evaluate integrands + ff_fs[itheta, 1] = bsq / dpsisq + ff_fs[itheta, 2] = 1.0 / dpsisq + ff_fs[itheta, 3] = 1.0 / bsq + ff_fs[itheta, 4] = 1.0 / (bsq * dpsisq) + ff_fs[itheta, 5] = bsq + + # Weight by jacobian and volume element + ff_fs[itheta, :] .*= jac / v1 + end + + ff = Spl.CubicSpline(Vector(rzphi.ys), ff_fs; bctype=2) # bctype=2 is periodic + + # Integrate quantities with respect to theta + Spl.spline_integrate!(ff) + avg = ff.fsi[end, :] + + # Evaluate Mercier criterion and related quantities + term = twopif * p1 * v1 / (q1 * chi1^3) * avg[2] + di = -0.25 + term * (1 - term) + + p1 * (v1 / (q1 * chi1^2))^2 * avg[1] * + (p1 * (avg[3] + (twopif / chi1)^2 * avg[4]) - v2 / v1) + h = twopif * p1 * v1 / (q1 * chi1^3) * (avg[2] - avg[1] / avg[5]) + + # Store results in output spline structure + locstab_fs[ipsi, 1] = di * sq.xs[ipsi] # is this the right 'psis'? + locstab_fs[ipsi, 2] = (di + (h - 0.5)^2) * sq.xs[ipsi] # is this the right 'psis'? + locstab_fs[ipsi, 3] = h + end +end diff --git a/src/DCON/Ode.jl b/src/DCON/Ode.jl new file mode 100644 index 000000000..55b2753d0 --- /dev/null +++ b/src/DCON/Ode.jl @@ -0,0 +1,1014 @@ +# This is used for various small tolerances throughout this file +const eps = 1e-10 + +""" +OdeState + +A mutable struct to hold the state of the ODE solver for DCON. +This struct contains all necessary fields to manage the ODE integration process, +including solution vectors, tolerances, and flags for the integration process. +""" +#TODO: variable description review by DCON expert (once finished), evaluate if all variables need to be part of the struct +# TODO: remove msol variable, I think it just makes things more confusing. Either use mpert or 2*mpert in loops. This might actually +# cause issues in ode_resist_cross, there's some logic I don't understand there where msol is increased. Might be better to keep it for now +@kwdef mutable struct OdeState + # Initialization parameters + mpert::Int # poloidal mode number count + msol::Int # number of solutions + numunorms_init::Int # initial storage size for unorm data + msing::Int # number of singular surfaces + numsteps_init::Int # initial size of data store + + # Saved data + psi_store::Vector{Float64} = Vector{Float64}(undef, numsteps_init) # psi at each step + u_store::Array{ComplexF64,4} = Array{ComplexF64}(undef, mpert, mpert, 2, numsteps_init) # store of u: mpert x mpert x 2 x nsteps + ud_store::Array{ComplexF64,4} = Array{ComplexF64}(undef, mpert, mpert, 2, numsteps_init) # store of ud: mpert x mpert x 2 x nsteps + step::Int = 1 # current number of stored steps (this is like istep in Fortran) + ca_r::Array{ComplexF64, 4} = Array{ComplexF64}(undef, mpert, 2*mpert, 2, msing) # asymptotic coefficients just right of singular surface + ca_l::Array{ComplexF64, 4} = Array{ComplexF64}(undef, mpert, 2*mpert, 2, msing) # asymptotic coefficients just left of singular surface + index::Array{Int,2} = zeros(Int, mpert, numunorms_init) # indices for sorting solutions + sing_flags::Vector{Bool} = falses(numunorms_init) # flags for singular solutions + fixfac::Array{ComplexF64,3} = zeros(ComplexF64, mpert, mpert, numunorms_init) # fixup factors for Gaussian reduction + fixstep::Vector{Float64} = zeros(Float64, numunorms_init) # psi values at which unorms were performed + + # Data for integrator + singfac::Float64 = 0.0 # separation from singular surface in terms of m - nq + psifac::Float64 = 0.0 # normalized flux coordinate + q::Float64 = 0.0 # q value at psifac + next::String = "" # next action ("cross" or "finish") + ising::Int = 0 # index of next singular surface + u::Array{ComplexF64, 3} = zeros(ComplexF64, mpert, mpert, 2) # solution vectors + ud::Array{ComplexF64, 3} = zeros(ComplexF64, mpert, mpert, 2) # derivative of solution vectors used in GPEC + m1::Int = 0 # poloidal mode number for the first singular surface (?) + psimax::Float64 = 0.0 # maximum psi value for the integrator + ua::Array{ComplexF64, 3} = Array{ComplexF64}(undef, mpert, 2*mpert, 2) # asympototic solutions at singular surface + ca::Array{ComplexF64, 3} = Array{ComplexF64}(undef, mpert, 2*mpert, 2) # asymptotic coefficients at singular surface + psi_prev::Float64 = 0.0 # previous psi value + crit_prev::Float64 = 0.0 # previous crit value + u_prev::Array{ComplexF64, 3} = zeros(ComplexF64, mpert, mpert, 2) # previous solution array + nzero::Int = 0 # count of zero crossings detected + + # Used for Gaussian reduction + new::Bool = true # flag for new solution + unorm::Vector{Float64} = zeros(Float64, 2*mpert) # norms of solution vectors + unorm0::Vector{Float64} = zeros(Float64, 2*mpert) # initial norms of solution vectors + ifix::Int = 0 # index for number of unorms performed + + # Temporary matrices for sing_der calculations + amat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2) + bmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2) + cmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2) + fmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2) + kmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2) + gmat::Vector{ComplexF64} = Vector{ComplexF64}(undef, mpert^2) + Afact::Union{Cholesky{ComplexF64,Matrix{ComplexF64}}, Nothing} = nothing + singfac_vec::Vector{Float64} = Vector{Float64}(undef, mpert) + + flag_count::Int = 0 # count of flags raised # TODO: remove this? Only used in ode_test if res_flag = true +end + +# Base struct that handles storage of the ODE solution throughout integration +mutable struct OdeDataStore + psi::Vector{Float64} + u::Vector{Array{ComplexF64,3}} + ud::Vector{Array{ComplexF64,3}} + step::Int +end + +# Initialize function for data storage object of a given size, will resize as needed +OdeDataStore(numsteps_init::Int) = OdeDataStore(Vector{Float64}(undef, numsteps_init), Vector{Array{ComplexF64,3}}(undef, numsteps_init), Vector{Array{ComplexF64,3}}(undef, numsteps_init), 0) + +# Initialize function for OdeState with relevant parameters for array initialization +OdeState(mpert::Int, msol::Int, numsteps_init::Int, numunorms_init::Int, msing::Int) = OdeState(; mpert, msol, numsteps_init, numunorms_init, msing) + +""" + `ode_run(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal)` + +Main driver for integrating plasma equilibrium and detecting singular surfaces. + +Initializes state and iterates through flux surfaces, calling appropriate update +routines and recording output. Terminates when a target singularity is reached +or integration ends. Support for `res_flag` and `kin_flag` is not yet implemented. + +# TODO: add a detailed description of how the integration loop varies from the Fortran version + +### Returns +nzero: number of zero crossings of the critical determinant detected during the integration. +""" +# TODO: We pass the same structs into most functions; however, do to our use of multiple ! functions that modify the structs +# and the convention that the modified struct comes first, the struct order is never consistent. Is there a better way? +# For now - going to try modified structs first, then alphabetical after +function ode_run(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal, ffit::FourFitVars, outp::DconOutput) + + # Initialization + odet = OdeState(intr.mpert, intr.mpert, ctrl.numsteps_init, ctrl.numunorms_init, intr.msing) + + if ctrl.sing_start <= 0 + ode_axis_init!(ctrl, equil, intr, odet) + elseif ctrl.sing_start <= intr.msing + error("sing_start > 0 not implemented yet!") + # ode_sing_init!(ctrl, equil, intr, odet) + else + error("Invalid value for sing_start: $(ctrl.sing_start) > msing = $(intr.msing)") + end + + if ctrl.verbose # mimicing an output from ode_output_open + println(" ψ=$(odet.psifac), q=$(Spl.spline_eval(equil.sq, odet.psifac, 0)[4])") + end + + # Write header data to files + ode_output_init(ctrl, equil, outp, intr, odet) + + # TODO: Ensure that this section exactly reproduces all functionality of the Fortran + # Might be good for ideal case, but maybe things I haven't considered break this + + # Always integrate once, even if no rational surfaces are crossed + ode_step!(odet, equil, intr, ctrl, ffit, outp) + + # If at a rational surface, do the appropriate crossing routine, then integrate again + while odet.ising != ctrl.ksing && odet.next == "cross" + if ctrl.res_flag + error("res_flag = true not implemented yet!") + elseif ctrl.kin_flag + error("kin_flag = true not implemented yet!") + else + ode_ideal_cross!(odet, equil, intr, ctrl, ffit, outp) + end + + odet.flag_count = 0 + ode_step!(odet, equil, intr, ctrl, ffit, outp) + end + + # Deallocate unused storage of integration data + odet.step -= 1 # step was incremented one extra time in ode_step! + trim_storage!(odet) + + if outp.write_euler_h5 + if ctrl.verbose + println("Writing saved integration data to euler.h5...") + end + write_output(outp, :euler_h5, odet.msol; dsetname="integration/msol") + write_output(outp, :euler_h5, odet.step; dsetname="integration/nstep") + write_output(outp, :euler_h5, odet.psi_store; dsetname="integration/psi") + write_output(outp, :euler_h5, Spl.spline_eval(equil.sq, odet.psi_store, 0)[4]; dsetname="integration/q") + write_output(outp, :euler_h5, odet.u_store; dsetname="integration/u") + write_output(outp, :euler_h5, odet.ud_store; dsetname="integration/ud") + write_output(outp, :euler_h5, odet.ifix; dsetname="normalizations/mfix") + write_output(outp, :euler_h5, odet.fixstep[1:odet.ifix]; dsetname="normalizations/psifix") + write_output(outp, :euler_h5, odet.fixfac[:,:,1:odet.ifix]; dsetname="normalizations/fixfac") + write_output(outp, :euler_h5, odet.sing_flags[1:odet.ifix]; dsetname="normalizations/sing_flags") + write_output(outp, :euler_h5, odet.index[:, 1:odet.ifix]; dsetname="normalizations/index") + write_output(outp, :euler_h5, intr.msing; dsetname="singular/msing") + write_output(outp, :euler_h5, [intr.sing[ising].psifac for ising in 1:intr.msing]; dsetname="singular/psi") + write_output(outp, :euler_h5, [intr.sing[ising].q for ising in 1:intr.msing]; dsetname="singular/q") + write_output(outp, :euler_h5, [intr.sing[ising].q1 for ising in 1:intr.msing]; dsetname="singular/q1") + write_output(outp, :euler_h5, odet.ca_l; dsetname="singular/ca_left") + write_output(outp, :euler_h5, odet.ca_r; dsetname="singular/ca_right") + # TODO: restype writing would also be added here, Matt says not needed for now (or maybe ever) + end + + # TODO: get rid of this eventually + # This is a rough sketch of the original Fortran logic for comparison + # while true # inside plasma (break out when at the edge) + # Rough sketch of Fortran logic for comparison + # while true # inside sing surface (break out when close to singular surface) + # if odet.istep > 0 + # ode_unorm!(odet, intr, ctrl, false) + # end + # Always record the first and last point in an inter-rational region + # these are important for resonant quantities + # recording the last point is critical for matching the nominal edge + # test = ode_test(odet, intr, ctrl) + # force_output = odet.first || test + # ode_output_step(odet, intr, ctrl, equil; force=force_output) + # ode_record_edge!(intr, odet, ctrl, equil) + # test && break # break out of loop if ode_test returns true + # ode_step!(odet, equil, intr, ctrl, ffit) + # odet.first = false + # end + + # # Re-initialize + # odet.ising == ctrl.ksing && break + # if odet.next == "cross" + # if ctrl.res_flag + # error("res_flag = true not implemented yet!") + # #ode_resist_cross() + # elseif ctrl.kin_flag + # error("kin_flag = true not implemented yet!") + # #ode_kin_cross() + # else + # ode_ideal_cross!(odet, equil, intr, ctrl, ffit) + # end + # else + # break + # end + # odet.flag_count = 0 + # end + return odet +end + + +""" + ode_axis_init!(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, + intr::DconInternal, odet::OdeState; itmax = 50) -> Int + +Initialize the ODE state for the case of sing_start = 0. + +Finds the starting flux surface where `q = qlow` using Newton iteration, locates +nearby singular surfaces, and sets integration bounds. Sorts mode indices and +initializes solution arrays for perturbation equations. + +Returns the index of the next relevant singular surface. +""" + +function ode_axis_init!(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal, odet::OdeState; itmax = 50) + + # Shorthand to evaluate q/q1 inside newton iteration + qval = psi -> Spl.spline_eval(equil.sq, psi, 0)[4] + q1val = psi -> Spl.spline_eval(equil.sq, psi, 1)[2][4] + + # Preliminary computations + odet.psifac = equil.sq.xs[1] + + # Use Newton iteration to find starting psi if qlow is above q0 + if ctrl.qlow > equil.sq.fs[1, 4] + # Start check from the edge for robustness in reverse shear cores + for jpsi = equil.sq.mx:-1:2 # avoid starting iteration on endpoints + if equil.sq.fs[jpsi - 1, 4] < ctrl.qlow + odet.psifac = equil.sq.xs[jpsi] + break + end + end + it = 0 + while it ≤ itmax + it += 1 + dpsi = (ctrl.qlow - qval(odet.psifac)) / q1val(odet.psifac) + odet.psifac += dpsi + if abs(dpsi) < eps * abs(odet.psifac) + break + end + end + end + + # Find inner singular surface + if false #(TODO: kin_flag) + # for ising = 1:kmsing + # if kinsing[ising].psifac > psifac + # break + # end + # end + else + odet.ising = 0 + for i in 1:intr.msing + if intr.sing[i].psifac > odet.psifac + odet.ising = max(0, i - 1) + break + end + end + end + + # Find next singular surface + if false # TODO: (kin_flag) + # while true + # ising += 1 + # if ising > kmsing + # break + # end + # if psilim < kinsing[ising].psifac + # break + # end + # odet.q = kinsing[ising].q + # if mlow <= nn * odet.q && mhigh >= nn * odet.q + # break + # end + # end + # if ising > kmsing || singfac_min == 0 + # psimax = psilim * (1 - eps) + # next = "finish" + # elseif psilim < kinsing[ising].psifac + # psimax = psilim * (1 - eps) + # next = "finish" + # else + # psimax = kinsing[ising].psifac - singfac_min / abs(nn * kinsing[ising].q1) + # next = "cross" + # end + else + while true + odet.ising += 1 + if odet.ising > intr.msing || intr.psilim < intr.sing[min(odet.ising, intr.msing)].psifac + break + end + if intr.mlow <= ctrl.nn * intr.sing[odet.ising].q && intr.mhigh >= ctrl.nn * intr.sing[odet.ising].q + break + end + end + if odet.ising > intr.msing || intr.psilim < intr.sing[min(odet.ising, intr.msing)].psifac || ctrl.singfac_min == 0 + odet.psimax = intr.psilim * (1 - eps) + odet.next = "finish" + else + odet.psimax = intr.sing[odet.ising].psifac - ctrl.singfac_min / abs(ctrl.nn * intr.sing[odet.ising].q1) + odet.next = "cross" + end + end + + # Allocate and sort solutions by increasing value of |m-ms1| + m = intr.mlow - 1 .+ collect(1:intr.mpert) + if ctrl.sort_type == "absm" + key = abs.(m) + elseif ctrl.sort_type == "sing" + key = m + if intr.msing > 0 + key .-= intr.sing[1].m + end + @. key = -abs(key) + else + error("Cannot recognize sort_type = $(ctrl.sort_type)") + end + index = sortperm(key, rev = true) # in original Fortran: bubble(key, index, 1, mpert) + + # Initialize solutions + for ipert = 1:intr.mpert + odet.u[index[ipert], ipert, 2] = 1 + end + odet.msol = intr.mpert + odet.u_prev .= odet.u + odet.psi_prev = odet.psifac + + # Compute conditions at next singular surface + if false #TODO: (kin_flag) + # if kmsing > 0 + # m1 = round(Int, nn * kinsing[ising].q) + # else + # m1 = round(Int, nn * qlim) + sign(one, nn * sq.fs1[mpsi, 5]) + # end + else + # note: Julia's default round does Banker's rounding, to match NINT in fortran we need to specify RoundFromZero + if intr.msing > 0 + odet.m1 = round(Int, ctrl.nn * intr.sing[odet.ising].q, RoundFromZero) + else + odet.m1 = round(Int, ctrl.nn * intr.qlim, RoundFromZero) + sign(ctrl.nn * equil.sq.fs1[end, 4]) + end + end + odet.singfac = abs(odet.m1 - ctrl.nn * equil.sq.fs[1, 4]) # Fortran: q=sq%fs(0,4) +end + +# TODO: NOT IMPLEMENTED YET! (low priority, just make sure sing_start = 0 in dcon.toml) +function ode_sing_init() + return +end +# # Declare and initialize local variables +# star = fill(' ', mpert) +# # local variables +# ua = Array{Complex{r8}}(undef, mpert, 2*mpert, 2) +# dpsi = 0.0 +# new = true + +# ising = sing_start +# dpsi = singfac_min/abs(nn*sing[ising].q1)*10 +# odet.psifac = sing[ising].psifac + dpsi +# odet.q = sing[ising].q + dpsi*sing[ising].q1 + +# # Allocate and initialize solution arrays +# u = zeros(Complex{r8}, mpert, mpert, 2) +# du = zeros(Complex{r8}, mpert, mpert, 2) +# u_prev = zeros(Complex{r8}, mpert, mpert, 2) +# unorm0 = zeros(r8, 2*mpert) +# unorm = zeros(r8, 2*mpert) +# index = zeros(Int, 2*mpert) + +# if old_init +# u .= 0.0 +# for ipert ∈ 1:mpert +# u[ipert, ipert, 2] = 1.0 +# end +# else +# sing_get_ua(ising, odet.psifac, ua) +# # Big slice: u = ua[:, mpert+1:2*mpert,:] +# for i = 1:mpert, j = 1:mpert, k = 1:2 +# u[i, j, k] = ua[i, mpert+j, k] +# end +# end +# u_prev .= u +# psi_prev = psifac +# msol = mpert +# neq = 4 * mpert * msol + +# # Compute conditions at next singular surface +# while true +# ising += 1 +# if ising > msing || psilim < sing[ising ≤ msing ? ising : msing].psifac +# break +# end +# odet.q = sing[ising].q +# if mlow ≤ nn*q && mhigh ≥ nn*q +# break +# end +# end +# This needs to be fixed up +# if ising > msing || psilim < sing[ising ≤ msing ? ising : msing].psifac +# m1 = round(Int, ctrl.nn*intr.qlim) + round(Int, sign(one, ctrl.nn*equil.sq.fs1[mpsi, 4])) +# psimax = psilim * (1-eps) +# next_ = "finish" +# else +# m1 = round(Int, nn*sing[ising].q) +# psimax = sing[ising].psifac - singfac_min/abs(nn*sing[ising].q1) +# next_ = "cross" +# end + +# # Set up integrator parameters +# istep = 0 +# istate = 1 +# iopt = 1 +# itask = 5 +# itol = 2 +# mf = 10 +# istate = 1 + +# # Set up work arrays +# liw = length(iwork) # iwork must exist! +# lrw = 22 + 64*mpert*msol +# rwork = zeros(r8, lrw) +# atol = zeros(r8, mpert, msol, 2) +# fixfac = zeros(r8, msol, msol) +# iwork = zeros(Int, liw) # or readjust as needed +# rwork[1] = psimax +# rwork[5] = dpsi +# rwork[11] = rwork[5] + +# # Terminate, or in Julia just return (no need for RETURN) +# return nothing # or could return a struct with all these values, for a more Julian approach +# end + +""" + ode_ideal_cross!(odet::OdeState, equil::Equilibrium.PlasmaEquilibrium, + intr::DconInternal, ctrl::DconControl) + +Handle the crossing of an ideal MHD singular surface during ODE integration +in a plasma equilibrium calculation. + +# Arguments +- `odet::OdeState`: The current state of the ODE system (mutable, updated in-place). +- `equil::Equilibrium.PlasmaEquilibrium`: Object representing plasma equilibrium parameters. +- `intr::DconInternal`: Structure containing internal data, including singular surface information. +- `ctrl::DconControl`: Holds control flags and integration parameters. + +# Description +This function updates the ODE solution as it crosses a (resonant) singular surface in the +ideal MHD calculation. It normalizes and reinitializes the solution vector at the singularity, +handles singular asymptotics, manages control flags, and updates relevant state variables +in `odet` for continued integration. It also determines the location and parameters of +the next singular surface, updates tolerance/stepping logic for the ODE solver, and may +write auxiliary diagnostic output or coefficients as configured. + +# Notes +- Handles resetting or reinitializing the solver after singular surface crossing. +- Assumes certain global state (such as `u`, `ua`, `index`, etc.) is properly managed. +- Intended for ideal MHD regions; kinetic surface handling is not included in this function. +""" +function ode_ideal_cross!(odet::OdeState, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal, ctrl::DconControl, ffit::FourFitVars, outp::DconOutput) + + # Fixup solution at singular surface + if ctrl.verbose + println(" ψ = $(intr.sing[odet.ising].psifac), q = $(intr.sing[odet.ising].q)") + end + ode_unorm!(odet, intr, ctrl, outp, true) + + # Get asymptotic coefficients before crossing rational surface + # TODO: remove odet.ua and ca and just have sing_get_ua and sing_get_ca return the arrays? + sing_get_ca!(odet, intr, ctrl) + odet.ca_l[:, :, :, odet.ising] .= odet.ca + + # Re-initialize on opposite side of rational surface + psi_old = odet.psifac + singp = intr.sing[odet.ising] + ipert0 = round(Int, ctrl.nn * singp.q, RoundFromZero) - intr.mlow + 1 + dpsi = singp.psifac - odet.psifac + odet.psifac = singp.psifac + dpsi + sing_get_ua!(odet, intr, ctrl) + if !ctrl.con_flag + odet.u[:, odet.index[1, odet.ifix], :] .= 0 + end + + # Update solution vectors + du1 = zeros(ComplexF64, intr.mpert, intr.mpert, 2) + du2 = zeros(ComplexF64, intr.mpert, intr.mpert, 2) + params = (ctrl, equil, intr, odet, ffit, outp) + sing_der!(du1, odet.u, params, psi_old) + sing_der!(du2, odet.u, params, odet.psifac) + odet.u .+= (du1 .+ du2) .* dpsi + if !ctrl.con_flag + odet.u[ipert0, :, :] .= 0 + odet.u[:, odet.index[1, odet.ifix], :] .= odet.ua[:, ipert0 + intr.mpert, :] + end + + # Get asymptotic coefficients after crossing rational surface + sing_get_ca!(odet, intr, ctrl) + odet.ca_r[:, :, :, odet.ising] .= odet.ca + + # Find next ising + while true + odet.ising += 1 + if odet.ising > intr.msing || intr.psilim < intr.sing[min(odet.ising, intr.msing)].psifac + break + end + if intr.mlow <= ctrl.nn * intr.sing[odet.ising].q && intr.mhigh >= ctrl.nn * intr.sing[odet.ising].q + break + end + end + + # Compute conditions at next singular surface + if odet.ising > intr.msing || intr.psilim < intr.sing[min(odet.ising, intr.msing)].psifac + odet.psimax = intr.psilim * (1 - eps) + odet.m1 = round(Int, ctrl.nn * intr.qlim, RoundFromZero) + sign(ctrl.nn * equil.sq.fs1[end, 4]) + odet.next = "finish" + else + singp = intr.sing[odet.ising] # Update singp + odet.psimax = singp.psifac - ctrl.singfac_min / abs(ctrl.nn * singp.q1) + odet.m1 = round(Int,ctrl.nn * singp.q, RoundFromZero) + write_output(outp, :crit_out, @sprintf(" ising psi q di re alpha im alpha\n")) + write_output(outp, :crit_out, @sprintf("%6d%11.3e%11.3e%11.3e%11.3e%11.3e\n", odet.ising, singp.psifac, singp.q, singp.di, real(singp.alpha), imag(singp.alpha))) + end + + # Restart ode solver + odet.new = true + odet.psi_store[odet.step] = odet.psifac # Store current psi + odet.u_store[:,:,:,odet.step] = odet.u # Store current u + odet.step += 1 # Advance step to account for crossing step + odet.u_prev .= odet.u + odet.psi_prev = odet.psifac + + # Write next header before continuing integration + write_output(outp, :crit_out, " psifac dpsi q singfac eval1") +end + +# Example stub for kinetic crossing +function ode_kin_cross() + # Implement kinetic crossing logic here + return +end + +# Example stub for resistive crossing +function ode_resist_cross() + # Implement resistive crossing logic here + return +end + +""" + ode_step!(odet::OdeState, equil::Equilibrium.PlasmaEquilibrium, + intr::DconInternal, ctrl::DconControl, ffit::FourFitVars) + +Integrate the Euler-Lagrange equations to the next rational surface or edge. + +# Arguments +- `odet::OdeState`: Structure storing the current ODE state and solution arrays. +- `equil::Equilibrium.PlasmaEquilibrium`: Plasma equilibrium parameters and profiles. +- `intr::DconInternal`: Internal data, including singular surfaces. +- `ctrl::DconControl`: Control and solver settings (e.g., tolerances, flags). +- `ffit::FourFitVars`: Additional fitting variables or Fourier fit coefficients. + +# Description +This function computes and sets appropriate relative and absolute tolerances +for the ODE integration depending on proximity to singular surfaces, +chooses the next integration endpoint, and advances the solution using +an adaptive ODE solver. The state in `odet` is updated in-place with +the solution at the new point. + +# Notes +- Tolerance logic distinguishes between "near-singular" and "regular" regions. +- ODE integration is performed using the DifferentialEquations.jl interface. +- Handles both node-based and maximal-psi stepping, depending on control flags. +""" +function ode_step!(odet::OdeState, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal, ctrl::DconControl, ffit::FourFitVars, outp::DconOutput) + + # print!(integrator) = begin + # u = integrator.u + # # params = integrator.p + # # params is a tuple: (ctrl, equil, intr, odet, ffit) + # # du = similar(u) + # # sing_der!(du, u, params, integrator.t) + # fmt(x) = @sprintf("%.5e", x) + # println(" ψ=", fmt(integrator.t), + # ", max|u|=", fmt(maximum(abs.(u)))) + # # ", max|du|=", fmt(maximum(abs.(du)))) + # last_psi[] = integrator.t + # end + + # Set up the callback to be run at every step + cb = DiscreteCallback((u,t,integrator)->true, integrator_callback!) + + # Choose integration bounds + if ctrl.node_flag # TODO: I can't find any mention of what this flag is for, can we get rid of it? + while odet.psifac >= equil.sq.xs[ix] + ix += 1 + end + psiout = equil.sq.xs[ix] + psiout = min(psiout, odet.psimax) + else + psiout = odet.psimax + end + + # Print out every tenth of the inter-rational interval + # Δψ = (odet.psimax - odet.psifac) / 10 + # last_psi = Ref(0.0) + + # TODO: need input here! Fortran emphasized that it was important to record data at the first and last step + # However, the recording for u, ud, psi is now done after integration. Is there anything still within + # ode_output_step that needs to be recorded with this precision, or can it just be called within the + # callback? Currently, ode_output_step does: ode_output_monitor (crit values), and in Fortran also does + # ode_output_get_evals, and ode_output_sol + # We don't use the `first` variable, and instead call the functions directly here before/after integration + ode_output_step!(odet, intr, ctrl, equil, outp) + + # Advance differential equation to next singular surface or edge + rtol, atol = compute_tols(intr, odet, ctrl) # initial tolerances + prob = ODEProblem(sing_der!, odet.u, (odet.psifac, psiout), (ctrl, equil, intr, odet, ffit, outp)) + sol = solve(prob, Tsit5(), reltol=rtol, abstol=atol, callback=cb) + # TODO: check absolute tolerances, check how sensitive outputs are to tolerances + + # Update u and psifac with the solution at the end of the interval + odet.u .= sol.u[end] + odet.psifac = sol.t[end] + + # Save the data after integration by evaluating stored solution + # (This used to be done during integration using ode_output_step) + # We use save nodes that include the first and last point in an interrational region, which are important + # for resonant quantities. Recording the last point is critical for matching the nominal edge + # TODO: does this get messed up by u_norming? + # for isave in (odet.ising-1)*ctrl.saves_per_region+1:odet.ising*ctrl.saves_per_region + # # Evaluate solution derivative ud at psi, u for GPEC (NOT du) + # u_interp = sol(odet.psi_saves[isave]) + # du_interp = similar(u_interp) + # sing_der!(du_interp, u_interp, (ctrl, equil, intr, odet, ffit, outp), odet.psi_saves[isave]) + + # # Store interpolated solutions at save points + # odet.u_saves[:, :, :, isave] .= u_interp + # odet.ud_saves[:, :, :, isave] .= odet.ud + # end + + # TODO: same as above, this might not be needed + ode_output_step!(odet, intr, ctrl, equil, outp) # always output final condition + + println(" ψ = $(odet.psifac), max u = $(maximum(abs, odet.u)), steps = $(odet.step-1)") +end + +""" + integrator_callback!(integrator) + +Callback function for ODE integrator to handle normalization, output, and storage at each step. +This handles the logic that was previously in a DO loop within ode_run and called every step +by running LSODE in one step mode in the Fortran code. +""" +function integrator_callback!(integrator) + ctrl, equil, intr, odet, ffit, outp = integrator.p + odet.u .= integrator.u + odet.psifac = integrator.t + + # Update integration tolerances + rtol, atol = compute_tols(intr, odet, ctrl) + integrator.opts.reltol = rtol + # integrator.opts.abstol = atol + + # TODO: Print status every Δψ, maybe get rid of this at some point? Good for debugging rn + # if integrator.t >= last_psi[] + Δψ + # print!(integrator) + # end + + # Note: no need for istep > 0 condition, since this is called after the first integration step always + ode_unorm!(odet, intr, ctrl, outp, false) + integrator.u .= odet.u # Update integrator.u with normalized odet.u + + # TODO: ode_test if res_flag = False effectively controls whether we print at the end of integration + # this then controls the output of ode_output_step and then has a break condition below + # Currently, all output logic is handled via psi_saves. There's a chance we will need other pieces + # of this ode_test logic (i.e. res_flag = True, compute powers) in the future, but for now this is sufficient + # force_output = ode_test(odet, intr, ctrl) + ode_output_step!(odet, intr, ctrl, equil, outp) + ode_record_edge!(intr, ctrl, equil, odet) + + # Grow arrays if needed + if odet.step >= size(odet.u_store, 4) + resize_storage!(odet) + end + # Save values + odet.psi_store[odet.step] = odet.psifac + odet.u_store[:,:,:,odet.step] = odet.u + odet.ud_store[:,:,:,odet.step] = odet.ud + # Advance stepper (just like in Fortran, a "step" starts with integration, does callback functions, then stores) + odet.step += 1 +end + +# Compute tolerances based on distance to singular surface during integration +function compute_tols(intr, odet, ctrl) + singfac_local = Inf + # Relative tolerance + if false # kin_flag (not implemented) + # Insert kin_flag branch if needed + else + # Note: odet.q is updated within the derivative calculation + if odet.ising <= intr.msing + singfac_local = abs(intr.sing[odet.ising].m - ctrl.nn * odet.q) + end + # If in between singular surfaces, check distance to both + if odet.ising > 1 + singfac_local = min(singfac_local, abs(intr.sing[odet.ising-1].m - ctrl.nn * odet.q)) + end + end + rtol = tol = singfac_local < ctrl.crossover ? ctrl.tol_r : ctrl.tol_nr + # Absolute tolerances + atol = similar(odet.u, Float64) + for ieq in 1:size(odet.u,3), isol in 1:size(odet.u,2) + atol0 = maximum(abs.(odet.u[:, isol, ieq])) * tol + if (atol0 == 0) atol0 = Inf end + atol[:, isol, ieq] .= atol0 + end + return rtol, atol +end + +""" + resize_storage!(odet::OdeState) + +Resize storage arrays in `odet` when the current step exceeds allocated size. +Doubles the size of the storage arrays for `u_store`, `ud_store`, and `psi_store`, +and copies over existing data to the new arrays. +""" +function resize_storage!(odet::OdeState) + oldlen = size(odet.u_store, 4) + newlen = 2 * oldlen + + # Allocate new arrays + u_new = Array{ComplexF64,4}(undef, odet.mpert, odet.mpert, 2, newlen) + ud_new = Array{ComplexF64,4}(undef, odet.mpert, odet.mpert, 2, newlen) + psi_new = Vector{Float64}(undef, newlen) + + # Copy old data + u_new[:,:,: ,1:odet.step] = odet.u_store[:,:,: ,1:odet.step] + ud_new[:,:,: ,1:odet.step] = odet.ud_store[:,:,: ,1:odet.step] + psi_new[1:odet.step] = odet.psi_store[1:odet.step] + + # Replace old arrays + odet.u_store = u_new + odet.ud_store = ud_new + odet.psi_store = psi_new +end + +""" + trim_storage!(odet::OdeState) + +Trim storage arrays in `odet` to the actual number of steps taken. +Resizes `u_store`, `ud_store`, and `psi_store` to the current step count, +removing any unused allocated space. +""" +function trim_storage!(odet::OdeState) + resize!(odet.psi_store, odet.step) + odet.u_store = odet.u_store[:,:,: ,1:odet.step] + odet.ud_store = odet.ud_store[:,:,: ,1:odet.step] +end + +""" + ode_unorm!(odet::OdeState, intr::DconInternal, sing_flag::Bool) + +Computes norms of the solution vectors, normalizes them +relative to initial values, and applies Gaussian reduction via `ode_fixup!` +if the variation exceeds a threshold or if `sing_flag` is true. +Throws an error if any vector norm is zero. +""" +function ode_unorm!(odet::OdeState, intr::DconInternal, ctrl::DconControl, outp::DconOutput, sing_flag::Bool) + # Compute norms of first solution vectors, abort if any are zero + odet.unorm[1:intr.mpert] .= [norm(odet.u[:, j, 1]) for j in 1:intr.mpert] + odet.unorm[intr.mpert+1:odet.msol] .= [norm(odet.u[:, j, 2]) for j in intr.mpert+1:odet.msol] + if minimum(odet.unorm[1:odet.msol]) == 0 + jmax = argmin(odet.unorm[1:odet.msol]) + error("One of the first solution vector norms unorm(1,$jmax) = 0") + end + + # Normalize unorm and perform Gaussian reduction if required + if odet.new + odet.new = false + odet.unorm0[1:odet.msol] .= odet.unorm[1:odet.msol] + else + odet.unorm[1:odet.msol] .= odet.unorm[1:odet.msol] ./ odet.unorm0[1:odet.msol] + uratio = maximum(odet.unorm[1:odet.msol]) / minimum(odet.unorm[1:odet.msol]) + if uratio > ctrl.ucrit || sing_flag + # TODO: add resizing logic here as well + if odet.ifix < ctrl.numunorms_init + odet.ifix += 1 + else + @warn "unorm storage reached, no longer saving fixfac data. Stability outputs and unorming will be correct, but cannot reconstruct `u`. \n + Increase `numunorms_init` in dcon.toml if needed. Automatic resizing will be added in a future version." + end + ode_fixup!(odet, intr, outp, sing_flag, false) + odet.new = true + end + end +end + +""" + ode_fixup!(odet::OdeState, intr::DconInternal, sing_flag::Bool, test::Bool) + +Applies Gaussian reduction to orthogonalize solution vectors in `odet.u`. + +Used when the spread in norms exceeds a threshold or a singularity is detected. +Sorts solutions by norm, eliminates dependencies using forward elimination, +and optionally computes the transformation matrix `fixfac`. +Behavior can be suppressed for testing via the `test` flag. +""" +function ode_fixup!(odet::OdeState, intr::DconInternal, outp::DconOutput, sing_flag::Bool, test::Bool) + + # TODO: seems like secondary is always false in fortran DCON (unless manually changed). is this needed? + secondary = false + + # TODO: can test be removed if we aren't implementing ode_test_fixup? + + # Write to output + if outp.write_crit_out + write_output(outp, :crit_out, "\n psifac dpsi q singfac eval1") + write_output(outp, :crit_out, @sprintf("\nGaussian Reduction at psi = %10.3e, q = %6.3f\n", odet.psifac, odet.q)) + if !sing_flag + write_output(outp, :crit_out, " psifac dpsi q singfac eval1\n") + end + end + odet.flag_count = 0 # TODO: is this used anywhere? + + # Store data for the current fixup + ifix = odet.ifix + odet.sing_flags[ifix] = sing_flag + odet.fixstep[ifix] = odet.step + + # Initialize fixfac + if !test + for isol in 1:odet.msol + odet.fixfac[isol, isol, ifix] = 1 + end + # Sort unorm + odet.index[1:odet.msol, ifix] .= collect(1:odet.msol) + odet.index[1:intr.mpert, ifix] .= sortperm_subrange(odet.unorm, 1:intr.mpert) # in original Fortran: bubble(unorm, index, 1, mpert) + odet.index[intr.mpert+1:odet.msol, ifix] .= sortperm_subrange(odet.unorm, intr.mpert+1:odet.msol) # in original Fortran: bubble(unorm, index, mpert + 1, msol) + end + + # Triangularize primary solutions + mask = trues(2, odet.msol) + for isol in 1:intr.mpert + ksol = odet.index[isol, ifix] + mask[2, ksol] = false + if !test + # Find max location + kpert = argmax(abs.(odet.u[:, ksol, 1]) .* mask[1, 1:intr.mpert]) + mask[1, kpert] = false + end + for jsol in 1:odet.msol + if mask[2, jsol] + if !test + odet.fixfac[ksol, jsol, ifix] = -odet.u[kpert, jsol, 1] / odet.u[kpert, ksol, 1] + end + odet.u[:, jsol, :] .= odet.u[:, jsol, :] .+ odet.u[:, ksol, :] .* odet.fixfac[ksol, jsol, ifix] + if !test + odet.u[kpert, jsol, 1] = 0 + end + end + end + end + + # Triangularize secondary solutions + if odet.msol > intr.mpert && secondary + mask = trues(2, odet.msol) + for isol in intr.mpert + 1:odet.msol + ksol = odet.index[isol, ifix] + mask[2, ksol] = false + if !test + absvals = abs.(odet.u[:, ksol, 2]) + masked = absvals .* mask[1, 1:intr.mpert] + kpert = argmax(masked) + mask[1, kpert] = false + end + for jsol in intr.mpert + 1:odet.msol + if mask[2, jsol] + if !test + odet.fixfac[ksol, jsol, ifix] = -odet.u[kpert, jsol, 2] / odet.u[kpert, ksol, 2] + end + odet.u[:, jsol, :] .= odet.u[:, jsol, :] .+ odet.u[:, ksol, :] .* odet.fixfac[ksol, jsol, ifix] + if !test + odet.u[kpert, jsol, 2] = 0 + end + end + end + end + end + + # Note: will dump to output later if needed +end + +""" + ode_test(odet::OdeState, intr::DconInternal, ctrl::DconControl)::Bool + +Returns `true` if integration is complete or if any stopping criteria are met. + +TODO: implement res_flag = true logic +""" +function ode_test(odet::OdeState, intr::DconInternal, ctrl::DconControl)::Bool + + # check if we are at end of integration + flag = odet.psifac == odet.psimax + + # if not running with res_flag = true this function will exit and return flag here) + if !ctrl.res_flag || flag || odet.ising > intr.msing || odet.singfac > ctrl.singfac_max + return flag + end + + @error "ode_test with res_flag = true not implemented yet!" + # TODO: none of this has been checked, wait until we implement res_flag = true + # ca_old .= ca # Save previous surface ca + # sing_get_ca(ising, psifac, u, ca) # Updates global ca + # dca = ca .- ca_old + # dsingfac = abs((singfac - singfac_old)/singfac) + # singfac_old = singfac + + # power = zeros(Float64, msol) + # powmax_old = powmax + # for isol in 1:msol + # # ca[:,isol,:]::matrix of size (mpert,2) + # # Flatten the relevant slice for norm calculation + # ca_isol = ca[:, isol, :] # mpert × 2 + # dca_isol = dca[:, isol, :] + # norm = abs(sum(conj.(ca_isol) .* ca_isol)) + # dnorm = abs(sum(conj.(ca_isol) .* dca_isol)) + # power[isol] = dnorm / (norm * dsingfac) + # end + # powmax = maximum(power) + + # odet.flag_count += 1 + # if odet.flag_count < 3 + # return flag + # end + # flag = flag || ((singfac < singfac_max) && (powmax > powmax_old)) + + # if ising == ksing + # println(err_unit, float(log10(singfac)), " ", float(log10(powmax))) + # end + + # return flag +end + +""" + ode_record_edge!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, odet::OdeState) + +Records edge quantities at the current integration point if edge conditions are met. + +Checks whether `psifac` and `q` exceed edge thresholds, and if so, +stores relevant values in `intr`. Currently, vacuum calculations are +not implemented; this function raises an error if invoked in a vacuum region. +""" +# TODO: this function requires integration the vacuum code for free_test +# for now, going to make it look ok and error out if we get to free_test +# I don't think this function is working properly, but I'm not sure what its doing +function ode_record_edge!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, odet::OdeState) + + q_psifac = Spl.spline_eval(equil.sq, odet.psifac, 0) + if intr.size_edge > 0 + #TODO: WTH? fortran has both a psiedge and psi_edge and they appear to be different. + # someone smarter than me please double check this + if q_psifac >= intr.q_edge[intr.i_edge] && odet.psifac >= ctrl.psiedge + @error "Vacuum code not yet integrated. This run has size_edge = $(intr.size_edge) > 0 and integrator passed psiedge/q_edge" + #free_test(plasma1, vacuum1, total1, odet.psifac) + intr.dw_edge[intr.i_edge] = total1 + intr.q_edge[intr.i_edge] = q_psifac + intr.psi_edge[intr.i_edge] = odet.psifac + intr.i_edge = min(intr.i_edge + 1, intr.size_edge) # just to be extra safe + end + end +end + +""" + get_psi_saves!(odet::OdeState, ctrl::DconControl, intr::DconInternal) + +Calculates the psi values at which to save the solution during ODE integration based on specified spacing type, +number of saves per region, and number of rational surfaces, and saves into `odet.psi_save_nodes`. Note that +`odet.psi_save_nodes` does not store the start/endpoints, since those are saved automatically. +""" +# TODO: this is no longer used, but might be useful code? Leaving for now, but likely can be removed +function get_psi_saves!(odet::OdeState, ctrl::DconControl, intr::DconInternal) + + # This function is called after the ode init functions, so the starting psi is stored in odet.psifac + # This repeats some logic used in the init and cross functions + + # Loop through interrational intervals (just one interval if no rational surfaces) + for ising in 1:intr.msing+1 + # Determine bottom of interrational interval + if ising == 1 + psibot = odet.psifac + else + psibot = intr.sing[ising - 1].psifac + ctrl.singfac_min / abs(ctrl.nn * intr.sing[ising - 1].q1) + end + # Determine top of interrational interval + if ising <= intr.msing + psitop = intr.sing[ising].psifac - ctrl.singfac_min / abs(ctrl.nn * intr.sing[ising].q1) + else + psitop = intr.psilim * (1 - eps) + end + # Calculate save nodes in interval + if ctrl.save_spacing == "Chebyshev" + odet.psi_saves[(ising-1)*ctrl.saves_per_region+1:ising*ctrl.saves_per_region] = chebyshev_nodes(psibot, psitop, ctrl.saves_per_region) + else + error("Cannot recognize save_spacing = $(ctrl.save_spacing)") + end + end +end \ No newline at end of file diff --git a/src/DCON/OdeOutput.jl b/src/DCON/OdeOutput.jl new file mode 100644 index 000000000..550431a29 --- /dev/null +++ b/src/DCON/OdeOutput.jl @@ -0,0 +1,306 @@ +""" + ode_output_init(ctrl, equil, outp, intr, odet) + + Write header info to output files at the start of the integration. +""" +function ode_output_init(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, outp::DconOutput, intr::DconInternal, odet::OdeState) + + # TODO: mess with this to condense the number of write_output calls? Maybe allow it to pass in dicts + # Write euler.bin header info + if outp.write_euler_h5 + # Write dcon run parameters + write_output(outp, :euler_h5, intr.mpert; dsetname="info/mpert") + write_output(outp, :euler_h5, intr.mband; dsetname="info/mband") + write_output(outp, :euler_h5, intr.mlow; dsetname="info/mlow") + write_output(outp, :euler_h5, intr.mhigh; dsetname="info/mhigh") + write_output(outp, :euler_h5, ctrl.nn; dsetname="info/nn") + write_output(outp, :euler_h5, ctrl.singfac_min; dsetname="info/singfac_min") + write_output(outp, :euler_h5, ctrl.kin_flag; dsetname="info/kin_flag") + write_output(outp, :euler_h5, ctrl.con_flag; dsetname="info/con_flag") + write_output(outp, :euler_h5, ctrl.mthvac; dsetname="info/mthvac") + write_output(outp, :euler_h5, intr.psilim; dsetname="info/psilim") + write_output(outp, :euler_h5, intr.qlim; dsetname="info/qlim") + write_output(outp, :euler_h5, outp.mthsurf0; dsetname="info/mthsurf0") #TODO: mthsurf0 is deprecated + + # Write equilibrium parameters + write_output(outp, :euler_h5, length(equil.rzphi.xs); dsetname="equil/nr") # TODO: equil save mpsi as really mpsi - 1, fix this + write_output(outp, :euler_h5, length(equil.rzphi.ys); dsetname="equil/nz") + write_output(outp, :euler_h5, equil.ro; dsetname="equil/ro") + write_output(outp, :euler_h5, equil.zo; dsetname="equil/zo") + write_output(outp, :euler_h5, equil.params.amean; dsetname="equil/amean") + write_output(outp, :euler_h5, equil.params.rmean; dsetname="equil/rmean") + write_output(outp, :euler_h5, equil.params.aratio; dsetname="equil/aratio") + write_output(outp, :euler_h5, equil.params.kappa; dsetname="equil/kappa") + write_output(outp, :euler_h5, equil.params.delta1; dsetname="equil/delta1") + write_output(outp, :euler_h5, equil.params.delta2; dsetname="equil/delta2") + write_output(outp, :euler_h5, equil.params.li1; dsetname="equil/li1") + write_output(outp, :euler_h5, equil.params.li2; dsetname="equil/li2") + write_output(outp, :euler_h5, equil.params.li3; dsetname="equil/li3") + write_output(outp, :euler_h5, equil.params.betap1; dsetname="equil/betap1") + write_output(outp, :euler_h5, equil.params.betap2; dsetname="equil/betap2") + write_output(outp, :euler_h5, equil.params.betap3; dsetname="equil/betap3") + write_output(outp, :euler_h5, equil.params.betat; dsetname="equil/betat") + write_output(outp, :euler_h5, equil.params.betan; dsetname="equil/betan") + write_output(outp, :euler_h5, equil.params.bt0; dsetname="equil/bt0") + write_output(outp, :euler_h5, equil.params.q0; dsetname="equil/q0") + write_output(outp, :euler_h5, equil.params.q95; dsetname="equil/q95") + write_output(outp, :euler_h5, equil.params.qmin; dsetname="equil/qmin") + write_output(outp, :euler_h5, equil.params.qmax; dsetname="equil/qmax") + write_output(outp, :euler_h5, equil.params.qa; dsetname="equil/qa") + write_output(outp, :euler_h5, equil.params.crnt; dsetname="equil/crnt") + write_output(outp, :euler_h5, equil.psio; dsetname="equil/psio") + write_output(outp, :euler_h5, equil.config.control.psilow; dsetname="equil/psilow") + write_output(outp, :euler_h5, equil.config.control.power_b; dsetname="equil/power_b") + write_output(outp, :euler_h5, equil.config.control.power_r; dsetname="equil/power_r") + write_output(outp, :euler_h5, equil.config.control.power_bp; dsetname="equil/power_bp") + write_output(outp, :euler_h5, 0; dsetname="equil/shotnum") # TODO: equil.params.shotnum) + write_output(outp, :euler_h5, 0; dsetname="equil/shottime") # TODO: equil.params.shottime) + + # Write spline arrays + write_output(outp, :euler_h5, Vector(equil.sq.xs); dsetname="splines/sq/xs") + # TODO: getting errors when trying to dump just fs, so splitting for now, which adds so many lines + # This should be fixed if we separate these like Nik mentioned + write_output(outp, :euler_h5, equil.sq.fs[:,1]; dsetname="splines/sq/fs/2piF") + write_output(outp, :euler_h5, equil.sq.fs[:,2]; dsetname="splines/sq/fs/mu0p") + write_output(outp, :euler_h5, equil.sq.fs[:,3]; dsetname="splines/sq/fs/dVdpsi") + write_output(outp, :euler_h5, equil.sq.fs[:,4]; dsetname="splines/sq/fs/q") + write_output(outp, :euler_h5, equil.sq.fs1[:,1]; dsetname="splines/sq/fs1/2piF") + write_output(outp, :euler_h5, equil.sq.fs1[:,2]; dsetname="splines/sq/fs1/mu0p") + write_output(outp, :euler_h5, equil.sq.fs1[:,3]; dsetname="splines/sq/fs1/dVdpsi") + write_output(outp, :euler_h5, equil.sq.fs1[:,4]; dsetname="splines/sq/fs1/q") + write_output(outp, :euler_h5, 0; dsetname="splines/sq/xpower") # TODO: equil.sq.xpower + write_output(outp, :euler_h5, Vector(equil.rzphi.xs); dsetname="splines/rzphi/xs") + write_output(outp, :euler_h5, Vector(equil.rzphi.ys); dsetname="splines/rzphi/ys") + write_output(outp, :euler_h5, equil.rzphi.fs[:,1]; dsetname="splines/rzphi/fs/rcoords") + write_output(outp, :euler_h5, equil.rzphi.fs[:,2]; dsetname="splines/rzphi/fs/offset") + write_output(outp, :euler_h5, equil.rzphi.fs[:,3]; dsetname="splines/rzphi/fs/nu") + write_output(outp, :euler_h5, equil.rzphi.fs[:,4]; dsetname="splines/rzphi/fs/jac") + write_output(outp, :euler_h5, equil.rzphi.fsx[:,1]; dsetname="splines/rzphi/fsx/rcoords") + write_output(outp, :euler_h5, equil.rzphi.fsx[:,2]; dsetname="splines/rzphi/fsx/offset") + write_output(outp, :euler_h5, equil.rzphi.fsx[:,3]; dsetname="splines/rzphi/fsx/nu") + write_output(outp, :euler_h5, equil.rzphi.fsx[:,4]; dsetname="splines/rzphi/fsx/jac") + write_output(outp, :euler_h5, equil.rzphi.fsy[:,1]; dsetname="splines/rzphi/fsy/rcoords") + write_output(outp, :euler_h5, equil.rzphi.fsy[:,2]; dsetname="splines/rzphi/fsy/offset") + write_output(outp, :euler_h5, equil.rzphi.fsy[:,3]; dsetname="splines/rzphi/fsy/nu") + write_output(outp, :euler_h5, equil.rzphi.fsy[:,4]; dsetname="splines/rzphi/fsy/jac") + write_output(outp, :euler_h5, equil.rzphi.fsxy[:,1]; dsetname="splines/rzphi/fsxy/rcoords") + write_output(outp, :euler_h5, equil.rzphi.fsxy[:,2]; dsetname="splines/rzphi/fsxy/offset") + write_output(outp, :euler_h5, equil.rzphi.fsxy[:,3]; dsetname="splines/rzphi/fsxy/nu") + write_output(outp, :euler_h5, equil.rzphi.fsxy[:,4]; dsetname="splines/rzphi/fsxy/jac") + write_output(outp, :euler_h5, 0; dsetname="splines/rzphi/x0") # TODO: equil.rzphi.x0 + write_output(outp, :euler_h5, 0; dsetname="splines/rzphi/y0") # TODO: equil.rzphi.y0 + write_output(outp, :euler_h5, 0; dsetname="splines/rzphi/xpower") # TODO: equil.rzphi.xpower + write_output(outp, :euler_h5, 0; dsetname="splines/rzphi/fpower") # TODO: equil.rzphi.fpower + end + + # Write crit.out header + if odet.ising > 0 && odet.ising <= intr.msing + singp = intr.sing[odet.ising] + write_output(outp, :crit_out, @sprintf(" ising psi q di re alpha im alpha\n")) + write_output(outp, :crit_out, @sprintf("%6d%11.3e%11.3e%11.3e%11.3e%11.3e\n", odet.ising, singp.psifac, singp.q, singp.di, real(singp.alpha), imag(singp.alpha))) + end + write_output(outp, :crit_out, " psifac dpsi q singfac eval1\n") +end + +""" + ode_output_step(odet, intr, ctrl, equil; force=false) + +Performs output and monitoring tasks at each integration step. + +This function calls `ode_output_monitor` to track critical eigenvalue behavior +and handle any diagnostics or logging associated with the current step. +Additional output (e.g., eigenvalue dumps, binary solution logging) may be added later. +""" +#TODO: depending on how we restructure our outputs, this function might be uncessary +# (i.e. if we don't need an ode_output_get_evals or ode_output_sol, can just replace calls with ode_output_monitor) +function ode_output_step!(odet::OdeState, intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, outp::DconOutput) + + # Compute and print critical data for each time step + ode_output_monitor!(odet, intr, ctrl, equil, outp) + # if dout.out_evals || dout.bin_evals + # ode_output_get_evals(intr, ctrl, dout, fNames, equil, odet) # this is just outputs + # end + + # All bin_euler logic performed after integration + + # if outp.bin_sol + # ode_output_sol() + # end +end + +# TODO: I don't think this function is essentially for the minimal working version - can convert later if needed +# function ode_output_get_evals(intr::DconInternal, ctrl::DconControl, dout::DconOutput, fNames::DconFileNames, equil::Equilibrium.PlasmaEquilibrium, odet::OdeState) +# # Access all variables from structs, not globals. +# # Pretty much just giving them all aliases so we don't have to type `intr.` and `ctrl.` every time. +# u = odet.u #TODO: is ud the same as u +# mpert = intr.mpert +# out_evals = dout.out_evals +# bin_evals = dout.bin_evals +# nn = intr.nn +# evals_out_unit = fNames.evals_out_unit +# evals_bin_unit = fNames.evals_bin_unit +# sq = equil.sq +# psifac = intr.sing.psifac +# q = equil.sq.f[4] + +# # Compute plasma response matrix +# temp = conj.(transpose(u[:, 1:mpert, 1])) +# wp = u[:, 1:mpert, 2] +# wp = conj.(transpose(wp)) + +# ipiv = zeros(Int, mpert) +# info = Ref{Int}(0) + +# temp_lapack = copy(temp) # copy just renames a function pretty much +# LAPACK.zgetrf!(temp_lapack, ipiv) +# wp_lapack = copy(wp) +# LAPACK.zgetrs!('N', temp_lapack, ipiv, wp_lapack) +# wp = (wp_lapack + conj.(transpose(wp_lapack))) / 2 + +# # Compute and sort eigenvalues +# evals = zeros(Float64, mpert) +# work = zeros(ComplexF64, 2*mpert-1) +# rwork = zeros(Float64, 3*mpert-2) +# evals, _ = LAPACK.zheev!('N', 'U', wp) +# index = sortperm(-abs.(1 ./ evals), rev=true) # TODO: Should this still be rev + +# # Compute and sort inverse eigenvalues +# evalsi, _ = LAPACK.zheev!('N', 'U', wp) +# indexi = sortperm(-abs.(evalsi), rev = true) # TODO: Should this still be rev + +# # Write ascii eigenvalues +# if out_evals && odet.istep > 0 +# @printf(evals_out_unit, "\nistep = %d, psifac = %.5e, q = %.5e\n", odet.istep, psifac, q) +# @printf(evals_out_unit, "\n i eval evali err\n") +# for ipert in 1:mpert +# @printf(evals_out_unit, "%6d %11.3e %11.3e %11.3e\n", +# ipert, +# evalsi[indexi[ipert]], +# evals[index[ipert]], +# evalsi[indexi[ipert]] * evals[index[ipert]] - 1) +# end +# @printf(evals_out_unit, "\n i eval evali err\n") +# end + +# # Write binary eigenvalues +# if bin_evals && psifac > 0.1 +# spline_eval(sq, psifac, 0) #TODO: Where does sq come from? +# q = sq.f[4] +# singfac = abs(odet.m1 - nn * q) +# logpsi1 = log10(psifac) +# logpsi2 = log10(singfac) +# for ipert in 2:mpert +# write(evals_bin_unit, Float32(ipert), Float32(psifac), +# Float32(logpsi1), Float32(logpsi2), +# Float32(q), Float32(1 / evals[index[ipert]])) +# end +# write(io, evals_bin_unit) # End record #TODO: Looks like the function call should be write(io, stuff). Will it be written to rhe right place? +# end + +# return +# end + +""" + ode_output_monitor!(odet, intr, ctrl, equil, outp) + +Monitor the evolution of a critical eigenvalue (`crit`) during ODE integration and detect zero crossings, which indicate resonant or singular behavior. +The function evaluates `crit` using `ode_output_get_crit`, and if a sign change is found, it estimates the crossing point via linear interpolation. +If the crossing satisfies sharpness and consistency conditions, it's logged and `nzero` is incremented. +A termination flag (`termbycross_flag`) set within DconControl can be used to stop integration upon detection. + +### Notes +- Zero-crossing detection is based on changes in the sign of `crit`. +- `u_med` is constructed as a linear interpolation between current and saved `u`. +- This function updates psi_prev, crit_prev, u_prev, and nzero in the `odet` state. + +### TODO +- Restore or redirect output to appropriate logging units. +- Replace `error(...)` with graceful shutdown if zero crossing is an intended exit condition. +""" +function ode_output_monitor!(odet::OdeState, intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, outp::DconOutput) + + # Compute new crit + dpsi = odet.psifac - odet.psi_prev + q, singfac, logpsi1, logpsi2, crit = ode_output_get_crit(odet.psifac, odet.u, intr.mpert, odet.m1, ctrl.nn, equil.sq) + + # Check for zero crossing + if crit * odet.crit_prev < 0 # if crit changes sign, zero crossing has occurred + fac = crit / (crit - odet.crit_prev) + psi_med = odet.psifac - fac * (odet.psifac - odet.psi_prev) + dpsi = psi_med - odet.psi_prev + u_med = odet.u .- fac .* (odet.u .- odet.u_prev) + q_med, singfac_med, logpsi1_med, logpsi2_med, crit_med = ode_output_get_crit(psi_med, u_med, intr.mpert, odet.m1, ctrl.nn, equil.sq) + + if (crit_med - crit) * (crit_med - odet.crit_prev) < 0 && + abs(crit_med) < 0.5 * min(abs(crit), abs(odet.crit_prev)) + println("Zero crossing detected at psi = $psi_med, q = $q_med") + write_output(outp, :dcon_out, @sprintf("Zero crossing at psi = %10.3e, q = %10.3e", psi_med, q_med)) + write_output(outp, :crit_out, @sprintf("Zero crossing at psi = %10.3e, q = %10.3e", psi_med, q_med)) + write_output(outp, :crit_out, @sprintf("%11.3e%11.3e%11.3e%11.3e%11.3e", psi_med,dpsi,q_med,singfac_med,crit_med)) + odet.nzero += 1 + end + if ctrl.termbycross_flag + #TODO: not sure if this is really an error, or just a user specified termination condition. So the program shoudln't error out, just stop integrating + # In fortran, these were both handled by program_stop() + error("Terminated by zero crossing.") + end + end + + # Write new crit + write_output(outp, :crit_out, @sprintf("%11.3e%11.3e%11.3e%11.3e%11.3e", odet.psifac,dpsi,odet.q,singfac,crit)) + + # Update saved values + odet.psi_prev = odet.psifac + odet.crit_prev = crit + odet.u_prev .= odet.u +end + +""" + ode_output_get_crit(psi, u, mpert, m1, nn, sq) -> (q, singfac, logpsi1, logpsi2, crit) + +Compute critical quantities at a given flux surface by constructing and inverting the plasma response matrix from the complex +array `u`, symmetrizing it, computing its Hermitian eigenvalues, and using the smallest (in magnitude) +inverse eigenvalue in combination with the equilibrium profiles to form `crit`. + +This uses Julia’s built-in linear algebra: +`lu(temp) = zgetrf`, `temp_fact \\ wp = zgetrs` +Under the hood, Julia calls optimized LAPACK routines via the LinearAlgebra standard library. + +### Main Arguments (others defined in main structs) +- `psi::Float64`: The flux surface at which to evaluate. +- `u::Array{ComplexF64, 3}`: Complex response data array of shape `(mpert, mpert, 2)`. + +### Returns +A tuple `(q, singfac, logpsi1, logpsi2, crit)` of critical data for the time step. +""" +# TODO: on self-contained functions like this, it feels silly to pass in these large structs when we only need one variable +# Should we just pass in the variables we need? This seems more readable to me personally +#function ode_output_get_crit(psi::Float64, u::Array{ComplexF64, 3}, intr::DconInternal, odet::OdeState, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium) # (alternate version) +function ode_output_get_crit(psi::Float64, u::Array{ComplexF64, 3}, mpert::Int, m1::Int, nn::Int, sq::Spl.CubicSpline) + + # Compute inverse plasma response matrix + uu = u[:, 1:mpert, :] + wp = adjoint(uu[:, :, 1]) # adjoint = conjugate transpose + temp = adjoint(uu[:, :, 2]) + + # Compute wp using LU decomposition + temp_fact = lu(temp) + wp = temp_fact \ wp + + # Symmetrize + wp = (wp + adjoint(wp)) / 2 + + # Compute and sort inverse eigenvalues + evalsi = eigen(Hermitian(wp)).values + indexi = sortperm(abs.(evalsi)) # bubble in Fortran sorts in descending order of -|evalsi|, we just do ascending order of |evalsi| + + # Compute critical data for each time step + profiles = Spl.spline_eval(sq, psi, 0) + q = profiles[4] + singfac = abs(m1 - nn * profiles[4]) + logpsi1 = log10(psi) + logpsi2 = log10(singfac) # TODO: why is this called logpsi2 and not logsingfac? + crit = evalsi[indexi[1]] # * profiles[3]^2 # TODO: appears to be a bug in profiles[3] + + return q, singfac, logpsi1, logpsi2, crit +end \ No newline at end of file diff --git a/src/DCON/Sing.jl b/src/DCON/Sing.jl new file mode 100644 index 000000000..e2492754b --- /dev/null +++ b/src/DCON/Sing.jl @@ -0,0 +1,671 @@ +""" + sing_scan!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, outp::DconOutput) + +Scan all singular surfaces and calculate asymptotic vmat and mmat matrices and Mericer criterion. +""" +function sing_scan!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, outp::DconOutput) + write_output(outp, :dcon_out, "\n Singular Surfaces:") + write_output(outp, :dcon_out, @sprintf("%3s %11s %11s %11s %11s %11s %11s %11s", "i", "psi", "rho", "q", "q1", "di0", "di", "err")) + # msol = intr.mpert # TODO: is msol used anywhere else? It's a global in Fortran and very confusing + for ising in 1:intr.msing + sing_vmat!(intr, ctrl, equil, ffit, outp, ising) + end + write_output(outp, :dcon_out, @sprintf("%3s %11s %11s %11s %11s %11s %11s %11s", "i", "psi", "rho", "q", "q1", "di0", "di", "err")) +end + +""" + sing_find!(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal; itmax=300) + +Locate singular rational q-surfaces (q = m/nn) using a bisection method between extrema of the q-profile, and store their properties in `intr.sing`. + +# Arguments +- 'itmax::Int`: Maximum number of iterations for the bisection method (default: 200) +""" +function sing_find!(ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, intr::DconInternal; itmax=200) + + # Shorthand to evaluate q inside bisection search + qval = psi -> Spl.spline_eval(equil.sq, psi, 0)[4] + + # Loop over extrema of q, find all rational values in between + for iex in 2:equil.params.mextrema + dq = equil.params.qextrema_q[iex] - equil.params.qextrema_q[iex-1] + m = trunc(Int, ctrl.nn * equil.params.qextrema_q[iex-1]) + if dq > 0 + m += 1 + end + dm = Int(sign(dq * ctrl.nn)) + + # Loop over possible m's in interval + while (m - ctrl.nn * equil.params.qextrema_q[iex-1]) * (m - ctrl.nn * equil.params.qextrema_q[iex]) <= 0 + it = 0 + psi0 = equil.params.qextrema_psi[iex-1] + psi1 = equil.params.qextrema_psi[iex] + psifac = (psi0 + psi1)/2 # initial guess for bisection + + # Bisection method to find singular surface + while it < itmax + it += 1 + psifac = (psi0 + psi1)/2 + singfac = (m - ctrl.nn * qval(psifac)) * dm + if abs(singfac) <= 1e-8 + break + elseif singfac > 0 + psi0 = psifac + else + psi1 = psifac + end + end + + if it == itmax + error("Bisection did not converge for m = $m") + else + push!(intr.sing, SingType( + m = m, + psifac = psifac, + rho = sqrt(psifac), + q = m / ctrl.nn, + q1 = Spl.spline_eval(equil.sq, psifac, 1)[2][4], + )) + intr.msing += 1 + end + m += dm + end + end +end + +""" + sing_lim!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, eqCtrl::Equilibrium.EquilibriumControl, eqPrm::Equilibrium.EquilibriumParameters) + +Compute and set limiter values for the DCON analysis - handles cases where user +truncates before the last singular surface. + +# Arguments +- `itmax::Int`: The maximum number of iterations allowed for the psilim search (default: 50) +- `eps::Float64`: The convergence tolerance for the psilim search (default: 1e-10) +""" +# JMH - this has been checked against the DIID_Ideal example (with psiedge = 0.95 to enter the last if statement). +# There are some discrepancies at the 4-5th digit between the two, not sure if this is numerical noise, +# an issue in the spline evals, or a bug here. However, the differences in the main internal parameters are small +# so ignoring for now, can address in a unit test later. +function sing_lim!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium; itmax=50, eps=1e-10) + + # Shorthand to evaluate q/q1 inside newton iteration + qval = psi -> Spl.spline_eval(equil.sq, psi, 0)[4] + q1val = psi -> Spl.spline_eval(equil.sq, psi, 1)[2][4] + + #compute and modify the DconInternal struct + intr.qlim = min(equil.params.qmax, ctrl.qhigh) + intr.q1lim = equil.sq.fs1[equil.config.control.mpsi+1, 4] + intr.psilim = equil.config.control.psihigh + #normalize dmlim to interval [0,1) + if ctrl.sas_flag + while ctrl.dmlim > 1.0 + ctrl.dmlim -= 1.0 + end + while ctrl.dmlim < 0.0 + ctrl.dmlim += 1.0 + end + #compute qlim + intr.qlim = (trunc(Int, ctrl.nn * intr.qlim) + ctrl.dmlim) / ctrl.nn + while intr.qlim > equil.params.qmax #could also be a while true with a break condition if (qlim <= qmax) like the Fortran code + intr.qlim -= 1.0 / ctrl.nn + end + end + + #use newton iteration to find psilim + if intr.qlim < equil.params.qmax + # Find index jpsi that minimizes |equil.sq.fs[:,4] - qlim| and ensure within mpsi limits + _, jpsi = findmin(abs.(equil.sq.fs[:,4] .- intr.qlim)) + jpsi = min(jpsi, equil.config.control.mpsi - 1) + + intr.psilim = equil.sq.xs[jpsi] + it = 0 + while it < itmax + it += 1 + dpsi = (intr.qlim - qval(intr.psilim)) / q1val(intr.psilim) + intr.psilim += dpsi + + if abs(dpsi) < eps * abs(intr.psilim) + intr.q1lim = q1val(intr.psilim) + break + end + end + + # abort if not found + if it > itmax + error("Can't find psilim.") + end + + else + intr.qlim = equil.params.qmax + intr.q1lim = equil.sq.fs1[equil.config.control.mpsi+1,4] + intr.psilim = equil.config.control.psihigh + end + + #set up record for determining the peak in dW near the boundary. + if ctrl.psiedge < intr.psilim + qedgestart = trunc(Int, Spl.spline_eval(equil.sq, ctrl.psiedge, 0)[4]) + intr.size_edge = ceil(Int, (intr.qlim - qedgestart) * ctrl.nn * ctrl.nperq_edge) + + intr.dw_edge = fill(-Inf * (1 + im), intr.size_edge) + intr.q_edge = [qedgestart + i / (ctrl.nperq_edge * ctrl.nn) for i in 0:intr.size_edge-1] + intr.psi_edge = zeros(intr.size_edge) + + # monitor some deeper points for an informative profile + intr.pre_edge = 1 + for i in 1:intr.size_edge + if intr.q_edge[i] < Spl.spline_eval(equil.sq, ctrl.psiedge, 0)[4] + intr.pre_edge += 1 + end + end + end +end + +# Main differences: using 1 indexing, so zeroth order is the first index, whereas Fortran used 0 indexing for these arrays +function sing_vmat!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, outp::DconOutput, ising::Int) + + # Allocations + singp = intr.sing[ising] + singp.vmat = zeros(ComplexF64, intr.mpert, 2*intr.mpert, 2, 2*ctrl.sing_order + 1) + singp.mmat = zeros(ComplexF64, intr.mpert, 2*intr.mpert, 2, 2*ctrl.sing_order + 3) + singp.power = zeros(ComplexF64, 2*intr.mpert) + + if ising < 1 || ising > intr.msing + return + end + + ipert0 = round(Int, ctrl.nn * singp.q, RoundFromZero) - intr.mlow + 1 # resonant perturbation + if ipert0 <= 0 || intr.mlow > ctrl.nn * singp.q || intr.mhigh < ctrl.nn * singp.q + singp.di = 0 + return + end + + # Compute ranges + singp.r1 = [ipert0] + singp.r2 = [ipert0, ipert0 + intr.mpert] + singp.n1 = [i for i in 1:intr.mpert if i != ipert0] + singp.n2 = vcat(singp.n1, [i + intr.mpert for i in singp.n1]) + + psifac = singp.psifac + q = singp.q + di0 = Spl.spline_eval(intr.locstab, singp.psifac, 0)[1] / singp.psifac + q1 = singp.q1 + rho = singp.rho + + # Compute Mercier criterion and singular power + sing_mmat!(intr, ctrl, equil, ffit, ising) + singp.m0mat = transpose(singp.mmat[singp.r1[1], singp.r2, :, 1]) + # TODO: this is a little odd. di is complex since m0 is complex (but the imaginaries are negligible), + # its then stored in singp where the type is real, and then converted to complex again for alpha and power. + # There's gotta be a more clear way to do this? But this is the most faithful to the Fortran + di = singp.m0mat[1,1]*singp.m0mat[2,2] - singp.m0mat[2,1]*singp.m0mat[1,2] + singp.di = real(di) + singp.alpha = sqrt(-complex(singp.di)) + singp.power[ipert0] = -singp.alpha + singp.power[ipert0 + intr.mpert] = singp.alpha + + write_output(outp, :dcon_out, @sprintf("%3d %11.3e %11.3e %11.3e %11.3e %11.3e %11.3e %11.3e", ising, psifac, rho, q, q1, di0, singp.di, singp.di/di0-1)) + + # Zeroth-order non-resonant solutions + singp.vmat .= 0 + for ipert in 1:intr.mpert + singp.vmat[ipert, ipert, 1, 1] = 1 + singp.vmat[ipert, ipert + intr.mpert, 2, 1] = 1 + end + + # Zeroth-order resonant solutions + singp.vmat[ipert0, ipert0, 1, 1] = 1 + singp.vmat[ipert0, ipert0 + intr.mpert, 1, 1] = 1 + singp.vmat[ipert0, ipert0, 2, 1] = -(singp.m0mat[1,1] + singp.alpha) / singp.m0mat[1,2] + singp.vmat[ipert0, ipert0 + intr.mpert, 2, 1] = -(singp.m0mat[1,1] - singp.alpha) / singp.m0mat[1,2] + det = conj(singp.vmat[ipert0, ipert0, 1, 1]) * singp.vmat[ipert0, ipert0 + intr.mpert, 2, 1] - + conj(singp.vmat[ipert0, ipert0 + intr.mpert, 1, 1]) * singp.vmat[ipert0, ipert0, 2, 1] + singp.vmat[ipert0, :, :, 1] ./= sqrt(det) + + # Higher order solutions + for k in 1:2*ctrl.sing_order + sing_solve!(singp, intr, k) + end +end + +# Main differences: using 1 indexing, so zeroth order is the first index, whereas Fortran used 0 indexing for these arrays. Also adapted for +# dense f/g/k arrays here, so a lot of the LAPACK operations go under the hood. +function sing_mmat!(intr::DconInternal, ctrl::DconControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, ising::Int) + + # ongoing TODO: list here + # figure out if there's a direct way of doing the banded->dense matrix conversion to Julia (very messy right now) + # avoided hardcoding of binomial coefficients for cleanup + + # Initial allocations + msol = 2 * intr.mpert # TODO: make sure this doesn't get updated as a global elsewhere in the Fortran + q = zeros(Float64, 4) + singfac = zeros(Float64, intr.mpert, 4) + f_interp = zeros(ComplexF64, intr.mpert, intr.mpert, 4) + g_interp = zeros(ComplexF64, intr.mpert, intr.mpert, 4) + k_interp = zeros(ComplexF64, intr.mpert, intr.mpert, 4) + f = zeros(ComplexF64, intr.mpert, intr.mpert, ctrl.sing_order + 1) + f0 = zeros(ComplexF64, intr.mpert, intr.mpert) + ff = zeros(ComplexF64, intr.mpert, intr.mpert, ctrl.sing_order + 1) + g = zeros(ComplexF64, intr.mpert, intr.mpert, ctrl.sing_order + 1) + k = zeros(ComplexF64, intr.mpert, intr.mpert, ctrl.sing_order + 1) + v = zeros(ComplexF64, intr.mpert, msol, 2) + x = zeros(ComplexF64, intr.mpert, msol, 2, ctrl.sing_order + 1) + + singp = intr.sing[ising] + + # Evaluate cubic splines + # TODO: third derivative has some error, but only included via sing_fac[ipert0] for sing_order < 3. Tests with solovev ideal indicate little sensitivity + # TODO: this is an annoying way to have to take apart this tuple of vectors, I think + # this is a planned fix already (i.e. separating cubic splines) + q .= getindex.(Spl.spline_eval(equil.sq, singp.psifac, 3), 4) + f_interp[:, :, 1], f_interp[:, :, 2], f_interp[:, :, 3], f_interp[:, :, 4] = Spl.spline_eval(ffit.fmats, singp.psifac, 3) + g_interp[:, :, 1], g_interp[:, :, 2], g_interp[:, :, 3], g_interp[:, :, 4] = Spl.spline_eval(ffit.gmats, singp.psifac, 3) + k_interp[:, :, 1], k_interp[:, :, 2], k_interp[:, :, 3], k_interp[:, :, 4] = Spl.spline_eval(ffit.kmats, singp.psifac, 3) + + # Evaluate singfac and its derivatives + ipert0 = singp.m - intr.mlow + 1 + mvec = intr.mlow:intr.mhigh + singfac[:, 1] .= mvec .- ctrl.nn * q[1] + singfac[:, 2] .= -ctrl.nn * q[2] + singfac[:, 3] .= -ctrl.nn * q[3] + singfac[:, 4] .= -ctrl.nn * q[4] + singfac[ipert0, 1] = -ctrl.nn * q[2] + singfac[ipert0, 2] = -ctrl.nn * q[3] / 2 + singfac[ipert0, 3] = -ctrl.nn * q[4] / 3 + singfac[ipert0, 4] = 0 + + # Compute factored Hermitian F and its derivatives + # TODO: only supports dense matrices for now, implement Banded? + for jpert in 1:intr.mpert + for ipert in jpert:min(intr.mpert, jpert + intr.mband) + f[ipert, jpert, 1] = singfac[ipert, 1] * f_interp[ipert, jpert, 1] + if ctrl.sing_order ≥ 1 + f[ipert, jpert, 2] = singfac[ipert, 1] * f_interp[ipert, jpert, 2] + + singfac[ipert, 2] * f_interp[ipert, jpert, 1] + end + if ctrl.sing_order ≥ 2 + f[ipert, jpert, 3] = singfac[ipert, 1] * f_interp[ipert, jpert, 3] + + 2 * singfac[ipert, 2] * f_interp[ipert, jpert, 2] + + singfac[ipert, 3] * f_interp[ipert, jpert, 1] + end + if ctrl.sing_order ≥ 3 + f[ipert, jpert, 4] = singfac[ipert, 1] * f_interp[ipert, jpert, 4] + + 3 * singfac[ipert, 2] * f_interp[ipert, jpert, 3] + + 3 * singfac[ipert, 3] * f_interp[ipert, jpert, 2] + + singfac[ipert, 4] * f_interp[ipert, jpert, 1] + end + if ctrl.sing_order ≥ 4 + f[ipert, jpert, 5] = 4 * singfac[ipert, 2] * f_interp[ipert, jpert, 4] + + 6 * singfac[ipert, 3] * f_interp[ipert, jpert, 3] + + 4 * singfac[ipert, 4] * f_interp[ipert, jpert, 2] + end + if ctrl.sing_order ≥ 5 + f[ipert, jpert, 6] = 10 * singfac[ipert, 3] * f_interp[ipert, jpert, 4] + + 10 * singfac[ipert, 4] * f_interp[ipert, jpert, 3] + end + if ctrl.sing_order ≥ 6 + f[ipert, jpert, 7] = 20 * singfac[ipert, 4] * f_interp[ipert, jpert, 4] + end + end + end + f0 .= f[:, :, 1] + + # Compute product of Hermitian matrix F + fac0 = 1 + for n in 0:ctrl.sing_order + fac1 = 1 + for j in 0:n + for jpert in 1:intr.mpert + for ipert in jpert:min(intr.mpert, jpert + intr.mband) + for kpert in max(1, ipert - intr.mband):jpert + ff[ipert, jpert, n + 1] += fac1 * f[ipert, kpert, j + 1] * conj(f[jpert, kpert, n - j + 1]) + end + end + end + fac1 *= (n - j) / (j + 1) + end + ff[:, :, n + 1] ./= fac0 + fac0 *= (n + 1) + end + + # NOTE: In Fortran, f, g, k are stored as banded Hermitian matrices (lower triangle only), + # with f already factored, this is passed into LAPACK which handles all of this under the hood. + # However, for now we are using dense matrices in Julia, so ff is stored as a full matrix (both triangles), + # and we need to fill in the upper triangle here. + # Use Hermitian property to fill the upper triangle + for n in 1:ctrl.sing_order + for i in 1:intr.mpert + for j in 1:i-1 + ff[j, i, n + 1] = conj(ff[i, j, n + 1]) + end + end + end + + # Compute non-Hermitian matrix K + for jpert in 1:intr.mpert + for ipert in max(1, jpert - intr.mband):min(intr.mpert, jpert + intr.mband) + k[ipert, jpert, 1] = singfac[ipert, 1] * k_interp[ipert, jpert, 1] + if ctrl.sing_order ≥ 1 + k[ipert, jpert, 2] = singfac[ipert, 1] * k_interp[ipert, jpert, 2] + + singfac[ipert, 2] * k_interp[ipert, jpert, 1] + end + if ctrl.sing_order ≥ 2 + k[ipert, jpert, 3] = singfac[ipert, 1] * k_interp[ipert, jpert, 3] / 2 + + singfac[ipert, 2] * k_interp[ipert, jpert, 2] + + singfac[ipert, 3] * k_interp[ipert, jpert, 1] / 2 + end + if ctrl.sing_order ≥ 3 + k[ipert, jpert, 4] = singfac[ipert, 1] * k_interp[ipert, jpert, 4] / 6 + + singfac[ipert, 2] * k_interp[ipert, jpert, 3] / 2 + + singfac[ipert, 3] * k_interp[ipert, jpert, 2] / 2 + + singfac[ipert, 4] * k_interp[ipert, jpert, 1] / 6 + end + if ctrl.sing_order ≥ 4 + k[ipert, jpert, 5] = singfac[ipert, 2] * k_interp[ipert, jpert, 4] / 6 + + singfac[ipert, 3] * k_interp[ipert, jpert, 3] / 4 + + singfac[ipert, 4] * k_interp[ipert, jpert, 2] / 6 + end + if ctrl.sing_order ≥ 5 + k[ipert, jpert, 6] = singfac[ipert, 3] * k_interp[ipert, jpert, 4] / 12 + + singfac[ipert, 4] * k_interp[ipert, jpert, 3] / 12 + end + if ctrl.sing_order ≥ 6 + k[ipert, jpert, 7] = singfac[ipert, 4] * k_interp[ipert, jpert, 4] / 36 + end + end + end + + # Compute Hermitian matrix G + for jpert in 1:intr.mpert + for ipert in jpert:min(intr.mpert, jpert + intr.mband) + g[ipert, jpert, 1] = g_interp[ipert, jpert, 1] + if ctrl.sing_order < 1 continue end + g[ipert, jpert, 2] = g_interp[ipert, jpert, 2] + if ctrl.sing_order < 2 continue end + g[ipert, jpert, 3] = g_interp[ipert, jpert, 3] / 2 + if ctrl.sing_order < 3 continue end + g[ipert, jpert, 4] = g_interp[ipert, jpert, 3] / 6 + end + end + + # Compute identity + for ipert in 1:intr.mpert + v[ipert, ipert, 1] = 1 + v[ipert, ipert + intr.mpert, 2] = 1 + end + + # Compute zeroth-order x1 + for isol=1:msol + x[:, isol, 1, 1] .= v[:, isol, 2] .- k[:, :, 1] * v[:, isol, 1] + end + # f is prefactorized so can just use this calculation to get F⁻¹x + x[:, :, 1, 1] = UpperTriangular(f0') \ (LowerTriangular(f0) \ x[:, :, 1, 1]) + + # Compute higher-order x1 + for i=1:ctrl.sing_order + for isol=1:msol + for j=1:i + x[:, isol, 1, i + 1] .-= ff[:, :, j + 1] * x[:, isol, 1, i - j + 1] + end + x[:, isol, 1, i + 1] .-= k[:, :, i + 1] * v[:, isol, 1] + end + x[:, :, 1, i + 1] = UpperTriangular(f0') \ (LowerTriangular(f0) \ x[:, :, 1, i + 1]) + end + + # Use Hermitian property to fill the upper triangle of g + # TODO: very hacky and unclear. Eventually, completely remove all mention of banding/Hermitian storage or make it cleaner + # Lots of stuff hidden in LAPACK calls in Fortran that we are doing manually here + for n in 0:ctrl.sing_order + for i in 1:intr.mpert + for j in 1:i-1 + g[j, i, n + 1] = conj(g[i, j, n + 1]) + end + end + end + + # Compute x2 + for i=0:ctrl.sing_order + for isol=1:msol + for j = 0:i + x[:, isol, 2, i + 1] .+= k[:, :, j + 1]' * x[:, isol, 1, i - j + 1] + end + x[:, isol, 2, i + 1] .+= g[:, :, i + 1] * v[:, isol, 1] + end + end + + # Principal terms of mmat + singp.mmat .= 0 + r1 = singp.r1 + r2 = singp.r2 + n1 = singp.n1 + n2 = singp.n2 + j = 0 + for i = 0:ctrl.sing_order + singp.mmat[r1, r2, :, j+1] .= x[r1, r2, :, i+1] + singp.mmat[r1, n2, :, j+2] .= x[r1, n2, :, i+1] + singp.mmat[n1, r2, :, j+2] .= x[n1, r2, :, i+1] + singp.mmat[n1, n2, :, j+3] .= x[n1, n2, :, i+1] + j += 2 + end + + # Shearing terms + singp.mmat[r1, r2[1], 1, 1] .+= 0.5 + singp.mmat[r1, r2[2], 2, 1] .-= 0.5 +end + +""" + sing_solve!(singp::SingType, k::Int) + +Solves iteratively for the next order in the power series `singp.vmat`. See equation 47 in the Glass 2016 DCON paper. + +Arguments +--------- +- `singp::SingType`: The singularity data structure containing all relevant matrices and parameters. +- `k::Int`: The current order in the power series expansion. +""" +function sing_solve!(singp::SingType, intr::DconInternal, k::Int) + for l in 1:k + singp.vmat[:,:,:,k + 1] .+= sing_matmul(singp.mmat[:,:,:,l + 1], singp.vmat[:,:,:,k - l + 1]) + end + for isol in 1:2*intr.mpert + a = copy(singp.m0mat) + a[1,1] -= k/2.0 + singp.power[isol] + a[2,2] -= k/2.0 + singp.power[isol] + det = a[1,1] * a[2,2] - a[1,2] * a[2,1] + x = -singp.vmat[singp.r1[1], isol, :, k+1] + singp.vmat[singp.r1[1], isol, 1, k+1] = (a[2,2]*x[1] - a[1,2]*x[2]) / det + singp.vmat[singp.r1[1], isol, 2, k+1] = (a[1,1]*x[2] - a[2,1]*x[1]) / det + singp.vmat[singp.n1, isol, :, k+1] ./= (singp.power[isol] + k/2.0) + end +end + +""" + sing_matmul(a, b) -> c + +Matrix multiplication specific to singular matrices. + +Arguments +--------- +- `a::Array{ComplexF64,3}`: shape (mpert, 2 * mpert, 2) +- `b::Array{ComplexF64,3}`: shape (mmpert, 2 * mpert, 2) + +Returns +------- +- `c::Array{ComplexF64,3}`: shape (mpert, 2 * mpert, 2) +""" +function sing_matmul(a::Array{ComplexF64,3}, b::Array{ComplexF64,3}) + m = size(b,1) + n = size(b,2) + + # consistency check + if size(a,2) != 2*m + error("Sing_matmul: size(a,2) = $(size(a,2)) != 2*size(b,1) = $(2*m)") + end + + c = zeros(ComplexF64, size(a,1), n, 2) + + # main computation + for i in 1:n + for j in 1:2 + c[:, i, j] .+= a[:, 1:m, j] * b[:, i, 1] + + a[:, m+1:2*m, j] * b[:, i, 2] + end + end + + return c +end + +""" + sing_get_ua!(odet::OdeState, intr::DconInternal, ctrl::DconControl) + +Compute the asymptotic series solution for a given singularity. + +- `odet`: Current ODE state (contains psifac, ua, ising, etc.) +- `intr`: DCON internal state (contains singularity data, mpert, etc.) +- `ctrl`: DCON control parameters (contains sing_order, etc.) + +Fills `ua` with the asymptotic solution vmat for the specified singular surface and psi value. +""" +function sing_get_ua!(odet::OdeState, intr::DconInternal, ctrl::DconControl) + + singp = intr.sing[odet.ising] + r1 = singp.r1 + r2 = singp.r2 + + # Compute distance from singular surface + dpsi = odet.psifac - singp.psifac + sqrtfac = sqrt(complex(dpsi)) + pfac = abs(dpsi)^singp.alpha + + # Compute power series via Horner's method + odet.ua .= singp.vmat[:,:,:,2 * ctrl.sing_order + 1] + for iorder in (2 * ctrl.sing_order - 1):-1:0 + odet.ua .= odet.ua .* sqrtfac .+ singp.vmat[:,:,:,iorder+1] + end + + # Restore powers + odet.ua[r1, :, 1] ./= sqrtfac + odet.ua[r1, :, 2] .*= sqrtfac + odet.ua[:, r2[1], :] ./= pfac + odet.ua[:, r2[2], :] .*= pfac + + # Renormalize + if odet.psifac < singp.psifac + odet.ua[:, r2[1], :] .*= abs(odet.ua[r1[1], r2[1], 1]) / odet.ua[r1[1], r2[1], 1] + odet.ua[:, r2[2], :] .*= abs(odet.ua[r1[1], r2[2], 1]) / odet.ua[r1[1], r2[2], 1] + end +end + +""" + sing_get_ca!(odet::OdeState, intr::DconInternal) + +Compute the asymptotic expansion coefficients according to equation 50 in Glasser 2016 DCON paper. +""" +function sing_get_ca!(odet::OdeState, intr::DconInternal, ctrl::DconControl) + + sing_get_ua!(odet, intr, ctrl) + + # Build temp1 + temp1 = zeros(ComplexF64, 2*intr.mpert, 2*intr.mpert) + temp1[1:intr.mpert, :] .= odet.ua[:, :, 1] + temp1[intr.mpert+1:2*intr.mpert, :] .= odet.ua[:, :, 2] + + # Built temp2 + temp2 = zeros(ComplexF64, 2*intr.mpert, odet.msol) + temp2[1:intr.mpert, :] .= odet.u[:, :, 1] + temp2[intr.mpert+1:2*intr.mpert, :] .= odet.u[:, :, 2] + + # LU factorization and solve + temp2 .= lu(temp1) \ temp2 + odet.ca[:, 1:odet.msol, 1] .= temp2[1:intr.mpert, :] + odet.ca[:, 1:odet.msol, 2] .= temp2[intr.mpert+1:2*intr.mpert, :] +end + +""" + sing_der!( + du::Array{ComplexF64,3}, + u::Array{ComplexF64,3}, + params::Tuple{DconControl, Equilibrium.PlasmaEquilibrium, DconInternal, FourFitVars, DconOutput}, + psieval::Float64 + ) + +Evaluate the derivative of the Euler-Lagrange equations, i.e. u' in equation 24 of Glasser 2016. +This follows the Julia DifferentialEquations package format for in place updating. + + ode_function!(du, u, p, t) + +# "Defining your ODE function to be in-place updating can have performance benefits. +# What this means is that, instead of writing a function which outputs its solution, +# you write a function which updates a vector that is designated to hold the solution. +# By doing this, DifferentialEquations.jl's solver packages are able to reduce the +# amount of array allocations and achieve better performance." + +Wherever possible, in-place operations on pre-allocated arrays are used to minimize memory allocations. +All LAPACK operations are handled under the hood by Julia's LinearAlgebra package, so we can obtain a much +more simplistic code with similar performance. +""" +function sing_der!(du::Array{ComplexF64, 3}, u::Array{ComplexF64, 3}, + params::Tuple{DconControl, Equilibrium.PlasmaEquilibrium, + DconInternal, OdeState, FourFitVars, DconOutput}, + psieval::Float64) + # Unpack structs + ctrl, equil, intr, odet, ffit, _ = params + + # Spline evaluation + odet.q = Spl.spline_eval(equil.sq, psieval, 0)[4] + odet.singfac_vec .= 1.0 ./ (intr.mlow .- ctrl.nn * odet.q .+ (0:intr.mpert-1)) + chi1 = 2π * equil.psio + + # kinetic stuff - skip for now + if false #(TODO: kin_flag) + error("kin_flag not implemented yet") + else + # Evaluate splines at psieval and reshape avoiding new allocations + # TODO: is this actually more efficient? + Spl.spline_eval!(odet.amat, ffit.amats, psieval; derivs=0) + amat = reshape(odet.amat, intr.mpert, intr.mpert) + Spl.spline_eval!(odet.bmat, ffit.bmats, psieval; derivs=0) + bmat = reshape(odet.bmat, intr.mpert, intr.mpert) + Spl.spline_eval!(odet.cmat, ffit.cmats, psieval; derivs=0) + cmat = reshape(odet.cmat, intr.mpert, intr.mpert) + Spl.spline_eval!(odet.fmat, ffit.fmats, psieval; derivs=0) + fmat = reshape(odet.fmat, intr.mpert, intr.mpert) + Spl.spline_eval!(odet.kmat, ffit.kmats, psieval; derivs=0) + kmat = reshape(odet.kmat, intr.mpert, intr.mpert) + Spl.spline_eval!(odet.gmat, ffit.gmats, psieval; derivs=0) + gmat = reshape(odet.gmat, intr.mpert, intr.mpert) + + # ldiv!(A,B): Compute A \ B in-place and overwriting B to store the result, + # where A is a factorization object. + odet.Afact = cholesky(Hermitian(amat)) + # bmat = A⁻¹ * bmat + ldiv!(odet.Afact, bmat) + # cmat = A⁻¹ * cmat + ldiv!(odet.Afact, cmat) + + # TODO: banded matrix calculations would go here + end + + # Compute du + if false #(TODO: kin_flag) + error("kin_flag not implemented yet") + else + # See equation 23 in Glasser 2016 DCON paper for derivation + # TODO: these comments are a work in progress and should be checked, but I think they're close + # main thing is I'm not sure where singfac comes from + + # du[1] = - K * u[1] + u[2] + du[:, :, 1] .= u[:, :, 2] .* odet.singfac_vec .- kmat * u[:, :, 1] + + # du[1] = - F⁻¹ * K * u[1] + F⁻¹ * u[2] (remember F is already stored in factored form) + du[:, :, 1] .= UpperTriangular(fmat') \ (LowerTriangular(fmat) \ du[:, :, 1]) + + # du[2] = G * u[1] + K' * du[1] = G * u[1] - K^† * F⁻¹ * K * u[1] + K^† * F⁻¹ * u[2] + du[:, :, 2] .= gmat * u[:, :, 1] .+ adjoint(kmat) * du[:, :, 1] + du[:, :, 1] .*= odet.singfac_vec + end + + # u-derivative used in GPEC + odet.ud[:,:,1] .= du[:,:,1] + odet.ud[:,:,2] .= -bmat * du[:,:,1] - cmat * u[:,:,1] +end diff --git a/src/DCON/Utils.jl b/src/DCON/Utils.jl new file mode 100644 index 000000000..c13999110 --- /dev/null +++ b/src/DCON/Utils.jl @@ -0,0 +1,126 @@ +# This is to implement the original bubble function found in equil/utils.f +# If you are sorting the entire array, just replace the call to bubble with +# +# index = sortperm(key) # for ascending order or +# index = sortperm(key; rev = true) # for descending order + +# This will return the indices of the sort range in descending order +function sortperm_subrange(key::Vector{Float64}, mrange::UnitRange{Int}; descend = true ) + sorted_inds = sort(mrange; by = i -> key[i], rev = descend) + return collect(sorted_inds) +end + +#If you want to mutate an existing index array like your original code: +function sortperm_subrange!(key::Vector{Float64}, index::Vector{Int}, mrange::UnitRange{Int}; descend = true ) + sorted_inds = sort(mrange; by = i -> key[i], rev = descend) + for (j, i) in enumerate(sorted_inds) + index[first(mrange) + j - 1] = i + end +end + +function load_u_matrix(filename) + lines = readlines(filename) + data = [parse.(Float64, split(l)) for l in lines[2:end]] + i_vals = Int.(getindex.(data, 1)) + j_vals = Int.(getindex.(data, 2)) + k_vals = Int.(getindex.(data, 3)) + imax = maximum(i_vals) + jmax = maximum(j_vals) + kmax = maximum(k_vals) + mat = zeros(ComplexF64, imax, jmax, kmax) + for row in data + i = Int(row[1]) + j = Int(row[2]) + k = Int(row[3]) + re = Float64(row[4]) + im = Float64(row[5]) + mat[i, j, k] = complex(re, im) + end + return mat +end + +""" + init_files(out::DconOutput, path::String) + +Open all requested output files into `path` and store handles. +""" +function init_files(out::DconOutput, path::String) + for pname in propertynames(out) + if startswith(String(pname), "write_") && getproperty(out, pname) + base_str = String(pname)[7:end] # remove write_ prefix + base = Symbol(base_str) # key for handles + fname_field = Symbol("fname_" * base_str) # add fname_ prefix + fname = getproperty(out, fname_field) + + full_path = joinpath(path, fname) + + if endswith(fname, ".out") || endswith(fname, ".txt") + out.handles[base] = open(full_path, "w") + + elseif endswith(fname, ".h5") && !haskey(out.handles, base) + fid = h5open(full_path, "w") + out.handles[base] = fid + + else + error("Unknown file extension for $fname, need to add to init_files!") + end + end + end + return out +end + +""" + write_output(out::DconOutput, key::Symbol, data; dsetname=nothing, slice=:) + +Writes `data` to the file corresponding to `key`. +- For text files: appends a line. +- For HDF5 files: writes into `dsetname` at `slice`. +""" +function write_output(out::DconOutput, key::Symbol, data; dsetname=nothing, slice=:) + handle = out.handles[key] + + if handle isa IOStream + println(handle, data) + + elseif handle isa HDF5.File + if dsetname === nothing + error("Must specify dsetname when writing to HDF5 file $key") + end + if haskey(handle, dsetname) + handle[dsetname][slice...] = data + else + # create dataset if not present + handle[dsetname] = data + end + + else + error("Unsupported handle type for key $key") + end +end + +""" + close_files(out::DconOutput) + +Closes all open files. +# TODO: is there a way to make the code run this if it errors out anywhere? +# In existing state, files will remain open if there is an error, so you have +# to manually exit and reopen Julia. +""" +function close_files(out::DconOutput) + for (key, handle) in out.handles + close(handle) + end + empty!(out.handles) +end + +""" + chebyshev_nodes(a::Float64, b::Float64, N::Int) +Generates `N` Chebyshev-Lobatto nodes in the interval `[a, b]` +in ascending order. +""" +# TODO: this is no longer used, but might be useful code? Leaving for now, but likely can be removed +function chebyshev_nodes(a::Float64, b::Float64, N::Int) + j = 0:N-1 + nodes = (a+b)/2 .+ (b-a)/2 .* cos.(π * j ./ (N - 1)) + return reverse(nodes) +end \ No newline at end of file diff --git a/src/DCON/fortran/README b/src/DCON/fortran/README new file mode 100644 index 000000000..b15071f57 --- /dev/null +++ b/src/DCON/fortran/README @@ -0,0 +1,897 @@ +Determining the MHD Stability of Axisymmetric Toroidal Plasmas +================================================================ + +:Version: + 3.60, September 5, 2002 +:Author: + Alan H. Glasser +:Location: + Los Alamos National Laboratory +:Phone: + 505-667-7723 +:Email: + ahg@lanl.gov + +Section 1. Introduction +----------------------- + +DCON is a code for determining the MHD stability of static +axisymmetric toroidal plasma. It uses a very efficient algorithm, +originally developed by Newcomb [W. A. Newcomb, Ann. Phys. 10, 232 +(1960)] for cylindrical plasmas and generalized by myself to +axisymmetric plasmas. A preprint of a manuscript containing the theory +of DCON is available in the tex subdirectory of this distribution in +both Plain TeX and PostScript formats. The algorithm involves +integrating a system of ordinary differential equations (ODE's), the +Euler-Lagrange equations for minimizing the potential energy delta_W +from the magnetic axis to the plasma edge. A plasma response matrix W_P +is constructed from the solutions. If the smallest inverse eigenvalue +of W_P changes sign, there is an unstable internal (fixed-boundary) +mode. The eigenvalues of W_P are combined with a vacuum response matrix +W_V to form a total response matrix W_T = W_P + W_V. If W_T has any +negative eigenvalues, there is an unstable external (free-boundary) +mode. The name DCON is an acronym for the Direct Criterion of Newcomb. +The code makes no effort to determine growth rates of unstable modes or +frequencies of the stable spectrum, but only to determine whether the +system supports unstable modes. The distance of a zero crossing from +the plasma edge can be used to quantify the degree of instability for an +internal mode, while the total perturbed potential energy can be used +for this purpose for a free-boundary mode. + +The present version of DCON evaluates the Mercier criterion D_I +> 0 for unstable localized ideal interchange modes; the related +criterion D_R > 0 of Glasser, Greene, and Johnson for localized +resistive interchange modes; the criterion C_A < 0 for ideal MHD +ballooning modes in the limit of large toroidal mode number; the +generalized Newcomb criterion for the internal ideal MHD stability of +one low toroidal mode number; and the plasma, vacuum, and total response +matrices and their eigenvalues for determining free-boundary stability. +A future version of DCON will treat resistive instabilities. + +In addition to MHD stability, there is a code ORBIT for tracking +the full Hamiltonian orbits of charged particles in the same equilibrium +fields used by DCON. The full-orbit equations are integrated with a +very efficient adaptive ODE solver with high accuracy, both inside and +outside the separatrix, and with extensive graphical output. Full +orbits and drift orbits have complementary uses. For particles with +small Larmor radius, such as thermal ions and electrons, drift orbits +are both more efficient and more accurate, especially for long +trajectories. For particles with large Larmor radius, such as beam +ions, full orbits are more efficient and more accurate. Drift orbits +will be added to ORBIT in a later release, allowing the best of both +worlds and comparisons between them. + +Both DCON and ORBIT are written entirely in high-level Fortran 90. +They make extensive use of dynamic allocation and deallocation to +allow maximum use of available memory. They use many other advanced +features of Fortran 90, such as derived types, array syntax, and +modules. There are no fixed dimensions of large arrays, no goto +statements, and no common blocks. Extensive use is made of BLAS and +LAPACK linear algebra routines for efficiency. There are interfaces to +a large number of commonly-used equilibrium data types for specifying +equilibria. Adding to these is usually very simple, and I would be glad +to help. Graphic output from DCON is viewed with the XDRAW graphics +code, which is distributed as part of the package and runs on any X +Window system. + +This document is a guide to preparing input for DCON and ORBIT +and interpreting their output. + + +Section 2. Straight-Fieldline Coordinates +----------------------------------------- + +A major new feature of dcon_3.50 is the use of generalized +straight-fieldline (SFL) coordinates. Previous versions have used only +one type of these, Hamada coordinates. + +For any flux coordinate system, one coordinate, psi, labels the +flux surface, and its gradient is orthogonal to the equillibrium +magnetic field; the other two, theta and zeta, are angle-like quantities +that parameterize the position around the torus the short and long way, +respectively. In DCON, psi is linear in the poloidal flux and +normalized to go from 0 at the magnetic axis to 1 at the last closed +flux surface. Occasionally, rho=sqrt(psi) is used for graphical +purposes as a radius-like variable. Theta and zeta are normalized to +increase by 1 (not twopi) in going one full turn around the torus. + +A flux coordinate system is an SFL coordinate system for which +the safety factor + +q = (B.del zeta) / (B.del theta) + +is a function of psi only. A particular SFL coordinate system is +defined by the variation of (B.del theta) (which is proportional to the +inverse of the Jacobian of the coordinate system) along the field line. +The coordinate systems incorporated into dcon have B.del theta +proportional to B_p**power_bp * B**power_b / R**power_r, with B_p the +poloidal field strength, B the total field strength, R the major radius, +and power_bp, power_b, and power_r input integers. Some commonly-used +and named coordinate systems are: + +========== ========== ======= ======== +name power_bp power_b power_r +========== ========== ======= ======== +hamada 0 0 0 +pest 0 0 2 +equal_arc 1 0 0 +boozer 0 2 0 +========== ========== ======= ======== + + +The (ignorable) toroidal coordinate is:: + + zeta = phi/twopi + nu(psi,theta), + +where nu is a single-valued function of theta. PEST coordinates have +the unique property that nu = 0 and the toroidal coordinate is +proportional to the conventional polar angle phi. For all other SLF +coordinate system, nu /= 0. + +PEST coordinates are well-adapted to high-aspect-ratio, circular +equilibria. For low-aspect-ratio, strongly-shaped equilibria, detailed +numerical comparisons with DCON show that Hamada coordinates generally +have the best Fourier convergence properties, and others are worse in +proportion to their departure from Hamada. Increasing power_r, as in +PEST coordinates, leads to reduced resolution on the outboard side of +the torus. Increasing power_b, as in equal_arc coordinates, leads to +reduced resolution in the neighborhood of an x-point. The user is +advised to use Hamada coordinates, the default. When using others, +proceed with caution, increase the number of Fourier components, and +monitor the convergence. + + +Section 3. Installation +----------------------------------------- + +The easiest way to unpack dcon_3.50.tar.gz is: + +gzip -cd dcon_3.50.tar.gz | tar -xvf - + +It will create a subdirectory ./dcon_3.50 and place its files there. +The contents of the dcon package are as follows: + +============ ======================================================= +README: this file. +equil: source code for equilibrium data processing +dcon: source code for DCON, stability code +match: source code for MATCH, future code for resistive modes +orbit: source code for ORBIT, full-orbit particle tracking +multi: source code for MULTI, multiple runs of DCON +sum: source code for SUM, data extraction from MULTI runs +draw: xdraw control files draw*.in +equilibria: sample equilibrium files +input: dcon control files +lsode: source code for ODE solver +makefile: master makefile for all codes on all machines +tex: preprint on the theory of DCON and equations for ORBIT +vacuum: source code for Morrell Chance's VACUUM code +xdraw: source code for XDRAW graphics code +============ ======================================================= + +DCON has been set up and tested on the following machines: + +SGI Octane running the IRIX 6.4 operating system +Sun SparcStations running the SunOS operating system +DEC Alpha running OSF1 operating system +PC Compatibles running Red Hat Linux 6.0 with Absoft Pro Fortran 6.0 +IBM running AIX + +If yours is one of these, do "cd dcon" and type make. It will +automatically make all its components, create a directory rundir and a +subdirectory with the name of your operating system, and copy the +executables and a few selected input files to that directory. This is +where you should work. You may want to do: + +nohup make > make.log & + +to launch a separate process which will keep a log of its actions and +any errors. + +If your machine is not among these, you should create a makefile in each +of the subdirectories with the name makefile_`uname`, where `uname` is +the first word of the output when you type the command "uname -a". The +makefile should contain definitions of your Fortran 90 compiler and +links to existing LAPACK, BLAS, and X11 libraries. Then type "make" +while in ./dcon_3.50. + + +Section 4. EQUIL Input +----------------------------------------- + +Both DCON and ORBIT use EQUIL to process the equilibrium data. +EQUIL is controlled primarily by equil.in. It contains two Fortran 90 +namelists: equil_control and equil_output. The equil_control namelist +contains most of the input parameters needed to control the equilibrium +operations of the code. The equil_output namelist controls auxiliary +output which is mostly used to diagnose problems. For the most part, +these may be left false and ignored. In this and other namelist input +files, all input parameters have reasonable default values. + +Here is an explanation of the input parameters in the first +namelist equil_control, along with typical input values and extensive +commentary. + +eq_type="efit" + +This specifies the type of the input file. It allows DCON to determine +whether the file is ascii or binary, whether it is direct or inverse, +and how to interpret the data. Here is a list of allowed types: + +============ ============================= ============ ======== +Name Description Data Type Format +============ ============================= ============ ======== +"fluxgrid" NIMROD data file inverse ascii +"miller" Bob Miller's TOQ code inverse binary_8 +"chease" Lausanne CHEASE code, 8-byte inverse binary_8 +"chease4" Lausanne CHEASE code inverse binary_4 +"chum" Modified Miller code inverse binary_4 +"galkin" Sergei Galkin's code inverse binary_8 +"efit" GA EFIT code direct ascii +"rsteq" ORNL RSTEQ code direct binary_8 +"ldp_d" Don Pearlstein's TEQ code direct binary_8 +"ldp_i" Don Pearlstein's inverse code inverse binary_8 +"jsolver" Steve Jardin's JSOLVER code inverse ascii +"lez" Leonid Zakharov'v code inverse binary_4 +"transp" Data from the TRANSP code inverse ascii +"sontag" Aaron Sontag's direct solver direct ascii +============ ============================= ============ ======== + +In addition, you may specify eq_type="lar" or "soloviev" to get the two +analytical equilibria. See below for more details. + +eq_filename="../equilibria/efit/82205-1.25X" + +This gives the path of the data file specifying the equilibrium. The +file may be ascii or binary. It may be the output of a direct +Grad-Shafranov solver, which specifies poloidal flux, R*B_phi, pressure, +and safety factor on a 1D grid of flux surfaces, and the poloidal flux +psi on a 2D grid in R and Z; or of an inverse solve, which replaces +psi(R,Z) with values of R and Z on a 2D grid of psi and theta on flux +surfaces. + +The next three input quantities, + +jac_type="hamada" +power_b=0 +power_r=0 + +are used to control the type of straight-fieldline coordinate system +used (see discussion above). If jac_type is one of those listed in the +table above, the code automatically chooses power_b and power_r +accordingly and ignores the input values. To use any other values, +choose jac_type="other" and set the integer variables power_b and +power_r. + +Next come specifications of grid parameters. + +=============== ============================================ +grid_type="ldp" type of radial grid packing +psilow=1e-4 minimum value of psi, normalized from 0 to 1 +psihigh=1 maximum value of psi, normalized from 0 to 1 +mpsi=128 number of radial grid intervals +mtheta=128 number of poloidal grid intervals +=============== ============================================ + +There are several options for radial grid types. The first, +grid_type="rho", distributes radial grid points uniformly in +rho=sqrt(psi), a generalized radius. The second, grid_type="ldp", uses +a method suggested by L. Don Pearlstein (LDP), which packs the grid in +the neighborhood of the axis and the edge. I have a slight preference +for "ldp", but they both work well. A third type, "original", uses the +same radial grid used in the input data. (Sorry, there's no "extra +crispy" option.) The poloidal grid is uniformly distributed in the +straight-fieldline coordinate theta. Throughout the code, cubic spline +and Fourier representations are used to minimize the effects of grid +discreteness. + +The input parameter psilow is used only for grid_type="ldp". A good +value is 1e-4. For the most part, results are insensitive to this +value, but substantially smaller values cause the code to run longer, +and substantially larger values may cause accuracy problems. + +The input parameter psihigh determines how close to the edge the ODE's +are integrated. It must be <= 1. For an inverse equilibrium, which +never has a separatrix in the computational domain, it may be set to 1. +For a direct equilibrium with a separatrix, psihigh determines how close +the code approaches the separatrix. Since the safety factor q goes +logarithmically to infinity at a separatrix, the required number of +poloidal harmonics increases with q (see below), and the run time +increases with both the number of harmonics and the number of singular +surfaces,it can be expensive to choose psihigh very close to 1. + +The next input parameter is + +newq0=0 + +For newq0 = 0, the code uses the original q profile specified in the +equilibrium file. For newq0 /= 0, it readjusts the q profile to give +the specified value of q at the axis, in such a way as to leave the +Grad-Shafranov solution invariant. This can be used to explore the +stability of a range of equilibria for each equilibrium file. + +The final input parameter in equil_control is + +input_only=f + +This is occasionally used in the course of debugging interfaces to new +equilibrium file types. It causes the code to generate information +about the input and then quit. + +The equil_output namelist of equil.in determines which auxiliary +output files are produced. These are primarily of interest to me, the +developer, and of very little interest to users. For most code +operation, they should all be left off (f). Turning them on (t) when +they are not used wastes cpu time and disk space. The ascii files are +readable by any text editor and can also be printed. The binary files +are intended for viewing with XDRAW. Here is a brief description of the +optional output files. + +=============== ====================================================== +gse_flag=f produces diagnostic output for accuracy of solution to + Grad-Shafranov equation + +out_eq_1d=f ascii output of 1D equilibrium file data +bin_eq_1d=f binary output of 1D equilibrium file data + +out_eq_2d=f ascii output of 1D equilibrium file data +bin_eq_2d=f binary output of 2D equilibrium file data + +out_2d=f ascii output of processed 2D data +bin_2d=f binary output of processed 2D data +=============== ====================================================== + +There are two other input files, each containing a single +namelist. The first, lar.in, is for large-aspect-ratio, circular cross, +low beta equilibrium, using the Shafranov expansion to second order. +The second, sol.in, is for the Soloviev equilibrium. + +The lar_input namelist of equil.in is used when eq_type="lar" +and eq_filename="lar.in". This allows the user to construct a +large-aspect-ratio, circular-cross-section equilibrium, using the +Shafranov expansion to second order, specifying minor radius a, major +radius r0, central pressure ratio beta0, and central safety factor q0. +The pressure profile is given by p0*(1-(r/a)**2)**p_pres, and the default +profile of sigma=J.B/B^2 is sigma0/(1+(r/a))**(2*p_sig))**(1+1/p_sig). +Specifying sigma_type="wesson" changes the functional form of sigma to a +simpler "Wesson-like" sigma0*(1-(r/a)**2)**p_sig. Additional profiles +would be simple to add. Here are sample input parameters: + +===================== ====================================================== +ma=64 number of radial grid points +mtau=64 number of azimuthal grid points + +lar_r0=10 major radium +lar_a=1 minor radius + +beta0=0 value of beta (pressure ratio) on axis +q0=3.2 value of q (safety factor) on axis + +p_pres=2 power used in specifying pressure profile +p_sig=2 power used in specifying current profile + +sigma_type='default' functional form of sigma profile + ('default' or 'wesson') +===================== ====================================================== + +The sol_input namelist of equil.in is used when +eq_type="soloviev" and eq_filename="sol.in". See Berger et al +[D. Berger,L.C. Bernard, R. Gruber,and 6. Troyon, J. Appl. Math. +Phys. (ZAMP) 31 (1980) 113] for a published stability analysis of this +equilibrium. Here are input parameters: + +=============== ====================================================== +mr=128 number of radial grid points +mz=128 number of axial grid points +ma=128 number of flux surfaces for surface quantities + +e=1 vertical elongation factor +a=1 minor radius +r0=3 major radius +q0=1.26 value of q (safety factor) on axis +=============== ====================================================== + + + +Section 5. DCON Input +----------------------------------------- + +The stability operations of DCON are controlled by the file +dcon.in, containing two namelists, dcon_control and dcon_output. The +first begins with a set of flags which determine which features of DCON +are exercised: + +=========== =========================================================================== +bal_flag=t Ideal MHD ballooning criterion for short wavelengths +mat_flag=t Construct coefficient matrices for diagnostic purposes +ode_flag=t Integrate ODE's for determining stability of internal long-wavelength mode +vac_flag=t Compute plasma, vacuum, and total energies for free-boundary modes +=========== =========================================================================== + +Next come values determining mode numbers: + +nn=1 +delta_mlow=4 +delta_mhigh=8 +delta_mband=0 +sing_start=0 + +For each run of the code, there is a single toroidal mode number nn and +a range of poloidal mode numbers from mlow to mhigh. The most unstable +modes are those which bend the field line lease, for which m-nn*q is as +small as possible. The code chooses mlow and mhigh as follows: + +mlow=MIN(nn*qmin,0._r8)-4-delta_mlow +mhigh=nn*qmax+delta_mhigh +mpert=mhigh-mlow+1 + +where mpert is the total number of perturbed mode numbers. The purpose +of delta_mlow and delta_mhigh is to give the user some control over the +range of mode numbers. For fixed-boundary modes, I have found +empirically that the code works well with delta_mlow = delta_mhigh = 0, +and increasing them increases the run time of the code without +substantially improving the accuracy (at least for Hamada coordinates). +For free-boundary modes, they should be positive, high enough to +accommodate the band width of the equilibrium shape. A good way to +choose them is to set newq0 = 0 and run the code several times with +increasing values of delta_mlow and delta_mhigh to find when convergence +is obtained. + +In principle, DCON should work for any toroidal mode number nn. In +practice, the larger the value of nn, the more singular surfaces there +are and the more harmonics it uses, so the longer it runs. Run time +increases quite fast with increasing nn. I have mostly used it for nn <= +15. There is an option controlled by the parameter + +sing_start=0 + +which is intended for operation with higher values of nn. With +sing_start=0, integration is initialized near the magnetic axis. For +sing_start > 0, it is initialized at singular surface number sing_start. +This reduces the work necessary, at the possible expense of accuracy. +With sing_start > 0, a different method is used to determine mlow. with +mmin the minimum value of nn*q between the starting singular surface and +the plasma edge, mlow is chosen as: + +mlow=mmin-delta_mlow + +Using sing_start > 0, I have tested DCON up to nn = 15. + +DCON is designed to use banded matrices, which couple each poloidal +harmonic m to only the nearest harmonics, out to m +/- mband. This was +intended to make it efficient to treat nearly cylindrical equilibria. +While there is no serious penalty for using banded form, in practice it +doesn't help much to reduce the band width mband from full. The +limiting factor is that if mband is chosen too small, factorization of a +key symmetric-positive-definite matrix F breaks because one or more of +its eigenvalues goes negative. The code chooses mband as: + +mband=mpert-1-MAX(delta_mband,0) + +using the input variable: + +delta_mband=0 + +For delta_mband = 0, it uses a full matrix, while for delta_mband > 0 it +reduces the band width. The safest choice is delta_mband = 0. If the +user chooses a value of delta_mband too large, causing F to become +non-positive definite, the code aborts with a message advising the user +to reduce delta_mband. + +The next two input variables are; + +mthvac=480 +thmax0=1 + +The vacuum energy is computed with the Morrell Chance's VACUUM code. +In general, the input to that code is controlled by vac.in. See +./tex/vacuum/vacinput.tex for details. An exception is that one of the +parameters in vac.in, mth, is overridden by a variable in dcon.in. +This is done because it is needed for dynamic memory allocation, which I +added. Mthvac is used by VACUUM as the number of points along the +plasma-vacuum interface. + +Thmax0 is used for the high-n ideal ballooning stability computation. +In principle, this requires integrating a 2nd-order ordinary +differential equation in the poloidal angle theta from -infinity to +infinity on each flux surface. In practice, it is done from -thmax to ++thmax, where thmax is the number of complete cycles around the torus +the short way. Thmax is chosen automatically to optimize both accuracy +and speed. The value of thmax chosen internally is multiplied by the +input variable thmax0 to allow some degree of user control. Its default +value is 1, and it is usually best left at 1. + +Next come variables controlling numerical accuracy: + +tol_nr=1e-5 +tol_r=1e-5 +crossover=1e-2 + +Tol_nr and tol_r are relative tolerances used in integrating the main +system of Euler-Lagrange equations. The first controls the tolerance +far from mode-rational surfaces, while the second controls the tolerance +near the rational surfaces. Crossover determines the distance from the +singular surface at which control passes from tol_nr to tol_r, expressed +in terms of the value of m-nn*q which goes to zero at the rational +surface. The ability to impose a tighter tolerance near the singular +surface will be of interest primarily for the later implementation of +resistive instabilities. + +singfac_min=1e-5 + +This is used to determine the position of closest apprach to each +singular surface. The integration terminates when m-nq reaches +singfac_min, then restarts on the other side of the singular surface. + +ucrit=1e4 + +This controls a feature of DCON required for preserving accuracy. +Starting near the magnetic axis, the code integrates a complex system of +ordinary differential equations of order 2*mpert, with mpert = mhigh - +mlow + 1. There are mpert regular solutions and mpert singular +solutions in the neighborhood of the magnetic axis; DCON follows all of +the regular solutions. Each regular solution grows roughly as r^|m| as +it comes out of the axis. The high-m solutions therefore grow much more +rapidly than the low-m solutions. After a short distance, the large +solutions could numerically overwhelm the small solutions, causing the +computation to lose all accuracy. To prevent this, the integration is +stopped occasionally, and the independent solution vectors are +reorganized to eliminate this problem. Ucrit determines how often this +is done. It should be left at 1e4 by the casual user. + +The final section of input, dcon_output controls stability +output options. Many of the optional outputs of interest only to the +developer have been removed to avoid confusion. The only remaining ones +are: + +============= ============================================================= +crit_break=t determines whether the color of the crit curve (see + below) changes after crossing a singular surface + +ahb_flag=f produces output on normal magnetic field eigenvalues and + eigenfunctions at plasma-vacuum interface (in honor of + Allen H. Boozer) + +mthsurf0 real variable, provides user control over number of boundary + points used to display surface eigenfunctions for + ahgb_flag=t. Default value 1, number of points + increases linearly with mthsurf0 +============= ============================================================= + + +Section 6. VACUUM Input +----------------------------------------- + +Computation of perturbed vacuum potential energy is performed +with Morrell Chance's VACUUM code. This is controlled by the file +vac.in, formerly named modivmc. It is safest to leave the variables in +this file unchanged, with one exception. The input variable a allows +the use of a conforming conducting wall surrounding the plasma, with a = +0 representing a wall right on the plasma boundary; a <= 10 a wall at a +relative distance a from form the plasma boundary, normalized to the +plasma radius; and a > 20 a wall at infinity. Beware of very small +values of a; the results may be inaccurate because of limited +resolution. See M. S. Chance, Phys. Plasma 4, 6, 2161 (1997) for theory +and code description. Subdirectory ./tex/vacuum of this directory +contains a complete description of the input. Use LaTeX. + + +Section 7. DCON Output +----------------------------------------- + +During the running of DCON, the code writes terse messages to +the screen to inform the user of its progress. Here is the output of a +typical run:: + + $ + $ dcon + Equilibrium: ../../equilibria/efit/82205-1.25X, Type: efit + Jac_type = hamada, power_b = 0, power_r = 0 + Diagnosing Grad-Shafranov solution + Evaluating Mercier criterion + Evaluating ballooning criterion + Fourier analysis of metric tensor components + q0 = 1.087E+00, qmin = 1.082E+00, qmax = 5.426E+00, qa = 6.119E+00 + betat = 2.843E-02, betan = 2.579E+00, betap1 = 1.033E+00 + nn = 1, mlow = -8, mhigh = 13, mpert = 22, mband = 21 + Computing F, G, and K Matrices + Starting integration of ODE's + psi = 1.000E-04, q = 1.087 + psi = 5.845E-01, q = 2.000 + psi = 8.024E-01, q = 3.000 + psi = 9.337E-01, q = 4.000 + psi = 9.813E-01, q = 5.000 + psi = 9.900E-01, q = 5.426 + Computing free boundary energies + Energies: plasma = -1.773E+00, vacuum = 3.050E+00, total = 1.277E+00 + All modes stable for nn = 1. + Total cpu time = 2.349E+01 seconds + PROGRAM_STOP => Normal termination. + $ + +If there are violations of the Newcomb stability criterion, indicating +the existence of internal (fixed-boundary) instabilities, the position +and q-value of the zero crossing(s) are also reported to the screen as +they occur. In that case, the free-boundary energies are not meaningful +and are not reported. + +The main results of DCON are reported in four files: dcon.out, +dcon,bin, crit.out, and crit.bin. Here is a description of their +contents. + +Dcon.out echoes input parameters; gives various global +properties of the equilibrium; lists a table of surfaces quantities, +including the ideal and resistive interchange criteria D_I and D_R; +lists all singular surfaces for the specified toroidal mode number nn +and their properties; and reports zero crossings of the DCON low-n +stability criterion. If there are any zero crossings, then the system +is unstable to internal, or fixed-boundary, modes, and the computation +of free-boundary energies is not meaningful and is skipped. If there +are no zero crossings, then dcon.out gives plasma, vacuum, and total +energy eigenvalues for free-boundary modes. The lowest total energy +reported in the table is the stability criterion for free-boundary +modes, also reported to the screen; negative means unstable. Following +the table of eigenvalues is a list of the eigenvectors corresponding to +each eigenvalue, normalized to unit magnitude. For each eigenvector, +the component with the largest absolute value is marked with an asterisk +"*". This is useful for identifying the dominant Fourier component of +the most unstable mode. It is also useful to note whether the +components for mlow and mhigh are sufficiently small, e.g. 1e-3. If +not, this is an indication the delta_mlow and/or delta_mhigh should be +increased. + +Dcon.bin contains data about equilibrium profiles and local +stability criteria. It is viewed by doing "xdraw dcon". + +Crit.out and crit.bin contain the low-n internal stability +results. Do "xdraw crit" to view the graphics file. The main result is +in the first frame, showing the stability criterion. If this changes +sign, the equilibrium is unstable to an internal ideal mode for the +specified toroidal mode number nn. If it is everywhere positive, the +system is stable to this mode number. The second frame shows the q +profile. The crit curve and the q curve are similarly color coded, +changing color as they cross singular surfaces. The color-change can be +suppressed by setting crit_break=f in dcon.in, namelist dcon_output. +This is useful for comparing different runs, using a different solid +color for each run. Multiple files can be compared by listing their +paths below the line "filename(s)" in drawcrit.in. + +If bin_2d=t in equil.in, then a graphics file 2d.bin is produced +and may be viewed with "xdraw 2d". It produces two windows, one showing +flux surfaces for the equilibrium, the other surfaces of constant theta. +The latter is especially useful for comparing the angular distribution +for different choices of straight-fieldline coordinates. + +If gse_flag=t in equil.in, then a graphics file gsei.bin is +prodcued and may be viewed with "xdraw gsei". It shows log_10 of the +Grad-Shafranov error, integrated over flux surfaces. This can be used +to assess the accuracy of the Grad-Shafranov solution. More detailed +local graphs of log10 error can be seen by doing "xdraw gse". A contour +plot can be seen with "xdraw gsec". The latter two require additional +input files, obtainable by "cp ../../draw/drawgse*.in .". + + +Section 8. ORBIT Input +----------------------------------------- + +This section describes input for controlling the ORBIT code for +following guiding-center or full-orbit trajectories of charged +particles, both inside and outside the separatrix. + +In order to follow the particle both inside and outside the +separatrix, account must be taken of the fact that the magnetic field +representation is different in these two regions. The Hamiltonian +equations of motion are expressed in terms of the vector potential A, +with the equilibrium magnetic field B = curl A and electric field E = +-grad phi - dA/dt. (The electrostatic potential phi is taken to be +uniform at present; this could easily be changed in the future for any +known configuration of phi.) Inside the separatrix, the flux surfaces +are closed, the vector potential is expressed in terms of the poloidal +coordinate theta, the toroidal field function f = R*B_T is constant on a +flux surface, and it is most convenient to express the equations of +motion in flux coordinates. Outside the separatrix, the flux surfaces +are not closed, the poloidal coordinate theta is not defined, f is +uniform, and it is most convenient to express the equations of motion in +cylindrical coordinates. ORBIT uses flux coordinates inside the +separatrix and cylindrical coordinates outside, and passes the particle +between the two when it crosses the separatrix. Graphs of the orbit +change color to indicate such a crossing. + +The equilibrium used by ORBIT is controlled by the same files +equil.in, lar.in, and sol.in, described above in Section 4. For +direct-type equilibria, the orbit is followed both inside and outside +the separatrix, terminating if the orbit crosses a boundary of the +computational domain. For inverse-type equilibria, the orbit is +followed only inside the separatrix, terminating if it crosses the +separatrix, this this is the boundary of the compuatational domain for +inverse-type data. + +The ORBIT code is controlled by orbit.in, containing one +namelist, orbit_input. The first two variables: + +gc_flag=t +orbit_type="inner" + +determine whether to use guiding-center or full orbits and whether the +initial particle position is specified inside or outside the separatrix +(see below for more detail). + +The next three variables: + +particle="ion" +ai=2 +zi=1 + +determine whether the particle to be followed is an ion or an electron, +and if it is an ion, its atomic weight ai and atomic number zi. If the +particle is an electon, then ai and zi are ignored. + +The next three variables: + +psi0=.85 +theta0=0 +zeta0=0 + +specify the particle position in straight-fieldline coordinates +(psi,theta,zeta) for orbit_type="inner", with psi linear in the poloidal +flux and normalized to go from 0 at the magnetic axis to 1 at the +separatrix; and theta and zeta parameterizing position the short and +long ways around the torus, increasing by 1 for each full circuit. + +The next three variables: + +r0=.5 +z0=0 +phi0=0 + +specify the particle position in cylindrical coordinates (r,z,phi) for +orbit_type="outer". The initial radial position is set to + +r=rs2+r0*(rmax-rs2) + +where rs2 is radius at which the last closed flux surface intersects the +horizontal line through the o-point, and rmax is the right edge of the +computational domain. The initial axial position is set to + +z=(zmax+zmin)/2+z0*(zmax-zmin)/2 + +where zmin and zmax are the bottom and top edges of the computational +domain. The initial azimuthal position phi0 is specified in radians. + +The next three variables: + +energy0=1e4 +alpha0=40 +phase0=45 + +specify the initial particle velocity, using spherical coordinates in +velocity space. The initial particle energy is specified in eV; alpha0 +and phase0 specify the angle of the initial velocity vector from the +z-axis and the from the r-axis in the r-phi plane, in degrees. + +The next three variables: + +taumax=10 +report=1 +stride=5 + +specify the duration of the run and the frequency of output. Tau is +time in units of the transit time of the particle with its given initial +energy at the o-point, if its velocity were purely toroidal. Taumax +specifies the length of the run in these units. Report specifies the +interval, in these units, at which the code reports progress to the +screen and writes a restart file (see below). Stride specifies the +number of internal integrator steps between graphic and tabular output +of the orbit. Increasing stride can be used to limit the size of the +output files, which decreasing it allows for more detail in the graphs. + +The next two variables: + +tol=1e-9 +errmax=1 + +control and monitor numerical error. Tol is the relative tolerance +specified to the adaptive ODE solver LSODE. Reducing tol gives tighter +tolerance at the expense of computation time. The code monitors the +relative change in the particle energy due to accumulated numerical +error. If this error exceeds errmax, the code quits. + +The next variable: + +break_flag=f + +determines whether the graphic output changes color every time tau +increments by report. Normally, a color change indicates the crossing +of the separatrix. Setting break_flag=t increases the frequency of +color change. This can be useful for cross-correlating different orbit +segments between graphs. + +The next variable: + +cross=t + +determines whether the orbit is allowed to cross the separatrix for +direct-type equilibrium data. If cross=f, the particle stops at the +separatrix. For inversse-type equilibrium data, the orbit can only be +followed inside the separatrix. + +The next variable: + +restart_flag=f + +is used to determine whether to restart the orbit from the last saved +restart.out file. The code saves this file each time tau -> tau + +report. If restart_flag=t, the code attempts to read this file. If it +exists, the code ignores input values for particle type and initial +conditions, restarts the trajectory from its last state, and uses taumax +to specify an increment on the runtime. If restart_flag=t but +restart.out is not found, the code resets restart_flag=f and proceeds as +if this were the input value. + +The final variables: + +orbit_out=f +orbit_bin=t + +determine whether to produce to produce tabular and graphic output for +the orbit. Normally the values are set as shown. Setting orbit_out=t +a tabular description of the orbit in orbit.out, which is usually not +very useful and is time-consuming. Setting orbit_bin=f causes the +graphical output to be suppressed. + +Section 9. ORBIT Input +----------------------------------------- + +This section describes output for the ORBIT code for following +full-orbit trajectories of charged particles, both inside and outside +the separatrix. + +There is an output file orbit.out which starts with the same +kind of equilibrium data as dcon.out, described in Section 7 above. +Then there are a few lines of information about the orbit that was run. +If orbit_out=t, this is followed by a long table of the orbit. This is +not recommended: it is not very useful, it wastes time, and the +information is better obtained in graphical form. + +To view the main graphical output, do "xdraw orbit". This +produces 9 graphs: + +1. Radial Position, R vs. tau +2. Axial Position, Z vs. tau +3. Orbit in Poloidal Plane, Z vs. R +4. Normalized Poloidal Flux, psi vs. tau +5. Parallel Velocity, v_parallel vs. tau +6. Orbit Viewed Along Axis, R*sin(phi) vs. R*cos(phi) +7. Relative Change in Energy, error vs. tau +8. Relative Change in Magnetic Moment, d_mu/mu_0 +9. Larmor Radius / Radius of Curvature, rl/R + +The color changes each time the particle crosses the separatrix. + + +Section 10. Other documentation +----------------------------------------- + +There is a subdirectory ./tex containing miscellaneous +documentation. Here is a brief description. + +1. tex/dcon/manuscript: + +An unpublished manuscript on the theory of DCON. + +2. tex/dcon/notebook: + +Raw equations on the theory of DCON: + +dcon.tex Raw equations on the theory of DCON +bal.tex High-n ballooning theory +mercier.tex Expressions for the Mercier criterion +metric.tex Expressions for the metric tensor + +tex/orbit: + +orbit.tex Raw Hamiltonian orbit equations in straight-fieldline coordinates + +tex/vacuum: + +vacinput.tex Latex file on preparing input to VACUUM. diff --git a/src/DCON/fortran/bal.f b/src/DCON/fortran/bal.f new file mode 100644 index 000000000..f31b6f031 --- /dev/null +++ b/src/DCON/fortran/bal.f @@ -0,0 +1,540 @@ +c----------------------------------------------------------------------- +c file bal.f. +c determines high-n ideal marginal MHD ballooning stability. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. bal_mod. +c 1. bal_scan. +c 2. bal_prep. +c 3. bal_der. +c 4. bal_int. +c 5. bal_pse. +c----------------------------------------------------------------------- +c subprogram 0. bal_mod. +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + MODULE bal_mod + USE dcon_mod + IMPLICIT NONE + + INTEGER, PRIVATE :: ipsi + REAL(r8), PRIVATE :: di,alpha,theta0=0 + REAL(r8), DIMENSION(2,2), PRIVATE :: v0 + TYPE(spline_type), PRIVATE :: bf,bg + + CONTAINS +c----------------------------------------------------------------------- +c subprogram 1. bal_scan. +c computes ballooning stability criterion. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE bal_scan +c----------------------------------------------------------------------- +c open output files. +c----------------------------------------------------------------------- + IF(out_bal1)CALL ascii_open(out_bal1_unit,"bal1.out","UNKNOWN") + IF(out_bal2)CALL ascii_open(out_bal2_unit,"bal2.out","UNKNOWN") + IF(bin_bal1)CALL bin_open(bin_bal1_unit,"bal1.bin","UNKNOWN", + $ "REWIND","none") + IF(bin_bal2)CALL bin_open(bin_bal2_unit,"bal2.bin","UNKNOWN", + $ "REWIND","none") +c----------------------------------------------------------------------- +c test ballooning stability. +c----------------------------------------------------------------------- + DO ipsi=0,mpsi + CALL bal_prep + IF(di <= 0 .AND. di >= -1e4 .AND. sq%xs(ipsi) <= 1)CALL bal_int + CALL spline_dealloc(bf) + CALL spline_dealloc(bg) + ENDDO +c----------------------------------------------------------------------- +c close output files. +c----------------------------------------------------------------------- + IF(out_bal1)CALL ascii_close(out_bal1_unit) + IF(out_bal2)CALL ascii_close(out_bal2_unit) + IF(bin_bal1)CALL bin_close(bin_bal1_unit) + IF(bin_bal2)CALL bin_close(bin_bal2_unit) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE bal_scan +c----------------------------------------------------------------------- +c subprogram 2. bal_prep. +c computes coefficients for the ideal marginal ballooning equations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE bal_prep + + LOGICAL, PARAMETER :: inverse_flag=.FALSE. + INTEGER :: itheta,info + INTEGER, DIMENSION(3) :: ipiv + REAL(r8) :: chi1,det,eta,fexp,p1,psifac,q,q1,r,rfac,theta, + $ twopif,v1 + REAL(r8), DIMENSION(2,2) :: c0,d0bar,d,v10 + REAL(r8), DIMENSION(2,2,0:mtheta) :: d1 + REAL(r8), DIMENSION(0:mtheta) :: b1,bsq,dbdb0,dbdb1,dbdb2, + $ kappan,kappas,jac,jacfac + REAL(r8), DIMENSION(3,3) :: v,w,temp + TYPE(spline_type) :: spl0,spl1,spl2,spl3 +c----------------------------------------------------------------------- +c compute surface quantities. +c----------------------------------------------------------------------- + psifac=sq%xs(ipsi) + twopif=sq%fs(ipsi,1) + p1=sq%fs1(ipsi,2) + v1=sq%fs(ipsi,3) + q=sq%fs(ipsi,4) + q1=sq%fs1(ipsi,4) + chi1=twopi*psio + v=0 + w=0 +c----------------------------------------------------------------------- +c compute coordinates and jacobian. +c----------------------------------------------------------------------- + DO itheta=0,mtheta + CALL bicube_eval(rzphi,rzphi%xs(ipsi),rzphi%ys(itheta),1) + theta=rzphi%ys(itheta) + rfac=SQRT(rzphi%f(1)) + eta=twopi*(theta+rzphi%f(2)) + r=ro+rfac*COS(eta) + jac(itheta)=rzphi%f(4) +c----------------------------------------------------------------------- +c compute contravariant basis vectors. +c----------------------------------------------------------------------- + v(1,1)=rzphi%fx(1)/(2*rfac*jac(itheta)) + v(1,2)=rzphi%fx(2)*twopi*rfac/jac(itheta) + v(1,3)=rzphi%fx(3)*r/jac(itheta) + v(2,1)=rzphi%fy(1)/(2*rfac*jac(itheta)) + v(2,2)=(1+rzphi%fy(2))*twopi*rfac/jac(itheta) + v(2,3)=rzphi%fy(3)*r/jac(itheta) + v(3,3)=twopi*r/jac(itheta) +c----------------------------------------------------------------------- +c compute covariant basis vectors, inverse method. +c----------------------------------------------------------------------- + IF(inverse_flag)THEN + temp=TRANSPOSE(v)*jac(itheta) + w=RESHAPE((/1,0,0,0,1,0,0,0,1/),(/3,3/)) + CALL dgetrf(3,3,temp,3,ipiv,info) + CALL dgetrs('N',3,3,temp,3,ipiv,w,3,info) +c----------------------------------------------------------------------- +c compute covariant basis vectors, direct method. +c----------------------------------------------------------------------- + ELSE + w(1,1)=(1+rzphi%fy(2))*twopi**2*rfac*r + $ /jac(itheta) + w(1,2)=-rzphi%fy(1)*pi*r/(rfac*jac(itheta)) + w(2,1)=-rzphi%fx(2)*twopi**2*r*rfac/jac(itheta) + w(2,2)=rzphi%fx(1)*pi*r/(rfac*jac(itheta)) + w(3,1)=(rzphi%fx(2)*rzphi%fy(3) + $ -rzphi%fx(3)*(1+rzphi%fy(2))) + $ *twopi*r*rfac/jac(itheta) + w(3,2)=(rzphi%fx(3)*rzphi%fy(1) + $ -rzphi%fx(1)*rzphi%fy(3)) + $ *r/(2*rfac*jac(itheta)) + w(3,3)=1/(twopi*r) + ENDIF +c----------------------------------------------------------------------- +c store physical quantities. +c----------------------------------------------------------------------- + b1(itheta)=SUM((v(2,:)+q*v(3,:))*v(1,:))*chi1 + bsq(itheta)=SUM((v(2,:)+q*v(3,:))**2)*chi1**2 + dbdb0(itheta)=SUM(w(1,:)**2)*q1**2 + dbdb1(itheta)=-SUM((w(3,:)-q*w(2,:))*w(1,:))*2*q1 + dbdb2(itheta)=SUM((w(3,:)-q*w(2,:))**2) + ENDDO +c----------------------------------------------------------------------- +c compute curvature terms. +c----------------------------------------------------------------------- + CALL spline_alloc(spl0,mtheta,2) + spl0%xs=rzphi%ys + spl0%fs(:,1)=1/bsq + spl0%fs(:,2)=jac*b1/bsq + CALL spline_fit(spl0,"periodic") + kappas=-spl0%fs1(:,1)*twopif/(2*jac) + DO itheta=0,mtheta + CALL bicube_eval(rzphi,rzphi%xs(ipsi),rzphi%ys(itheta),1) + kappan(itheta)=((p1/bsq(itheta)-rzphi%fx(4)/jac(itheta))/chi1 + $ +twopif*q1/(bsq(itheta)*jac(itheta))+spl0%fs1(itheta,2) + $ /jac(itheta))/2 + ENDDO + CALL spline_dealloc(spl0) +c----------------------------------------------------------------------- +c compute coefficients for ballooning equation. +c----------------------------------------------------------------------- + CALL spline_alloc(bf,mtheta,5) + bf%xs=rzphi%ys + jacfac=jac/chi1 + bf%fs(:,1)=dbdb0/(bsq*jacfac) + bf%fs(:,2)=dbdb1/(2*dbdb0) + bf%fs(:,3)=(dbdb2-dbdb1**2/(4*dbdb0))/(bsq*jacfac) + bf%fs(:,4)=2*kappan*p1/chi1*jacfac + bf%fs(:,5)=-2*kappas*p1/chi1*q1*jacfac + CALL spline_fit(bf,"periodic") +c----------------------------------------------------------------------- +c diagnose bf. +c----------------------------------------------------------------------- + bf%title=(/"theta ","dbdb0 ","dbdb1 ","dbdb2 ","kappas","kappan"/) + CALL spline_write1(bf,out_bal1,bin_bal1, + $ out_bal1_unit,bin_bal1_unit,.TRUE.) +c----------------------------------------------------------------------- +c initialize bg. +c----------------------------------------------------------------------- + CALL spline_alloc(spl0,mtheta,1) + spl0%xs=rzphi%ys + spl0%fs(:,1)=-p1*q1*twopif/(bsq*chi1**2) + CALL spline_fit(spl0,"periodic") + CALL spline_int(spl0) + CALL spline_alloc(bg,mtheta,5) + bg%xs=rzphi%ys + bg%fs(:,5)=spl0%fs(:,1)-spl0%fsi(mtheta,1) + CALL spline_dealloc(spl0) +c----------------------------------------------------------------------- +c compute c0. +c----------------------------------------------------------------------- + CALL spline_alloc(spl1,mtheta,4) + spl1%xs=rzphi%ys + DO itheta=0,mtheta + c0(1,1)=.5 + c0(1,2)=1/bf%fs(itheta,1) + c0(2,1)=-bf%fs(itheta,4) + c0(2,2)=-.5 +c----------------------------------------------------------------------- +c compute d0. +c----------------------------------------------------------------------- + spl1%fs(itheta,1)=c0(1,1)+c0(1,2)*bg%fs(itheta,5) + spl1%fs(itheta,2)=c0(1,2) + spl1%fs(itheta,3)=c0(2,1) + $ +(c0(2,2)-c0(1,1)-c0(1,2)*bg%fs(itheta,5))*bg%fs(itheta,5) + spl1%fs(itheta,4)=-spl1%fs(itheta,1) +c----------------------------------------------------------------------- +c compute d1. +c----------------------------------------------------------------------- + fexp=-c0(1,2)*bf%fs(itheta,2)*2 + d1(1,1,itheta)=fexp*bg%fs(itheta,5) + d1(1,2,itheta)=fexp + d1(2,1,itheta)=-fexp*bg%fs(itheta,5)**2 + d1(2,2,itheta)=-d1(1,1,itheta) + ENDDO +c----------------------------------------------------------------------- +c fit to cubic splines and write output. +c----------------------------------------------------------------------- + CALL spline_fit(spl1,"periodic") + CALL spline_int(spl1) + d0bar(1,1)=spl1%fsi(mtheta,1) + d0bar(1,2)=spl1%fsi(mtheta,2) + d0bar(2,1)=spl1%fsi(mtheta,3) + d0bar(2,2)=spl1%fsi(mtheta,4) +c----------------------------------------------------------------------- +c compute mercier criterion and alpha. +c----------------------------------------------------------------------- + di=d0bar(1,1)*d0bar(2,2)-d0bar(1,2)*d0bar(2,1) + IF(di > 0)THEN + CALL spline_dealloc(spl1) + RETURN + ENDIF + alpha=SQRT(-di) +c----------------------------------------------------------------------- +c compute zeroth-order eigenfunctions. +c----------------------------------------------------------------------- + v0(1,1)=1 + v0(1,2)=1 + v0(2,1)=-(d0bar(1,1)-alpha)/d0bar(1,2) + v0(2,2)=-(d0bar(1,1)+alpha)/d0bar(1,2) +c----------------------------------------------------------------------- +c store derivatives for first-order terms. +c----------------------------------------------------------------------- + CALL spline_alloc(spl2,mtheta,4) + spl2%xs=rzphi%ys + DO itheta=0,mtheta + spl2%fs(itheta,1) + $ =(spl1%fs(itheta,1)-alpha)*v0(1,1) + $ +spl1%fs(itheta,2)*v0(2,1) + spl2%fs(itheta,2) + $ =spl1%fs(itheta,3)*v0(1,1) + $ +(spl1%fs(itheta,4)-alpha)*v0(2,1) + spl2%fs(itheta,3) + $ =(spl1%fs(itheta,1)+alpha)*v0(1,2) + $ +spl1%fs(itheta,2)*v0(2,2) + spl2%fs(itheta,4) + $ =spl1%fs(itheta,3)*v0(1,2) + $ +(spl1%fs(itheta,4)+alpha)*v0(2,2) + ENDDO +c----------------------------------------------------------------------- +c fit to cubic spines and integrate. +c----------------------------------------------------------------------- + CALL spline_fit(spl2,"periodic") + CALL spline_int(spl2) + spl2%fs=spl2%fsi +c----------------------------------------------------------------------- +c store derivatives for second-order terms. +c----------------------------------------------------------------------- + CALL spline_alloc(spl3,mtheta,4) + spl3%xs=rzphi%ys + DO itheta=0,mtheta + spl3%fs(itheta,1) + $ =(spl1%fs1(itheta,1)+1-alpha)*spl2%fs(itheta,1) + $ +spl1%fs(itheta,2)*spl2%fs(itheta,2) + $ +d1(1,1,itheta)*v0(1,1)+d1(1,2,itheta)*v0(2,1) + spl3%fs(itheta,2) + $ =spl1%fs(itheta,3)*spl2%fs(itheta,1) + $ +(spl1%fs(itheta,4)+1-alpha)*spl2%fs(itheta,2) + $ +d1(2,1,itheta)*v0(1,1)+d1(2,2,itheta)*v0(2,1) + spl3%fs(itheta,3) + $ =(spl1%fs(itheta,1)+1+alpha)*spl2%fs(itheta,3) + $ +spl1%fs(itheta,2)*spl2%fs(itheta,4) + $ +d1(1,1,itheta)*v0(1,2)+d1(1,2,itheta)*v0(2,2) + spl3%fs(itheta,4) + $ =spl1%fs(itheta,3)*spl2%fs(itheta,3) + $ +(spl1%fs(itheta,4)+1+alpha)*spl2%fs(itheta,4) + $ +d1(2,1,itheta)*v0(1,2)+d1(2,2,itheta)*v0(2,2) + ENDDO +c----------------------------------------------------------------------- +c fit to cubic spines and integrate. +c----------------------------------------------------------------------- + CALL spline_fit(spl3,"periodic") + CALL spline_int(spl3) +c----------------------------------------------------------------------- +c compute first order constants, first eigenfunction. +c----------------------------------------------------------------------- + d(2,1)=d0bar(2,1) + d(1,2)=d0bar(1,2) + d(1,1)=d0bar(1,1)+1-alpha + d(2,2)=d0bar(2,2)+1-alpha + det=d(1,1)*d(2,2)-d(1,2)*d(2,1) + v10(1,1)=(d(1,2)*spl3%fsi(mtheta,2)-d(2,2)*spl3%fsi(mtheta,1))/det + v10(2,1)=(d(2,1)*spl3%fsi(mtheta,1)-d(1,1)*spl3%fsi(mtheta,2))/det +c----------------------------------------------------------------------- +c compute first order constants, second eigenfunction. +c----------------------------------------------------------------------- + d(1,1)=d0bar(1,1)+1+alpha + d(2,2)=d0bar(2,2)+1+alpha + det=d(1,1)*d(2,2)-d(1,2)*d(2,1) + v10(1,2)=(d(1,2)*spl3%fsi(mtheta,4)-d(2,2)*spl3%fsi(mtheta,3))/det + v10(2,2)=(d(2,1)*spl3%fsi(mtheta,3)-d(1,1)*spl3%fsi(mtheta,4))/det +c----------------------------------------------------------------------- +c add constants to v1 and fit to cubic splines. +c----------------------------------------------------------------------- + bg%fs(:,1)=spl2%fs(:,1)+v10(1,1) + bg%fs(:,2)=spl2%fs(:,2)+v10(2,1) + bg%fs(:,3)=spl2%fs(:,3)+v10(1,2) + bg%fs(:,4)=spl2%fs(:,4)+v10(2,2) + CALL spline_fit(bg,"periodic") +c----------------------------------------------------------------------- +c diagnose bg. +c----------------------------------------------------------------------- +c bg%title=(/" bg1 "," bg2 "," bg2 "," bg2 "," bg2 "/) +c CALL spline_write1(bg,out_bal1,bin_bal1, +c $ out_bal1_unit,bin_bal1_unit,.FALSE.) +c----------------------------------------------------------------------- +c deallocate local splines. +c----------------------------------------------------------------------- + CALL spline_dealloc(spl1) + CALL spline_dealloc(spl2) + CALL spline_dealloc(spl3) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE bal_prep +c----------------------------------------------------------------------- +c subprogram 3. bal_der +c differential equations for the marginal ballooning. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE bal_der(neq,theta,y,dy) + + INTEGER, INTENT(IN) :: neq + REAL(r8), INTENT(IN) :: theta + REAL(r8), DIMENSION(neq), INTENT(IN) :: y + REAL(r8), DIMENSION(neq), INTENT(OUT) :: dy + + REAL(r8) :: dbdb,kappaw,thfac +c----------------------------------------------------------------------- +c compute coefficients. +c----------------------------------------------------------------------- + CALL spline_eval(bf,theta,0) + thfac=theta-theta0 + dbdb=bf%f(1)*(thfac+bf%f(2))**2+bf%f(3) + kappaw=bf%f(4)+thfac*bf%f(5) +c----------------------------------------------------------------------- +c compute derivatives. +c----------------------------------------------------------------------- + dy(1)=y(2)/dbdb + dy(2)=-y(1)*kappaw +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE bal_der +c----------------------------------------------------------------------- +c subprogram 4. bal_int +c integrates the ideal marginal ballooning equations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE bal_int + + INTEGER, PARAMETER :: neq=2,liw=20,lrw=22+neq*16 + INTEGER, DIMENSION(liw) :: iwork=0 + INTEGER :: iopt,iside,istate,itask,itol,jac,mf + INTEGER :: istep,nstep=HUGE(0),icross + REAL(r8), PARAMETER :: tol=1e-5,thmin=1,hu_min=1e-10 + REAL(r8) :: thmax,atol,ca1,ca2,det,rtol,theta,thout + REAL(r8), DIMENSION(lrw) :: rwork=0 + REAL(r8), DIMENSION(neq) :: y,dy + REAL(r8), DIMENSION(2,2) :: u +c----------------------------------------------------------------------- +c write formats. +c----------------------------------------------------------------------- + 10 FORMAT(/2x,"ist",2x,"nqu",1x,"icr",4x,"theta",6x,"dtheta",4x, + $ "asinh y1",2x,"asinh ca1",2x,"asinh ca2"/) + 20 FORMAT(i5,2i4,1x,1p,5e11.3) +c----------------------------------------------------------------------- +c initialize independent variables. +c----------------------------------------------------------------------- + thmax=SQRT(MAXVAL(ABS(bf%fs(:,3)/bf%fs(:,1))))*10*thmax0 + thmax=MIN(thmax,100._r8) + theta=-thmax + thout=thmax + istep=0 +c----------------------------------------------------------------------- +c compute equilibrium quantities and asymptotic solutions. +c----------------------------------------------------------------------- + CALL bal_pse(theta,u) + y(1)=u(1,2)*sinh(1.) + y(2)=u(2,2)*sinh(1.) +c----------------------------------------------------------------------- +c set up integrator parameters. +c----------------------------------------------------------------------- + icross=0 + iside=1 + istate=1 + itask=5 + mf=10 + rwork(1)=thout + iopt=1 + itol=1 + rtol=tol + atol=tol*tol +c----------------------------------------------------------------------- +c write header. +c----------------------------------------------------------------------- + IF(out_bal2)WRITE(out_bal2_unit,10) +c----------------------------------------------------------------------- +c check for crossings. +c----------------------------------------------------------------------- + DO + IF(iside*y(1) < 0)THEN + icross=icross+1 + iside=-iside + ENDIF +c----------------------------------------------------------------------- +c compute and print asymptotic coefficient. +c----------------------------------------------------------------------- + IF(out_bal2 .OR. bin_bal2)THEN + IF(ABS(theta) > thmin)THEN + CALL bal_pse(theta,u) + det=u(1,1)*u(2,2)-u(1,2)*u(2,1) + ca1=(y(1)*u(2,2)-y(2)*u(1,2))/det + ca2=(y(2)*u(1,1)-y(1)*u(2,1))/det + CALL bal_der(neq,theta,y,dy) + IF(out_bal2) + $ WRITE(out_bal2_unit,20)istep,iwork(14),icross, + $ theta,rwork(11),asinh(y(1)),asinh(ca1),asinh(ca2) + IF(bin_bal2) + $ WRITE(bin_bal2_unit)REAL(theta,4), + $ REAL(asinh(y(1)),4),REAL(asinh(y(2)),4), + $ REAL(y(2)/dy(1),4),REAL(dy(2)/y(1),4), + $ REAL(asinh(ca1),4),REAL(asinh(ca2),4),REAL(u,4) + ELSE + ca1=0 + ca2=0 + det=0 + ENDIF + ENDIF +c----------------------------------------------------------------------- +c advance. +c----------------------------------------------------------------------- + IF(istep >= nstep .OR. theta >= thmax .OR. istate < 0)EXIT + istep=istep+1 + CALL lsode(bal_der,neq,y,theta,thout,itol,rtol,atol,itask, + $ istate,iopt,rwork,lrw,iwork,liw,jac,mf) + IF(rwork(11) < hu_min)EXIT + ENDDO +c----------------------------------------------------------------------- +c write trailer. +c----------------------------------------------------------------------- + IF(out_bal2)WRITE(out_bal2_unit,10) + IF(bin_bal2)WRITE(bin_bal2_unit) +c----------------------------------------------------------------------- +c compute and store final asymptotic coefficients. +c----------------------------------------------------------------------- + IF(theta >= thmax)THEN + CALL bal_pse(theta,u) + det=u(1,1)*u(2,2)-u(1,2)*u(2,1) + ca1=(y(1)*u(2,2)-y(2)*u(1,2))/det + ca2=(y(2)*u(1,1)-y(1)*u(2,1))/det + locstab%fs(ipsi,4:5)=(/ca1,ca2/) + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE bal_int +c----------------------------------------------------------------------- +c subprogram 5. bal_pse. +c computes alpha series solutions. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE bal_pse(theta,u) + + REAL(r8), INTENT(IN) :: theta + REAL(r8), INTENT(OUT), DIMENSION(2,2) :: u + + REAL(r8) :: dtheta,thfac + REAL(r8), DIMENSION(2,2) :: v +c----------------------------------------------------------------------- +c compute alpha series. +c----------------------------------------------------------------------- + CALL spline_eval(bg,theta,0) + dtheta=theta-theta0 + v(1,1)=v0(1,1)+bg%f(1)/dtheta + v(2,1)=v0(2,1)+bg%f(2)/dtheta + v(1,2)=v0(1,2)+bg%f(3)/dtheta + v(2,2)=v0(2,2)+bg%f(4)/dtheta +c----------------------------------------------------------------------- +c compute transformed solutions. +c----------------------------------------------------------------------- + u(1,1)=v(1,1) + u(1,2)=v(1,2) + u(2,1)=bg%f(5)*v(1,1)+v(2,1) + u(2,2)=bg%f(5)*v(1,2)+v(2,2) +c----------------------------------------------------------------------- +c multiply by alphas. +c----------------------------------------------------------------------- + thfac=ABS(dtheta)**(alpha+.5)/dtheta + u(1,1)=u(1,1)*thfac + u(2,1)=u(2,1)*thfac*dtheta + u(1,2)=u(1,2)/(thfac*dtheta) + u(2,2)=u(2,2)/thfac +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE bal_pse + END MODULE bal_mod diff --git a/src/DCON/fortran/dcon b/src/DCON/fortran/dcon new file mode 100644 index 000000000..9c799258f Binary files /dev/null and b/src/DCON/fortran/dcon differ diff --git a/src/DCON/fortran/dcon.F b/src/DCON/fortran/dcon.F new file mode 100644 index 000000000..0fe960de8 --- /dev/null +++ b/src/DCON/fortran/dcon.F @@ -0,0 +1,430 @@ +c----------------------------------------------------------------------- +c file dcon.f. +c performs ideal MHD stability analysis. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 1. dcon. +c 2. dcon_dealloc. +c----------------------------------------------------------------------- +c subprogram 1. dcon. +c performs ideal & kinetic MHD stability analysis. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + PROGRAM dcon + USE equil_mod + USE equil_out_mod + USE bal_mod + USE mercier_mod + USE ode_mod + USE free_mod + USE resist_mod + USE pentrc_interface, ! rename overlapping names + $ pentrc_verbose=>verbose, ! should get a more fundamental fix + $ pentrc_mpert=>mpert, + $ pentrc_nn=>nn, + $ pentrc_r8=>r8, + $ pentrc_timer=>timer + IMPLICIT NONE + + LOGICAL :: use_classic_splines_for_dcon=.FALSE., cyl_flag=.FALSE., + $ reform_eq_with_psilim=.FALSE. + INTEGER :: mmin,ipsi,m,peak_index + COMPLEX(r8) :: plasma1,vacuum1,total1 + + INTEGER, DIMENSION(:), ALLOCATABLE :: mtmp + REAL(r8), DIMENSION(:), ALLOCATABLE :: psitmp + COMPLEX(r8), DIMENSION(:,:), ALLOCATABLE :: xtmp + + ! harvest variables + INCLUDE 'harvest_lib.inc77' + INTEGER :: ierr + INTEGER :: hint = 0 + REAL(r8) :: hdbl = 0 + CHARACTER(LEN=16) :: hkey + CHARACTER(LEN=50000) :: hnml + CHARACTER(LEN=65507) :: hlog + CHARACTER, PARAMETER :: nul = char(0) + + NAMELIST/dcon_control/bal_flag,mat_flag,ode_flag,vac_flag, + $ mer_flag,res_flag,fft_flag,node_flag,mthvac,sing_start,nn, + $ delta_mlow,delta_mhigh,delta_mband,thmax0,nstep,ksing, + $ tol_nr,tol_r,crossover,ucrit,singfac_min,singfac_max, + $ cyl_flag,dmlim,lim_flag,sas_flag,sing_order,sort_type, + $ termbycross_flag,qhigh,kin_flag,con_flag,kinfac1,kinfac2, + $ kingridtype,ktanh_flag,passing_flag,trapped_flag, + $ ion_flag,electron_flag,ktc,ktw,qlow, + $ use_classic_splines,reform_eq_with_psilim, + $ psiedge,nperq_edge,wv_farwall_flag, + $ dcon_kin_threads,parallel_threads + NAMELIST/dcon_output/interp,crit_break,out_bal1, + $ bin_bal1,out_bal2,bin_bal2,out_metric,bin_metric,out_fmat, + $ bin_fmat,out_gmat,bin_gmat,out_kmat,bin_kmat,out_sol, + $ out_sol_min,out_sol_max,bin_sol,bin_sol_min,bin_sol_max, + $ out_fl,bin_fl,out_evals,bin_evals,bin_euler,euler_stride, + $ bin_vac,ahb_flag,mthsurf0,msol_ahb,netcdf_out,out_fund, + $ out_ahg2msc +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(/'ipsi',2x,'psifac',6x,'f',7x,'mu0 p',5x,'dvdpsi', + $ 6x,'q',10x,'di',9x,'dr',8x,'ca1'/) + 20 FORMAT(i4,1p,8e11.3) + 30 FORMAT(/3x,"mlow",1x,"mhigh",1x,"mpert",1x,"mband",3x,"nn",2x, + $ "lim_fl",2x,"dmlim",7x,"qlim",6x,"psilim"//5i6,l6,1p,3e11.3/) +c----------------------------------------------------------------------- +c read input data. +c----------------------------------------------------------------------- + IF(verbose) WRITE(*,*)"" + IF(verbose) WRITE(*,*)"DCON START => "//TRIM(version) + IF(verbose) WRITE(*,*)"__________________________________________" + CALL timer(0,out_unit) + CALL ascii_open(in_unit,"dcon.in","OLD") + READ(UNIT=in_unit,NML=dcon_control) + READ(UNIT=in_unit,NML=dcon_output) + CALL ascii_close(in_unit) + + IF (out_ahg2msc) THEN + WRITE(*,*) "WARNING: ahg2msc.out is deprecated and will be " // + $ "removed in a future version. Set out_ahg2msc = .FALSE." + WRITE(*,*) " to disable this warning." + vac_memory=.FALSE. + ELSE + vac_memory=.TRUE. + ENDIF + +c----------------------------------------------------------------------- +c set variables +c----------------------------------------------------------------------- + IF(parallel_threads > 0)THEN + WRITE(*,*) "!! WARNING: parallel_threads has been deprecated. " + $ //"Use dcon_kin_threads" + ENDIF +#ifdef _OPENMP +c The code is compiled with the OpenMP option so the preprocessor +c will pick include the following line + IF(dcon_kin_threads > 0)THEN + CALL OMP_SET_NUM_THREADS(dcon_kin_threads) + ENDIF +#else +c No OpenMP so the following line will appear in source code + dcon_kin_threads = 1 +#endif + delta_mhigh=delta_mhigh*2 + use_classic_splines_for_dcon = use_classic_splines +c----------------------------------------------------------------------- +c open output files, read, process, and diagnose equilibrium. +c----------------------------------------------------------------------- + CALL ascii_open(out_unit,"dcon.out","UNKNOWN") + CALL equil_read(out_unit) + CALL equil_out_global + CALL equil_out_qfind +c----------------------------------------------------------------------- +c optionally reform the eq splines to concentrate at true truncation +c----------------------------------------------------------------------- + CALL sing_lim ! determine if qhigh is truncating before psihigh + IF(psilim /= psihigh .AND. reform_eq_with_psilim)THEN + CALL equil_read(out_unit, psilim) + CALL equil_out_global + CALL equil_out_qfind + ENDIF +c----------------------------------------------------------------------- +c record the equilibrium properties +c----------------------------------------------------------------------- + CALL equil_out_diagnose(.FALSE.,out_unit) + CALL equil_out_write_2d + IF(dump_flag .AND. eq_type /= "dump")CALL equil_out_dump + IF(direct_flag)CALL bicube_dealloc(psi_in) +c----------------------------------------------------------------------- +c enable different settings for dcon and equilibrium splines +c----------------------------------------------------------------------- + use_classic_splines = use_classic_splines_for_dcon +c----------------------------------------------------------------------- +c prepare local stability criteria. +c----------------------------------------------------------------------- + CALL spline_alloc(locstab,mpsi,5) + locstab%xs=sq%xs + locstab%fs=0 + locstab%name="locstb" + locstab%title=(/" di "," dr "," h "," ca1 "," ca2 "/) + IF (mer_flag) THEN + WRITE(*,*)"Evaluating Mercier criterion" + CALL mercier_scan + ENDIF + IF(bal_flag)THEN + IF(verbose) WRITE(*,*)"Evaluating ballooning criterion" + CALL bal_scan + ENDIF + CALL spline_fit(locstab,"extrap") +c----------------------------------------------------------------------- +c output surface quantities. +c----------------------------------------------------------------------- + CALL bin_open(bin_unit,"dcon.bin","UNKNOWN","REWIND","none") + WRITE(out_unit,10) + DO ipsi=0,mpsi + WRITE(out_unit,20)ipsi,sq%xs(ipsi),sq%fs(ipsi,1)/twopi, + $ sq%fs(ipsi,2),sq%fs(ipsi,3),sq%fs(ipsi,4), + $ locstab%fs(ipsi,1)/sq%xs(ipsi), + $ locstab%fs(ipsi,2)/sq%xs(ipsi),locstab%fs(ipsi,4) + WRITE(bin_unit) + $ REAL(sq%xs(ipsi),4), + $ REAL(SQRT(sq%xs(ipsi)),4), + $ REAL(sq%fs(ipsi,1)/twopi,4), + $ REAL(sq%fs(ipsi,2),4), + $ REAL(sq%fs(ipsi,4),4), + $ REAL(asinh(locstab%fs(ipsi,1)/sq%xs(ipsi)),4), + $ REAL(asinh(locstab%fs(ipsi,2)/sq%xs(ipsi)),4), + $ REAL(asinh(locstab%fs(ipsi,3)),4), + $ REAL(asinh(locstab%fs(ipsi,4)),4) + ENDDO + WRITE(out_unit,10) + WRITE(bin_unit) + CALL bin_close(bin_unit) +c----------------------------------------------------------------------- +c define poloidal mode numbers. +c----------------------------------------------------------------------- + CALL sing_find + !CALL sing_lim ! now done in above test for re-forming equil + IF(cyl_flag)THEN + mlow=delta_mlow + mhigh=delta_mhigh + ELSEIF(sing_start == 0)THEN + mlow=MIN(nn*qmin,zero)-4-delta_mlow + mhigh=nn*qmax+delta_mhigh + ELSE + mmin=HUGE(mmin) + DO ising=INT(sing_start),msing + mmin=MIN(mmin,sing(ising)%m) + ENDDO + mlow=mmin-delta_mlow + mhigh=nn*qmax+delta_mhigh + ENDIF + mpert=mhigh-mlow+1 + mband=mpert-1-delta_mband + mband=MIN(MAX(mband,0),mpert-1) +c----------------------------------------------------------------------- +c fit equilibrium quantities to Fourier-spline functions. +c----------------------------------------------------------------------- + IF(mat_flag .OR. ode_flag)THEN + IF(verbose) WRITE(*,'(3x,1p,4(a,es10.3))')"q0 = ",q0, + $ ", qmin = ",qmin,", qmax = ",qmax,", q95 = ",q95 + IF(verbose) WRITE(*,'(3x,a,l1,1p,3(a,es10.3))') + $ "sas_flag = ",sas_flag,", dmlim = ",dmlim, + $ ", qlim = ",qlim,", psilim = ",psilim + IF(verbose) WRITE(*,'(3x,1p,3(a,es10.3))')"betat = ",betat, + $ ", betan = ",betan,", betap1 = ",betap1 + IF(verbose) WRITE(*,'(3x,5(a,i4))')"nn = ",nn,", mlow = ",mlow, + $ ", mhigh = ",mhigh,", mpert = ",mpert,", mband = ",mband + IF(verbose) WRITE(*,'(1x,a)') + $ "Fourier analysis of metric tensor components" + CALL fourfit_make_metric + IF(verbose) WRITE(*,*)"Computing F, G, and K Matrices" + CALL fourfit_make_matrix(out_fund) + WRITE(out_unit,30)mlow,mhigh,mpert,mband,nn,sas_flag,dmlim, + $ qlim,psilim + IF(kin_flag)THEN + CALL fourfit_action_matrix + IF(verbose) WRITE(*,*) "Initializing PENTRC" + ! call the automatic reading and distributing of inputs + CALL initialize_pentrc(op_kin=.FALSE.,op_deq=.FALSE., + $ op_peq=.FALSE.) + ! manually set the pentrc equilibrium description + CALL set_eq(eqfun,sq,rzphi,smats,tmats,xmats,ymats,zmats, + $ twopi*psio,ro,nn,jac_type,mlow,mhigh,mpert,mthvac) + ! manually set the kinetic profiles + CALL read_kin(kinetic_file,zi,zimp,mi,mimp,nfac, + $ tfac,wefac,wpfac,indebug) + ! manually set the perturbed equilibrium displacements + ! use false flat xi and xi' for equal weighting + ALLOCATE(psitmp(sq%mx+1),mtmp(mpert),xtmp(sq%mx+1,mpert)) + psitmp(:) = sq%xs(0:) + mtmp = (/(m,m=mlow,mhigh)/) + xtmp = 1e-4 + CALL set_peq(psitmp,mtmp,xtmp,xtmp,xtmp,.false.,tdebug) + DEALLOCATE(xtmp,mtmp,psitmp) + IF(verbose) WRITE(*,*)"Computing Kinetic Matrices" + CALL fourfit_kinetic_matrix(kingridtype,out_fund) + ENDIF + CALL sing_scan + DO ising=1,msing + CALL resist_eval(sing(ising)) + ENDDO + IF (kin_flag)THEN + CALL ksing_find + ENDIF + ENDIF +c----------------------------------------------------------------------- +c integrate main ODE's. +c----------------------------------------------------------------------- + ALLOCATE(ud(mpert,mpert,2)) + IF(ode_flag)THEN + IF(verbose) WRITE(*,*)"Starting integration of ODE's" + CALL ode_run + IF(size_edge > 0)THEN + peak_index = MAXLOC(REAL(dw_edge(pre_edge:i_edge)),dim=1) + + $ (pre_edge - 1) + qhigh = q_edge(peak_index) + sas_flag = .FALSE. + psiedge = psihigh + CALL sing_lim + WRITE(*,'(1x,a34,f10.6,a10,f10.6)') "Re-Integrating to "// + $ "peak dW @ qlim =",qlim,", psilim =",psilim + ! full re-run because outputs were written to disk each step + ! making it hard to backtrack + IF(bin_euler)CALL bin_close(euler_bin_unit) + CALL ode_run + ENDIF + ENDIF + DEALLOCATE(ud) +c----------------------------------------------------------------------- +c compute free boundary energies. +c----------------------------------------------------------------------- + IF(vac_flag .AND. .NOT. + $ (ksing > 0 .AND. ksing <= msing+1 .AND. bin_sol))THEN + IF(verbose) WRITE(*,*)"Computing free boundary energies" + ALLOCATE(ud(mpert,mpert,2)) + CALL free_run(plasma1,vacuum1,total1,nzero,netcdf_out) + DEALLOCATE(ud) + ELSE + plasma1=0 + vacuum1=0 + total1=0 + CALL dcon_dealloc + ENDIF + IF(mat_flag .OR. ode_flag)DEALLOCATE(asmat,bsmat,csmat,ipiva,jmat) + IF(bin_euler)CALL bin_close(euler_bin_unit) +c----------------------------------------------------------------------- +c the bottom line. +c----------------------------------------------------------------------- + IF(nzero /= 0)THEN + IF(verbose) WRITE(*,'(1x,a,i2,".")') + $ "Fixed-boundary mode unstable for nn = ",nn + ENDIF + IF(vac_flag .AND. .NOT. + $ (ksing > 0 .AND. ksing <= msing+1 .AND. bin_sol))THEN + IF(REAL(total1) < 0)THEN + IF(verbose) WRITE(*,'(1x,a,i2,".")') + $ "Free-boundary mode unstable for nn = ",nn + ELSE + IF(verbose) WRITE(*,'(1x,a,i2,".")') + $ "All free-boundary modes stable for nn = ",nn + ENDIF + ENDIF +c----------------------------------------------------------------------- +c save output in sum1.bin. +c----------------------------------------------------------------------- + CALL bin_open(sum_unit,"sum1.bin","UNKNOWN","REWIND","none") + WRITE(sum_unit)mpsi,mtheta,mlow,mhigh,mpert,mband, + $ REAL(psilow,4),REAL(psihigh,4),REAL(amean,4),REAL(rmean,4), + $ REAL(aratio,4),REAL(kappa,4),REAL(delta1,4),REAL(delta2,4), + $ REAL(li1,4),REAL(li2,4),REAL(li3,4),REAL(ro,4),REAL(zo,4), + $ REAL(psio,4),REAL(betap1,4),REAL(betap2,4),REAL(betap3,4), + $ REAL(betat,4),REAL(betan,4),REAL(bt0,4),REAL(q0,4), + $ REAL(qmin,4),REAL(qmax,4),REAL(qa,4),REAL(crnt,4), + $ REAL(plasma1,4),REAL(vacuum1,4),REAL(total1,4),REAL(q95,4), + $ REAL(bwall,4),REAL(betaj,4) + CALL bin_close(sum_unit) +c----------------------------------------------------------------------- +c log inputs/outputs with harvest +c----------------------------------------------------------------------- + ierr=init_harvest('CODEDB_DCON'//nul,hlog,LEN(hlog)) + ierr=set_harvest_verbose(0) + ! standard CODEDB records + ierr=set_harvest_payload_str(hlog,'CODE'//nul,'DCON'//nul) + ierr=set_harvest_payload_str(hlog,'VERSION'//nul,version//nul) + if(shotnum>0) + $ ierr=set_harvest_payload_int(hlog,'SHOT'//nul,INT(shotnum)) + if(shottime>0) + $ ierr=set_harvest_payload_int(hlog,'TIME'//nul,INT(shottime)) + ! DCON specifc records + ierr=set_harvest_payload_int(hlog,'mpsi'//nul,mpsi) + ierr=set_harvest_payload_int(hlog,'mtheta'//nul,mtheta) + ierr=set_harvest_payload_int(hlog,'mlow'//nul,mlow) + ierr=set_harvest_payload_int(hlog,'mhigh'//nul,mhigh) + ierr=set_harvest_payload_int(hlog,'mpert'//nul,mpert) + ierr=set_harvest_payload_int(hlog,'mband'//nul,mband) + ierr=set_harvest_payload_dbl(hlog,'psilow'//nul,psilow) + ierr=set_harvest_payload_dbl(hlog,'psilim'//nul,psilim) + ierr=set_harvest_payload_dbl(hlog,'amean'//nul,amean) + ierr=set_harvest_payload_dbl(hlog,'rmean'//nul,rmean) + ierr=set_harvest_payload_dbl(hlog,'aratio'//nul,aratio) + ierr=set_harvest_payload_dbl(hlog,'kappa'//nul,kappa) + ierr=set_harvest_payload_dbl(hlog,'delta1'//nul,delta1) + ierr=set_harvest_payload_dbl(hlog,'delta2'//nul,delta2) + ierr=set_harvest_payload_dbl(hlog,'li1'//nul,li1) + ierr=set_harvest_payload_dbl(hlog,'li2'//nul,li2) + ierr=set_harvest_payload_dbl(hlog,'li3'//nul,li3) + ierr=set_harvest_payload_dbl(hlog,'ro'//nul,ro) + ierr=set_harvest_payload_dbl(hlog,'zo'//nul,zo) + ierr=set_harvest_payload_dbl(hlog,'psio'//nul,psio) + ierr=set_harvest_payload_dbl(hlog,'betap1'//nul,betap1) + ierr=set_harvest_payload_dbl(hlog,'betap2'//nul,betap2) + ierr=set_harvest_payload_dbl(hlog,'betap3'//nul,betap3) + ierr=set_harvest_payload_dbl(hlog,'betat'//nul,betat) + ierr=set_harvest_payload_dbl(hlog,'betan'//nul,betan) + ierr=set_harvest_payload_dbl(hlog,'bt0'//nul,bt0) + ierr=set_harvest_payload_dbl(hlog,'q0'//nul,q0) + ierr=set_harvest_payload_dbl(hlog,'qmin'//nul,qmin) + ierr=set_harvest_payload_dbl(hlog,'qmax'//nul,qmax) + ierr=set_harvest_payload_dbl(hlog,'qa'//nul,qa) + ierr=set_harvest_payload_dbl(hlog,'crnt'//nul,crnt) + ierr=set_harvest_payload_dbl(hlog,'q95'//nul,q95) + ierr=set_harvest_payload_dbl(hlog,'betan'//nul,betan) + ierr=set_harvest_payload_dbl(hlog,'plasma1'//nul,plasma1) + ierr=set_harvest_payload_dbl(hlog,'vacuum1'//nul,vacuum1) + ierr=set_harvest_payload_dbl(hlog,'total1'//nul,total1) + ierr=harvest_send(hlog) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + CALL program_stop("Normal termination.") + END PROGRAM dcon +c----------------------------------------------------------------------- +c subprogram 2. dcon_dealloc. +c deallocates internal memory. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE dcon_dealloc + USE ode_mod + IMPLICIT NONE + +c----------------------------------------------------------------------- +c deallocate internal memory. +c----------------------------------------------------------------------- + CALL spline_dealloc(sq) + CALL spline_dealloc(locstab) + CALL bicube_dealloc(rzphi) + IF(mat_flag .OR. ode_flag)THEN + CALL cspline_dealloc(amats) + CALL cspline_dealloc(bmats) + CALL cspline_dealloc(cmats) + CALL cspline_dealloc(dmats) + CALL cspline_dealloc(emats) + CALL cspline_dealloc(hmats) + CALL cspline_dealloc(dbats) + CALL cspline_dealloc(ebats) + CALL cspline_dealloc(fbats) + CALL cspline_dealloc(fmats) + CALL cspline_dealloc(gmats) + CALL cspline_dealloc(kmats) + + DO ising=1,msing + DEALLOCATE(sing(ising)%vmat) + DEALLOCATE(sing(ising)%mmat) + DEALLOCATE(sing(ising)%power) + DEALLOCATE(sing(ising)%n1) + DEALLOCATE(sing(ising)%n2) + ENDDO + DEALLOCATE(sing) + ENDIF + IF(ode_flag)DEALLOCATE(u,du,u_save) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE dcon_dealloc diff --git a/src/DCON/fortran/dcon_mod.f b/src/DCON/fortran/dcon_mod.f new file mode 100644 index 000000000..6ad7bb64d --- /dev/null +++ b/src/DCON/fortran/dcon_mod.f @@ -0,0 +1,128 @@ +c----------------------------------------------------------------------- +c file dcon_mod.f. +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c subprogram 0. dcon_mod. +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + MODULE dcon_mod + USE spline_mod + USE global_mod + USE equil_mod + USE equil_out_mod + USE pentrc_interface, ONLY: version + + IMPLICIT NONE + + INTEGER :: out_bal1_unit=21 + INTEGER :: out_bal2_unit=22 + INTEGER :: bin_bal1_unit=23 + INTEGER :: bin_bal2_unit=24 + INTEGER :: fourfit_out_unit=21 + INTEGER :: fourfit_bin_unit=22 + INTEGER :: evals_out_unit=23 + INTEGER :: evals_bin_unit=24 + INTEGER :: crit_out_unit=25 + INTEGER :: crit_bin_unit=26 + INTEGER :: euler_bin_unit=27 + INTEGER :: init_out_unit=28 + INTEGER :: dcon_unit=1 + INTEGER :: unorm_unit=29 + INTEGER :: ca_unit=30 + INTEGER :: err_unit=31 + + LOGICAL :: out_bal1=.FALSE. + LOGICAL :: out_bal2=.FALSE. + LOGICAL :: bin_bal1=.FALSE. + LOGICAL :: bin_bal2=.FALSE. + LOGICAL :: out_fund=.FALSE. + LOGICAL :: out_fmat=.FALSE. + LOGICAL :: out_gmat=.FALSE. + LOGICAL :: out_kmat=.FALSE. + LOGICAL :: out_metric=.FALSE. + LOGICAL :: bin_fmat=.FALSE. + LOGICAL :: bin_gmat=.FALSE. + LOGICAL :: bin_kmat=.FALSE. + LOGICAL :: bin_metric=.FALSE. + LOGICAL :: feval_flag=.FALSE. + LOGICAL :: fft_flag=.FALSE. + LOGICAL :: bin_euler=.FALSE. + LOGICAL :: bin_vac=.FALSE. + LOGICAL :: out_evals=.FALSE. + LOGICAL :: bin_evals=.FALSE. + LOGICAL :: out_sol=.FALSE. + LOGICAL :: bin_sol=.FALSE. + LOGICAL :: netcdf_out=.TRUE. + + LOGICAL :: bal_flag=.FALSE. + LOGICAL :: mat_flag=.FALSE. + LOGICAL :: ode_flag=.FALSE. + LOGICAL :: vac_flag=.FALSE. + LOGICAL :: mer_flag=.FALSE. + + LOGICAL :: crit_break=.TRUE. + LOGICAL :: node_flag=.FALSE. + LOGICAL :: res_flag=.FALSE. + LOGICAL :: ahb_flag=.FALSE. + LOGICAL :: out_ahg2msc=.TRUE. + LOGICAL :: vac_memory=.FALSE. + + INTEGER, PARAMETER :: sol_base=50 + INTEGER :: mlow,mhigh,mpert,mband,nn,nstep=HUGE(0),bin_sol_min, + $ bin_sol_max,euler_stride=1,mthvac=480,ksing=-1,delta_mlow=0, + $ delta_mhigh=0,delta_mband=0,out_sol_min,out_sol_max + REAL(r8) :: thmax0=1,ucrit=1e4,tol_r=1e-5,tol_nr=1e-5, + $ crossover=1e-2,sing_start=0,mthsurf0=1 + + TYPE(spline_type) :: locstab + + TYPE :: resist_type + REAL(r8) :: e,f,h,m,g,k,eta,rho,taua,taur + END TYPE resist_type + + TYPE :: sing_type + INTEGER :: m + INTEGER :: order + INTEGER, DIMENSION(1) :: r1 + INTEGER, DIMENSION(2) :: r2 + INTEGER, DIMENSION(:), POINTER :: n1,n2 + REAL(r8) :: psifac,rho,q,q1,di + COMPLEX(r8) :: alpha + COMPLEX(r8), DIMENSION(:), POINTER :: power + COMPLEX(r8), DIMENSION(:,:,:,:), POINTER :: vmat,mmat + TYPE(resist_type) :: restype + END TYPE sing_type + + INTEGER :: msing,kmsing + TYPE(sing_type), DIMENSION(:), POINTER :: sing + TYPE(sing_type), DIMENSION(:), POINTER :: kinsing + + LOGICAL :: sas_flag=.FALSE.,lim_flag + EQUIVALENCE (sas_flag,lim_flag) + REAL(r8) :: psilim,qlim,q1lim,dmlim=.5_r8,qhigh=1e3,qlow=0 + + INTEGER :: kingridtype=0 + REAL(r8) :: kinfac1=1.0,kinfac2=1.0,ktc=0.1,ktw=50 + LOGICAL :: kin_flag = .FALSE. + LOGICAL :: con_flag = .FALSE. + LOGICAL :: ktanh_flag = .FALSE. + LOGICAL :: passing_flag = .FALSE. + LOGICAL :: trapped_flag = .TRUE. + LOGICAL :: electron_flag = .FALSE. + LOGICAL :: ion_flag = .TRUE. + LOGICAL :: fkg_kmats_flag = .FALSE. + LOGICAL :: keq_out = .FALSE. + LOGICAL :: theta_out = .FALSE. + LOGICAL :: xlmda_out = .FALSE. + + ! for recording dw(q) near the boundary + REAL(r8) :: psiedge = 1.0 + REAL(r8), DIMENSION(:), ALLOCATABLE :: q_edge, psi_edge + COMPLEX(r8), DIMENSION(:), ALLOCATABLE :: dw_edge + INTEGER :: nperq_edge=20, size_edge=0, pre_edge=1, i_edge=1 + + END MODULE dcon_mod diff --git a/src/DCON/fortran/dcon_netcdf.f b/src/DCON/fortran/dcon_netcdf.f new file mode 100644 index 000000000..9fac3b1f9 --- /dev/null +++ b/src/DCON/fortran/dcon_netcdf.f @@ -0,0 +1,276 @@ +c----------------------------------------------------------------------- +c file dcon_netcdf.f +c writes dcon.out information to a netcdf file +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. dcon_netcdf_mod +c 1. check +c 2. dcon_netcdf_out +c----------------------------------------------------------------------- +c subprogram 0. dcon_netcdf_mod +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + MODULE dcon_netcdf_mod + USE dcon_mod + USE sing_mod, ONLY: sing_detf + USE local_mod, ONLY: r8, r4 + USE netcdf + IMPLICIT NONE + + CONTAINS +c----------------------------------------------------------------------- +c subprogram 1. check. +c Check status of netcdf file. +c----------------------------------------------------------------------- + SUBROUTINE check(stat) +c----------------------------------------------------------------------- +c declaration. +c----------------------------------------------------------------------- + INTEGER, INTENT (IN) :: stat +c----------------------------------------------------------------------- +c stop if it is an error. +c----------------------------------------------------------------------- + IF(stat /= nf90_noerr) THEN + PRINT *, TRIM(nf90_strerror(stat)) + STOP "ERROR: failed to write/read netcdf file" + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE check +c----------------------------------------------------------------------- +c subprogram 2. dcon_netcdf_out. +c Replicate dcon.out information in netcdf format. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE dcon_netcdf_out(wp,wv,wt,wt0,ep,ev,et) + + COMPLEX(r8), DIMENSION(mpert), INTENT(IN) :: ep,ev,et + COMPLEX(r8), DIMENSION(mpert,mpert), INTENT(IN) :: wp,wv,wt,wt0 + + INTEGER :: i, ncid, + $ i_dim, m_dim, mo_dim, p_dim, ep_dim, i_id, m_id, mo_id, p_id, + $ f_id, q_id, dv_id, mu_id, di_id, dr_id, ca_id, + $ wp_id, wpv_id, wv_id, wvv_id, wt_id, wtv_id, wt0_id, + $ pd_dim, pd_id, df_id, ep_id, ew_id, eq_id + REAL(r4) :: cpusec, wallsec + CHARACTER(2) :: sn + CHARACTER(64) :: ncfile + + LOGICAL, PARAMETER :: debug_flag = .FALSE. +c----------------------------------------------------------------------- +c set variables +c----------------------------------------------------------------------- + IF(debug_flag) PRINT *,"Called dcon_netcdf_out" + IF (nn<10) THEN + WRITE(UNIT=sn,FMT='(I1)')nn + sn=ADJUSTL(sn) + ELSE + WRITE(UNIT=sn,FMT='(I2)')nn + ENDIF + ncfile = "dcon_output_n"//TRIM(sn)//".nc" + CALL timer(1,0,cpusec,wallsec) +c----------------------------------------------------------------------- +c open files +c----------------------------------------------------------------------- + IF(debug_flag) PRINT *," - Creating netcdf files" + CALL check( nf90_create(ncfile, + $ cmode=or(NF90_CLOBBER,NF90_64BIT_OFFSET), ncid=ncid) ) +c----------------------------------------------------------------------- +c define global file attributes +c----------------------------------------------------------------------- + IF(debug_flag) PRINT *," - Defining modal netcdf globals" + CALL check( nf90_put_att(ncid,nf90_global,"title", + $ "DCON outputs")) + ! define global attributes + CALL check( nf90_put_att(ncid,nf90_global,"jacobian", + $ trim(jac_type))) + CALL check( nf90_put_att(ncid,nf90_global,"power_bp", power_bp)) + CALL check( nf90_put_att(ncid,nf90_global,"power_b", power_b)) + CALL check( nf90_put_att(ncid,nf90_global,"power_r", power_r)) + CALL check( nf90_put_att(ncid,nf90_global,'mpsi', mpsi)) + CALL check( nf90_put_att(ncid,nf90_global,'mtheta', mtheta)) + CALL check( nf90_put_att(ncid,nf90_global,'mlow', mlow)) + CALL check( nf90_put_att(ncid,nf90_global,'mhigh', mhigh)) + CALL check( nf90_put_att(ncid,nf90_global,'mpert', mpert)) + CALL check( nf90_put_att(ncid,nf90_global,'mband', mband)) + CALL check( nf90_put_att(ncid,nf90_global,'psilow', psilow)) + CALL check( nf90_put_att(ncid,nf90_global,'amean', amean)) + CALL check( nf90_put_att(ncid,nf90_global,'rmean', rmean)) + CALL check( nf90_put_att(ncid,nf90_global,'aratio', aratio)) + CALL check( nf90_put_att(ncid,nf90_global,'kappa', kappa)) + CALL check( nf90_put_att(ncid,nf90_global,'delta1', delta1)) + CALL check( nf90_put_att(ncid,nf90_global,'delta2', delta2)) + CALL check( nf90_put_att(ncid,nf90_global,'li1', li1)) + CALL check( nf90_put_att(ncid,nf90_global,'li2', li2)) + CALL check( nf90_put_att(ncid,nf90_global,'li3', li3)) + CALL check( nf90_put_att(ncid,nf90_global,'ro', ro)) + CALL check( nf90_put_att(ncid,nf90_global,'zo', zo)) + CALL check( nf90_put_att(ncid,nf90_global,'psio', psio)) + CALL check( nf90_put_att(ncid,nf90_global,'betap1', betap1)) + CALL check( nf90_put_att(ncid,nf90_global,'betap2', betap2)) + CALL check( nf90_put_att(ncid,nf90_global,'betap3', betap3)) + CALL check( nf90_put_att(ncid,nf90_global,'betat', betat)) + CALL check( nf90_put_att(ncid,nf90_global,'betan', betan)) + CALL check( nf90_put_att(ncid,nf90_global,'bt0', bt0)) + CALL check( nf90_put_att(ncid,nf90_global,'q0', q0)) + CALL check( nf90_put_att(ncid,nf90_global,'qmin', qmin)) + CALL check( nf90_put_att(ncid,nf90_global,'qmax', qmax)) + CALL check( nf90_put_att(ncid,nf90_global,'qa', qa)) + CALL check( nf90_put_att(ncid,nf90_global,'crnt', crnt)) + CALL check( nf90_put_att(ncid,nf90_global,'q95', q95)) + CALL check( nf90_put_att(ncid,nf90_global,'betan', betan)) + CALL check( nf90_put_att(ncid,nf90_global,"qlim", qlim)) + CALL check( nf90_put_att(ncid,nf90_global,"psilim", psilim)) + CALL check( nf90_put_att(ncid,nf90_global,"shot", INT(shotnum)) ) + CALL check( nf90_put_att(ncid,nf90_global,"time",INT(shottime)) ) + CALL check( nf90_put_att(ncid,nf90_global,"n", nn)) + CALL check( nf90_put_att(ncid,nf90_global,"version", version)) + CALL check( nf90_put_att(ncid,nf90_global,"cpu_time",cpusec) ) + CALL check( nf90_put_att(ncid,nf90_global,"wall_time",wallsec)) + ! define dimensions + CALL check( nf90_def_dim(ncid, "i", 2, i_dim) ) + CALL check( nf90_def_var(ncid, "i", nf90_int, i_dim, i_id) ) + CALL check( nf90_def_dim(ncid, "m", mpert, m_dim) ) + CALL check( nf90_def_var(ncid, "m", nf90_int, m_dim, m_id) ) + CALL check( nf90_def_dim(ncid, "mode", mpert, mo_dim) ) + CALL check( nf90_def_var(ncid, "mode", nf90_int, mo_dim, mo_id)) + CALL check( nf90_def_dim(ncid, "psi_n", sq%mx+1, p_dim) ) + CALL check( nf90_def_var(ncid, "psi_n", nf90_double, p_dim, p_id)) + CALL check( nf90_put_att(ncid,p_id, "long_name", + $ "Normalized Poloidal Flux") ) + IF(size_edge > 0)THEN + CALL check( nf90_def_dim(ncid, "psi_n_edge", size_edge,ep_dim)) + CALL check( nf90_def_var(ncid, "psi_n_edge", nf90_double, + $ ep_dim, ep_id)) + CALL check( nf90_put_att(ncid,ep_id,"long_name", + $ "Normalized Poloidal Flux") ) + ENDIF + IF(ALLOCATED(sing_detf))THEN + CALL check( nf90_def_dim(ncid, "psi_n_detf", + $ SIZE(sing_detf, 2), pd_dim) ) + CALL check( nf90_def_var(ncid, "psi_n_detf", nf90_double, + $ pd_dim, pd_id)) + CALL check( nf90_put_att(ncid,pd_id,"long_name", + $ "Normalized Poloidal Flux") ) + ENDIF + ! define variables + CALL check( nf90_def_var(ncid, "f", nf90_double, p_dim, f_id) ) + CALL check( nf90_def_var(ncid, "mu0p", nf90_double, p_dim, mu_id)) + CALL check( nf90_def_var(ncid, "dvdpsi", nf90_double,p_dim,dv_id)) + CALL check( nf90_def_var(ncid, "q", nf90_double, p_dim, q_id) ) + CALL check( nf90_put_att(ncid,q_id,"long_name", + $ "Safety Factor") ) + CALL check( nf90_def_var(ncid, "di", nf90_double, p_dim, di_id) ) + CALL check( nf90_def_var(ncid, "dr", nf90_double, p_dim, dr_id) ) + CALL check( nf90_def_var(ncid, "ca1", nf90_double, p_dim, ca_id)) + CALL check( nf90_def_var(ncid, "W_p_eigenvector", nf90_double, + $ (/m_dim, mo_dim, i_dim/), wp_id) ) + CALL check( nf90_def_var(ncid, "W_p_eigenvalue", nf90_double, + $ (/mo_dim, i_dim/), wpv_id) ) + CALL check( nf90_put_att(ncid,wp_id,"long_name", + $ "Plasma Energy Eigenmodes") ) + CALL check( nf90_put_att(ncid,wpv_id,"long_name", + $ "Plasma Energy Eigenvalues") ) + CALL check( nf90_def_var(ncid, "W_v_eigenvector", nf90_double, + $ (/m_dim, mo_dim, i_dim/), wv_id) ) + CALL check( nf90_def_var(ncid, "W_v_eigenvalue", nf90_double, + $ (/mo_dim, i_dim/), wvv_id) ) + CALL check( nf90_put_att(ncid,wv_id,"long_name", + $ "Vacuum Energy Eigenmodes") ) + CALL check( nf90_put_att(ncid,wvv_id,"long_name", + $ "Vacuum Energy Eigenvalues") ) + CALL check( nf90_def_var(ncid, "W_t_eigenvector", nf90_double, + $ (/m_dim, mo_dim, i_dim/), wt_id) ) + CALL check( nf90_def_var(ncid, "W_t_eigenvalue", nf90_double, + $ (/mo_dim, i_dim/), wtv_id) ) + CALL check( nf90_put_att(ncid,wt_id,"long_name", + $ "Total Energy Eigenmodes") ) + CALL check( nf90_put_att(ncid,wtv_id,"long_name", + $ "Total Energy Eigenvalues") ) + CALL check( nf90_def_var(ncid, "W_t", nf90_double, + $ (/m_dim, mo_dim, i_dim/), wt0_id) ) + CALL check( nf90_put_att(ncid,wt0_id,"long_name", + $ "Total Energy Matrix") ) + IF(size_edge > 0)THEN + CALL check( nf90_def_var(ncid, "dW_edge", nf90_double, + $ (/ep_dim, i_dim/), ew_id) ) + CALL check( nf90_put_att(ncid,ew_id,"long_name", + $ "Least Stable Total Energy Eigenvalues") ) + CALL check( nf90_def_var(ncid, "q_edge", nf90_double, + $ ep_dim, eq_id) ) + CALL check( nf90_put_att(ncid,eq_id,"long_name", + $ "Safety Factor") ) + ENDIF + IF(ALLOCATED(sing_detf))THEN + CALL check( nf90_def_var(ncid, "detF", nf90_double, + $ (/pd_dim, i_dim/), df_id) ) + ENDIF + ! end definitions + CALL check( nf90_enddef(ncid) ) +c----------------------------------------------------------------------- +c set variables +c----------------------------------------------------------------------- + IF(debug_flag) PRINT *," - Putting dimension variables in netcdf" + CALL check( nf90_put_var(ncid,i_id, (/0,1/)) ) + CALL check( nf90_put_var(ncid,m_id, (/(i+mlow, i=0,mpert-1)/)) ) + CALL check( nf90_put_var(ncid,mo_id, (/(i, i=1,mpert)/)) ) + CALL check( nf90_put_var(ncid,p_id, sq%xs(:))) + IF(size_edge > 0)THEN + CALL check( nf90_put_var(ncid,ep_id, psi_edge)) + ENDIF + + IF(debug_flag) PRINT *," - Putting profile variables in netcdf" + CALL check( nf90_put_var(ncid,f_id, sq%fs(:,1)/twopi)) + CALL check( nf90_put_var(ncid,mu_id, sq%fs(:,2))) + CALL check( nf90_put_var(ncid,dv_id, sq%fs(:,3))) + CALL check( nf90_put_var(ncid,q_id, sq%fs(:,4))) + CALL check( nf90_put_var(ncid,di_id, locstab%fs(:,1)/sq%xs(:))) + CALL check( nf90_put_var(ncid,dr_id, locstab%fs(:,2)/sq%xs(:))) + CALL check( nf90_put_var(ncid,ca_id, locstab%fs(:,4))) + IF(size_edge > 0)THEN + CALL check( nf90_put_var(ncid,ew_id, RESHAPE((/REAL(dw_edge), + $ AIMAG(dw_edge)/),(/size_edge,2/))) ) + CALL check( nf90_put_var(ncid,eq_id, q_edge)) + ENDIF + + IF(debug_flag) PRINT *," - Putting matrix variables in netcdf" + CALL check( nf90_put_var(ncid,wp_id,RESHAPE((/REAL(wp), + $ AIMAG(wp)/),(/mpert,mpert,2/))) ) + CALL check( nf90_put_var(ncid,wpv_id,RESHAPE((/REAL(ep), + $ AIMAG(ep)/),(/mpert,2/))) ) + CALL check( nf90_put_var(ncid,wv_id,RESHAPE((/REAL(wv), + $ AIMAG(wv)/),(/mpert,mpert,2/))) ) + CALL check( nf90_put_var(ncid,wvv_id,RESHAPE((/REAL(ev), + $ AIMAG(ev)/),(/mpert,2/))) ) + CALL check( nf90_put_var(ncid,wt_id,RESHAPE((/REAL(wt), + $ AIMAG(wt)/),(/mpert,mpert,2/))) ) + CALL check( nf90_put_var(ncid,wtv_id,RESHAPE((/REAL(et), + $ AIMAG(et)/),(/mpert,2/))) ) + CALL check( nf90_put_var(ncid,wt0_id,RESHAPE((/REAL(wt0), + $ AIMAG(wt0)/),(/mpert,mpert,2/))) ) + IF(ALLOCATED(sing_detf))THEN + CALL check( nf90_put_var(ncid,pd_id, REAL(sing_detf(1,:))) ) + CALL check( nf90_put_var(ncid,df_id,RESHAPE( + $ (/REAL(sing_detf(2,:)), AIMAG(sing_detf(2,:))/), + $ (/SIZE(sing_detf,2),2/))) ) + ENDIF +c----------------------------------------------------------------------- +c close file +c----------------------------------------------------------------------- + IF(debug_flag) PRINT *," - Closing netcdf file" + CALL check( nf90_close(ncid) ) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE dcon_netcdf_out + + END MODULE dcon_netcdf_mod \ No newline at end of file diff --git a/src/DCON/fortran/debug.f b/src/DCON/fortran/debug.f new file mode 100644 index 000000000..e38ab233c --- /dev/null +++ b/src/DCON/fortran/debug.f @@ -0,0 +1,160 @@ +c----------------------------------------------------------------------- +c file debug2.f. +c prints large us. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. debug_mod. +c 1. debug1. +c 2. debug2. +c 3. debug3. +c----------------------------------------------------------------------- +c subprogram 0. debug_mod. +c module declarations. +c----------------------------------------------------------------------- + MODULE debug_mod + USE local_mod + IMPLICIT NONE + + CONTAINS +c----------------------------------------------------------------------- +c subprogram 1. debug1. +c prints 1d arrays. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE debug1(u,name,unit) + + REAL(r8), DIMENSION(:,0:), INTENT(IN) :: u + CHARACTER(*), INTENT(IN) :: name + INTEGER, INTENT(IN) :: unit + + CHARACTER(80) :: format1,format2 + INTEGER :: nqty,nx,iqty,i +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT('(/3x,"i",',i2,'(6x,i2,4x)/)') + 20 FORMAT('(i4,1p,',i2,'e11.3)') +c----------------------------------------------------------------------- +c define sizes. +c----------------------------------------------------------------------- + nqty=SIZE(u,1) + nx=SIZE(u,2) +c----------------------------------------------------------------------- +c create formats. +c----------------------------------------------------------------------- + WRITE(format1,10)nqty + WRITE(format2,20)nqty +c----------------------------------------------------------------------- +c write array. +c----------------------------------------------------------------------- + WRITE(unit,'(a)')TRIM(name)//":" + WRITE(unit,format1)(iqty,iqty=1,nqty) + DO i=0,nx-1 + WRITE(unit,format2)i,u(:,i) + ENDDO + WRITE(unit,format1)(iqty,iqty=1,nqty) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE debug1 +c----------------------------------------------------------------------- +c subprogram 2. debug2. +c prints 2d arrays. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE debug2(u,name,unit) + + REAL(r8), DIMENSION(:,0:,0:), INTENT(IN) :: u + CHARACTER(*), INTENT(IN) :: name + INTEGER, INTENT(IN) :: unit + + CHARACTER(80) :: format1,format2 + INTEGER :: nqty,nx,ny,iqty,ix,iy +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT('(/2x,"iy",2x,"ix",',i2,'(5x,i2,4x)/)') + 20 FORMAT('(2i4,1p,',i2,'e11.3)') +c----------------------------------------------------------------------- +c define sizes. +c----------------------------------------------------------------------- + nqty=SIZE(u,1) + nx=SIZE(u,2) + ny=SIZE(u,3) +c----------------------------------------------------------------------- +c create formats. +c----------------------------------------------------------------------- + WRITE(format1,10)nqty + WRITE(format2,20)nqty +c----------------------------------------------------------------------- +c write array. +c----------------------------------------------------------------------- + WRITE(unit,'(a)')TRIM(name)//":" + WRITE(unit,format1)(iqty,iqty=1,nqty) + DO iy=0,ny-1 + DO ix=0,nx-1 + WRITE(unit,format2)iy,ix,u(:,ix,iy) + ENDDO + WRITE(unit,format1)(iqty,iqty=1,nqty) + ENDDO +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE debug2 +c----------------------------------------------------------------------- +c subprogram 3. debug3. +c prints 2d arrays. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE debug3(u,name,unit) + + REAL(r8), DIMENSION(:,:,0:,0:), INTENT(IN) :: u + CHARACTER(*), INTENT(IN) :: name + INTEGER, INTENT(IN) :: unit + + CHARACTER(80) :: format1,format2 + INTEGER :: nqty1,nqty2,nx,ny,iqty,jqty,ix,iy +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT('(/2y,"iy",2x,"ix",',i3,'(5x,i2,",",i2,3x)/)') + 20 FORMAT('(2i4,1p,',i3,'e11.3)') +c----------------------------------------------------------------------- +c define sizes. +c----------------------------------------------------------------------- + nqty1=SIZE(u,1) + nqty2=SIZE(u,2) + nx=SIZE(u,3) + ny=SIZE(u,4) +c----------------------------------------------------------------------- +c create formats. +c----------------------------------------------------------------------- + WRITE(format1,10)nqty1*nqty2 + WRITE(format2,20)nqty1*nqty2 +c----------------------------------------------------------------------- +c write array. +c----------------------------------------------------------------------- + WRITE(unit,'(a)')TRIM(name)//":" + WRITE(unit,format1)((iqty,jqty,iqty=1,nqty1),jqty=1,nqty2) + DO iy=0,ny-1 + DO ix=0,nx-1 + WRITE(unit,format2)iy,ix,u(:,:,ix,iy) + ENDDO + WRITE(unit,format1)((iqty,jqty,iqty=1,nqty1),jqty=1,nqty2) + ENDDO +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE debug3 + END MODULE debug_mod diff --git a/src/DCON/fortran/diagnostic b/src/DCON/fortran/diagnostic new file mode 100644 index 000000000..6bc52d72f --- /dev/null +++ b/src/DCON/fortran/diagnostic @@ -0,0 +1,8 @@ +sunfire02:~/dcon/dcon% dcon + +lib-4324 : UNRECOVERABLE library error +' is unrecognized in namelist input. + +Encountered during a namelist READ from unit 1 +Fortran unit 1 is connected to a sequential formatted text file: "dcon.in" +Abort (core dumped) diff --git a/src/DCON/fortran/fourfit.F b/src/DCON/fortran/fourfit.F new file mode 100644 index 000000000..11b4ea1c7 --- /dev/null +++ b/src/DCON/fortran/fourfit.F @@ -0,0 +1,1611 @@ +c----------------------------------------------------------------------- +c file fourfit.f +c fits equilibrium quantities to Fourier series, evaluates matrices. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. fourfit_mod. +c 1. fourfit_make_metric. +c 2. fourfit_make_matrix. +c 3. fourfit_action_matrix. +c 4. fourfit_write_metric. +c 5. fourfit_write_matrix. +c 6. fourfit_evals. +c 7. fourfit_diagnose_1. +c 8. fourfit_kinetic_matrix. +c----------------------------------------------------------------------- +c subprogram 0. fourfit_mod. +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + MODULE fourfit_mod + USE fspline_mod + USE dcon_mod + USE pentrc_interface, ! rename overlapping names + $ pentrc_verbose=>verbose, ! should get a more fundamental fix + $ pentrc_mpert=>mpert, + $ pentrc_nn=>nn, + $ pentrc_r8=>r8, + $ pentrc_timer=>timer + USE utilities, only : progressbar + USE torque, only : kelmm ! cspline Euler-Lagrange mats for local use + USE inputs, only : dbob_m,divx_m,kin,xs_m,fnml + USE energy_integration + USE pitch_integration + USE dcon_interface, only: geom, + $ dcon_int_rzphi=>rzphi, + $ dcon_int_eqfun=>eqfun, + $ dcon_int_sq=>sq, + $ dcon_int_smats=>smats, + $ dcon_int_tmats=>tmats, + $ dcon_int_xmats=>xmats, + $ dcon_int_ymats=>ymats, + $ dcon_int_zmats=>zmats + IMPLICIT NONE + + TYPE(fspline_type), PRIVATE :: metric,fmodb + TYPE(cspline_type) :: dmats,emats,hmats,dbats,ebats,fbats, + $ fmats,kmats,gmats,kaats,gaats, + $ f0mats,pmats,paats,kkmats,kkaats,r1mats,r2mats,r3mats, + $ akmats,bkmats,ckmats + TYPE(spline_type) :: k0s + INTEGER, DIMENSION(:), POINTER :: ipiva + COMPLEX(r8), DIMENSION(:,:), POINTER :: asmat,bsmat,csmat + COMPLEX(r8), DIMENSION(:), POINTER :: jmat + + INTEGER :: parallel_threads = 0, dcon_kin_threads = 0 + + ! kientic ABCDEH mats for sing_mod + TYPE(cspline_type) :: kwmats(6),ktmats(6) + + CONTAINS +c----------------------------------------------------------------------- +c subprogram 1. fourfit_make_metric. +c computes fourier series of metric tensor components. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE fourfit_make_metric + + INTEGER :: ipsi,itheta + REAL(r8) :: theta,rfac,eta,r,jac,jac1,psifac,p1,q, + $ g12,g22,g13,g23,g33,b2h,b2hp,b2ht,chi1 + REAL(r8), DIMENSION(3,3) :: v +c----------------------------------------------------------------------- +c set up Fourier-spline type. +c----------------------------------------------------------------------- + CALL fspline_alloc(metric,mpsi,mtheta,mband,8) + metric%xs=rzphi%xs + metric%ys=rzphi%ys*twopi + metric%name="metric" + metric%xtitle=" psi " + metric%ytitle="theta " + metric%title=(/" g11 "," g22 "," g33 "," g23 "," g31 ", + $ " g12 "," jmat ","jmat1 "/) +c----------------------------------------------------------------------- +c set up kinetic Fourier-spline type. +c----------------------------------------------------------------------- + CALL fspline_alloc(fmodb,mpsi,mtheta,mband,8) + fmodb%xs=rzphi%xs + fmodb%ys=rzphi%ys*twopi + fmodb%name="fmodb" + fmodb%xtitle=" psi " + fmodb%ytitle="theta " + fmodb%title=(/" smat "," tmat "," xmat ", + $ " ymat1 "," ymat2 "," zmat1 ", " zmat2 "," zmat3 "/) +c----------------------------------------------------------------------- +c begin loop over nodes. +c----------------------------------------------------------------------- + chi1=twopi*psio + DO ipsi=0,mpsi + psifac=sq%xs(ipsi) + p1=sq%fs1(ipsi,2) + q=sq%fs(ipsi,4) + DO itheta=0,mtheta + CALL bicube_eval(rzphi,rzphi%xs(ipsi),rzphi%ys(itheta),1) + CALL bicube_eval(eqfun,rzphi%xs(ipsi),rzphi%ys(itheta),1) + theta=rzphi%ys(itheta) + rfac=SQRT(rzphi%f(1)) + eta=twopi*(theta+rzphi%f(2)) + r=ro+rfac*COS(eta) + jac=rzphi%f(4) + jac1=rzphi%fx(4) + b2h=eqfun%f(1)**2/2 + b2hp=eqfun%f(1)*eqfun%fx(1) + b2ht=eqfun%f(1)*eqfun%fy(1) +c----------------------------------------------------------------------- +c compute contravariant basis vectors. +c----------------------------------------------------------------------- + v(1,1)=rzphi%fx(1)/(2*rfac*jac) + v(1,2)=rzphi%fx(2)*twopi*rfac/jac + v(1,3)=rzphi%fx(3)*r/jac + v(2,1)=rzphi%fy(1)/(2*rfac*jac) + v(2,2)=(1+rzphi%fy(2))*twopi*rfac/jac + v(2,3)=rzphi%fy(3)*r/jac + v(3,3)=twopi*r/jac + g12=SUM(v(1,:)*v(2,:))*jac**2 + g13=v(3,3)*v(1,3)*jac**2 + g22=SUM(v(2,:)**2)*jac**2 + g23=v(2,3)*v(3,3)*jac**2 + g33=v(3,3)*v(3,3)*jac**2 +c----------------------------------------------------------------------- +c compute metric tensor components. +c----------------------------------------------------------------------- + metric%fs(ipsi,itheta,1)=SUM(v(1,:)**2)*jac + metric%fs(ipsi,itheta,2)=SUM(v(2,:)**2)*jac + metric%fs(ipsi,itheta,3)=v(3,3)*v(3,3)*jac + metric%fs(ipsi,itheta,4)=v(2,3)*v(3,3)*jac + metric%fs(ipsi,itheta,5)=v(3,3)*v(1,3)*jac + metric%fs(ipsi,itheta,6)=SUM(v(1,:)*v(2,:))*jac + metric%fs(ipsi,itheta,7)=jac + metric%fs(ipsi,itheta,8)=jac1 +c----------------------------------------------------------------------- +c compute kinetic metric tensor components. +c----------------------------------------------------------------------- + fmodb%fs(ipsi,itheta,1)=jac*(p1+b2hp) + $ -chi1**2*b2ht*(g12+q*g13)/(jac*b2h*2) + fmodb%fs(ipsi,itheta,2)= + $ chi1**2*b2ht*(g23+q*g33)/(jac*b2h*2) + fmodb%fs(ipsi,itheta,3)=jac*b2h*2 + fmodb%fs(ipsi,itheta,4)=jac1*b2h*2-chi1**2*b2h*2*eqfun%fy(2) + fmodb%fs(ipsi,itheta,5)=-twopi*chi1**2/jac*(g12+q*g13) + fmodb%fs(ipsi,itheta,6)=chi1**2*b2h*2*eqfun%fy(3) + fmodb%fs(ipsi,itheta,7)=twopi*chi1**2/jac*(g23+q*g33) + fmodb%fs(ipsi,itheta,8)=twopi*chi1**2/jac*(g22+q*g23) + ENDDO + ENDDO +c----------------------------------------------------------------------- +c fit Fourier-spline type. +c----------------------------------------------------------------------- + IF(fft_flag)THEN + CALL fspline_fit_2(metric,"extrap",.FALSE.) + CALL fspline_fit_2(fmodb,"extrap",.FALSE.) + ELSE + CALL fspline_fit_1(metric,"extrap",.FALSE.) + CALL fspline_fit_1(fmodb,"extrap",.FALSE.) + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE fourfit_make_metric +c----------------------------------------------------------------------- +c subprogram 2. fourfit_make_matrix. +c constructs the coefficient matrices and fits them to cubic splines. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE fourfit_make_matrix(op_diagnose) + + LOGICAL, OPTIONAL, INTENT(IN) :: op_diagnose + + CHARACTER(128) :: message + INTEGER :: ipsi,ipert,jpert,m1,m2,m,dm,info,iqty,l,i,j,iindex + REAL(r8) :: chi1,jtheta,nq,p1,psifac,q,q1,singfac1,singfac2,ileft + COMPLEX(r8) :: tphi + + INTEGER, DIMENSION(mpert) :: mfac,ipiv + + COMPLEX(r8), DIMENSION(mpert*mpert) :: work + COMPLEX(r8), DIMENSION(mband+1,mpert) :: fmatb + COMPLEX(r8), DIMENSION(2*mband+1,mpert) :: kmatb + COMPLEX(r8), DIMENSION(-mband:mband) :: + $ g11,g22,g33,g23,g31,g12,jmat1,imat + COMPLEX(r8), DIMENSION(mpert,mpert) :: amat,bmat,cmat,dmat,emat, + $ fmat,gmat,hmat,kmat,temp0,temp1,temp2,dbat,ebat,fbat + COMPLEX(r8), DIMENSION(3*mband+1,mpert) :: amatlu,fmatlu + + LOGICAL :: diagnose=.FALSE. + INTEGER, PARAMETER :: unit=99 + + mfac =(/(m,m=mlow,mhigh)/) + IF(PRESENT(op_diagnose)) diagnose = op_diagnose +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(/5x,"i",5x,"j",4x,"re fb",6x,"im fb"/) + 20 FORMAT(2i6,1p,2e11.3) +c----------------------------------------------------------------------- +c set up complex cubic splines for matrices. +c----------------------------------------------------------------------- + IF(diagnose)CALL bin_open(unit,"coefs.bin","UNKNOWN","REWIND", + $ "none") + ALLOCATE(asmat(mpert,mpert),bsmat(mpert,mpert),csmat(mpert,mpert), + $ jmat(-mband:mband),ipiva(mpert)) + CALL cspline_alloc(fmats,mpsi,(mband+1)*(2*mpert-mband)/2) + CALL cspline_alloc(gmats,mpsi,(mband+1)*(2*mpert-mband)/2) + CALL cspline_alloc(kmats,mpsi,(2*mband+1)*mpert) + fmats%xs=rzphi%xs + gmats%xs=rzphi%xs + kmats%xs=rzphi%xs + fmats%fs=0 + gmats%fs=0 + kmats%fs=0 + imat=0 + imat(0)=1 +c----------------------------------------------------------------------- +c set up cubic splines for interpolation to psilim. +c----------------------------------------------------------------------- + CALL cspline_alloc(amats,mpsi,mpert**2) + CALL cspline_alloc(bmats,mpsi,mpert**2) + CALL cspline_alloc(cmats,mpsi,mpert**2) + CALL cspline_alloc(dmats,mpsi,mpert**2) + CALL cspline_alloc(emats,mpsi,mpert**2) + CALL cspline_alloc(hmats,mpsi,mpert**2) + CALL cspline_alloc(dbats,mpsi,mpert**2) + CALL cspline_alloc(ebats,mpsi,mpert**2) + CALL cspline_alloc(fbats,mpsi,mpert**2) + + amats%xs=rzphi%xs + bmats%xs=rzphi%xs + cmats%xs=rzphi%xs + dmats%xs=rzphi%xs + emats%xs=rzphi%xs + hmats%xs=rzphi%xs + dbats%xs=rzphi%xs + ebats%xs=rzphi%xs + fbats%xs=rzphi%xs + + amats%fs=0 + bmats%fs=0 + cmats%fs=0 + dmats%fs=0 + emats%fs=0 + hmats%fs=0 + dbats%fs=0 + ebats%fs=0 + fbats%fs=0 +c----------------------------------------------------------------------- +c define flux surface quantities. +c----------------------------------------------------------------------- + DO ipsi=0,mpsi + psifac=sq%xs(ipsi) + p1=sq%fs1(ipsi,2) + q=sq%fs(ipsi,4) + q1=sq%fs1(ipsi,4) + chi1=twopi*psio + nq=nn*q + jtheta=-sq%fs1(ipsi,1) +c----------------------------------------------------------------------- +c compute lower half of matrices. +c----------------------------------------------------------------------- + g11(0:-mband:-1)=metric%cs%fs(ipsi,1:mband+1) + g22(0:-mband:-1)=metric%cs%fs(ipsi,mband+2:2*mband+2) + g33(0:-mband:-1)=metric%cs%fs(ipsi,2*mband+3:3*mband+3) + g23(0:-mband:-1)=metric%cs%fs(ipsi,3*mband+4:4*mband+4) + g31(0:-mband:-1)=metric%cs%fs(ipsi,4*mband+5:5*mband+5) + g12(0:-mband:-1)=metric%cs%fs(ipsi,5*mband+6:6*mband+6) + jmat(0:-mband:-1)=metric%cs%fs(ipsi,6*mband+7:7*mband+7) + jmat1(0:-mband:-1)=metric%cs%fs(ipsi,7*mband+8:8*mband+8) +c----------------------------------------------------------------------- +c compute upper half of matrices. +c----------------------------------------------------------------------- + g11(1:mband)=CONJG(g11(-1:-mband:-1)) + g22(1:mband)=CONJG(g22(-1:-mband:-1)) + g33(1:mband)=CONJG(g33(-1:-mband:-1)) + g23(1:mband)=CONJG(g23(-1:-mband:-1)) + g31(1:mband)=CONJG(g31(-1:-mband:-1)) + g12(1:mband)=CONJG(g12(-1:-mband:-1)) + jmat(1:mband)=CONJG(jmat(-1:-mband:-1)) + jmat1(1:mband)=CONJG(jmat1(-1:-mband:-1)) +c----------------------------------------------------------------------- +c begin loops over perturbed fourier components. +c----------------------------------------------------------------------- + ipert=0 + DO m1=mlow,mhigh + ipert=ipert+1 + singfac1=m1-nq + DO dm=MAX(1-ipert,-mband),MIN(mpert-ipert,mband) + m2=m1+dm + singfac2=m2-nq + jpert=ipert+dm +c----------------------------------------------------------------------- +c construct primitive matrices. +c----------------------------------------------------------------------- + amat(ipert,jpert)=twopi**2*(nn*nn*g22(dm) + $ +nn*(m1+m2)*g23(dm)+m1*m2*g33(dm)) + bmat(ipert,jpert)=-twopi*ifac*chi1 + $ *(nn*g22(dm)+(m1+nq)*g23(dm)+m1*q*g33(dm)) + cmat(ipert,jpert)=twopi*ifac*( + $ twopi*ifac*chi1*singfac2*(nn*g12(dm)+m1*g31(dm)) + $ -q1*chi1*(nn*g23(dm)+m1*g33(dm))) + $ -twopi*ifac*(jtheta*singfac1*imat(dm) + $ +nn*p1/chi1*jmat(dm)) + dmat(ipert,jpert)=twopi*chi1*(g23(dm)+g33(dm)*m1/nn) + emat(ipert,jpert)=-chi1/nn*(q1*chi1*g33(dm) + $ -twopi*ifac*chi1*g31(dm)*singfac2 + $ +jtheta*imat(dm)) + hmat(ipert,jpert)=(q1*chi1)**2*g33(dm) + $ +(twopi*chi1)**2*singfac1*singfac2*g11(dm) + $ -twopi*ifac*chi1*dm*q1*chi1*g31(dm) + $ +jtheta*q1*chi1*imat(dm)+p1*jmat1(dm) + fmat(ipert,jpert)=(chi1/nn)**2*g33(dm) + kmat(ipert,jpert)=twopi*ifac*chi1*(g23(dm)+g33(dm)*m1/nn) + ENDDO + ENDDO + dbat=dmat + ebat=emat + fbat=fmat +c----------------------------------------------------------------------- +c factor A. +c----------------------------------------------------------------------- + temp0=amat + CALL zhetrf('L',mpert,amat,mpert,ipiv,work,mpert*mpert,info) + IF(info /= 0)THEN + WRITE(message,'(2(a,i2))') + $ "zhetrf: amat singular at ipsi = ",ipsi, + $ ", ipert = ",info,", increase delta_mband" + CALL program_stop(message) + ENDIF +c----------------------------------------------------------------------- +c compute composite matrices F, G, and K. +c----------------------------------------------------------------------- + temp1=dmat + temp2=cmat + CALL zhetrs('L',mpert,mpert,amat,mpert,ipiv,temp1,mpert,info) + CALL zhetrs('L',mpert,mpert,amat,mpert,ipiv,temp2,mpert,info) + fmat=fmat-MATMUL(CONJG(TRANSPOSE(dmat)),temp1) + kmat=emat-MATMUL(CONJG(TRANSPOSE(kmat)),temp2) + gmat=hmat-MATMUL(CONJG(TRANSPOSE(cmat)),temp2) + amat=temp0 +c----------------------------------------------------------------------- +c kinetic matrices. +c----------------------------------------------------------------------- + ipert=0 + DO m1=mlow,mhigh + ipert=ipert+1 + singfac1=m1-nq + DO dm=MAX(1-ipert,-mband),MIN(mpert-ipert,mband) + m2=m1+dm + singfac2=m2-nq + jpert=ipert+dm + dmat(ipert,jpert)=chi1**2*(g22(dm)+q*g23(dm)+ + $ q*(g23(dm)+q*g33(dm))) + emat(ipert,jpert)=chi1**2*(q1*(g23(dm)+q*g33(dm))- + $ twopi*ifac*(g12(dm)+q*g31(dm))*singfac2)+ + $ p1*jmat(dm) + ENDDO + ENDDO +c----------------------------------------------------------------------- +c store matrices for interpolation. +c----------------------------------------------------------------------- + amats%fs(ipsi,:)=RESHAPE(amat,(/mpert**2/)) + bmats%fs(ipsi,:)=RESHAPE(bmat,(/mpert**2/)) + cmats%fs(ipsi,:)=RESHAPE(cmat,(/mpert**2/)) + dmats%fs(ipsi,:)=RESHAPE(dmat,(/mpert**2/)) + emats%fs(ipsi,:)=RESHAPE(emat,(/mpert**2/)) + hmats%fs(ipsi,:)=RESHAPE(hmat,(/mpert**2/)) + dbats%fs(ipsi,:)=RESHAPE(dbat,(/mpert**2/)) + ebats%fs(ipsi,:)=RESHAPE(ebat,(/mpert**2/)) + fbats%fs(ipsi,:)=RESHAPE(fbat,(/mpert**2/)) +c----------------------------------------------------------------------- +c diagnose. +c----------------------------------------------------------------------- + IF(feval_flag)CALL fourfit_evals(ipsi,psifac,fmat) + IF(diagnose)WRITE(unit)REAL(psifac,4), + $ REAL(fmat(1,1),4),REAL(kmat(1,1),4), + $ REAL(gmat(1,1)*psifac,4),REAL(g11(0)*psifac,4), + $ REAL(g22(0),4),REAL(g33(0),4) +c----------------------------------------------------------------------- +c transfer F to banded matrix. +c----------------------------------------------------------------------- + DO jpert=1,mpert + DO ipert=jpert,MIN(mpert,jpert+mband) + fmatb(1+ipert-jpert,jpert)=fmat(ipert,jpert) + ENDDO + ENDDO +c----------------------------------------------------------------------- +c factor F. +c----------------------------------------------------------------------- + CALL zpbtrf('L',mpert,mband,fmatb,mband+1,info) + IF(info /= 0)THEN + WRITE(message,'(2(a,i3),a)') + $ "zpbtrf: fmat singular at ipsi = ",ipsi, + $ ", ipert = ",info,", reduce delta_mband" + CALL program_stop(message) + ENDIF +c----------------------------------------------------------------------- +c store Hermitian matrices F and G. +c----------------------------------------------------------------------- + iqty=1 + DO jpert=1,mpert + DO ipert=jpert,MIN(mpert,jpert+mband) + fmats%fs(ipsi,iqty)=fmatb(1+ipert-jpert,jpert) + gmats%fs(ipsi,iqty)=gmat(ipert,jpert) + iqty=iqty+1 + ENDDO + ENDDO +c----------------------------------------------------------------------- +c store non-Hermitian matrix K. +c----------------------------------------------------------------------- + iqty=1 + DO jpert=1,mpert + DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband) + kmats%fs(ipsi,iqty)=kmat(ipert,jpert) + iqty=iqty+1 + ENDDO + ENDDO + ENDDO +c----------------------------------------------------------------------- +c close diagnostic file. +c----------------------------------------------------------------------- + IF(diagnose)THEN + WRITE(unit) + CALL bin_close(unit) + ENDIF +c----------------------------------------------------------------------- +c set powers. +c----------------------------------------------------------------------- + gmats%xpower(1,:)=-1 + IF(power_flag)THEN + IF (kin_flag)THEN + hmats%x0(2)=1.0 + hmats%xpower(1,:)=-1 + hmats%xpower(2,:)=-1 + gmats%x0(2)=1.0 + gmats%xpower(2,:)=-1 + ENDIF + m=mlow + iqty=1 + DO jpert=1,mpert + DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband) + dm=ipert-jpert + IF(m == 1 .AND. dm == -1 .OR. m == -1 .AND. dm == 1) + $ kmats%xpower(1,iqty)=-1 + iqty=iqty+1 + ENDDO + m=m+1 + ENDDO + ENDIF +c----------------------------------------------------------------------- +c cubic spline fit banded matrices. +c----------------------------------------------------------------------- + CALL cspline_fit(amats,"extrap") + CALL cspline_fit(bmats,"extrap") + CALL cspline_fit(cmats,"extrap") + CALL cspline_fit(dmats,"extrap") + CALL cspline_fit(emats,"extrap") + CALL cspline_fit(hmats,"extrap") + CALL cspline_fit(fmats,"extrap") + CALL cspline_fit(kmats,"extrap") + CALL cspline_fit(gmats,"extrap") + CALL cspline_fit(dbats,"extrap") + CALL cspline_fit(ebats,"extrap") + CALL cspline_fit(fbats,"extrap") + +c----------------------------------------------------------------------- +c write binary output for diagnosis. +c----------------------------------------------------------------------- + IF(diagnose)THEN + WRITE(*,*)"Write binary output for graphs." + mfac =(/(i,i=mlow,mhigh)/) + CALL ascii_open(fourfit_out_unit,"imats.out","UNKNOWN") + WRITE(fourfit_out_unit,*)"DCON ideal energy matrices" + WRITE(fourfit_out_unit,'(1/,1x,a12,1x,I6,1x,1(a12,I4),1/)') + $ "mpsi =",mpsi,"mpert =",mpert + WRITE(fourfit_out_unit,'(1x,a16,2(1x,a4),12(1x,a16))') + $ "psi","m1","m2", + $ "real(Ai)","imag(Ai)","real(Bi)","imag(Bi)", + $ "real(Ci)","imag(Ci)","real(Di)","imag(Di)", + $ "real(Ei)","imag(Ei)","real(Hi)","imag(Hi)" + DO ipsi=0,mpsi + DO i=1,mpert + DO j=1,mpert + ipert = (i-1)*mpert + j + WRITE(fourfit_out_unit,'(1x,es16.8,2(1x,I4),'// + $ '12(1x,es16.8))') + $ REAL(amats%xs(ipsi),4),mfac(i),mfac(j), + $ REAL(REAL(amats%fs(ipsi,ipert)),4), + $ REAL(AIMAG(amats%fs(ipsi,ipert)),4), + $ REAL(REAL(bmats%fs(ipsi,ipert)),4), + $ REAL(AIMAG(bmats%fs(ipsi,ipert)),4), + $ REAL(REAL(cmats%fs(ipsi,ipert)),4), + $ REAL(AIMAG(cmats%fs(ipsi,ipert)),4), + $ REAL(REAL(dmats%fs(ipsi,ipert)),4), + $ REAL(AIMAG(dmats%fs(ipsi,ipert)),4), + $ REAL(REAL(emats%fs(ipsi,ipert)),4), + $ REAL(AIMAG(emats%fs(ipsi,ipert)),4), + $ REAL(REAL(hmats%fs(ipsi,ipert)),4), + $ REAL(AIMAG(hmats%fs(ipsi,ipert)),4) + ENDDO + ENDDO + ENDDO + WRITE(fourfit_out_unit,*) + CALL ascii_close(fourfit_out_unit) + + WRITE(*,*)"Write binary output for graphs." + CALL bin_open(bin_unit,"fs.bin","UNKNOWN","REWIND","none") + DO ipert=1,(mband+1)*(2*mpert-mband)/2 + DO ipsi=0,mpsi + WRITE(bin_unit)REAL(sq%xs(ipsi),4), + $ REAL(sq%fs(ipsi,4),4), + $ REAL(REAL(fmats%fs(ipsi,ipert)),4), + $ REAL(AIMAG(fmats%fs(ipsi,ipert)),4) + ENDDO + WRITE(bin_unit) + ENDDO + CALL bin_close(bin_unit) + CALL bin_open(bin_unit,"ks.bin","UNKNOWN","REWIND","none") + DO ipert=1,(2*mband+1)*mpert + DO ipsi=0,mpsi + WRITE(bin_unit)REAL(sq%xs(ipsi),4), + $ REAL(sq%fs(ipsi,4),4), + $ REAL(REAL(kmats%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kmats%fs(ipsi,ipert)),4) + ENDDO + WRITE(bin_unit) + ENDDO + CALL bin_close(bin_unit) + CALL bin_open(bin_unit,"gs.bin","UNKNOWN","REWIND","none") + DO ipert=1,(mband+1)*(2*mpert-mband)/2 + DO ipsi=0,mpsi + WRITE(bin_unit)REAL(sq%xs(ipsi),4), + $ REAL(sq%fs(ipsi,4),4), + $ REAL(REAL(gmats%fs(ipsi,ipert)),4), + $ REAL(AIMAG(gmats%fs(ipsi,ipert)),4) + ENDDO + WRITE(bin_unit) + ENDDO + CALL bin_close(bin_unit) + ENDIF +c----------------------------------------------------------------------- +c interpolate matrices to psilim (need modification for valen3d). +c----------------------------------------------------------------------- + IF(sas_flag)THEN + CALL cspline_eval(amats,psilim,0) + CALL cspline_eval(bmats,psilim,0) + CALL cspline_eval(cmats,psilim,0) + asmat=RESHAPE(amats%f,(/mpert,mpert/)) + bsmat=RESHAPE(bmats%f,(/mpert,mpert/)) + csmat=RESHAPE(cmats%f,(/mpert,mpert/)) + CALL zhetrf('L',mpert,asmat,mpert,ipiva,work,mpert*mpert,info) + ENDIF +c----------------------------------------------------------------------- +c diagnose and deallocate. +c----------------------------------------------------------------------- + IF(bin_metric)CALL fourfit_write_metric + IF(bin_fmat)CALL fourfit_write_matrix(fmats,"fmat",.TRUE.) + IF(bin_gmat)CALL fourfit_write_matrix(gmats,"gmat",.TRUE.) + IF(bin_kmat)CALL fourfit_write_matrix(kmats,"kmat",.FALSE.) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE fourfit_make_matrix +c----------------------------------------------------------------------- +c subprogram 3. fourfit_action_matrix. +c equilibrium matrices necessary to calc perturbed mod b. +c----------------------------------------------------------------------- + SUBROUTINE fourfit_action_matrix +c----------------------------------------------------------------------- +c declaration. +c----------------------------------------------------------------------- + INTEGER :: ipsi,istep,ipert,jpert,itheta,dm,m1,m2 + REAL(r8) :: q,singfac2 + COMPLEX(r8), DIMENSION(-mband:mband) :: + $ sband,tband,xband,yband1,yband2,zband1,zband2,zband3 + COMPLEX(r8), DIMENSION(mpert,mpert) :: smat,tmat,xmat,ymat,zmat + + WRITE(*,*)"Computing action matrices" +c----------------------------------------------------------------------- +c set up fourier-spline type. +c----------------------------------------------------------------------- + CALL cspline_alloc(smats,mpsi,mpert**2) + CALL cspline_alloc(tmats,mpsi,mpert**2) + CALL cspline_alloc(xmats,mpsi,mpert**2) + CALL cspline_alloc(ymats,mpsi,mpert**2) + CALL cspline_alloc(zmats,mpsi,mpert**2) + + smats%xs=sq%xs + tmats%xs=sq%xs + xmats%xs=sq%xs + ymats%xs=sq%xs + zmats%xs=sq%xs + DO ipsi=0,mpsi + q=sq%fs(ipsi,4) + sband(0:-mband:-1)=fmodb%cs%fs(ipsi,1:mband+1) + tband(0:-mband:-1)=fmodb%cs%fs(ipsi,mband+2:2*mband+2) + xband(0:-mband:-1)=fmodb%cs%fs(ipsi,2*mband+3:3*mband+3) + yband1(0:-mband:-1)=fmodb%cs%fs(ipsi,3*mband+4:4*mband+4) + yband2(0:-mband:-1)=fmodb%cs%fs(ipsi,4*mband+5:5*mband+5) + zband1(0:-mband:-1)=fmodb%cs%fs(ipsi,5*mband+6:6*mband+6) + zband2(0:-mband:-1)=fmodb%cs%fs(ipsi,6*mband+7:7*mband+7) + zband3(0:-mband:-1)=fmodb%cs%fs(ipsi,7*mband+8:8*mband+8) + + sband(1:mband)=CONJG(sband(-1:-mband:-1)) + tband(1:mband)=CONJG(tband(-1:-mband:-1)) + xband(1:mband)=CONJG(xband(-1:-mband:-1)) + yband1(1:mband)=CONJG(yband1(-1:-mband:-1)) + yband2(1:mband)=CONJG(yband2(-1:-mband:-1)) + zband1(1:mband)=CONJG(zband1(-1:-mband:-1)) + zband2(1:mband)=CONJG(zband2(-1:-mband:-1)) + zband3(1:mband)=CONJG(zband3(-1:-mband:-1)) + + ipert=0 + DO m1=mlow,mhigh + ipert=ipert+1 + DO dm=MAX(1-ipert,-mband),MIN(mpert-ipert,mband) + m2=m1+dm + singfac2=m2-nn*q + jpert=ipert+dm + smat(ipert,jpert)=sband(dm) + tmat(ipert,jpert)=tband(dm) + xmat(ipert,jpert)=xband(dm) + ymat(ipert,jpert)=yband1(dm)+ifac*singfac2*yband2(dm) + zmat(ipert,jpert)=zband1(dm)+ + $ ifac*(m2*zband2(dm)+nn*zband3(dm)) + ENDDO + ENDDO + smats%fs(ipsi,:)=RESHAPE(smat,(/mpert**2/)) + tmats%fs(ipsi,:)=RESHAPE(tmat,(/mpert**2/)) + xmats%fs(ipsi,:)=RESHAPE(xmat,(/mpert**2/)) + ymats%fs(ipsi,:)=RESHAPE(ymat,(/mpert**2/)) + zmats%fs(ipsi,:)=RESHAPE(zmat,(/mpert**2/)) + ENDDO + + CALL cspline_fit(smats,"extrap") + CALL cspline_fit(tmats,"extrap") + CALL cspline_fit(xmats,"extrap") + CALL cspline_fit(ymats,"extrap") + CALL cspline_fit(zmats,"extrap") + + CALL fspline_dealloc(metric) + CALL fspline_dealloc(fmodb) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE fourfit_action_matrix +c----------------------------------------------------------------------- +c subprogram 4. fourfit_write_metric. +c uses cspline_write_log to diagnose cspline_types. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE fourfit_write_metric + + REAL(r8), DIMENSION(2) :: xend=(/zero,one/) +c----------------------------------------------------------------------- +c computations. +c----------------------------------------------------------------------- + CALL bin_open(bin_unit,"metric.bin","UNKNOWN","REWIND","none") + CALL cspline_write_log(metric%cs,.FALSE.,.TRUE.,out_unit, + $ bin_unit,.FALSE.,mband+1,xend) + CALL bin_close(fourfit_bin_unit) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE fourfit_write_metric +c----------------------------------------------------------------------- +c subprogram 5. fourfit_write_matrix +c produces ascii and binary output of logs. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE fourfit_write_matrix(matrix,name,sym_flag) + + TYPE(cspline_type) :: matrix + CHARACTER(*), INTENT(IN) :: name + LOGICAL, INTENT(IN) :: sym_flag + + INTEGER :: iqty,ix,jx,j,ipert,jpert,iband,iband0,mband0=8,imin + REAL(r8) :: dx + REAL(r8), DIMENSION(2) :: xend=(/zero,one/) + REAL(r8), DIMENSION(0:4*mpsi) :: x + REAL(r8), DIMENSION(0:4*mpsi,2) :: xlog + + REAL(r8), DIMENSION(:), POINTER :: epsilon + REAL(r8), DIMENSION(:,:,:), POINTER :: flog + COMPLEX(r8), DIMENSION(:,:,:), POINTER :: f +c----------------------------------------------------------------------- +c set limits and allocate arrays. +c----------------------------------------------------------------------- + mband0=MIN(mband0,mband) + IF(sym_flag)THEN + iband0=0 + ELSE + iband0=-mband0 + ENDIF + ALLOCATE(f(0:4*mpsi,mpert,iband0:mband0), + $ flog(0:4*mpsi,mpert,iband0:mband0), + $ epsilon(iband0:mband0)) +c----------------------------------------------------------------------- +c compute values. +c----------------------------------------------------------------------- + f=0 + jx=0 + DO ix=1,mpsi + dx=(matrix%xs(ix)-matrix%xs(ix-1))/4 + DO j=0,4 + IF(j == 4 .AND. ix < mpsi)CYCLE + x(jx)=matrix%xs(ix-1)+j*dx + xlog(jx,:)=LOG10(ABS(x(jx)-xend)) + CALL cspline_eval(matrix,x(jx),0) + iqty=1 + DO jpert=1,mpert + IF(sym_flag)THEN + imin=jpert + ELSE + imin=MAX(1,jpert-mband) + ENDIF + DO ipert=imin,MIN(mpert,jpert+mband) + IF(ipert-jpert <= mband0 + $ .AND. ipert-jpert >= -mband0) + $ f(jx,jpert,ipert-jpert)=matrix%f(iqty) + iqty=iqty+1 + ENDDO + ENDDO + jx=jx+1 + ENDDO + ENDDO +c----------------------------------------------------------------------- +c compute logs. +c----------------------------------------------------------------------- + flog=HUGE(flog) + WHERE(f /= 0) + flog=LOG(f) + ELSEWHERE + flog=HUGE(flog) + ENDWHERE + DO iband=iband0,mband0 + epsilon(iband)=MINVAL(flog(:,:,iband)) + WHERE(f(:,:,iband) == 0) + flog(:,:,iband)=epsilon(iband) + ENDWHERE + ENDDO + flog=flog/alog10 +c----------------------------------------------------------------------- +c open output file. +c----------------------------------------------------------------------- + CALL bin_open(bin_unit,TRIM(name)//".bin","UNKNOWN","REWIND", + $ "none") +c----------------------------------------------------------------------- +c print node values. +c----------------------------------------------------------------------- + DO ipert=1,mpert + DO ix=0,4*mpsi,4 + WRITE(bin_unit)REAL(x(ix),4),REAL(xlog(ix,:),4), + $ REAL(flog(ix,ipert,:),4) + ENDDO + WRITE(bin_unit) + ENDDO +c----------------------------------------------------------------------- +c print interpolated values. +c----------------------------------------------------------------------- + DO ipert=1,mpert + DO ix=0,4*mpsi + WRITE(bin_unit)REAL(x(ix),4),REAL(xlog(ix,:),4), + $ REAL(flog(ix,ipert,:),4) + ENDDO + WRITE(bin_unit) + ENDDO +c----------------------------------------------------------------------- +c close output file and deallocate arrays. +c----------------------------------------------------------------------- + CALL bin_close(bin_unit) + DEALLOCATE(f,flog,epsilon) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE fourfit_write_matrix +c----------------------------------------------------------------------- +c subprogram 6. fourfit_evals +c computes and prints eigenvalues Hermitian matrix. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE fourfit_evals(ipsi,psifac,matrix) + USE global_mod + IMPLICIT NONE + + INTEGER, INTENT(IN) :: ipsi + REAL(r8), INTENT(IN) :: psifac + COMPLEX(r8), DIMENSION(mpert,mpert), INTENT(IN) :: matrix + + INTEGER :: info,lwork + COMPLEX(r8), DIMENSION(mpert,mpert) :: temp + COMPLEX(r8), DIMENSION(2*(mpert+1)*mpert) :: work + REAL(r8), DIMENSION(3*mpert-2) :: rwork + REAL(r8), DIMENSION(mpert) :: evals +c----------------------------------------------------------------------- +c write formats. +c----------------------------------------------------------------------- + 10 FORMAT(/3x,"ipsi",3x,"psifac",5x,"eval1",6x,"eval2"/) + 20 FORMAT(i6,1p,3e11.3) +c----------------------------------------------------------------------- +c open output files. +c----------------------------------------------------------------------- + IF(ipsi == 0)THEN + CALL ascii_open(evals_out_unit,"feval.out","UNKNOWN") + WRITE(evals_out_unit,10) + CALL bin_open(evals_bin_unit,"feval.bin","UNKNOWN","REWIND", + $ "none") + ENDIF +c----------------------------------------------------------------------- +c compute eigenvalues. +c----------------------------------------------------------------------- + lwork=SIZE(work) + temp=matrix + CALL zheev('N','U',mpert,temp,mpert,evals,work,lwork,rwork,info) +c----------------------------------------------------------------------- +c print results. +c----------------------------------------------------------------------- + WRITE(evals_out_unit,20)ipsi,psifac,evals(1:2) + WRITE(evals_bin_unit)REAL(psifac,4),REAL(evals(1:2),4) +c----------------------------------------------------------------------- +c close output files. +c----------------------------------------------------------------------- + IF(ipsi == mpsi)THEN + WRITE(evals_out_unit,10) + CALL ascii_close(evals_out_unit) + CALL bin_close(evals_bin_unit) + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE fourfit_evals +c----------------------------------------------------------------------- +c subprogram 7. fourfit_diagnose_1. +c diagnoses coefficient matrices. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE fourfit_diagnose_1(g11,g22,g33,g23,g31,g12) + + COMPLEX(r8), DIMENSION(-mband:mband), INTENT(IN) :: + $ g11,g22,g33,g23,g31,g12 + + INTEGER :: dm,unit=98 +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(/4x,"dm",5x,"g11",8x,"g22",8x,"g33",8x,"g23",8x,"g31",8x, + $ "g12"/) + 20 FORMAT(i6,1p,8e11.3) +c----------------------------------------------------------------------- +c write binary output. +c----------------------------------------------------------------------- + CALL ascii_open(unit,"metric.out","UNKNOWN") + WRITE(unit,10) + DO dm=0,mband + WRITE(unit,20)dm, + $ REAL(g11(dm),4),REAL(g22(dm),4),REAL(g33(dm),4), + $ REAL(g23(dm),4),REAL(g31(dm),4),REAL(g12(dm),4) + ENDDO + WRITE(unit,10) + CALL ascii_close(unit) + CALL program_stop("Termination by fourfit_diagnose_1") +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE fourfit_diagnose_1 +c----------------------------------------------------------------------- +c subprogram 8. fourfit_kinetic_matrix. +c Use PENTRC to calculated the coefficient matrices on a dynamic +c grid and fit them to cubic splines. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE fourfit_kinetic_matrix(methodin,writein) + IMPLICIT NONE + + LOGICAL, OPTIONAL :: writein + INTEGER, OPTIONAL :: methodin + + LOGICAL :: output + INTEGER :: ipsi,ipert,l,i,j,iindex,method = 0 + CHARACTER(1) :: ft + INTEGER, DIMENSION(mpert) :: mfac + REAL(r8) :: ileft,psifac,chi1,plim(2) + COMPLEX(r8) :: tphi + COMPLEX(r8), DIMENSION(mpert,mpert,6) :: kwmat,kwmat_l, + $ ktmat,ktmat_l + COMPLEX(r8), DIMENSION(:,:,:,:,:), ALLOCATABLE :: kwmatls, ktmatls +c----------------------------------------------------------------------- +c declarations for diagnostics. +c----------------------------------------------------------------------- + INTEGER :: info,iqty,jpert,ix,idone + INTEGER, DIMENSION(mpert) :: ipiv + CHARACTER(128) :: message + COMPLEX(r8), DIMENSION(mpert*mpert) :: work,amats_f,bmats_f, + $ cmats_f,dmats_f,emats_f,hmats_f,dbats_f,ebats_f,fbats_f + COMPLEX(r8), DIMENSION(mpert,mpert) :: amat,bmat,cmat,dmat,emat, + $ fmat,gmat,hmat,kmat,temp0,temp1,temp2,caat,gaat, + $ f0mat,pmat,paat,kkmat,kkaat,r1mat,r2mat,r3mat, + $ dbat,ebat,umat,aamat,bkmat,bkaat,b1mat + COMPLEX(r8), DIMENSION(3*mband+1,mpert) :: amatlu +c----------------------------------------------------------------------- +c declarations for parallelization. +c----------------------------------------------------------------------- + LOGICAL :: debug_omp = .FALSE. + INTEGER :: t_start, t_end, cr, num_threads, ithread + REAL(r8) :: t_sec + INTEGER :: OMP_GET_NUM_THREADS, OMP_GET_THREAD_NUM +c----------------------------------------------------------------------- +c output formats +c----------------------------------------------------------------------- + IF(debug_omp)THEN + PRINT *,"In serial region..." +#ifdef _OPENMP + num_threads = OMP_GET_NUM_THREADS() + PRINT *,"# of OMP threads = ",num_threads +#else + num_threads = 1 + PRINT *,"# NO OPENMP MULTITHREADING" +#endif + ENDIF +c----------------------------------------------------------------------- +c some basic variables +c----------------------------------------------------------------------- + IF(PRESENT(methodin)) method = methodin + output=.FALSE. + IF(PRESENT(writein)) output = writein + chi1=twopi*psio + plim = (/0.0,1.0/) + IF (passing_flag .AND. trapped_flag) THEN + ft="f" + ELSE IF (trapped_flag) THEN + ft="t" + ELSE IF (passing_flag) THEN + ft="p" + ELSE + CALL program_stop("Kinetic calculations require "// + $ "passing_flag and/or trapped_flag") + ENDIF + ALLOCATE(kwmatls(mpert,mpert,6,0:mpsi,-nl:nl), + $ ktmatls(mpert,mpert,6,0:mpsi,-nl:nl)) + kwmatls(:,:,:,:,:)=0 + ktmatls(:,:,:,:,:)=0 +c----------------------------------------------------------------------- +c Original approach using eqgrid loop to calculate kinetic matrices +c----------------------------------------------------------------------- + CALL cspline_alloc(kaats,mpsi,(2*mband+1)*mpert) + CALL cspline_alloc(gaats,mpsi,(2*mband+1)*mpert) + kaats%xs=rzphi%xs + gaats%xs=rzphi%xs + kaats%fs=0 + gaats%fs=0 + + IF(method==-1)THEN + output = .FALSE. + ELSEIF(method==0)THEN + fkg_kmats_flag=.TRUE. + + CALL cspline_alloc(akmats,mpsi,mpert**2) + CALL cspline_alloc(bkmats,mpsi,mpert**2) + CALL cspline_alloc(ckmats,mpsi,mpert**2) + CALL cspline_alloc(f0mats,mpsi,mpert**2) + CALL cspline_alloc(pmats,mpsi,mpert**2) + CALL cspline_alloc(paats,mpsi,mpert**2) + CALL cspline_alloc(kkmats,mpsi,mpert**2) + CALL cspline_alloc(kkaats,mpsi,mpert**2) + CALL cspline_alloc(r1mats,mpsi,mpert**2) + CALL cspline_alloc(r2mats,mpsi,mpert**2) + CALL cspline_alloc(r3mats,mpsi,mpert**2) + + akmats%xs=rzphi%xs + bkmats%xs=rzphi%xs + ckmats%xs=rzphi%xs + f0mats%xs=rzphi%xs + pmats%xs=rzphi%xs + paats%xs=rzphi%xs + kkmats%xs=rzphi%xs + kkaats%xs=rzphi%xs + r1mats%xs=rzphi%xs + r2mats%xs=rzphi%xs + r3mats%xs=rzphi%xs + + akmats%fs=0 + bkmats%fs=0 + ckmats%fs=0 + f0mats%fs=0 + pmats%fs=0 + paats%fs=0 + kkmats%fs=0 + kkaats%fs=0 + r1mats%fs=0 + r2mats%fs=0 + r3mats%fs=0 + + DO i=1,6 + CALL cspline_alloc(kwmats(i),mpsi,mpert**2) + CALL cspline_alloc(ktmats(i),mpsi,mpert**2) + kwmats(i)%xs=rzphi%xs + ktmats(i)%xs=rzphi%xs + ENDDO + +c----------------------------------------------------------------------- +c Parallel calls of expensive kinetic calculations for each psi,ell +c----------------------------------------------------------------------- + idone = 0 + CALL SYSTEM_CLOCK(COUNT_RATE=cr) +!$OMP PARALLEL DO SCHEDULE(DYNAMIC,8) DEFAULT(NONE) COLLAPSE(2) +!$OMP& PROC_BIND(CLOSE) +!$OMP& PRIVATE( +!$OMP& ipsi,ix,psifac,l,num_threads,t_start,t_end,t_sec, +!$OMP& tphi,kwmat_l,ktmat_l,kwmat,ktmat) +!$OMP& SHARED( +!$OMP& rzphi,ion_flag,electron_flag,debug_omp,verbose,cr,idone, +!$OMP& nn,nl,ft,zi,mi,wdfac,divxfac,mpsi,kwmatls,ktmatls, +c!!!!!!... these can be SHARED because all calls use spline_*_external +c!!!!!!... to avoid conflicts +!$OMP& dcon_int_smats,dcon_int_tmats,dcon_int_xmats,dcon_int_ymats, +!$OMP& dcon_int_zmats) + +!$OMP& COPYIN( +c!!!!!!...from inputs.f90... +!$OMP& dbob_m,divx_m,kin,xs_m,fnml, +c!!!!!!...from dcon_interface.f90 +!$OMP& geom, dcon_int_sq,dcon_int_eqfun,dcon_int_rzphi) + + DO ipsi=0,mpsi + DO l=-nl,nl + CALL SYSTEM_CLOCK(COUNT=t_start) +#ifdef _OPENMP + IF(ipsi==0 .AND. l==-nl)THEN + num_threads = OMP_GET_NUM_THREADS() + WRITE(*,'(1x,a,i3,a)') "Running in parallel with ", + $ num_threads," OMP threads" + ENDIF +#endif + psifac=rzphi%xs(ipsi) + IF (ion_flag) THEN + kwmat_l = 0 + ktmat_l = 0 + call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac, + $ .FALSE.,ft//"wmm",op_wmats=kwmat_l) + call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac, + $ .FALSE.,ft//"tmm",op_wmats=ktmat_l) + kwmatls(:,:,:,ipsi,l) = kwmatls(:,:,:,ipsi,l)+kwmat_l + ktmatls(:,:,:,ipsi,l) = ktmatls(:,:,:,ipsi,l)+ktmat_l + ENDIF + IF (electron_flag) THEN + kwmat_l = 0 + ktmat_l = 0 + call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,.TRUE., + $ ft//"wmm",op_wmats=kwmat_l) + call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,.TRUE., + $ ft//"tmm",op_wmats=ktmat_l) + kwmatls(:,:,:,ipsi,l) = kwmatls(:,:,:,ipsi,l)+kwmat_l + ktmatls(:,:,:,ipsi,l) = ktmatls(:,:,:,ipsi,l)+ktmat_l + ENDIF + ! helpful status messages +!$OMP CRITICAL + idone = idone + 1 + IF(verbose) CALL progressbar(idone,1,(mpsi+1)*(2*nl+1), + $ op_percent=10) +!$OMP END CRITICAL + IF(debug_omp)THEN + CALL SYSTEM_CLOCK(COUNT=t_end) + t_sec = REAL(t_end-t_start,r8)/REAL(cr,r8) + WRITE(*,'(1x,a5,i3,a6,es16.8,a8)') + $ "ipsi=",ipsi," took ",t_sec," seconds" + ENDIF + ENDDO + ENDDO +!$OMP END PARALLEL DO + +c----------------------------------------------------------------------- +c Now go back totypical serial psi operations +c----------------------------------------------------------------------- + DO ipsi=0,mpsi + psifac=rzphi%xs(ipsi) + + ! collect all the ell for a given psi from the collapsed parallel calcs + kwmat = 0 + ktmat = 0 + DO l=-nl,nl + kwmat = kwmat + kwmatls(:,:,:,ipsi,l) + ktmat = ktmat + ktmatls(:,:,:,ipsi,l) + ENDDO + + ! apply normalizations and hypertangent smoothing for core + IF (ktanh_flag) THEN + kwmat=kinfac1*kwmat*(1+tanh((psifac-ktc)*ktw)) + ktmat=kinfac2*ktmat*(1+tanh((psifac-ktc)*ktw)) + ELSE + kwmat=kinfac1*kwmat + ktmat=kinfac2*ktmat + ENDIF + ! store to splines + DO i=1,6 + kwmats(i)%fs(ipsi,:)=RESHAPE(kwmat(:,:,i),(/mpert**2/)) + ktmats(i)%fs(ipsi,:)=RESHAPE(ktmat(:,:,i),(/mpert**2/)) + ENDDO +c----------------------------------------------------------------------- +c Pass only essential matrices to splines +c----------------------------------------------------------------------- + ix = ipsi + CALL cspline_eval_external(amats,psifac,ix,amats_f) + CALL cspline_eval_external(bmats,psifac,ix,bmats_f) + CALL cspline_eval_external(cmats,psifac,ix,cmats_f) + CALL cspline_eval_external(dmats,psifac,ix,dmats_f) + CALL cspline_eval_external(emats,psifac,ix,emats_f) + CALL cspline_eval_external(hmats,psifac,ix,hmats_f) + CALL cspline_eval_external(dbats,psifac,ix,dbats_f) + CALL cspline_eval_external(ebats,psifac,ix,ebats_f) + CALL cspline_eval_external(fbats,psifac,ix,fbats_f) + + amat=RESHAPE(amats_f,(/mpert,mpert/)) + bmat=RESHAPE(bmats_f,(/mpert,mpert/)) + cmat=RESHAPE(cmats_f,(/mpert,mpert/)) + dmat=RESHAPE(dmats_f,(/mpert,mpert/)) + emat=RESHAPE(emats_f,(/mpert,mpert/)) + hmat=RESHAPE(hmats_f,(/mpert,mpert/)) + dbat=RESHAPE(dbats_f,(/mpert,mpert/)) + ebat=RESHAPE(ebats_f,(/mpert,mpert/)) + fmat=RESHAPE(fbats_f,(/mpert,mpert/)) + + amat=amat+kwmat(:,:,1)+ktmat(:,:,1) + bmat=bmat+kwmat(:,:,2)+ktmat(:,:,2) + cmat=cmat+kwmat(:,:,3)+ktmat(:,:,3) + dmat=dmat+kwmat(:,:,4)+ktmat(:,:,4) + emat=emat+kwmat(:,:,5)+ktmat(:,:,5) + hmat=hmat+kwmat(:,:,6)+ktmat(:,:,6) + caat=cmat-2*ktmat(:,:,3) + b1mat=ifac*dbat + + ! invert non-hermitian a matrix + amatlu=0 + umat=0 + DO jpert=1,mpert + DO ipert=1,mpert + amatlu(2*mband+1+ipert-jpert,jpert)= + $ amat(ipert,jpert) + IF(ipert==jpert)umat(ipert,jpert)=1 + ENDDO + ENDDO + CALL zgbtrf(mpert,mpert,mband,mband,amatlu,3*mband+1, + $ ipiv,info) + IF(info /= 0)THEN + WRITE(message,'(2(a,i2))') + $ "zgbtrf: amat singular at ipsi = ",ipsi, + $ ", ipert = ",info,", increase delta_mband" + CALL program_stop(message) + ENDIF + + temp1=dbat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp1,mpert,info) + f0mat=fmat-MATMUL(CONJG(TRANSPOSE(dbat)),temp1) + + ! calculate 3 submatrices for kinetic f matrix + temp2=amat + CALL zgbtrs("C",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) ! close to unit matrix. + aamat=CONJG(TRANSPOSE(temp2)) + umat=umat-aamat + + bkmat=kwmat(:,:,2)+ktmat(:,:,2)+ifac*chi1/(twopi*nn)* + $ (kwmat(:,:,1)+ktmat(:,:,1)) + bkaat=kwmat(:,:,2)-ktmat(:,:,2)+ifac*chi1/(twopi*nn)* + $ (kwmat(:,:,1)+ktmat(:,:,1)) + temp2=bkmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + pmat=MATMUL(CONJG(TRANSPOSE(b1mat)),temp2) + + temp2=b1mat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + paat=MATMUL(CONJG(TRANSPOSE(bkaat)),temp2) + $ -ifac*chi1/(twopi*nn)*MATMUL(umat,b1mat) + paat=CONJG(TRANSPOSE(paat)) + + temp1=kwmat(:,:,1)+ktmat(:,:,1) + temp2=bkmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + r1mat=kwmat(:,:,4)+ktmat(:,:,4)- + $ (chi1/(twopi*nn))**2*CONJG(TRANSPOSE(temp1))+ + $ ifac*chi1/(twopi*nn)*CONJG(TRANSPOSE(bkaat))- + $ ifac*chi1/(twopi*nn)*MATMUL(aamat,bkmat)- + $ MATMUL(CONJG(TRANSPOSE(bkaat)),temp2) + + ! calculate 4 submatrices for kinetic k matrix + temp1=cmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp1,mpert,info) + kkmat=ebat-MATMUL(CONJG(TRANSPOSE(b1mat)),temp1) + + temp1=b1mat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp1,mpert,info) + kkaat=CONJG(TRANSPOSE(ebat))- + $ MATMUL(CONJG(TRANSPOSE(caat)),temp1) + + temp1=kwmat(:,:,5)+ktmat(:,:,5)-ifac*chi1/(twopi*nn)* + $ (kwmat(:,:,3)+ktmat(:,:,3)) + temp2=cmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + r2mat=temp1+ifac*chi1/(twopi*nn)*MATMUL(umat,cmat)- + $ MATMUL(CONJG(TRANSPOSE(bkaat)),temp2) + + temp1=kwmat(:,:,5)-ktmat(:,:,5)-ifac*chi1/(twopi*nn)* + $ (kwmat(:,:,3)-ktmat(:,:,3)) + temp2=bkmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + r3mat=CONJG(TRANSPOSE(temp1))- + $ MATMUL(CONJG(TRANSPOSE(caat)),temp2) + + ! calculate kinetic g matrix + temp2=cmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + gaat=hmat-MATMUL(CONJG(TRANSPOSE(caat)),temp2) + + ! pass only essential kinetic matrices + akmats%fs(ipsi,:)=RESHAPE(amat,(/mpert**2/)) + bkmats%fs(ipsi,:)=RESHAPE(bmat,(/mpert**2/)) + ckmats%fs(ipsi,:)=RESHAPE(cmat,(/mpert**2/)) + f0mats%fs(ipsi,:)=RESHAPE(f0mat,(/mpert**2/)) + pmats%fs(ipsi,:)=RESHAPE(pmat,(/mpert**2/)) + paats%fs(ipsi,:)=RESHAPE(paat,(/mpert**2/)) + kkmats%fs(ipsi,:)=RESHAPE(kkmat,(/mpert**2/)) + kkaats%fs(ipsi,:)=RESHAPE(kkaat,(/mpert**2/)) + r1mats%fs(ipsi,:)=RESHAPE(r1mat,(/mpert**2/)) + r2mats%fs(ipsi,:)=RESHAPE(r2mat,(/mpert**2/)) + r3mats%fs(ipsi,:)=RESHAPE(r3mat,(/mpert**2/)) + + ! pass banded g matrix directly + iqty=1 + DO jpert=1,mpert + DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband) + gaats%fs(ipsi,iqty)=gaat(ipert,jpert) + iqty=iqty+1 + ENDDO + ENDDO + ENDDO + DEALLOCATE(kwmatls, ktmatls) ! these are really big, get rid of them asap +c----------------------------------------------------------------------- +c fit splines +c----------------------------------------------------------------------- + DO i=1,6 + CALL cspline_fit(kwmats(i),"extrap") + CALL cspline_fit(ktmats(i),"extrap") + ENDDO + + CALL cspline_fit(akmats,"extrap") + CALL cspline_fit(bkmats,"extrap") + CALL cspline_fit(ckmats,"extrap") + CALL cspline_fit(f0mats,"extrap") + CALL cspline_fit(pmats,"extrap") + CALL cspline_fit(paats,"extrap") + CALL cspline_fit(kkmats,"extrap") + CALL cspline_fit(kkaats,"extrap") + CALL cspline_fit(r1mats,"extrap") + CALL cspline_fit(r2mats,"extrap") + CALL cspline_fit(r3mats,"extrap") +c----------------------------------------------------------------------- +c Use built in PENTRC spline integration options to form matrixes +c----------------------------------------------------------------------- + ELSEIF(method==1)THEN + DO i=1,6 + CALL cspline_alloc(kwmats(i),mpsi,mpert**2) + CALL cspline_alloc(ktmats(i),mpsi,mpert**2) + kwmats(i)%xs=rzphi%xs + ktmats(i)%xs=rzphi%xs + ENDDO + DO ipsi=0,mpsi + iindex = FLOOR(REAL(ipsi+1,r8)/FLOOR((mpsi+1)/10.0))*10 + ileft = REAL(ipsi+1,r8)/FLOOR((mpsi+1)/10.0)*10-iindex + IF ((ipsi /= 0) .AND. (ileft == 0) .AND. verbose) + $ WRITE(*,*)" ...",iindex,"% of kinetic computations" + kwmat = 0 + ktmat = 0 + psifac=rzphi%xs(ipsi) + ! get matrices for all ell at this one psi + IF (ion_flag) THEN + DO l=-nl,nl + kwmat_l = 0 + ktmat_l = 0 + call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac, + $ .FALSE.,ft//"wmm",op_wmats=kwmat_l) + kwmat = kwmat+kwmat_l + call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac, + $ .FALSE.,ft//"tmm",op_wmats=ktmat_l) + ktmat = ktmat+ktmat_l + ENDDO + ENDIF + IF (electron_flag) THEN + DO l=-nl,nl + kwmat_l = 0 + ktmat_l = 0 + call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,.TRUE., + $ ft//"wmm",op_wmats=kwmat_l) + kwmat = kwmat+kwmat_l + call tpsi(tphi,psifac,nn,l,zi,mi,wdfac,divxfac,.TRUE., + $ ft//"tmm",op_wmats=ktmat_l) + ktmat = ktmat+ktmat_l + ENDDO + ENDIF + ! apply normalizations and hypertangent smoothing for core + IF (ktanh_flag) THEN + kwmat=kinfac1*kwmat*(1+tanh((psifac-ktc)*ktw)) + ktmat=kinfac2*ktmat*(1+tanh((psifac-ktc)*ktw)) + ELSE + kwmat=kinfac1*kwmat + ktmat=kinfac2*ktmat + ENDIF + ! store to splines + DO i=1,6 + kwmats(i)%fs(ipsi,:)=RESHAPE(kwmat(:,:,i),(/mpert**2/)) + ktmats(i)%fs(ipsi,:)=RESHAPE(ktmat(:,:,i),(/mpert**2/)) + ENDDO + ENDDO + DO i=1,6 + CALL cspline_fit(kwmats(i),"extrap") + CALL cspline_fit(ktmats(i),"extrap") + ENDDO +c----------------------------------------------------------------------- +c Use built in PENTRC spline integration options to form matrixes +c----------------------------------------------------------------------- + ELSEIF(method==2)THEN + WRITE(*,*) " Kinetic energy calculation using MXM euler "// + $ "lagrange matrix on equilibrium grid" + tphi = tintgrl_grid('equil',plim,nn,nl,zi,mi,wdfac,divxfac, + $ .FALSE.,ft//"wmm") + ! copy and apply factor to splines + DO i=1,6 + CALL cspline_copy(kelmm(i),kwmats(i)) + IF (ktanh_flag) THEN + DO ipsi=0,kwmats(1)%mx + kwmats(i)%fs(ipsi,:) = kinfac1*kwmats(i)%fs(ipsi,:)* + $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw)) + kwmats(i)%fs1(ipsi,:) = kinfac1*kwmats(i)%fs1(ipsi,:)* + $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw)) + ENDDO + ELSE + kwmats(i)%fs = kinfac1*kwmats(i)%fs + kwmats(i)%fs1 = kinfac1*kwmats(i)%fs1 + ENDIF + ENDDO + WRITE(*,*) " Kinetic torque calculation using MXM euler "// + $ "lagrange matrix on equilibrium grid" + tphi = tintgrl_grid('equil',plim,nn,nl,zi,mi,wdfac,divxfac, + $ .FALSE.,ft//"tmm") + ! copy and apply factor to splines + DO i=1,6 + CALL cspline_copy(kelmm(i),ktmats(i)) + IF (ktanh_flag) THEN + DO ipsi=0,kwmats(1)%mx + ktmats(i)%fs(ipsi,:) = kinfac2*ktmats(i)%fs(ipsi,:)* + $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw)) + ktmats(i)%fs1(ipsi,:) = kinfac2*ktmats(i)%fs1(ipsi,:)* + $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw)) + ENDDO + ELSE + ktmats(i)%fs = kinfac2*ktmats(i)%fs + ktmats(i)%fs1 = kinfac2*ktmats(i)%fs1 + ENDIF + ENDDO +c----------------------------------------------------------------------- +c Use built in PENTRC LSODE integration options to form matrixes +c -> Grid determined by T & dW from flat xi spectrum +c----------------------------------------------------------------------- + ELSEIF(method==3)THEN + WRITE(*,*) " Kinetic energy calculation using MXM euler "// + $ "lagrange matrix" + tphi = tintgrl_lsode(plim,nn,nl,zi,mi,wdfac,divxfac,.FALSE., + $ ft//"wmm") + ! copy and apply factor to splines + DO i=1,6 + CALL cspline_copy(kelmm(i),kwmats(i)) + IF (ktanh_flag) THEN + DO ipsi=0,kwmats(1)%mx + kwmats(i)%fs(ipsi,:) = kinfac1*kwmats(i)%fs(ipsi,:)* + $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw)) + kwmats(i)%fs1(ipsi,:) = kinfac1*kwmats(i)%fs1(ipsi,:)* + $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw)) + ENDDO + ELSE + kwmats(i)%fs = kinfac1*kwmats(i)%fs + kwmats(i)%fs1 = kinfac1*kwmats(i)%fs1 + ENDIF + ENDDO + WRITE(*,*) " Kinetic torque calculation using MXM euler "// + $ "lagrange matrix" + tphi = tintgrl_lsode(plim,nn,nl,zi,mi,wdfac,divxfac,.FALSE., + $ ft//"tmm") + ! copy and apply factor to splines + DO i=1,6 + CALL cspline_copy(kelmm(i),ktmats(i)) + IF (ktanh_flag) THEN + DO ipsi=0,kwmats(1)%mx + ktmats(i)%fs(ipsi,:) = kinfac2*ktmats(i)%fs(ipsi,:)* + $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw)) + ktmats(i)%fs1(ipsi,:) = kinfac2*ktmats(i)%fs1(ipsi,:)* + $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw)) + ENDDO + ELSE + ktmats(i)%fs = kinfac2*ktmats(i)%fs + ktmats(i)%fs1 = kinfac2*ktmats(i)%fs1 + ENDIF + ENDDO +c----------------------------------------------------------------------- +c Use built in PENTRC LSODE integration options to form matrixes +c -> Grid determined by norm of EL matrices +c----------------------------------------------------------------------- + ELSEIF(method==4)THEN + WRITE(*,*) " Kinetic MXM euler lagrange energy matrix norm " + $ //"calculation" + tphi = tintgrl_lsode(plim,nn,nl,zi,mi,wdfac,divxfac,.FALSE., + $ ft//"kmm") + ! copy and apply factor to splines + DO i=1,6 + CALL cspline_copy(kelmm(i),kwmats(i)) + IF (ktanh_flag) THEN + DO ipsi=0,kwmats(1)%mx + kwmats(i)%fs(ipsi,:) = kinfac1*kwmats(i)%fs(ipsi,:)* + $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw)) + kwmats(i)%fs1(ipsi,:) = kinfac1*kwmats(i)%fs1(ipsi,:)* + $ (1+tanh((kwmats(i)%xs(ipsi)-ktc)*ktw)) + ENDDO + ELSE + kwmats(i)%fs = kinfac1*kwmats(i)%fs + kwmats(i)%fs1 = kinfac1*kwmats(i)%fs1 + ENDIF + ENDDO + WRITE(*,*) " Kinetic MXM euler lagrange torque matrix norm " + $ //"calculation" + tphi = tintgrl_lsode(plim,nn,nl,zi,mi,wdfac,divxfac,.FALSE., + $ ft//"rmm") + ! copy and apply factor to splines + DO i=1,6 + CALL cspline_copy(kelmm(i),ktmats(i)) + IF (ktanh_flag) THEN + DO ipsi=0,kwmats(1)%mx + ktmats(i)%fs(ipsi,:) = kinfac2*ktmats(i)%fs(ipsi,:)* + $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw)) + ktmats(i)%fs1(ipsi,:) = kinfac2*ktmats(i)%fs1(ipsi,:)* + $ (1+tanh((ktmats(i)%xs(ipsi)-ktc)*ktw)) + ENDDO + ELSE + ktmats(i)%fs = kinfac2*ktmats(i)%fs + ktmats(i)%fs1 = kinfac2*ktmats(i)%fs1 + ENDIF + ENDDO + ELSE + CALL program_stop("ERROR: Valid kingridtypes are 0,1,2,3,4") + ENDIF + gaats%x0(2)=1.0 + gaats%xpower(1,:)=-1 + gaats%xpower(2,:)=-1 + CALL cspline_fit(kaats,"extrap") + CALL cspline_fit(gaats,"extrap") +c----------------------------------------------------------------------- +c Optionally write matrices to binary files for diagnostics +c----------------------------------------------------------------------- + IF(output)THEN + ! binary output + CALL bin_open(bin_unit,"kwmats.bin","UNKNOWN","REWIND","none") + DO ipert=1,mpert**2 + DO ipsi=0,kwmats(1)%mx + WRITE(bin_unit) REAL(kwmats(1)%xs(ipsi),4), + $ REAL(REAL(kwmats(1)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(1)%fs(ipsi,ipert)),4), + $ REAL(REAL(kwmats(2)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(2)%fs(ipsi,ipert)),4), + $ REAL(REAL(kwmats(3)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(3)%fs(ipsi,ipert)),4), + $ REAL(REAL(kwmats(4)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(4)%fs(ipsi,ipert)),4), + $ REAL(REAL(kwmats(5)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(5)%fs(ipsi,ipert)),4), + $ REAL(REAL(kwmats(6)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(6)%fs(ipsi,ipert)),4) + ENDDO + WRITE(bin_unit) + ENDDO + CALL bin_close(bin_unit) + CALL bin_open(bin_unit,"ktmats.bin","UNKNOWN","REWIND","none") + DO ipert=1,mpert**2 + DO ipsi=0,ktmats(1)%mx + WRITE(bin_unit) REAL(ktmats(1)%xs(ipsi),4), + $ REAL(REAL(ktmats(1)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(1)%fs(ipsi,ipert)),4), + $ REAL(REAL(ktmats(2)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(2)%fs(ipsi,ipert)),4), + $ REAL(REAL(ktmats(3)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(3)%fs(ipsi,ipert)),4), + $ REAL(REAL(ktmats(4)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(4)%fs(ipsi,ipert)),4), + $ REAL(REAL(ktmats(5)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(5)%fs(ipsi,ipert)),4), + $ REAL(REAL(ktmats(6)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(6)%fs(ipsi,ipert)),4) + ENDDO + WRITE(bin_unit) + ENDDO + CALL bin_close(bin_unit) + + mfac =(/(i,i=mlow,mhigh)/) + CALL ascii_open(fourfit_out_unit,"kwmats.out","UNKNOWN") + WRITE(fourfit_out_unit,*)"DCON Kinetic energy matrices" + WRITE(fourfit_out_unit,'(1/,1x,a12,1x,I6,1x,1(a12,I4),1/)') + $ "mpsi =",mpsi,"mpert =",mpert + WRITE(fourfit_out_unit,'(1x,a16,2(1x,a4),12(1x,a16))') + $ "psi","m1","m2", + $ "real(Ak)","imag(Ak)","real(Bk)","imag(Bk)", + $ "real(Ck)","imag(Ck)","real(Dk)","imag(Dk)", + $ "real(Ek)","imag(Ek)","real(Hk)","imag(Hk)" + DO ipsi=0,kwmats(1)%mx + DO i=1,mpert + DO j=1,mpert + ipert = (i-1)*mpert + j + WRITE(fourfit_out_unit,'(1x,es16.8,2(1x,I4),'// + $ '12(1x,es16.8))') + $ REAL(kwmats(1)%xs(ipsi),4),mfac(i),mfac(j), + $ REAL(REAL(kwmats(1)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(1)%fs(ipsi,ipert)),4), + $ REAL(REAL(kwmats(2)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(2)%fs(ipsi,ipert)),4), + $ REAL(REAL(kwmats(3)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(3)%fs(ipsi,ipert)),4), + $ REAL(REAL(kwmats(4)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(4)%fs(ipsi,ipert)),4), + $ REAL(REAL(kwmats(5)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(5)%fs(ipsi,ipert)),4), + $ REAL(REAL(kwmats(6)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(kwmats(6)%fs(ipsi,ipert)),4) + ENDDO + ENDDO + ENDDO + WRITE(fourfit_out_unit,*) + CALL ascii_close(fourfit_out_unit) + CALL ascii_open(fourfit_out_unit,"ktmats.out","UNKNOWN") + WRITE(fourfit_out_unit,*) "DCON Kinetic torque matrices" + WRITE(fourfit_out_unit,'(1/,1x,a12,1x,I6,1x,1(a12,I4),1/)') + $ "mpsi =",mpsi,"mpert =",mpert + WRITE(fourfit_out_unit,'(1x,a16,2(1x,a4),12(1x,a16))') + $ "psi","m1","m2", + $ "real(Ak)","imag(Ak)","real(Bk)","imag(Bk)", + $ "real(Ck)","imag(Ck)","real(Dk)","imag(Dk)", + $ "real(Ek)","imag(Ek)","real(Hk)","imag(Hk)" + DO ipsi=0,kwmats(1)%mx + DO i=1,mpert + DO j=1,mpert + ipert = (i-1)*mpert + j + WRITE(fourfit_out_unit,'(1x,es16.8,2(1x,I4),'// + $ '12(1x,es16.8))') + $ REAL(kwmats(1)%xs(ipsi),4),mfac(i),mfac(j), + $ REAL(REAL(ktmats(1)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(1)%fs(ipsi,ipert)),4), + $ REAL(REAL(ktmats(2)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(2)%fs(ipsi,ipert)),4), + $ REAL(REAL(ktmats(3)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(3)%fs(ipsi,ipert)),4), + $ REAL(REAL(ktmats(4)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(4)%fs(ipsi,ipert)),4), + $ REAL(REAL(ktmats(5)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(5)%fs(ipsi,ipert)),4), + $ REAL(REAL(ktmats(6)%fs(ipsi,ipert)),4), + $ REAL(AIMAG(ktmats(6)%fs(ipsi,ipert)),4) + ENDDO + ENDDO + ENDDO + WRITE(fourfit_out_unit,*) + CALL ascii_close(fourfit_out_unit) + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE fourfit_kinetic_matrix + END MODULE fourfit_mod diff --git a/src/DCON/fortran/free.f b/src/DCON/fortran/free.f new file mode 100644 index 000000000..2baf6a2c7 --- /dev/null +++ b/src/DCON/fortran/free.f @@ -0,0 +1,845 @@ +c----------------------------------------------------------------------- +c file free.f. +c stability of free-boundary modes. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. free_mod. +c 1. free_run. +c 2. free_write_msc. +c 3. free_ahb_prep. +c 4. free_ahb_write. +c 5. free_test. +c 6. free_wvmats +c----------------------------------------------------------------------- +c subprogram 0. free_mod. +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + MODULE free_mod + USE vacuum_mod, ONLY: mscvac + USE global_mod, ONLY: wv_farwall_flag + USE sing_mod, ONLY: sing_der, msol + USE fourfit_mod, ONLY: asmat, bsmat, csmat, jmat, ipiva, + $ cspline_type + USE ode_output_mod, ONLY: u,du + USE dcon_netcdf_mod + IMPLICIT NONE + + INTEGER :: msol_ahb=-1 + INTEGER, PRIVATE :: mthsurf + REAL(r8), PRIVATE :: qsurf,q1surf + REAL(r8), DIMENSION(:), POINTER, PRIVATE :: theta,dphi,r,z + REAL(r8), DIMENSION(:,:), POINTER, PRIVATE :: thetas + REAL(r8), DIMENSION(:,:,:), POINTER, PRIVATE :: project + REAL(r8), DIMENSION(:,:), POINTER :: grri,xzpts + + TYPE(cspline_type) :: wvmats + CONTAINS +c----------------------------------------------------------------------- +c subprogram 1. free_run. +c computes plasma, vacuum, and total potential energies. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE free_run(plasma1,vacuum1,total1,nzero,op_netcdf_out) + + COMPLEX(r8), INTENT(OUT) :: plasma1,vacuum1,total1 + INTEGER, INTENT(IN) :: nzero + LOGICAL, OPTIONAL :: op_netcdf_out + + LOGICAL, PARAMETER :: normalize=.TRUE. + CHARACTER(1), DIMENSION(mpert,msol) :: star + INTEGER :: ipert,jpert,isol,info,lwork + INTEGER, DIMENSION(mpert) :: ipiv,m,eindex + INTEGER, DIMENSION(1) :: imax + REAL(r8) :: v1 + REAL(r8), DIMENSION(mpert) :: singfac + ! eigenvalues are complex for gpec + COMPLEX(r8), DIMENSION(mpert) :: ep,ev,et,tt + + REAL(r8), DIMENSION(3*mpert-2) :: rwork + REAL(r8), DIMENSION(2*mpert) :: rwork2 + COMPLEX(r8) :: phase,norm + COMPLEX(r8), DIMENSION(2*mpert-1) :: work + COMPLEX(r8), DIMENSION(2*mpert+1) :: work2 + COMPLEX(r8), DIMENSION(mpert,mpert) :: wp,wv,wt,wt0,temp,wpt,wvt + COMPLEX(r8), DIMENSION(mpert,mpert) :: nmat,smat + COMPLEX(r8), DIMENSION(mpert,mpert) :: vl,vr + CHARACTER(24), DIMENSION(mpert) :: message + LOGICAL, PARAMETER :: complex_flag=.TRUE.,wall_flag=.FALSE. + LOGICAL :: farwal_flag + REAL(r8) :: kernelsignin + INTEGER :: vac_unit + COMPLEX(r8), DIMENSION(mpert) :: diff + CHARACTER(128) :: ahg_file +c----------------------------------------------------------------------- +c write formats. +c----------------------------------------------------------------------- + 10 FORMAT(1x,"Energies: plasma = ",es10.3,", vacuum = ",es10.3, + $ ", real = ",es10.3,", imaginary = ",es10.3) + 20 FORMAT(/3x,"isol",3x,"plasma",5x,"vacuum",2x,"re total",2x, + $ "im total"/) + 30 FORMAT(i6,1p,4e11.3,a) + 40 FORMAT(/3x,"isol",2x,"imax",3x,"plasma",5x,"vacuum",2x,"re total", + $ 2x,"im total"/) + 50 FORMAT(2i6,1p,4e11.3,a) + 60 FORMAT(/2x,"ipert",4x,"m",4x,"re wt",6x,"im wt",6x,"abs wt"/) + 70 FORMAT(2i6,1p,3e11.3,2x,a) + 80 FORMAT(/3x,"isol",3x,"plasma",5x,"vacuum"/) + 90 FORMAT(i6,1p,2e11.3) +c----------------------------------------------------------------------- +c Basic parameters at this psi +c----------------------------------------------------------------------- + CALL spline_eval(sq,psilim,0) + v1=sq%f(3) +c----------------------------------------------------------------------- +c compute plasma response matrix. +c----------------------------------------------------------------------- + IF(ode_flag)THEN + temp=CONJG(TRANSPOSE(u(:,1:mpert,1))) + wp=u(:,1:mpert,2) + wp=CONJG(TRANSPOSE(wp)) + CALL zgetrf(mpert,mpert,temp,mpert,ipiv,info) + CALL zgetrs('N',mpert,mpert,temp,mpert,ipiv,wp,mpert,info) + wp=CONJG(TRANSPOSE(wp))/psio**2 + ELSE + wp=0 + ENDIF +c----------------------------------------------------------------------- +c write file for mscvac, prepare input for ahb (deallocate moved to end). +c----------------------------------------------------------------------- + ahg_file="ahg2msc_dcon.out" + CALL free_write_msc(psilim,vac_memory,ahgstr_op=ahg_file) + IF(ahb_flag)THEN + CALL free_ahb_prep(wp,nmat,smat,asmat,bsmat,csmat,ipiva) + ENDIF +c----------------------------------------------------------------------- +c compute vacuum response matrix. +c----------------------------------------------------------------------- + vac_unit=4 + farwal_flag=.TRUE. ! self-inductance for plasma boundary. + kernelsignin=-1.0 + ALLOCATE(grri(2*(mthvac+5),mpert*2),xzpts(mthvac+5,4)) + ! xzpts has a dimension of [mthvac+2] with 2 exrta repeating pts + CALL mscvac(wv,mpert,mtheta,mthvac,complex_flag,kernelsignin, + $ wall_flag,farwal_flag,grri,xzpts,ahg_file) + IF(bin_vac)THEN + WRITE(*,*) "!! WARNING: Use of vacuum.bin is deprecated in"// + $ " GPEC. Set bin_vac = f in dcon.in to reduce file IO." + CALL bin_open(vac_unit,"vacuum.bin","UNKNOWN","REWIND","none") + WRITE(vac_unit)grri + ENDIF + + kernelsignin=1.0 + CALL mscvac(wv,mpert,mtheta,mthvac,complex_flag,kernelsignin, + $ wall_flag,farwal_flag,grri,xzpts,ahg_file) + IF(bin_vac)THEN + WRITE(vac_unit)grri + ENDIF + IF(wv_farwall_flag)THEN + temp=wv + ENDIF + + farwal_flag=.FALSE. ! self-inductance with the wall. + kernelsignin=-1.0 + CALL mscvac(wv,mpert,mtheta,mthvac,complex_flag,kernelsignin, + $ wall_flag,farwal_flag,grri,xzpts,ahg_file) + IF(bin_vac)THEN + WRITE(vac_unit)grri + ENDIF + + kernelsignin=1.0 + CALL mscvac(wv,mpert,mtheta,mthvac,complex_flag,kernelsignin, + $ wall_flag,farwal_flag,grri,xzpts,ahg_file) + IF(bin_vac)THEN + WRITE(vac_unit)grri + WRITE(vac_unit)xzpts + + CALL bin_close(vac_unit) + ENDIF + + DEALLOCATE(grri,xzpts) + + IF(wv_farwall_flag)THEN + wv=temp + ENDIF + + singfac=mlow-nn*qlim+(/(ipert,ipert=0,mpert-1)/) + DO ipert=1,mpert + wv(ipert,:)=wv(ipert,:)*singfac + wv(:,ipert)=wv(:,ipert)*singfac + ENDDO +c----------------------------------------------------------------------- +c compute complex energy eigenvalues. +c----------------------------------------------------------------------- + wt=wp+wv + wt0=wt + lwork=2*mpert+1 + CALL zgeev('V','V',mpert,wt,mpert,et, + $ vl,mpert,vr,mpert,work2,lwork,rwork2,info) + eindex(1:mpert)=(/(ipert,ipert=1,mpert)/) + CALL bubble(REAL(et),eindex,1,mpert) + tt=et + DO ipert=1,mpert + wt(:,ipert)=vr(:,eindex(mpert+1-ipert)) + et(ipert)=tt(eindex(mpert+1-ipert)) + ENDDO +c----------------------------------------------------------------------- +c normalize eigenfunction and energy. +c----------------------------------------------------------------------- + IF(normalize)THEN + DO isol=1,mpert + norm=0 + DO ipert=1,mpert + DO jpert=1,mpert + norm=norm+jmat(jpert-ipert) + $ *wt(ipert,isol)*CONJG(wt(jpert,isol)) + ENDDO + ENDDO + norm=norm/v1 + wt(:,isol)=wt(:,isol)/SQRT(norm) + et(isol)=et(isol)/norm + ENDDO + ENDIF +c----------------------------------------------------------------------- +c normalize phase and label largest component. +c----------------------------------------------------------------------- + DO isol=1,mpert + imax=MAXLOC(ABS(wt(:,isol))) + phase=ABS(wt(imax(1),isol))/wt(imax(1),isol) + wt(:,isol)=wt(:,isol)*phase + star(:,isol)=' ' + star(imax(1),isol)='*' + ENDDO +c----------------------------------------------------------------------- +c compute plasma and vacuum contributions. +c----------------------------------------------------------------------- + wpt=MATMUL(CONJG(TRANSPOSE(wt)),MATMUL(wp,wt)) + wvt=MATMUL(CONJG(TRANSPOSE(wt)),MATMUL(wv,wt)) + DO ipert=1,mpert + ep(ipert)=wpt(ipert,ipert) + ev(ipert)=wvt(ipert,ipert) + ENDDO + plasma1=REAL(ep(1)) + vacuum1=REAL(ev(1)) + total1=REAL(et(1)) +c----------------------------------------------------------------------- +c write data for ahb and deallocate. +c----------------------------------------------------------------------- + IF(ahb_flag)THEN + CALL free_ahb_write(nmat,smat,wt,et) + DEALLOCATE(r,z,theta,dphi,thetas,project) + ENDIF + + IF(vac_memory) CALL unset_dcon_params +c----------------------------------------------------------------------- +c save eigenvalues and eigenvectors to file. +c----------------------------------------------------------------------- + IF(bin_euler)THEN + WRITE(euler_bin_unit)3 + WRITE(euler_bin_unit)ep + WRITE(euler_bin_unit)et + WRITE(euler_bin_unit)wt + WRITE(euler_bin_unit)wt0 + WRITE(euler_bin_unit)wv_farwall_flag + ENDIF +c----------------------------------------------------------------------- +c write to screen and copy to output. +c----------------------------------------------------------------------- + IF(verbose) WRITE(*,10) REAL(ep(1)),REAL(ev(1)), + $ REAL(et(1)),AIMAG(et(1)) +c----------------------------------------------------------------------- +c write eigenvalues to file. +c----------------------------------------------------------------------- + message="" + WRITE(out_unit,'(/1x,a)')"Total Energy Eigenvalues:" + WRITE(out_unit,20) + WRITE(out_unit,30)(isol,REAL(ep(isol)),REAL(ev(isol)), + $ REAL(et(isol)),AIMAG(et(isol)), + $ TRIM(message(isol)),isol=1,mpert) + WRITE(out_unit,20) +c----------------------------------------------------------------------- +c write eigenvectors to file. +c----------------------------------------------------------------------- + WRITE(out_unit,*)"Total Energy Eigenvectors:" + m=mlow+(/(isol,isol=0,mpert-1)/) + DO isol=1,mpert + WRITE(out_unit,40) + WRITE(out_unit,50)isol,imax(1),REAL(ep(isol)),REAL(ev(isol)), + $ REAL(et(isol)),AIMAG(et(isol)),TRIM(message(isol)) + WRITE(out_unit,60) + WRITE(out_unit,70)(ipert,m(ipert),wt(ipert,isol), + $ ABS(wt(ipert,isol)),star(ipert,isol),ipert=1,mpert) + WRITE(out_unit,60) + ENDDO +c----------------------------------------------------------------------- +c write the plasma matrix. +c----------------------------------------------------------------------- + WRITE(out_unit,'(/1x,a/)')"Plasma Energy Matrix:" + DO isol=1,mpert + WRITE(out_unit,'(1x,2(a,i3))')"isol = ",isol,", m = ",m(isol) + WRITE(out_unit,'(/2x,"i",5x,"re wp",8x,"im wp",8x,"abs wp"/)') + WRITE(out_unit,'(i3,1p,3e13.5)') + $ (ipert,wp(ipert,isol),ABS(wp(ipert,isol)),ipert=1,mpert) + WRITE(out_unit,'(/2x,"i",5x,"re wp",8x,"im wp",8x,"abs wp"/)') + ENDDO +c----------------------------------------------------------------------- +c compute separate plasma and vacuum eigenvalues. +c----------------------------------------------------------------------- + lwork=2*mpert+1 + CALL zgeev('V','V',mpert,wp,mpert,ep, + $ vl,mpert,vr,mpert,work2,lwork,rwork2,info) + eindex(1:mpert)=(/(ipert,ipert=1,mpert)/) + CALL bubble(REAL(ep),eindex,1,mpert) + tt=ep + DO ipert=1,mpert + wp(:,ipert)=vr(:,eindex(mpert+1-ipert)) + ep(ipert)=tt(eindex(mpert+1-ipert)) + ENDDO + CALL zheev('V','U',mpert,wv,mpert,ev,work,lwork,rwork,info) +c----------------------------------------------------------------------- +c optionally write netcdf file. +c----------------------------------------------------------------------- + IF(netcdf_out) CALL dcon_netcdf_out(wp,wv,wt,wt0,ep,ev,et) +c----------------------------------------------------------------------- +c deallocate +c----------------------------------------------------------------------- + CALL dcon_dealloc +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE free_run +c----------------------------------------------------------------------- +c subprogram 2. free_write_msc. +c writes boundary data for Morrell Chance's vacuum code. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE free_write_msc(psifac, inmemory_op, ahgstr_op) + + REAL(r8), INTENT(IN) :: psifac + LOGICAL, OPTIONAL :: inmemory_op + LOGICAL :: inmemory = .FALSE. + + CHARACTER(1), PARAMETER :: tab=CHAR(9) + INTEGER :: itheta,n + REAL(r8) :: qa + REAL(r8), DIMENSION(0:mtheta) :: angle,r,z,delta,rfac,theta + CHARACTER(128) :: ahgstr + CHARACTER(128), optional :: ahgstr_op + + IF(PRESENT(inmemory_op))THEN + inmemory = inmemory_op + ELSE + inmemory = .FALSE. + ENDIF + + IF(PRESENT(ahgstr_op))THEN + ahgstr = ahgstr_op + ELSE + ahgstr = "ahg2msc_dcon.out" + ENDIF + +c----------------------------------------------------------------------- +c compute output. +c----------------------------------------------------------------------- + CALL spline_eval(sq,psifac,1) + qa=sq%f(4) + + theta=rzphi%ys + DO itheta=0,mtheta + CALL bicube_eval(rzphi,psifac,theta(itheta),0) + rfac(itheta)=SQRT(rzphi%f(1)) + angle(itheta)=twopi*(theta(itheta)+rzphi%f(2)) + delta(itheta)=-rzphi%f(3)/qa + ENDDO + r=ro+rfac*COS(angle) + z=zo+rfac*SIN(angle) +c----------------------------------------------------------------------- +c invert values for nn < 0. +c----------------------------------------------------------------------- + n=nn + IF(nn < 0)THEN + qa=-qa + delta=-delta + n=-n + ENDIF +c----------------------------------------------------------------------- +c pass all values in memory instead of over ascii io (faster). +c----------------------------------------------------------------------- + IF(inmemory)THEN + CALL set_dcon_params(mtheta,mlow,mhigh,n,qa,r(mtheta:0:-1), + $ z(mtheta:0:-1),delta(mtheta:0:-1)) + ELSE +c----------------------------------------------------------------------- +c write scalars. +c----------------------------------------------------------------------- + CALL ascii_open(bin_unit,ahgstr,"UNKNOWN") + WRITE(bin_unit,'(i4,a)')mtheta,tab//tab//"mtheta"//tab//"mthin" + $ //tab//"Number of poloidal nodes" + WRITE(bin_unit,'(i4,a)')mlow,tab//tab//"mlow"//tab//"lmin"//tab + $ //"Lowest poloidal harmonic" + WRITE(bin_unit,'(i4,a,a)')mhigh,tab//tab//"mhigh"//tab//"lmax" + $ //tab//"Highest poloidal harmonic" + WRITE(bin_unit,'(i4,a)')n,tab//tab//"nn"//tab//"nadj"//tab + $ //"Toroidal harmonic" + WRITE(bin_unit,'(f13.10,a)')qa,tab//"qa"//tab//"qa1"//tab + $ //"Safety factor at plasma edge" +c----------------------------------------------------------------------- +c write arrays. +c----------------------------------------------------------------------- + WRITE(bin_unit,'(/a/)')"Poloidal Coordinate Theta:" + WRITE(bin_unit,'(1p,4e18.10)')(1-theta(itheta), + $ itheta=mtheta,0,-1) + WRITE(bin_unit,'(/a/)')"Polar Angle Eta:" + WRITE(bin_unit,'(1p,4e18.10)')(twopi-angle(itheta), + $ itheta=mtheta,0,-1) + WRITE(bin_unit,'(/a/)')"Radial Coordinate X:" + WRITE(bin_unit,'(1p,4e18.10)')(r(itheta),itheta=mtheta,0,-1) + WRITE(bin_unit,'(/a/)')"Axial Coordinate Z:" + WRITE(bin_unit,'(1p,4e18.10)')(z(itheta),itheta=mtheta,0,-1) + WRITE(bin_unit,'(/a/)')"Toroidal Angle Difference Delta:" + WRITE(bin_unit,'(1p,4e18.10)')(delta(itheta), + $ itheta=mtheta,0,-1) + CALL ascii_close(bin_unit) + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE free_write_msc +c----------------------------------------------------------------------- +c subprogram 3. free_ahb_prep. +c prepares boundary data for Allen H. Boozers's feedback problem. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE free_ahb_prep(wp,nmat,smat,asmat,bsmat,csmat,ipiva) + + COMPLEX(r8), DIMENSION(mpert,mpert), INTENT(IN) :: wp + COMPLEX(r8), DIMENSION(mpert,mpert), INTENT(OUT) :: nmat,smat + COMPLEX(r8), DIMENSION(:,:), INTENT(IN) :: asmat,bsmat,csmat + INTEGER, DIMENSION(:), INTENT(INOUT) :: ipiva + + INTEGER :: itheta,iqty,ipert,info,neq + REAL(r8) :: rfac,angle,bpfac,btfac,bfac,fac,jac,delpsi,psifac + REAL(r8), DIMENSION(2,2) :: w + COMPLEX(r8), DIMENSION(mpert,mpert,2) :: u,du + TYPE(spline_type) :: spl +c----------------------------------------------------------------------- +c preliminary computations. +c----------------------------------------------------------------------- + mthsurf=40*mthsurf0*MAX(ABS(mlow),ABS(mhigh)) + ALLOCATE(r(0:mthsurf),z(0:mthsurf),theta(0:mthsurf), + $ dphi(0:mthsurf),thetas(0:mthsurf,4),project(3,3,0:mthsurf)) + CALL spline_alloc(spl,mthsurf,4) + theta=(/(itheta,itheta=0,mthsurf)/)/REAL(mthsurf,r8) + spl%xs=theta + psifac=psilim + qsurf=qlim + q1surf=q1lim + CALL spline_eval(sq,psilim,0) +c----------------------------------------------------------------------- +c compute geometric factors. +c----------------------------------------------------------------------- + DO itheta=0,mthsurf + CALL bicube_eval(rzphi,psilim,theta(itheta),1) + rfac=SQRT(rzphi%f(1)) + angle=twopi*(theta(itheta)+rzphi%f(2)) + r(itheta)=ro+rfac*COS(angle) + z(itheta)=zo+rfac*SIN(angle) + dphi(itheta)=rzphi%f(3) + jac=rzphi%f(4) +c----------------------------------------------------------------------- +c compute covariant basis vectors. +c----------------------------------------------------------------------- + w(1,1)=(1+rzphi%fy(2))*twopi**2*rfac*r(itheta)/jac + w(1,2)=-rzphi%fy(1)*pi*r(itheta)/(rfac*jac) + w(2,1)=-rzphi%fx(2)*twopi**2*r(itheta)*rfac/jac + w(2,2)=rzphi%fx(1)*pi*r(itheta)/(rfac*jac) +c----------------------------------------------------------------------- +c compute project. +c----------------------------------------------------------------------- + delpsi=SQRT(w(1,1)**2+w(1,2)**2) + project(1,1,itheta)=1/(delpsi*jac) + project(2,1,itheta) + $ =-(w(1,1)*w(2,1)+w(1,2)*w(2,2))/(twopi*r(itheta)*delpsi) + project(2,2,itheta)=delpsi/(twopi*r(itheta)) + project(3,1,itheta)=rzphi%fx(3)*r(itheta)/jac + project(3,2,itheta)=rzphi%fy(3)*r(itheta)/jac + project(3,3,itheta)=twopi*r(itheta)/jac +c----------------------------------------------------------------------- +c compute alternative theta coordinates. +c----------------------------------------------------------------------- + bpfac=psio*delpsi/r(itheta) + btfac=sq%f(1)/(twopi*r(itheta)) + bfac=SQRT(bpfac*bpfac+btfac*btfac) + fac=r(itheta)**power_r/(bpfac**power_bp*bfac**power_b) + spl%fs(itheta,1)=fac + spl%fs(itheta,2)=fac/r(itheta)**2 + spl%fs(itheta,3)=fac*bpfac + !modified for boozer coordinates. + spl%fs(itheta,4)=fac*bfac**2 + ENDDO +c----------------------------------------------------------------------- +c compute alternative poloidal coordinates. +c----------------------------------------------------------------------- + CALL spline_fit(spl,"periodic") + CALL spline_int(spl) + DO iqty=1,4 + thetas(:,iqty)=spl%fsi(:,iqty)/spl%fsi(mthsurf,iqty) + ENDDO + CALL spline_dealloc(spl) +c----------------------------------------------------------------------- +c compute displacements and their derivatives. +c----------------------------------------------------------------------- + msol=mpert + neq=4*mpert*msol + psifac=psilim + u(:,:,1)=0 + DO ipert=1,mpert + u(ipert,ipert,1)=1 + ENDDO + u(:,:,2)=wp*psio**2 + CALL sing_der(neq,psifac,u,du) + nmat=du(:,:,1) + smat=-(MATMUL(bsmat,du(:,:,1))+MATMUL(csmat,u(:,:,1))) + CALL zhetrs('L',mpert,mpert,asmat,mpert,ipiva,smat,mpert,info) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE free_ahb_prep +c----------------------------------------------------------------------- +c subprogram 4. free_ahb_write. +c writes boundary data for Allen H. Boozers's feedback problem. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE free_ahb_write(nmat,smat,wt,et) + + COMPLEX(r8), DIMENSION(mpert,mpert), INTENT(IN) :: nmat,smat,wt + COMPLEX(r8), DIMENSION(mpert), INTENT(IN) :: et + + INTEGER :: itheta,ipert,isol,m + INTEGER, DIMENSION(mpert) :: mvec + REAL(r8) :: chi1 + COMPLEX(r8) :: expfac,expfac0,expfac1,phase + COMPLEX(r8), DIMENSION(mpert) :: singfac + COMPLEX(r8), DIMENSION(mpert,mpert) :: xin,xis + COMPLEX(r8), DIMENSION(mpert,mpert,3) :: jqvec + COMPLEX(r8), DIMENSION(mpert,0:mthsurf,3) :: bvec0,bvec +c----------------------------------------------------------------------- +c compute Fourier components: xsp1_mn = xin, xss_mn = xis. +c----------------------------------------------------------------------- + xin=MATMUL(nmat,wt) + xis=MATMUL(smat,wt) + mvec=(/(m,m=mlow,mhigh)/) + chi1=twopi*psio + singfac=chi1*twopi*ifac*(mvec-nn*qsurf) + DO isol=1,mpert + jqvec(:,isol,1)=wt(:,isol)*singfac + jqvec(:,isol,2)=-chi1*xin(:,isol)-twopi*ifac*nn*xis(:,isol) + jqvec(:,isol,3)=-chi1*(qsurf*xin(:,isol)+q1surf*wt(:,isol)) + $ -twopi*ifac*mvec*xis(:,isol) + ENDDO +c----------------------------------------------------------------------- +c transform to configuration space. +c----------------------------------------------------------------------- + expfac0=EXP(twopi*ifac*theta(1)) + expfac1=1 + bvec0=0 + DO itheta=0,mthsurf-1 + expfac=EXP(ifac*(twopi*mlow*theta(itheta)+nn*dphi(itheta))) + DO ipert=1,mpert + bvec0(:,itheta,:)=bvec0(:,itheta,:)+jqvec(ipert,:,:)*expfac + expfac=expfac*expfac1 + ENDDO + expfac1=expfac1*expfac0 + ENDDO + bvec0(:,mthsurf,:)=bvec0(:,0,:) +c----------------------------------------------------------------------- +c compute orthogonal components of perturbed magnetic field. +c----------------------------------------------------------------------- + DO isol=1,msol + bvec(isol,:,1)=project(1,1,:)*bvec0(isol,:,1) + bvec(isol,:,2) + $ =project(2,1,:)*bvec0(isol,:,1) + $ +project(2,2,:)*bvec0(isol,:,2) + bvec(isol,:,3) + $ =project(3,1,:)*bvec0(isol,:,1) + $ +project(3,2,:)*bvec0(isol,:,2) + $ +project(3,3,:)*bvec0(isol,:,3) + phase=bvec(isol,0,1)/ABS(bvec(isol,0,1)) + bvec(isol,:,:)=bvec(isol,:,:)/phase + ENDDO +c----------------------------------------------------------------------- +c open dcon_surf.out, write geometry and eigenvalues. +c----------------------------------------------------------------------- + CALL ascii_open(bin_unit,"dcon_surf.out","UNKNOWN") + WRITE(bin_unit,'(a/a/a/)')"Output from DCON, ", + $ "total perturbed energy eigenvalues", + $ "and normal magnetic field eigenvectors" + WRITE(bin_unit,'(3(a,i4),a,1p,e16.8)') + $ "mthsurf = ",mthsurf,", msol = ",msol,", nn = ",nn, + $ ", qsurf = ",qsurf + WRITE(bin_unit,'(/a//(1p,5e16.8))')"radial position r:",r + WRITE(bin_unit,'(/a//(1p,5e16.8))')"axial position z:",z + WRITE(bin_unit,'(/a//(1p,5e16.8))') + $ "total energy eigenvalues et:",et*psio**2/(2*mu0) +c----------------------------------------------------------------------- +c write perturbed normal magnetic field. +c----------------------------------------------------------------------- + DO isol=1,mpert + WRITE(bin_unit,'(/a,i3,a/)')"normal magnetic eigenvector" + $ //", isol = ",isol,", cos factor:" + WRITE(bin_unit,'(1p,5e16.8)')REAL(bvec(isol,:,1)) + WRITE(bin_unit,'(/a,i3,a/)')"normal magnetic eigenvector" + $ //", isol = ",isol,", sin factor:" + WRITE(bin_unit,'(1p,5e16.8)')AIMAG(bvec(isol,:,1)) + ENDDO +c----------------------------------------------------------------------- +c write perturbed poloidal magnetic field. +c----------------------------------------------------------------------- + DO isol=1,mpert + WRITE(bin_unit,'(/a,i3,a/)')"poloidal magnetic eigenvector" + $ //", isol = ",isol,", cos factor:" + WRITE(bin_unit,'(1p,5e16.8)')REAL(bvec(isol,:,2)) + WRITE(bin_unit,'(/a,i3,a/)')"poloidal magnetic eigenvector," + $ //" isol = ",isol,", sin factor:" + WRITE(bin_unit,'(1p,5e16.8)')AIMAG(bvec(isol,:,2)) + ENDDO +c----------------------------------------------------------------------- +c write perturbed toroidal magnetic field. +c----------------------------------------------------------------------- + DO isol=1,mpert + WRITE(bin_unit,'(/a,i3,a/)')"toroidal magnetic eigenvector," + $ //" isol = ",isol,", cos factor:" + WRITE(bin_unit,'(1p,5e16.8)')REAL(bvec(isol,:,3)) + WRITE(bin_unit,'(/a,i3,a/)')"toroidal magnetic eigenvector" + $ //", isol = ",isol,", sin factor:" + WRITE(bin_unit,'(1p,5e16.8)')AIMAG(bvec(isol,:,3)) + ENDDO + CALL ascii_close(bin_unit) +c----------------------------------------------------------------------- +c draw graphs. +c----------------------------------------------------------------------- + CALL bin_open(bin_unit,"ahb.bin","UNKNOWN","REWIND","none") + DO isol=1,mpert + DO itheta=0,mthsurf + WRITE(bin_unit)REAL(theta(itheta),4), + $ REAL(REAL(bvec(isol,itheta,:)),4), + $ REAL(AIMAG(bvec(isol,itheta,:)),4), + $ REAL(thetas(itheta,:),4), + $ REAL(thetas(itheta,:)-theta(itheta),4) + ENDDO + WRITE(bin_unit) + IF(isol == msol_ahb)EXIT + ENDDO + CALL bin_close(bin_unit) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE free_ahb_write +c----------------------------------------------------------------------- +c subprogram 5. free_test. +c Trimmed down version of free_run computing total dW. +c Can also calculate plasma and vacuum eigenvalues IFF debugging +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE free_test(plasma1,vacuum1,total1,psifac) + + COMPLEX(r8), INTENT(OUT) :: plasma1,vacuum1,total1 + REAL(r8), INTENT(IN) :: psifac + + LOGICAL, PARAMETER :: normalize=.TRUE., debug=.FALSE. + LOGICAL, SAVE :: first_call=.TRUE. + INTEGER :: ipert,jpert,isol,info,lwork,i + INTEGER, DIMENSION(mpert) :: ipiv,m,eindex + REAL(r8) :: v1 + REAL(r8), DIMENSION(mpert) :: singfac + ! eigenvalues are complex for gpec + COMPLEX(r8), DIMENSION(mpert) :: et,tt + + REAL(r8), DIMENSION(2*mpert) :: rwork2 + COMPLEX(r8) :: norm + COMPLEX(r8), DIMENSION(2*mpert+1) :: work2 + COMPLEX(r8), DIMENSION(mpert,mpert) :: wp,wv,wt,wt0,temp + COMPLEX(r8), DIMENSION(mpert,mpert) :: vl,vr + LOGICAL, PARAMETER :: complex_flag=.TRUE. + REAL(r8) :: kernelsignin +c----------------------------------------------------------------------- +c Basic parameters at this psi +c----------------------------------------------------------------------- + CALL spline_eval(sq,psifac,0) + v1=sq%f(3) +c----------------------------------------------------------------------- +c compute plasma response matrix. +c----------------------------------------------------------------------- + temp=CONJG(TRANSPOSE(u(:,1:mpert,1))) + wp=u(:,1:mpert,2) + wp=CONJG(TRANSPOSE(wp)) + CALL zgetrf(mpert,mpert,temp,mpert,ipiv,info) + CALL zgetrs('N',mpert,mpert,temp,mpert,ipiv,wp,mpert,info) + wp=CONJG(TRANSPOSE(wp))/psio**2 +c----------------------------------------------------------------------- +c compute vacuum response matrix. +c----------------------------------------------------------------------- + wv = 0 + ! calc a rough spline of wv so we don't call mscvac (slow) every time + IF(first_call)THEN + CALL free_wvmats + CALL spline_eval(sq,psifac,0) + first_call = .FALSE. + ENDIF + CALL cspline_eval(wvmats, psifac,0) + wv=RESHAPE(wvmats%f,(/mpert,mpert/)) +c----------------------------------------------------------------------- +c compute complex energy eigenvalues. +c----------------------------------------------------------------------- + wt=wp+wv + wt0=wt + lwork=2*mpert+1 + CALL zgeev('V','V',mpert,wt,mpert,et, + $ vl,mpert,vr,mpert,work2,lwork,rwork2,info) + eindex(1:mpert)=(/(ipert,ipert=1,mpert)/) + CALL bubble(REAL(et),eindex,1,mpert) + tt=et + DO ipert=1,mpert + wt(:,ipert)=vr(:,eindex(mpert+1-ipert)) + et(ipert)=tt(eindex(mpert+1-ipert)) + ENDDO +c----------------------------------------------------------------------- +c normalize eigenfunction and energy. +c----------------------------------------------------------------------- + IF(normalize)THEN + isol=1 ! only bother with the first one + norm=0 + DO ipert=1,mpert + DO jpert=1,mpert + norm=norm+jmat(jpert-ipert) + $ *wt(ipert,isol)*CONJG(wt(jpert,isol)) + ENDDO + ENDDO + norm=norm/v1 + et(isol)=et(isol)/norm + ENDIF + total1=et(1) +c----------------------------------------------------------------------- +c compute plasma and vacuum eigenvalues +c DIFFERS FROM free_run, which calcs energies of the total eigenmode +c----------------------------------------------------------------------- + IF(debug)THEN + wt=wp + wt0=wt + lwork=2*mpert+1 + CALL zgeev('V','V',mpert,wt,mpert,et, + $ vl,mpert,vr,mpert,work2,lwork,rwork2,info) + eindex(1:mpert)=(/(ipert,ipert=1,mpert)/) + CALL bubble(REAL(et),eindex,1,mpert) + tt=et + DO ipert=1,mpert + wt(:,ipert)=vr(:,eindex(mpert+1-ipert)) + et(ipert)=tt(eindex(mpert+1-ipert)) + ENDDO + plasma1=et(1) + + wt=wv + wt0=wt + lwork=2*mpert+1 + CALL zgeev('V','V',mpert,wt,mpert,et, + $ vl,mpert,vr,mpert,work2,lwork,rwork2,info) + eindex(1:mpert)=(/(ipert,ipert=1,mpert)/) + CALL bubble(REAL(et),eindex,1,mpert) + tt=et + DO ipert=1,mpert + wt(:,ipert)=vr(:,eindex(mpert+1-ipert)) + et(ipert)=tt(eindex(mpert+1-ipert)) + ENDDO + vacuum1=et(1) + ELSE + plasma1 = 0.0 + vacuum1 = 0.0 + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE free_test +c----------------------------------------------------------------------- +c subprogram 6. free_wvmats. +c Forms a spline of the vacuum matrix over a specified range +c for rapid calls to free_test. Range is expected to be be between +c rationals. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE free_wvmats + + INTEGER :: npsi,i,ipert,it,itmax=50 + REAL(r8) :: qi, psii, dpsi, eps=1e-9 + REAL(r8), DIMENSION(mpert) :: singfac + COMPLEX(r8), DIMENSION(mpert,mpert) :: wv + LOGICAL, PARAMETER :: complex_flag=.TRUE.,wall_flag=.FALSE. + LOGICAL :: farwal_flag=.FALSE. + REAL(r8) :: kernelsignin + INTEGER :: vac_unit + CHARACTER(128) :: ahgstr +c----------------------------------------------------------------------- +c Basic parameters for course scan of psi +c----------------------------------------------------------------------- + npsi = MAX(4, CEILING((qlim - q_edge(1)) * nn * 4)) ! 4 pts per q window, 4 if q edge spans less than one full window + psii = psiedge ! should start exactly here + CALL cspline_alloc(wvmats,npsi,mpert**2) + DO i=0,npsi + ! file name is ahg2msc_{i}.out + ahgstr = "ahg2msc_"//CHAR(i)//".out" + ! space point evenly in q + qi = q_edge(1) + (qlim - q_edge(1)) * i * 1.0/npsi + ! use newton iteration to find psilim. + it=0 + DO + it=it+1 + CALL spline_eval(sq, psii, 1) + dpsi=(qi-sq%f(4)) / sq%f1(4) + psii = psii + dpsi + IF(ABS(dpsi) < eps*ABS(psii) .OR. it > itmax)EXIT + ENDDO + ! call mscvac and save matrices to spline + wvmats%xs(i) = psii + CALL spline_eval(sq, wvmats%xs(i), 0) + CALL free_write_msc(wvmats%xs(i), inmemory_op=.TRUE., + $ ahgstr_op=ahgstr) + kernelsignin=1.0 + ALLOCATE(grri(2*(mthvac+5),mpert*2),xzpts(mthvac+5,4)) + CALL mscvac(wv,mpert,mtheta,mthvac,complex_flag,kernelsignin, + $ wall_flag,farwal_flag,grri,xzpts,ahgstr) + singfac=mlow-nn*sq%f(4)+(/(ipert,ipert=0,mpert-1)/) + DO ipert=1,mpert + wv(ipert,:)=wv(ipert,:)*singfac + wv(:,ipert)=wv(:,ipert)*singfac + ENDDO + wvmats%fs(i,:)=RESHAPE(wv,(/mpert**2/)) + DEALLOCATE(grri,xzpts) + ENDDO + CALL unset_dcon_params + CALL cspline_fit(wvmats,"extrap") +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE free_wvmats + END MODULE free_mod diff --git a/src/DCON/fortran/makefile b/src/DCON/fortran/makefile new file mode 100644 index 000000000..b17442383 --- /dev/null +++ b/src/DCON/fortran/makefile @@ -0,0 +1,87 @@ + +include ../install/DEFAULTS.inc + +IFLAGS = -I../equil -I../harvest -I../pentrc -I../vacuum -I$(MATHINC) -I$(NETCDFINC) +F90 = $(FC) $(FFLAGS) $(OMPFLAG) $(IFLAGS) $(RECURSFLAG) $(LEGACYFLAG) +export FFLAGS # for sub-makes + +.f.o: + $(F90) -c $*.f + +.F.o: + $(F90) -c $*.F + +LIBDIR = ../lib + +LIBS = \ + -lpentrc \ + -llsode \ + -lequil \ + -lvac \ + -lharvest \ + +OBJS = \ + debug.o \ + dcon_mod.o \ + mercier.o \ + bal.o \ + fourfit.o \ + sing.o \ + ode_output.o \ + free.o \ + ode.o \ + dcon_netcdf.o \ + resist.o \ + dcon.o + +# targets + +all: harvest lsode equil vacuum pentrc dcon + +harvest: + cd ../; git submodule init; git submodule update + cd ../harvest; make FC=$(FC) CC=$(CC) GACODE_ROOT= -f Makefile libharvest.a + mkdir -p ../lib + cp -f ../harvest/libharvest.a ../lib/ + +lsode: + cd ../lsode; make + +equil: + cd ../equil; make + +vacuum: + cd ../vacuum; make + +pentrc: + cd ../pentrc; make pentrc + +# note we explicitly make pentrc to force sync the compile-time version variable +dcon: pentrc $(OBJS) + $(F90) -o dcon $(OBJS) -L$(LIBDIR) $(LIBS) -L$(MATHDIR) $(MATHLIBS) -L$(NETCDFDIR) $(NETCDFLIBS) $(NETCDF_EXTRA_LIBS) $(LDFLAGS) + mkdir -p ../bin + cp -f dcon ../bin + +clean: + rm -f *.o *.mod *.out *.bin sum.dat *~ *.diff dcon *.original + +# dependencies + +dcon_mod.o: ../equil/spline_mod.mod ../equil/global_mod.mod \ + ../equil/equil_mod.mod ../equil/equil_out_mod.mod ../pentrc/dcon_interface.mod +mercier.o: dcon_mod.o +bal.o: dcon_mod.o +fourfit.o: ../equil/fspline_mod.mod ../equil/global_mod.mod \ + ../pentrc/pentrc_interface.mod ../pentrc/utilities.mod ../pentrc/torque.mod ../pentrc/inputs.mod \ + ../pentrc/energy_integration.mod ../pentrc/pitch_integration.mod ../pentrc/dcon_interface.mod \ + dcon_mod.o +sing.o: fourfit.o +debug.o: ../equil/local_mod.mod +ode_output.o: dcon_mod.o sing.o debug.o +ode.o: ode_output.o free.o +dcon_netcdf.o: dcon_mod.o +free.o: ../equil/global_mod.mod dcon_netcdf.o ode_output.o +resist.o: dcon_mod.o +dcon.o: ../equil/equil_mod.mod ../equil/equil_out_mod.mod \ + ../pentrc/inputs.o ../pentrc/pentrc_interface.o \ + bal.o mercier.o ode.o free.o resist.o diff --git a/src/DCON/fortran/mercier.f b/src/DCON/fortran/mercier.f new file mode 100644 index 000000000..ac312ad14 --- /dev/null +++ b/src/DCON/fortran/mercier.f @@ -0,0 +1,105 @@ +c----------------------------------------------------------------------- +c file mercier.f. +c computes mercier criterion and related quantities. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. mercier_mod. +c 1. mercier_scan. +c----------------------------------------------------------------------- +c subprogram 0. mercier_mod. +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + MODULE mercier_mod + USE dcon_mod + IMPLICIT NONE + + CONTAINS +c----------------------------------------------------------------------- +c subprogram 1. mercier_scan. +c evaluates mercier criterion and related quantities. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE mercier_scan + + INTEGER :: ipsi,itheta + REAL(r8) :: bsq,chi1,di,dpsisq,eta,h,jac,p1,psifac,q,q1,r, + $ rfac,term,theta,twopif,v1,v2,v21,v22,v23,v33 + REAL(r8), DIMENSION(:), POINTER :: avg + TYPE(spline_type), TARGET :: ff +c----------------------------------------------------------------------- +c prepare spline types. +c----------------------------------------------------------------------- + CALL spline_alloc(ff,mtheta,5) + ff%xs=rzphi%ys +c----------------------------------------------------------------------- +c compute surface quantities. +c----------------------------------------------------------------------- + DO ipsi=0,mpsi + psifac=sq%xs(ipsi) + twopif=sq%fs(ipsi,1) + p1=sq%fs1(ipsi,2) + v1=sq%fs(ipsi,3) + v2=sq%fs1(ipsi,3) + q=sq%fs(ipsi,4) + q1=sq%fs1(ipsi,4) + chi1=twopi*psio +c----------------------------------------------------------------------- +c evaluate coordinates and jacobian. +c----------------------------------------------------------------------- + DO itheta=0,mtheta + CALL bicube_eval(rzphi,rzphi%xs(ipsi),rzphi%ys(itheta),1) + theta=rzphi%ys(itheta) + rfac=SQRT(rzphi%f(1)) + eta=twopi*(theta+rzphi%f(2)) + r=ro+rfac*COS(eta) + jac=rzphi%f(4) +c----------------------------------------------------------------------- +c evaluate other local quantities. +c----------------------------------------------------------------------- + v21=rzphi%fy(1)/(2*rfac*jac) + v22=(1+rzphi%fy(2))*twopi*rfac/jac + v23=rzphi%fy(3)*r/jac + v33=twopi*r/jac + bsq=chi1**2*(v21**2+v22**2+(v23+q*v33)**2) + dpsisq=(twopi*r)**2*(v21**2+v22**2) +c----------------------------------------------------------------------- +c evaluate integrands. +c----------------------------------------------------------------------- + ff%fs(itheta,1)=bsq/dpsisq + ff%fs(itheta,2)=1/dpsisq + ff%fs(itheta,3)=1/bsq + ff%fs(itheta,4)=1/(bsq*dpsisq) + ff%fs(itheta,5)=bsq + ff%fs(itheta,:)=ff%fs(itheta,:)*jac/v1 + ENDDO +c----------------------------------------------------------------------- +c integrate quantities with respect to theta. +c----------------------------------------------------------------------- + CALL spline_fit(ff,"periodic") + CALL spline_int(ff) + avg => ff%fsi(mtheta,:) +c----------------------------------------------------------------------- +c evaluate mercier criterion and related quantities. +c----------------------------------------------------------------------- + term=twopif*p1*v1/(q1*chi1**3)*avg(2) + di=-.25+term*(1-term)+p1*(v1/(q1*chi1**2))**2*avg(1) + $ *(p1*(avg(3)+(twopif/chi1)**2*avg(4))-v2/v1) + h=twopif*p1*v1/(q1*chi1**3)*(avg(2)-avg(1)/avg(5)) + locstab%fs(ipsi,1)=di*locstab%xs(ipsi) + locstab%fs(ipsi,2)=(di+(h-0.5)**2)*locstab%xs(ipsi) + locstab%fs(ipsi,3)=h + ENDDO + CALL spline_dealloc(ff) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE mercier_scan + END MODULE mercier_mod diff --git a/src/DCON/fortran/ode.f b/src/DCON/fortran/ode.f new file mode 100644 index 000000000..5acdaa8d1 --- /dev/null +++ b/src/DCON/fortran/ode.f @@ -0,0 +1,1320 @@ +c----------------------------------------------------------------------- +c file ode.f. +c sets up and integrates Euler-Lagrange differential equations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. ode_mod. +c 1. ode_run. +c 2. ode_axis_init. +c 3. ode_sing_init. +c 4. ode_ideal_cross. +c 5. ode_kin_cross. +c 6. ode_resist_cross. +c 7. ode_step. +c 8. ode_unorm. +c 9. ode_fixup. +c 10. ode_test. +c 11. ode_test_fixup. +c 12. ode_record_edge +c----------------------------------------------------------------------- +c subprogram 0. ode_mod. +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + MODULE ode_mod + USE fourfit_mod + USE ode_output_mod + USE debug_mod + USE free_mod + IMPLICIT NONE + + LOGICAL :: new + LOGICAL, PARAMETER :: diagnose_ca=.FALSE. + CHARACTER(12) :: next + INTEGER, PRIVATE :: istate,liw,lrw,iopt,itask,itol,mf,ix + INTEGER, DIMENSION(20), PRIVATE :: iwork + REAL(r8), PRIVATE :: psiout + REAL(r8), PARAMETER, PRIVATE :: eps=1e-10 + REAL(r8), DIMENSION(:), POINTER, PRIVATE :: rwork + COMPLEX(r8), DIMENSION(:,:,:), POINTER :: atol + + INTEGER, DIMENSION(:), POINTER :: index + REAL(r8), DIMENSION(:), POINTER :: unorm,unorm0 + COMPLEX(r8), DIMENSION(:,:), POINTER :: fixfac + + CHARACTER(4) :: sort_type="absm" + INTEGER :: flag_count + + CONTAINS +c----------------------------------------------------------------------- +c subprogram 1. ode_run. +c integrates the differential equations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_run + + CHARACTER(64) :: message + LOGICAL :: force_output, test, first +c----------------------------------------------------------------------- +c initialize. +c----------------------------------------------------------------------- + IF(sing_start <= 0)THEN + CALL ode_axis_init + ELSE IF(sing_start <= msing)THEN + CALL ode_sing_init + ELSE + WRITE(message,'(2(a,i2))') + $ "sing_start = ",sing_start," > msing = ",msing + CALL program_stop(message) + ENDIF + flag_count=0 + CALL ode_output_open + IF(diagnose_ca)CALL ascii_open(ca_unit,"ca.out","UNKNOWN") +c----------------------------------------------------------------------- +c integrate. +c----------------------------------------------------------------------- + DO + first = .TRUE. + DO + IF(istep > 0)CALL ode_unorm(.FALSE.) + ! always record the first and last point in an inter-rational region + ! these are important for resonant quantities + ! recording the last point is cirtical for matching the nominal edge + test = ode_test() + force_output = first .OR. test + CALL ode_output_step(unorm, op_force=force_output) + CALL ode_record_edge + IF(test)EXIT + CALL ode_step + first = .FALSE. + ENDDO +c----------------------------------------------------------------------- +c re-initialize. +c----------------------------------------------------------------------- + IF(ising == ksing)EXIT + IF(next == "cross")THEN + IF(res_flag)THEN + CALL ode_resist_cross + ELSE + IF(kin_flag)THEN + CALL ode_kin_cross + ELSE + CALL ode_ideal_cross + ENDIF + ENDIF + ELSE + EXIT + ENDIF + flag_count=0 + ENDDO +c----------------------------------------------------------------------- +c finalize. +c----------------------------------------------------------------------- + CALL ode_output_close + DEALLOCATE(rwork,atol,unorm0,unorm,index,fixfac) + IF(diagnose_ca)CALL ascii_close(ca_unit) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_run +c----------------------------------------------------------------------- +c subprogram 2. ode_axis_init. +c initializes variables near axis. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_axis_init + + INTEGER :: ipert + REAL(r8), DIMENSION(mpert) :: key,m + INTEGER :: jpsi,it,itmax=50 + REAL(r8) :: dpsi,q,q1,eps=1e-10 +c----------------------------------------------------------------------- +c preliminary computations. +c----------------------------------------------------------------------- + new=.TRUE. + ix=0 + psiout=1 + psifac=sq%xs(0) +c----------------------------------------------------------------------- +c use newton iteration to find starting psi if qlow it is above q0 +c----------------------------------------------------------------------- + IF(qlow > sq%fs(0, 4))THEN + ! start check from the edge for robustness in reverse shear cores + DO jpsi = sq%mx-1, 1, -1 ! avoid starting iteration on endpoints + IF(sq%fs(jpsi - 1, 4) < qlow) EXIT + ENDDO + psifac=sq%xs(jpsi) + it=0 + DO + it=it+1 + CALL spline_eval(sq,psifac,1) + q=sq%f(4) + q1=sq%f1(4) + dpsi=(qlow-q)/q1 + psifac=psifac+dpsi + IF(ABS(dpsi) < eps*ABS(psifac) .OR. it > itmax)EXIT + ENDDO + ENDIF +c----------------------------------------------------------------------- +c find inner singular surface. +c----------------------------------------------------------------------- + ising=0 + IF(kin_flag)THEN + DO ising=1,kmsing + IF(kinsing(ising)%psifac > psifac) EXIT + ENDDO + ELSE + DO ising=1,msing + IF(sing(ising)%psifac > psifac) EXIT + ENDDO + ENDIF + ising = MAX(0, ising-1) +c----------------------------------------------------------------------- +c find next singular surface. +c----------------------------------------------------------------------- + IF(kin_flag)THEN + DO + ising=ising+1 + IF(ising > kmsing)EXIT + IF(psilim=nn*q)EXIT + ENDDO + IF(ising>kmsing.OR.singfac_min==0)THEN + psimax=psilim*(1-eps) + next="finish" + ELSEIF(psilim msing.OR.psilim=nn*q)EXIT + ENDDO + IF(ising>msing.OR.psilim 0)key=key-sing(1)%m + key=-ABS(key) + CASE DEFAULT + CALL program_stop("Cannot recognize sort_type = " + $ //TRIM(sort_type)) + END SELECT + CALL bubble(key,index,1,mpert) +c----------------------------------------------------------------------- +c initialize solutions. +c----------------------------------------------------------------------- + u=0 + DO ipert=1,mpert + u(index(ipert),ipert,2)=1 + ENDDO + msol=mpert + neq=4*mpert*msol + u_save=u + psi_save=psifac +c----------------------------------------------------------------------- +c initialize integrator parameters. +c----------------------------------------------------------------------- + istep=0 + iopt=1 + itask=5 + itol=2 + mf=10 + istate=1 +c----------------------------------------------------------------------- +c compute conditions at next singular surface. +c----------------------------------------------------------------------- + q=sq%fs(0,4) + IF(kin_flag)THEN + IF(kmsing > 0)THEN + m1=NINT(nn*kinsing(ising)%q) + ELSE + m1=NINT(nn*qlim)+NINT(SIGN(one,nn*sq%fs1(mpsi,4))) + ENDIF + ELSE + IF(msing > 0)THEN + m1=NINT(nn*sing(ising)%q) + ELSE + m1=NINT(nn*qlim)+NINT(SIGN(one,nn*sq%fs1(mpsi,4))) + ENDIF + ENDIF + singfac=ABS(m1-nn*q) +c----------------------------------------------------------------------- +c set up work arrays. +c----------------------------------------------------------------------- + liw=SIZE(iwork) + lrw=22+64*mpert*msol + ALLOCATE(rwork(lrw),atol(mpert,msol,2),fixfac(msol,msol)) + iwork=0 + rwork=0 + rwork(1)=psimax + rwork(5)=psifac*1e-3 + rwork(11)=rwork(5) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_axis_init +c----------------------------------------------------------------------- +c subprogram 3. ode_sing_init. +c re-initializes solution across singular surface. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_sing_init + + LOGICAL, PARAMETER :: diagnose=.FALSE.,old_init=.FALSE. + CHARACTER(1), DIMENSION(mpert) :: star + INTEGER :: ipert,isol,ipert0,ieq,m + REAL(r8) :: dpsi + COMPLEX(r8), DIMENSION(mpert,2*mpert,2) :: ua +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(3x,"mlow",1x,"mhigh",1x,"mpert",5x,"q",8x,"psifac",6x, + $ "dpsi",4x,"order"//3i6,1p,3e11.3,i6/) + 20 FORMAT(1x,a,i2,a,i3,": ",a) + 30 FORMAT(/5x,"i", + $ 2x,2(3x,"re u(",i1,")",4x,"im u(",i1,")",1x), + $ 2x,2(3x,"re du(",i1,")",3x,"im du(",i1,")")/) + 40 FORMAT((i6,1p,2(2x,4e11.3),a3)) +c----------------------------------------------------------------------- +c initialize position. +c----------------------------------------------------------------------- + new=.TRUE. + ising=sing_start + dpsi=singfac_min/ABS(nn*sing(ising)%q1)*10 + psifac=sing(ising)%psifac+dpsi + q=sing(ising)%q+dpsi*sing(ising)%q1 +c----------------------------------------------------------------------- +c allocate and initialize solutions. +c----------------------------------------------------------------------- + ALLOCATE(u(mpert,mpert,2),du(mpert,mpert,2),u_save(mpert,mpert,2), + $ unorm0(2*mpert),unorm(2*mpert),index(2*mpert)) + IF(old_init)THEN + u=0 + DO ipert=1,mpert + u(ipert,ipert,2)=1 + ENDDO + ELSE + CALL sing_get_ua(ising,psifac,ua) + u=ua(:,mpert+1:2*mpert,:) + ENDIF + u_save=u + psi_save=psifac + msol=mpert + neq=4*mpert*msol +c----------------------------------------------------------------------- +c diagnose output. +c----------------------------------------------------------------------- + IF(diagnose)THEN + CALL sing_der(neq,psifac,u,du) + CALL ascii_open(init_out_unit,"init.out","UNKNOWN") + WRITE(init_out_unit,'(1x,a/)')"Output from ode_sing_init" + WRITE(init_out_unit,10)mlow,mhigh,mpert,q,psifac,dpsi, + $ sing_order + ipert0=sing(ising)%m-mlow+1 + star=" " + star(ipert0)="*" + m=mlow + DO isol=1,msol + WRITE(init_out_unit,20)"isol = ",isol,", m = ",m,star(isol) + WRITE(init_out_unit,30)(ieq,ieq,ieq=1,2),(ieq,ieq,ieq=1,2), + $ (ieq,ieq,ieq=1,2) + WRITE(init_out_unit,40)(ipert,u(ipert,isol,:), + $ du(ipert,isol,:),star(ipert),ipert=1,mpert) + WRITE(init_out_unit,30)(ieq,ieq,ieq=1,2),(ieq,ieq,ieq=1,2), + $ (ieq,ieq,ieq=1,2) + m=m+1 + ENDDO + CALL ascii_close(init_out_unit) + CALL program_stop("Termination by ode_sing_init.") + ENDIF +c----------------------------------------------------------------------- +c compute conditions at next singular surface. +c----------------------------------------------------------------------- + DO + ising=ising+1 + IF(ising>msing.OR.psilim=nn*q)EXIT + ENDDO + IF(ising>msing.OR.psilimmsing.OR.psilim=nn*q)EXIT + ENDDO +c----------------------------------------------------------------------- +c compute conditions at next singular surface. +c----------------------------------------------------------------------- + IF(ising>msing.OR.psilim msing .OR. psilim < sing(ising)%psifac)EXIT + q=sing(ising)%q + IF(mlow <= nn*q .AND. mhigh >= nn*q)EXIT + ENDDO +c----------------------------------------------------------------------- +c compute conditions at next singular surface. +c----------------------------------------------------------------------- + IF(ising > msing .OR. psilim < sing(ising)%psifac)THEN + psimax=psilim*(1-eps) + m1=NINT(nn*qlim)+NINT(SIGN(one,nn*sq%fs1(mpsi,4))) + next="finish" + ELSE + psimax=sing(ising)%psifac-singfac_min/ABS(nn*sing(ising)%q1) + m1=NINT(nn*sing(ising)%q) + WRITE(crit_out_unit,20)ising,sing(ising)%psifac, + $ sing(ising)%q,sing(ising)%di,sing(ising)%alpha + ENDIF +c----------------------------------------------------------------------- +c restart ode solver. +c----------------------------------------------------------------------- + istate=1 + istep=istep+1 + rwork(1)=psimax + new=.TRUE. + u_save=u + psi_save=psifac +c----------------------------------------------------------------------- +c write to files. +c----------------------------------------------------------------------- + WRITE(crit_out_unit,30) + IF(crit_break)WRITE(crit_bin_unit) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_resist_cross +c----------------------------------------------------------------------- +c subprogram 7. ode_step. +c takes a step of the integrator. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_step + + INTEGER :: ipert,isol,ieq,jac,errloc(3) + REAL(r8) :: singfac,rtol,atol0,tol,dt,errmax,ewtmax + REAL(r8), PARAMETER :: dpsimax=1e-3,dpsimin=1e-5,dpsifac=2e-2 + COMPLEX(r8) :: err(mpert,msol,2),ewt(mpert,msol,2) + + LOGICAL, PARAMETER :: diagnose=.FALSE. + CHARACTER(256) :: message +c----------------------------------------------------------------------- +c compute relative tolerances. +c----------------------------------------------------------------------- + singfac=HUGE(singfac) + IF(kin_flag)THEN + IF(ising==1 .AND. kmsing>=1)THEN + singfac = abs(psifac - kinsing(ising)%psifac) / + $ (kinsing(ising)%psifac - psilow) + ELSEIF(ising<=kmsing)THEN + singfac = MIN(abs(psifac - kinsing(ising)%psifac), + $ abs(psifac - kinsing(ising-1)%psifac)) / + $ abs(kinsing(ising)%psifac - kinsing(ising-1)%psifac) + ENDIF + ELSE + IF(ising<=msing)singfac=ABS(sing(ising)%m-nn*q) + IF(ising>1)singfac=MIN(singfac,ABS(sing(ising-1)%m-nn*q)) + ENDIF + IF(singfac ucrit .OR. sing_flag)THEN + CALL ode_fixup(sing_flag,.FALSE.) + IF(diagnose)CALL ode_test_fixup + new=.TRUE. + ENDIF + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_unorm +c----------------------------------------------------------------------- +c subprogram 9. ode_fixup. +c performs Gaussian reduction of solution matrix. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_fixup(sing_flag,test) + + LOGICAL, INTENT(IN) :: sing_flag,test + + LOGICAL, PARAMETER :: diagnose=.FALSE.,secondary=.FALSE. + LOGICAL, SAVE :: new=.TRUE. + LOGICAL, DIMENSION(2,msol) :: mask + INTEGER :: ipert,isol,jsol,kpert,ksol + INTEGER, DIMENSION(1) :: jmax +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(/3x,"is",4x,"psifac",6x,"dpsi",8x,"q",7x,"singfac",5x, + $ "eval1"/) + 20 FORMAT(1x,a,i6,a,es10.3,a,f6.3) + 40 FORMAT(2(a,i3)) + 30 FORMAT(3x,"mlow",1x,"mhigh",1x,"mpert",2x,"msol",3x,"psifac", + $ 6x,"q"//4i6,1p,2e11.3/) + 50 FORMAT(/1x,"i",2(3x,"re u(",i1,")",4x,"im u(",i1,")",1x)/) + 60 FORMAT(i2,1p,4e11.3) +c----------------------------------------------------------------------- +c open output file and write initial values. +c----------------------------------------------------------------------- + IF(diagnose)THEN + IF(new)THEN + CALL ascii_open(init_out_unit,"fixup.out","UNKNOWN") + new=.FALSE. + ENDIF + WRITE(init_out_unit,30)mlow,mhigh,mpert,msol,psifac,q + WRITE(init_out_unit,'(/a/)')"input values:" + DO isol=1,msol + WRITE(init_out_unit,40)"isol = ",isol,", m = ",mlow+isol-1 + WRITE(init_out_unit,50)(ipert,ipert,ipert=1,2) + WRITE(init_out_unit,60)(ipert, + $ u(ipert,isol,:)/MAXVAL(ABS(u(:,isol,1))),ipert=1,mpert) + WRITE(init_out_unit,50)(ipert,ipert,ipert=1,2) + ENDDO + ENDIF +c----------------------------------------------------------------------- +c initial output. +c----------------------------------------------------------------------- + WRITE(crit_out_unit,10) + WRITE(crit_out_unit,20) + $ "Gaussian Reduction at istep = ",istep, + $ ", psi =",psifac,", q = ",q + IF(.NOT. sing_flag)WRITE(crit_out_unit,10) + istate=1 + flag_count=0 +c----------------------------------------------------------------------- +c initialize fixfac. +c----------------------------------------------------------------------- + IF(.NOT. test)THEN + fixfac=0 + DO isol=1,msol + fixfac(isol,isol)=1 + ENDDO +c----------------------------------------------------------------------- +c sort unorm. +c----------------------------------------------------------------------- + index(1:msol)=(/(ipert,ipert=1,msol)/) + CALL bubble(unorm,index,1,mpert) + CALL bubble(unorm,index,mpert+1,msol) + ENDIF +c----------------------------------------------------------------------- +c triangularize primary solutions. +c----------------------------------------------------------------------- + mask=.TRUE. + DO isol=1,mpert + ksol=index(isol) + mask(2,ksol)=.FALSE. + IF(.NOT. test)THEN + jmax=MAXLOC(ABS(u(:,ksol,1)),mask(1,1:mpert)) + kpert=jmax(1) + mask(1,kpert)=.FALSE. + ENDIF + DO jsol=1,msol + IF(mask(2,jsol))THEN + IF(.NOT. test)fixfac(ksol,jsol) + $ =-u(kpert,jsol,1)/u(kpert,ksol,1) + u(:,jsol,:)=u(:,jsol,:)+u(:,ksol,:)*fixfac(ksol,jsol) + IF(.NOT. test)u(kpert,jsol,1)=0 + ENDIF + ENDDO + ENDDO +c----------------------------------------------------------------------- +c triangularize secondary solutions. +c----------------------------------------------------------------------- + IF(msol > mpert .AND. secondary)THEN + mask=.TRUE. + DO isol=mpert+1,msol + ksol=index(isol) + mask(2,ksol)=.FALSE. + IF(.NOT. test)THEN + jmax=MAXLOC(ABS(u(:,ksol,2)),mask(1,1:mpert)) + kpert=jmax(1) + mask(1,kpert)=.FALSE. + ENDIF + DO jsol=mpert+1,msol + IF(mask(2,jsol))THEN + IF(.NOT. test)fixfac(ksol,jsol) + $ =-u(kpert,jsol,2)/u(kpert,ksol,2) + u(:,jsol,:)=u(:,jsol,:)+u(:,ksol,:)*fixfac(ksol,jsol) + IF(.NOT. test)u(kpert,jsol,2)=0 + ENDIF + ENDDO + ENDDO + ENDIF +c----------------------------------------------------------------------- +c save fixfac to file. +c----------------------------------------------------------------------- + IF(bin_euler. AND. .NOT. test)THEN + WRITE(euler_bin_unit)2 + WRITE(euler_bin_unit)sing_flag,msol + WRITE(euler_bin_unit)fixfac,index(1:msol) + ENDIF +c----------------------------------------------------------------------- +c write output values and close output file. +c----------------------------------------------------------------------- + IF(diagnose)THEN + WRITE(init_out_unit,'(/a/)')"output values:" + DO isol=1,msol + WRITE(init_out_unit,40)"isol = ",isol,", m = ",mlow+isol-1 + WRITE(init_out_unit,50)(ipert,ipert,ipert=1,2) + WRITE(init_out_unit,60)(ipert,u(ipert,isol,:),ipert=1,mpert) + WRITE(init_out_unit,50)(ipert,ipert,ipert=1,2) + ENDDO + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_fixup +c----------------------------------------------------------------------- +c subprogram 10. ode_test. +c tests for optimum approach to singular surface. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c delcarations. +c----------------------------------------------------------------------- + FUNCTION ode_test() RESULT(flag) + + LOGICAL :: flag + + INTEGER :: isol + REAL(r8), SAVE :: singfac_old,powmax + REAL(r8) :: dsingfac,norm,dnorm,powmax_old + REAL(r8), DIMENSION(msol) :: power + COMPLEX(r8), DIMENSION(mpert,msol,2) :: dca + COMPLEX(r8), DIMENSION(mpert,mpert,2) :: ufree +c----------------------------------------------------------------------- +c truncation test: lsode limit +c----------------------------------------------------------------------- + flag = psifac == psimax .OR. istep == nstep .OR. istate < 0 +c----------------------------------------------------------------------- +c simple return. +c----------------------------------------------------------------------- + IF(.NOT. res_flag .OR. flag + $ .OR. ising > msing .OR. singfac > singfac_max)RETURN +c----------------------------------------------------------------------- +c update values. +c----------------------------------------------------------------------- + ca_old=ca + CALL sing_get_ca(ising,psifac,u,ca) + dca=ca-ca_old + dsingfac=ABS((singfac-singfac_old)/singfac) + singfac_old=singfac +c----------------------------------------------------------------------- +c update powers. +c----------------------------------------------------------------------- + powmax_old=powmax + DO isol=1,msol + norm=ABS(SUM(CONJG(ca(:,isol,:))*ca(:,isol,:))) + dnorm=ABS(SUM(CONJG(ca(:,isol,:))*dca(:,isol,:))) + power(isol)=dnorm/(norm*dsingfac) + ENDDO + powmax=MAXVAL(power) +c----------------------------------------------------------------------- +c compute derivatives and flag. +c----------------------------------------------------------------------- + flag_count=flag_count+1 + IF(flag_count < 3)RETURN + flag=flag .OR. singfac < singfac_max .AND. powmax > powmax_old +c----------------------------------------------------------------------- +c diagnose. +c----------------------------------------------------------------------- + IF(ising == ksing)THEN + WRITE(err_unit)REAL(LOG10(singfac),4),REAL(LOG10(powmax),4) + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END FUNCTION ode_test +c----------------------------------------------------------------------- +c subprogram 11. ode_test_fixup. +c tests fixup routine. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_test_fixup + + CHARACTER(16)filename + INTEGER :: isol,ipert + INTEGER, SAVE :: ifix=0 + REAL(r8), DIMENSION(:,:,:), POINTER :: re,im + COMPLEX(r8), DIMENSION(:,:,:), POINTER :: u_old +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(/2x,"isol",2x,"index"/) + 20 FORMAT(2i6) + 30 FORMAT(2(a,i3)) + 40 FORMAT(/1x,"i",2(3x,"re u(",i1,")",4x,"im u(",i1,")",1x)/) + 50 FORMAT(i2,1p,4e11.3) +c----------------------------------------------------------------------- +c create initial u. +c----------------------------------------------------------------------- + ALLOCATE(u_old(mpert,msol,2),re(mpert,msol,2),im(mpert,msol,2)) + u_old=u + CALL put_seed(0) + CALL RANDOM_NUMBER(re) + CALL RANDOM_NUMBER(im) + u=CMPLX(re,im) + DEALLOCATE(re,im) +c----------------------------------------------------------------------- +c diagnose index. +c----------------------------------------------------------------------- + ifix=ifix+1 + WRITE(filename,'(a,i2.2,a)')"fixup_",ifix,".out" + CALL ascii_open(debug_unit,TRIM(filename),"UNKNOWN") + WRITE(debug_unit,10) + DO isol=1,msol + WRITE(debug_unit,20)isol,index(isol) + ENDDO + WRITE(debug_unit,10) +c----------------------------------------------------------------------- +c diagnose initial u. +c----------------------------------------------------------------------- + WRITE(debug_unit,'(/a/)')"initial values:" + DO isol=1,msol + WRITE(debug_unit,30)"isol = ",isol,", m = ",mlow+isol-1 + WRITE(debug_unit,40)(ipert,ipert,ipert=1,2) + WRITE(debug_unit,50)(ipert,u(ipert,isol,:),ipert=1,mpert) + WRITE(debug_unit,40)(ipert,ipert,ipert=1,2) + ENDDO +c----------------------------------------------------------------------- +c diagnose final u. +c----------------------------------------------------------------------- + CALL ode_fixup(.FALSE.,.TRUE.) + WRITE(debug_unit,'(/a/)')"final values:" + DO isol=1,msol + WRITE(debug_unit,30)"isol = ",isol,", m = ",mlow+isol-1 + WRITE(debug_unit,40)(ipert,ipert,ipert=1,2) + WRITE(debug_unit,50)(ipert,u(ipert,isol,:),ipert=1,mpert) + WRITE(debug_unit,40)(ipert,ipert,ipert=1,2) + ENDDO + CALL ascii_close(debug_unit) + u=u_old + DEALLOCATE(u_old) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_test_fixup +c----------------------------------------------------------------------- +c subprogram 12. ode_record_edge. +c record the energy in the edge +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_record_edge + LOGICAL, PARAMETER :: debug=.FALSE. + INTEGER, SAVE :: calc_number = 0 + COMPLEX(r8) :: total1, vacuum1, plasma1 + + CALL spline_eval(sq,psifac,0) + IF(size_edge > 0)THEN + IF(sq%f(4) >= q_edge(i_edge) .AND. psifac >= psiedge)THEN ! second codition handles initialization plasmas with q0~qa + CALL free_test(plasma1,vacuum1,total1,psifac) + IF(debug) WRITE(*,'(2(i4),6(es12.3))') calc_number, + $ i_edge,psifac,sq%f(4),q_edge(i_edge), + $ REAL(total1),REAL(vacuum1),REAL(plasma1) + calc_number = calc_number + 1 + dw_edge(i_edge) = total1 + q_edge(i_edge) = sq%f(4) + psi_edge(i_edge) = psifac + i_edge = MIN(i_edge + 1, size_edge) ! just to be extra safe + ENDIF + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_record_edge + + END MODULE ode_mod diff --git a/src/DCON/fortran/ode_output.f b/src/DCON/fortran/ode_output.f new file mode 100644 index 000000000..35b7adf51 --- /dev/null +++ b/src/DCON/fortran/ode_output.f @@ -0,0 +1,570 @@ +c----------------------------------------------------------------------- +c file ode_output.f. +c diagnoses main differential equations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. ode_output_mod. +c 1. ode_output_open +c 2. ode_output_step +c 3. ode_output_close +c 4. ode_output_get_evals. +c 5. ode_output_monitor. +c 6. ode_output_get_crit. +c 7. ode_output_sol. +c----------------------------------------------------------------------- +c subprogram 0. ode_mod. +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + MODULE ode_output_mod + USE sing_mod + USE dcon_mod, ONLY : shotnum,shottime + IMPLICIT NONE + + CHARACTER(6), DIMENSION(:), POINTER :: name + INTEGER, DIMENSION(:), POINTER :: sol_out_unit,sol_bin_unit + + INTEGER :: neq,ising,istep,m1,nzero + REAL(r8) :: psifac,psizero,singfac,q,psi_save,psimax,singfac_old, + $ psifac_old + REAL(r8) :: singfac_min=1e-5,singfac_max=1e-4 + COMPLEX(r8), DIMENSION(:,:,:), POINTER :: u,u_old,u_save,du, + $ ca,ca_old + + LOGICAL :: termbycross_flag=.FALSE. + + CONTAINS +c----------------------------------------------------------------------- +c subprogram 1. ode_output_open +c integrates the differential equations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_output_open + + INTEGER :: isol,iunit + REAL(r8), DIMENSION(:), POINTER :: xs,ys + REAL(r8), DIMENSION(:,:,:), POINTER :: fs,fsx,fsy,fsxy +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(/3x,"ising",3x,"psi",9x,"q",10x,"di",6x,"re alpha", + $ 3x,"im alpha"//i6,1p,5e11.3/) + 20 FORMAT(/3x,"is",4x,"psifac",6x,"dpsi",8x,"q",7x,"singfac",5x, + $ "eval1"/) + 30 FORMAT(3x,"mlow",4x,"m",2x,"mhigh",2x,"isol",2x,"msol"//5i6/) + 40 FORMAT(1x,2x,a,es10.3,a,f6.3) +c----------------------------------------------------------------------- +c allocate space for asymptotic coefficients. +c----------------------------------------------------------------------- + nzero=0 + ALLOCATE(ca(mpert,msol,2),ca_old(mpert,msol,2)) +c----------------------------------------------------------------------- +c open file for solutions. +c----------------------------------------------------------------------- + IF(bin_euler)THEN + xs => rzphi%xs + ys => rzphi%ys + fs => rzphi%fs + fsx => rzphi%fsx + fsy => rzphi%fsy + fsxy => rzphi%fsxy + CALL bin_open(euler_bin_unit,"euler.bin","UNKNOWN","REWIND", + $ "none") + WRITE(euler_bin_unit)mlow,mhigh,nn,mpsi,mtheta,ro,zo +c----------------------------------------------------------------------- +c +c----------------------------------------------------------------------- + WRITE(euler_bin_unit)mband,mthsurf0,mthvac,psio, + $ psilow,psilim,qlim,singfac_min + WRITE(euler_bin_unit)power_b,power_r,power_bp + WRITE(euler_bin_unit)kin_flag,con_flag + ! from sum1 equilibrium descriptions + WRITE(euler_bin_unit) amean,rmean,aratio,kappa,delta1,delta2, + $ li1,li2,li3,betap1,betap2,betap3,betat,betan,bt0, + $ q0,qmin,qmax,qa,crnt,q95,shotnum,shottime +c----------------------------------------------------------------------- + WRITE(euler_bin_unit)sq%xs,sq%fs,sq%fs1,sq%xpower + WRITE(euler_bin_unit)rzphi%xs,rzphi%ys, + $ rzphi%fs,rzphi%fsx,rzphi%fsy,rzphi%fsxy, + $ rzphi%x0,rzphi%y0,rzphi%xpower,rzphi%ypower + ENDIF +c----------------------------------------------------------------------- +c open output files for crit and write header. +c----------------------------------------------------------------------- + CALL ascii_open(crit_out_unit,"crit.out","UNKNOWN") + CALL bin_open(crit_bin_unit,"crit.bin","UNKNOWN","REWIND","none") + IF(out_evals)CALL ascii_open(evals_out_unit,"evals.out","UNKNOWN") + IF(bin_evals)CALL bin_open(evals_bin_unit,"evals.bin","UNKNOWN", + $ "REWIND","none") + IF(ising > 0 .AND. ising <= msing) + $ WRITE(crit_out_unit,10)ising,sing(ising)%psifac, + $ sing(ising)%q,sing(ising)%di,sing(ising)%alpha + WRITE(crit_out_unit,20) +c----------------------------------------------------------------------- +c define file names. +c----------------------------------------------------------------------- + IF(bin_sol)THEN + ALLOCATE(name(2*mpert)) + DO isol=1,2*mpert + WRITE(name(isol),'(a,i2.2)')"sol",isol + ENDDO + ENDIF +c----------------------------------------------------------------------- +c open binary output files for solutions. +c----------------------------------------------------------------------- + IF(bin_sol)THEN + bin_sol_min=1 + bin_sol_min=MAX(bin_sol_min,1) + IF(res_flag)THEN + bin_sol_max=MIN(bin_sol_max,mpert+2*msing,2*mpert) + ELSE + bin_sol_max=MIN(bin_sol_max,mpert) + ENDIF + IF(res_flag)THEN + bin_sol_max=MIN(2*mpert,9) + ELSE + bin_sol_max=MIN(mpert,9) + ENDIF + bin_sol_max=MIN(bin_sol_max,98+bin_sol_min-sol_base) + ALLOCATE(sol_bin_unit(bin_sol_min:bin_sol_max)) + sol_bin_unit=sol_base-bin_sol_min + $ +(/(isol,isol=bin_sol_min,bin_sol_max)/) + DO isol=bin_sol_min,bin_sol_max + iunit=sol_bin_unit(isol) + CALL bin_open(iunit,TRIM(name(isol))//".bin", + $ "UNKNOWN","REWIND","none") + ENDDO + CALL bin_open(unorm_unit,"unorm.bin","UNKNOWN","REWIND","none") + ENDIF +c----------------------------------------------------------------------- +c print initial point of integration. +c----------------------------------------------------------------------- + CALL spline_eval(sq,psifac,0) + q=sq%f(4) + IF(verbose) WRITE(*,40)"psi =",psifac,", q = ",q +c----------------------------------------------------------------------- +c open file for error output. +c----------------------------------------------------------------------- + IF(ksing > 0 .AND. ksing <= msing)THEN + CALL bin_open(err_unit,"error.bin","UNKNOWN","REWIND","none") + ALLOCATE(u_old(mpert,msol,2)) + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_output_open +c----------------------------------------------------------------------- +c subprogram 2. ode_output_step +c integrates the differential equations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_output_step(unorm, op_force) + + REAL(r8), DIMENSION(:), INTENT(IN) :: unorm + LOGICAL, OPTIONAL :: op_force + LOGICAL :: force + ! set optional parameters + force = .FALSE. + IF(PRESENT(op_force)) force = op_force +c----------------------------------------------------------------------- +c compute and print critical data for each time step. +c----------------------------------------------------------------------- + CALL ode_output_monitor + IF(out_evals .OR. bin_evals)CALL ode_output_get_evals +c----------------------------------------------------------------------- +c write solutions. +c----------------------------------------------------------------------- + IF(bin_euler .AND. (mod(istep,euler_stride) == 0 .OR. force))THEN + CALL sing_der(neq,psifac,u,du) + WRITE(euler_bin_unit)1 + WRITE(euler_bin_unit)psifac,q,msol + WRITE(euler_bin_unit)u + WRITE(euler_bin_unit)ud + ENDIF +c----------------------------------------------------------------------- +c output solutions components for each time step. +c----------------------------------------------------------------------- + IF(bin_sol)CALL ode_output_sol(psifac,u,unorm) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_output_step +c----------------------------------------------------------------------- +c subprogram 3. ode_output_close. +c produces ascii output for each step. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_output_close + + INTEGER :: isol +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + 10 FORMAT(1x,2x,a,es10.3,a,f6.3) + 20 FORMAT(/3x,"is",4x,"psifac",6x,"dpsi",8x,"q",7x,"singfac",5x, + $ "eval1"/) +c----------------------------------------------------------------------- +c close crit files. +c----------------------------------------------------------------------- + WRITE(term_unit,10)"psi =",psifac,", q = ",q + WRITE(crit_out_unit,20) + CALL ascii_close(crit_out_unit) + WRITE(crit_bin_unit) + CALL bin_close(crit_bin_unit) + DEALLOCATE(ca,ca_old) +c----------------------------------------------------------------------- +c close other files. +c----------------------------------------------------------------------- + IF(out_evals)CALL ascii_close(evals_out_unit) + IF(bin_evals)CALL bin_close(evals_bin_unit) + IF(ksing > 0 .AND. ksing <= msing)THEN + CALL bin_close(err_unit) + DEALLOCATE(u_old) + ENDIF +c----------------------------------------------------------------------- +c close binary output files. +c----------------------------------------------------------------------- + IF(bin_sol)DEALLOCATE(name) + IF(bin_sol)THEN + DO isol=bin_sol_min,bin_sol_max + CALL bin_close(sol_bin_unit(isol)) + ENDDO + CALL bin_close(unorm_unit) + DEALLOCATE(sol_bin_unit) + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_output_close +c----------------------------------------------------------------------- +c subprogram 4. ode_output_get_evals. +c computes critical criterminant. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_output_get_evals + + INTEGER :: info,ipert,lwork + INTEGER, DIMENSION(mpert) :: ipiv,index,indexi + + REAL(r8) :: logpsi1,logpsi2 + REAL(r8), DIMENSION(3*mpert-2) :: rwork + REAL(r8), DIMENSION(mpert) :: key,evals,evalsi + + COMPLEX(r8), DIMENSION(mpert,mpert) :: temp,wp + COMPLEX(r8), DIMENSION(2*mpert-1) :: work +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(/a,i4,1p,2(a,es10.3)) + 20 FORMAT(/5x,"i",5x,"eval",7x,"evali",7x,"err"/) + 30 FORMAT(i6,1p,3e11.3) +c----------------------------------------------------------------------- +c compute plasma response matrix. +c----------------------------------------------------------------------- + temp=CONJG(TRANSPOSE(u(:,1:mpert,1))) + wp=u(:,1:mpert,2) + wp=CONJG(TRANSPOSE(wp)) + CALL zgetrf(mpert,mpert,temp,mpert,ipiv,info) + CALL zgetrs('N',mpert,mpert,temp,mpert,ipiv,wp,mpert,info) + wp=(wp+CONJG(TRANSPOSE(wp)))/2 +c----------------------------------------------------------------------- +c compute and sort eigenvalues. +c----------------------------------------------------------------------- + lwork=2*mpert-1 + CALL zheev('N','U',mpert,wp,mpert,evals,work,lwork,rwork,info) + index=(/(ipert,ipert=1,mpert)/) + key=-ABS(1/evals) + CALL bubble(key,index,1,mpert) +c----------------------------------------------------------------------- +c compute and sort inverse eigenvalues. +c----------------------------------------------------------------------- + lwork=2*mpert-1 + CALL zheev('N','U',mpert,wp,mpert,evalsi,work,lwork,rwork,info) + indexi=(/(ipert,ipert=1,mpert)/) + key=-ABS(evalsi) + CALL bubble(key,indexi,1,mpert) +c----------------------------------------------------------------------- +c write ascii eigenvalues. +c----------------------------------------------------------------------- + IF(out_evals .AND. istep > 0)THEN + WRITE(evals_out_unit,10)"istep = ",istep, + $ ", psifac = ",psifac,", q = ",q + WRITE(evals_out_unit,20) + WRITE(evals_out_unit,30)(ipert, + $ evalsi(indexi(ipert)),evals(index(ipert)), + $ evalsi(indexi(ipert))*evals(index(ipert))-1, + $ ipert=1,mpert) + WRITE(evals_out_unit,20) + ENDIF +c----------------------------------------------------------------------- +c write binary eigenvalues. +c----------------------------------------------------------------------- + IF(bin_evals .AND. psifac > .1)THEN + CALL spline_eval(sq,psifac,0) + q=sq%f(4) + singfac=ABS(m1-nn*q) + logpsi1=LOG10(psifac) + logpsi2=LOG10(singfac) + DO ipert=2,mpert + WRITE(evals_bin_unit)REAL(ipert,4),REAL(psifac,4), + $ REAL(logpsi1,4),REAL(logpsi2,4), + $ REAL(q,4),REAL(1/evals(index(ipert)),4) + ENDDO + WRITE(evals_bin_unit) + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_output_get_evals +c----------------------------------------------------------------------- +c subprogram 5. ode_output_monitor. +c writes crit and monitors zero crossings. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_output_monitor + + REAL(r8) :: logpsi1,logpsi2,crit,fac, + $ psi_med,crit_med,q_med,singfac_med,logpsi1_med,logpsi2_med + REAL(r8), SAVE :: crit_save=0,psi_save=0,dpsi + COMPLEX(r8), DIMENSION(mpert,msol,2) :: u_med +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(i5,1p,6e11.3) + 20 FORMAT(1x,a,1p,e10.3,a,e10.3) +c----------------------------------------------------------------------- +c compute new crit. +c----------------------------------------------------------------------- + dpsi=psifac-psi_save + CALL ode_output_get_crit(psifac,u,q,singfac,logpsi1,logpsi2,crit) +c----------------------------------------------------------------------- +c check for zero crossing. +c----------------------------------------------------------------------- + IF(crit*crit_save < 0)THEN + fac=crit/(crit-crit_save) + psi_med=psifac-fac*(psifac-psi_save) + dpsi=psi_med-psi_save + u_med=u-fac*(u-u_save) + CALL ode_output_get_crit(psi_med,u_med,q_med,singfac_med, + $ logpsi1_med,logpsi2_med,crit_med) + IF((crit_med-crit)*(crit_med-crit_save) < 0 .AND. + $ ABS(crit_med) < .5*MIN(ABS(crit),ABS(crit_save)))THEN + WRITE(term_unit,20) + $ "Zero crossing at psi =",psi_med,", q =",q_med + WRITE(out_unit,20) + $ "Zero crossing at psi =",psi_med,", q =",q_med + WRITE(crit_out_unit,20) + $ "Zero crossing at psi =",psi_med,", q =",q_med + WRITE(crit_out_unit,10)istep,psi_med,dpsi,q_med, + $ singfac_med,crit_med + WRITE(crit_bin_unit)REAL(psi_med,4),REAL(logpsi1_med,4), + $ REAL(logpsi2_med,4),REAL(q_med,4),REAL(crit_med,4) + nzero=nzero+1 + ENDIF + IF (termbycross_flag) THEN + CALL program_stop("Terminated by zero crossing.") + ENDIF + ENDIF +c----------------------------------------------------------------------- +c write new crit. +c----------------------------------------------------------------------- + WRITE(crit_out_unit,10)istep,psifac,dpsi,q,singfac,crit + WRITE(crit_bin_unit)REAL(psifac,4),REAL(logpsi1,4), + $ REAL(logpsi2,4),REAL(q,4),REAL(crit,4) +c----------------------------------------------------------------------- +c update saved values. +c----------------------------------------------------------------------- + psi_save=psifac + crit_save=crit + u_save=u +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_output_monitor +c----------------------------------------------------------------------- +c subprogram 6. ode_output_get_crit. +c computes critical criterminant. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_output_get_crit(psi,u,q,singfac, + $ logpsi1,logpsi2,crit) + + REAL(r8), INTENT(IN) :: psi + COMPLEX(r8), DIMENSION(:,:,:), INTENT(IN) :: u + REAL(r8), INTENT(OUT) :: q,singfac,logpsi1,logpsi2,crit + + INTEGER :: info,ipert,lwork + INTEGER, DIMENSION(mpert) :: ipiv,indexi + REAL(r8), DIMENSION(3*mpert-2) :: rwork + REAL(r8), DIMENSION(mpert) :: key,evalsi + COMPLEX(r8), DIMENSION(mpert,mpert) :: temp,wp + COMPLEX(r8), DIMENSION(2*mpert-1) :: work + COMPLEX(r8), DIMENSION(mpert,mpert,2) :: uu +c----------------------------------------------------------------------- +c compute dependent variables. +c----------------------------------------------------------------------- + uu=u(:,1:mpert,:) +c----------------------------------------------------------------------- +c compute inverse plasma response matrix. +c----------------------------------------------------------------------- + wp=CONJG(TRANSPOSE(uu(:,:,1))) + temp=uu(:,:,2) + temp=CONJG(TRANSPOSE(temp)) + CALL zgetrf(mpert,mpert,temp,mpert,ipiv,info) + CALL zgetrs('N',mpert,mpert,temp,mpert,ipiv,wp,mpert,info) + wp=(wp+CONJG(TRANSPOSE(wp)))/2 +c----------------------------------------------------------------------- +c compute and sort inverse eigenvalues. +c----------------------------------------------------------------------- + lwork=2*mpert-1 + CALL zheev('N','U',mpert,wp,mpert,evalsi,work,lwork,rwork,info) + indexi=(/(ipert,ipert=1,mpert)/) + key=-ABS(evalsi) + CALL bubble(key,indexi,1,mpert) +c----------------------------------------------------------------------- +c compute critical data for each time step. +c----------------------------------------------------------------------- + CALL spline_eval(sq,psi,0) + q=sq%f(4) + singfac=ABS(m1-nn*q) + logpsi1=LOG10(psi) + logpsi2=LOG10(singfac) + crit=evalsi(indexi(1))*sq%f(3)**2 +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_output_get_crit +c----------------------------------------------------------------------- +c subprogram 7. ode_output_sol. +c produces binary output for each step. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE ode_output_sol(psifac,u,unorm) + + REAL(r8), INTENT(IN) :: psifac + COMPLEX(r8), DIMENSION(mpert,msol,2), INTENT(IN) :: u + REAL(r8), DIMENSION(:), INTENT(IN) :: unorm + + INTEGER :: isol,ipert,iunit,jsing + REAL(r8) :: psil,psir,psiminl,psiminr,a,b,x,singlog + REAL(r8), DIMENSION(mpert) :: logunorm + COMPLEX(r8), DIMENSION(mpert,msol,2) :: uu,ca + COMPLEX(r8), DIMENSION(mpert,2) :: logu,logca +c----------------------------------------------------------------------- +c determine singular interval. +c----------------------------------------------------------------------- + jsing=1 + DO + IF(jsing > msing)EXIT + IF(sing(jsing)%psifac > psifac)EXIT + jsing=jsing+1 + ENDDO +c----------------------------------------------------------------------- +c compute left edge of interval. +c----------------------------------------------------------------------- + IF(jsing == 1)THEN + psil=0 + psiminl=psilow + ELSE + psil=sing(jsing-1)%psifac + psiminl=singfac_min/ABS(nn*sing(jsing-1)%q1) + ENDIF +c----------------------------------------------------------------------- +c compute right edge of interval. +c----------------------------------------------------------------------- + IF(jsing > msing)THEN + psiminr=psiminl + psir=psilim+psiminr + ELSE + psir=sing(jsing)%psifac + psiminr=singfac_min/ABS(nn*sing(jsing)%q1) + ENDIF +c----------------------------------------------------------------------- +c compute abscissa. +c----------------------------------------------------------------------- + b=2/(LOG10((psir-psil-psiminl)/psiminl) + $ +LOG10((psir-psil-psiminr)/psiminr)) + a=b*LOG10((psir-psil-psiminl)/psiminl)+2*jsing-2 + x=a+b*LOG10((psifac-psil)/(psir-psifac)) + singlog=LOG10(ABS(singfac)) +c----------------------------------------------------------------------- +c compute solutions and asymptotic coefficients. +c----------------------------------------------------------------------- + uu=u + IF(psil < psir .AND. jsing > 1 .AND. psifac-psil < psir-psifac + $ .OR. jsing > msing)THEN + CALL sing_get_ca(jsing-1,psifac,uu,ca) + ELSE + CALL sing_get_ca(jsing,psifac,uu,ca) + ENDIF +c----------------------------------------------------------------------- +c compute logu and logca +c----------------------------------------------------------------------- + DO isol=MAX(1,bin_sol_min),MIN(bin_sol_max,msol) + iunit=sol_bin_unit(isol) + WHERE(uu(:,isol,:) /= 0) + logu=LOG(uu(:,isol,:)) + ELSEWHERE + logu=0 + END WHERE + WHERE(ca(:,isol,:) /= 0) + logca=LOG(ca(:,isol,:)) + ELSEWHERE + logca=0 + END WHERE +c----------------------------------------------------------------------- +c write binary output. +c----------------------------------------------------------------------- + DO ipert=1,mpert + WRITE(iunit)REAL(psifac,4),REAL(LOG10(psifac),4),REAL(x,4), + $ REAL(DREAL(logu(ipert,:))/alog10,4), + $ REAL(DREAL(logca(ipert,:))/alog10,4), + $ REAL(LOG10(ABS((psifac-sing(1)%psifac) + $ /(nn*sing(1)%q1)))),REAL(singlog,4) + ENDDO + WRITE(iunit) + ENDDO +c----------------------------------------------------------------------- +c diagnose unorm. +c----------------------------------------------------------------------- + WHERE(unorm(1:mpert) > 1) + logunorm=LOG10(unorm(1:mpert)) + ELSEWHERE + logunorm=0 + ENDWHERE + DO isol=1,mpert + WRITE(unorm_unit)REAL(isol,4),REAL(psifac,4), + $ REAL(LOG10(psifac),4),REAL(x,4), + $ REAL(logunorm(isol),4) + ENDDO + WRITE(unorm_unit) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE ode_output_sol + END MODULE ode_output_mod diff --git a/src/DCON/fortran/resist.f b/src/DCON/fortran/resist.f new file mode 100644 index 000000000..0aa572cf9 --- /dev/null +++ b/src/DCON/fortran/resist.f @@ -0,0 +1,155 @@ +c----------------------------------------------------------------------- +c file resist.f. +c computes resistive surface quantities. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. resist_mod. +c 1. resist_eval. +c----------------------------------------------------------------------- +c subprogram 0. resist_mod. +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + MODULE resist_mod + USE dcon_mod + IMPLICIT NONE + + CONTAINS +c----------------------------------------------------------------------- +c subprogram 1. resist_eval. +c computes resistive surface quantities. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE resist_eval(sing) + + TYPE(sing_type), INTENT(INOUT) :: sing + + LOGICAL, PARAMETER :: diagnose=.FALSE. + INTEGER :: itheta + REAL(r8) :: bsq,chi1,dpsisq,eta,jac,lambda,p,p1,psifac,q,q1,r, + $ rfac,taue,theta,twopif,v1,v2,v21,v22,v23,v33 + REAL(r8), PARAMETER :: ne=1e14,te=3e3,mi=2*mp,gamma=5._r8/3._r8 + REAL(r8), DIMENSION(:), POINTER :: avg + TYPE(spline_type), TARGET :: ff +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(a,1p,e10.3) +c----------------------------------------------------------------------- +c prepare spline types. +c----------------------------------------------------------------------- + CALL spline_alloc(ff,mtheta,6) + ff%xs=rzphi%ys +c----------------------------------------------------------------------- +c compute surface quantities. +c----------------------------------------------------------------------- + psifac=sing%psifac + CALL spline_eval(sq,psifac,1) + twopif=sq%f(1) + p=sq%f(2) + p1=sq%f1(2) + v1=sq%f(3) + v2=sq%f1(3) + q=sq%f(4) + q1=sq%f1(4) + chi1=twopi*psio +c----------------------------------------------------------------------- +c evaluate coordinates and jacobian. +c----------------------------------------------------------------------- + DO itheta=0,mtheta + theta=rzphi%ys(itheta) + CALL bicube_eval(rzphi,psifac,theta,1) + rfac=SQRT(rzphi%f(1)) + eta=twopi*(theta+rzphi%f(2)) + r=ro+rfac*COS(eta) + jac=rzphi%f(4) +c----------------------------------------------------------------------- +c evaluate other local quantities. +c----------------------------------------------------------------------- + v21=rzphi%fy(1)/(2*rfac*jac) + v22=(1+rzphi%fy(2))*twopi*rfac/jac + v23=rzphi%fy(3)*r/jac + v33=twopi*r/jac + bsq=chi1**2*(v21**2+v22**2+(v23+q*v33)**2) + dpsisq=(twopi*r)**2*(v21**2+v22**2) +c----------------------------------------------------------------------- +c evaluate integrands. +c----------------------------------------------------------------------- + ff%fs(itheta,1)=bsq/dpsisq + ff%fs(itheta,2)=1/dpsisq + ff%fs(itheta,3)=1/bsq + ff%fs(itheta,4)=1/(bsq*dpsisq) + ff%fs(itheta,5)=bsq + ff%fs(itheta,6)=dpsisq/bsq + ff%fs(itheta,:)=ff%fs(itheta,:)*jac/v1 + ENDDO +c----------------------------------------------------------------------- +c integrate quantities with respect to theta. +c----------------------------------------------------------------------- + CALL spline_fit(ff,"periodic") + CALL spline_int(ff) + avg => ff%fsi(mtheta,:) +c----------------------------------------------------------------------- +c compute resistive curvature terms E, F, and H. +c----------------------------------------------------------------------- + sing%restype%e=p1*v1/(q1*chi1**2)**2*avg(1) + $ *(twopif*q1*chi1/avg(5)-v2) + sing%restype%f=(p1*v1/(q1*chi1**2))**2*(avg(1)*avg(3) + $ +(twopif/chi1)**2*(avg(1)*avg(4)-avg(2)**2)) + sing%restype%h=twopif*p1*v1/(q1*chi1**3)*(avg(2)-avg(1)/avg(5)) +c----------------------------------------------------------------------- +c computes mass factor and related terms, M, G, and K. +c----------------------------------------------------------------------- + sing%restype%m=avg(1)*(avg(6)+(twopif/chi1)**2*(avg(3)-1/avg(5))) + sing%restype%g=avg(5)/(sing%restype%m*gamma*p) + sing%restype%k=(q1*chi1**2/(p1*v1))**2 + $ *avg(5)/(sing%restype%m*avg(1)) +c----------------------------------------------------------------------- +c compute resistivity and density. +c----------------------------------------------------------------------- + lambda=24-.5*LOG(ne)+LOG(te) + taue=3.44e5*te**1.5/(ne*lambda) + sing%restype%eta=me/(ne*1e6*e**2*taue*1.96) + sing%restype%rho=ne*mi*1e6 +c----------------------------------------------------------------------- +c compute Alfven and resistive time scales. +c----------------------------------------------------------------------- + sing%restype%taua=SQRT(sing%restype%rho*sing%restype%m*mu0) + $ /ABS(twopi*nn*sing%q1*chi1/v1) + sing%restype%taur=avg(1)/avg(5)*mu0/sing%restype%eta +c----------------------------------------------------------------------- +c diagnose. +c----------------------------------------------------------------------- + IF(diagnose)THEN + WRITE(*,10)"q = ",sing%q + WRITE(*,10)"q1 = ",sing%q1 + WRITE(*,10)"e = ",sing%restype%e + WRITE(*,10)"f = ",sing%restype%f + WRITE(*,10)"h = ",sing%restype%h + WRITE(*,10)"m = ",sing%restype%m + WRITE(*,10)"g = ",sing%restype%g + WRITE(*,10)"k = ",sing%restype%k + WRITE(*,10)"rho = ",sing%restype%rho + WRITE(*,10)"taue = ",taue + WRITE(*,10)"taua = ",sing%restype%taua + WRITE(*,10)"taur = ",sing%restype%taur + WRITE(*,10)"sfac = ",sing%restype%taur/sing%restype%taua + WRITE(*,10)"eta = ",sing%restype%eta + CALL program_stop("Termination by resist_eval.") + ENDIF +c----------------------------------------------------------------------- +c deallocate. +c----------------------------------------------------------------------- + CALL spline_dealloc(ff) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE resist_eval + END MODULE resist_mod diff --git a/src/DCON/fortran/sing.f b/src/DCON/fortran/sing.f new file mode 100644 index 000000000..5ffb77e86 --- /dev/null +++ b/src/DCON/fortran/sing.f @@ -0,0 +1,1817 @@ +c----------------------------------------------------------------------- +c file sing.f. +c computations relating to singular surfaces. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. sing_mod. +c 1. sing_scan. +c 2. sing_find. +c 3. sing_lim. +c 4. sing_vmat. +c 5. sing_mmat. +c 6. sing_solve. +c 7. sing_matmul. +c 8. sing_vmat_diagnose. +c 9. sing_get_ua. +c 10. sing_get_ca. +c 11. sing_der. +c 12. sing_ua_diagnose. +c 13. sing_get_f_det. +c 14. ksing_find. +c 15. sing_adp_find_sing. +c 16. sing_newton. +c----------------------------------------------------------------------- +c subprogram 0. sing_mod. +c module declarations. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + MODULE sing_mod + USE fourfit_mod + IMPLICIT NONE + + INTEGER :: msol,sing_order=2 + REAL(r8) :: det_max + INTEGER, DIMENSION(:), POINTER :: r1,r2,n1,n2 + COMPLEX(r8), DIMENSION(2,2) :: m0mat + COMPLEX(r8), DIMENSION(:,:), ALLOCATABLE :: sing_detf + + CONTAINS +c----------------------------------------------------------------------- +c subprogram 1. sing_scan. +c scans singular surfaces and prints information about them. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_scan + + INTEGER :: ising +c----------------------------------------------------------------------- +c write formats. +c----------------------------------------------------------------------- + 10 FORMAT(/2x,"i",5x,"psi",8x,"rho",9x,"q",10x,"q1",8x,"di0",9x,"di", + $ 8x,"err"/) +c----------------------------------------------------------------------- +c scan over singular surfaces and print output. +c----------------------------------------------------------------------- + WRITE(out_unit,'(/1x,a)')"Singular Surfaces:" + WRITE(out_unit,10) + msol=mpert + DO ising=1,msing + CALL sing_vmat(ising) + ENDDO + WRITE(out_unit,10) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_scan +c----------------------------------------------------------------------- +c subprogram 2. sing_find. +c finds positions of singular values of q. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_find + + INTEGER, PARAMETER :: itmax=200,nsing=1000 + INTEGER :: iex,ising,m,dm,it + INTEGER, DIMENSION(nsing) :: m_sing + REAL(r8) :: dq,psifac,psifac0,psifac1,singfac + REAL(r8), DIMENSION(nsing) :: psising,qsing,q1sing +c----------------------------------------------------------------------- +c start loop over extrema to find singular surfaces. +c----------------------------------------------------------------------- + ising=0 + DO iex=1,mex + dq=qex(iex)-qex(iex-1) + m=nn*qex(iex-1) + IF(dq > 0)m=m+1 + dm=SIGN(one,dq*nn) +c----------------------------------------------------------------------- +c find singular surfaces by binary search. +c----------------------------------------------------------------------- + DO + IF((m-nn*qex(iex-1))*(m-nn*qex(iex)) > 0)EXIT + it=0 + psifac0=psiex(iex-1) + psifac1=psiex(iex) + DO + it=it+1 + psifac=(psifac0+psifac1)/2 + CALL spline_eval(sq,psifac,0) + singfac=(m-nn*sq%f(4))*dm + IF(singfac > 0)THEN + psifac0=psifac + psifac=(psifac+psifac1)/2 + ELSE + psifac1=psifac + psifac=(psifac+psifac0)/2 + ENDIF + IF(ABS(singfac) <= 1e-12)EXIT + IF(it > itmax) + $ CALL program_stop("sing_find can't find root") + ENDDO +c----------------------------------------------------------------------- +c store singular surfaces. +c----------------------------------------------------------------------- + ising=ising+1 + CALL spline_eval(sq,psifac,1) + m_sing(ising)=m + qsing(ising)=REAL(m,r8)/nn + q1sing(ising)=sq%f1(4) + psising(ising)=psifac + m=m+dm + ENDDO + ENDDO +c----------------------------------------------------------------------- +c transfer to permanent storage. +c----------------------------------------------------------------------- + msing=ising + ALLOCATE(sing(msing)) + DO ising=1,msing + sing(ising)%m=m_sing(ising) + sing(ising)%psifac=psising(ising) + sing(ising)%rho=SQRT(psising(ising)) + sing(ising)%q=qsing(ising) + sing(ising)%q1=q1sing(ising) + ENDDO + DEALLOCATE(psiex,qex) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_find +c----------------------------------------------------------------------- +c subprogram 3. sing_lim. +c computes limiter values. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_lim + + INTEGER :: it,itmax=50 + INTEGER, DIMENSION(1) :: jpsi + REAL(r8) :: dpsi,q,q1,eps=1e-10 + + INTEGER :: i + REAL(r8) :: qedgestart +c----------------------------------------------------------------------- +c compute psilim and qlim. +c----------------------------------------------------------------------- + qlim=MIN(qmax,qhigh) + q1lim=sq%fs1(mpsi,4) + psilim=psihigh + IF(sas_flag)THEN +c----------------------------------------------------------------------- +c normalze dmlim to interval [0,1). +c----------------------------------------------------------------------- + DO + IF(dmlim < 1)EXIT + dmlim=dmlim-1 + ENDDO + DO + IF(dmlim >= 0)EXIT + dmlim=dmlim+1 + ENDDO +c----------------------------------------------------------------------- +c compute qlim. +c----------------------------------------------------------------------- + qlim=(INT(nn*qlim)+dmlim)/nn + DO + IF(qlim <= qmax)EXIT + qlim=qlim-1._r8/nn + ENDDO + ENDIF +c----------------------------------------------------------------------- +c use newton iteration to find psilim. +c----------------------------------------------------------------------- + IF(qlim= mpsi) jpsi(1)=mpsi-1 + psilim=sq%xs(jpsi(1)) + it=0 + DO + it=it+1 + CALL spline_eval(sq,psilim,1) + q=sq%f(4) + q1=sq%f1(4) + dpsi=(qlim-q)/q1 + psilim=psilim+dpsi + IF(ABS(dpsi) < eps*ABS(psilim) .OR. it > itmax)EXIT + ENDDO + q1lim=q1 +c----------------------------------------------------------------------- +c abort if not found. +c----------------------------------------------------------------------- + IF(it > itmax)THEN + CALL program_stop("Can't find psilim.") + ENDIF + ELSE + qlim = qmax + q1lim=sq%fs1(mpsi,4) + psilim=psihigh + ENDIF +c----------------------------------------------------------------------- +c set up record for determining the peak in dW near the boundary. +c----------------------------------------------------------------------- + IF(psiedge < psilim)THEN + CALL spline_eval(sq, psiedge, 0) + qedgestart = INT(sq%f(4)) + size_edge = CEILING((qlim - qedgestart) * nn * nperq_edge) + ALLOCATE(dw_edge(size_edge), q_edge(size_edge), + $ psi_edge(size_edge)) + q_edge(:) = qedgestart + (/(i*1.0,i=0,size_edge-1)/) / + $ (nperq_edge*nn) + psi_edge(:) = 0.0 + dw_edge(:) = -huge(0.0_r8) * (1 + ifac) + ! we monitor some deeper points for an informative profile + ! output over a full rational window + ! but we still respect the user psiedge when looking for peak dW + pre_edge = 1 + DO i=1,size_edge + IF(q_edge(i) < sq%f(4)) pre_edge = pre_edge + 1 + ENDDO + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_lim +c----------------------------------------------------------------------- +c subprogram 4. sing_vmat. +c computes asymptotic behavior at the singular surface. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_vmat(ising) + + INTEGER, INTENT(IN) :: ising + + LOGICAL, PARAMETER :: diagnose=.FALSE. + INTEGER :: ipert0,ipert,k + REAL(r8) :: psifac,di,di0,q,q1,rho,dpsi + REAL(r8), PARAMETER :: half=.5_r8 + COMPLEX(r8) :: det + TYPE(sing_type), POINTER :: singp +c----------------------------------------------------------------------- +c allocate and initialize solution array. +c----------------------------------------------------------------------- + IF(ising < 1 .OR. ising > msing)RETURN + singp => sing(ising) + ALLOCATE(singp%vmat(mpert,2*mpert,2,0:2*sing_order), + $ singp%mmat(mpert,2*mpert,2,0:2*sing_order+2)) +c----------------------------------------------------------------------- +c zero di if out of range. +c----------------------------------------------------------------------- + ipert0=NINT(nn*singp%q)-mlow+1 + q=singp%q + IF(ipert0 <= 0 .OR. mlow > nn*q .OR. mhigh < nn*q)THEN + singp%di=0 + RETURN + ENDIF +c----------------------------------------------------------------------- +c allocate and compute ranges. +c----------------------------------------------------------------------- + ALLOCATE(sing(ising)%n1(mpert-1),sing(ising)%n2(2*mpert-2)) + singp%r1=(/ipert0/) + singp%r2=(/ipert0,ipert0+mpert/) + singp%n1=(/(ipert,ipert=1,ipert0-1),(ipert,ipert=ipert0+1,mpert)/) + singp%n2=(/singp%n1,singp%n1+mpert/) + r1 => singp%r1 + r2 => singp%r2 + n1 => singp%n1 + n2 => singp%n2 +c----------------------------------------------------------------------- +c interpolate local values. +c----------------------------------------------------------------------- + psifac=singp%psifac + CALL spline_eval(locstab,psifac,0) + di0=locstab%f(1)/psifac + q1=singp%q1 + rho=singp%rho +c----------------------------------------------------------------------- +c compute Mercier criterion and singular power. +c----------------------------------------------------------------------- + CALL sing_mmat(ising) + m0mat=TRANSPOSE(singp%mmat(r1(1),r2,:,0)) + di=m0mat(1,1)*m0mat(2,2)-m0mat(2,1)*m0mat(1,2) + singp%di=di + singp%alpha=SQRT(-CMPLX(singp%di)) + ALLOCATE(singp%power(2*mpert)) + singp%power=0 + singp%power(ipert0)=-singp%alpha + singp%power(ipert0+mpert)=singp%alpha + WRITE(out_unit,'(i3,1p,7e11.3)')ising,psifac,rho,q,q1,di0, + $ singp%di,singp%di/di0-1 +c----------------------------------------------------------------------- +c zeroth-order non-resonant solutions. +c----------------------------------------------------------------------- + singp%vmat=0 + DO ipert=1,mpert + singp%vmat(ipert,ipert,1,0)=1 + singp%vmat(ipert,ipert+mpert,2,0)=1 + ENDDO +c----------------------------------------------------------------------- +c zeroth-order resonant solutions. +c----------------------------------------------------------------------- + singp%vmat(ipert0,ipert0,1,0)=1 + singp%vmat(ipert0,ipert0+mpert,1,0)=1 + singp%vmat(ipert0,ipert0,2,0) + $ =-(m0mat(1,1)+singp%alpha)/m0mat(1,2) + singp%vmat(ipert0,ipert0+mpert,2,0) + $ =-(m0mat(1,1)-singp%alpha)/m0mat(1,2) + det=CONJG(singp%vmat(ipert0,ipert0,1,0)) + $ *singp%vmat(ipert0,ipert0+mpert,2,0) + $ -CONJG(singp%vmat(ipert0,ipert0+mpert,1,0)) + $ *singp%vmat(ipert0,ipert0,2,0) + singp%vmat(ipert0,:,:,0)=singp%vmat(ipert0,:,:,0)/SQRT(det) +c----------------------------------------------------------------------- +c compute higher-order solutions. +c----------------------------------------------------------------------- + DO k=1,2*sing_order + CALL sing_solve(k,singp%power,singp%mmat,singp%vmat) + ENDDO +c----------------------------------------------------------------------- +c diagnose. +c----------------------------------------------------------------------- + IF(diagnose)THEN + CALL sing_vmat_diagnose(ising) + dpsi=-1e-2 + CALL sing_ua_diagnose(ising,dpsi) + CALL program_stop("Termination by sing_vmat.") + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_vmat +c----------------------------------------------------------------------- +c subprogram 5. sing_mmat. +c computes series expansion of coefficient matrix. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_mmat(ising) + + INTEGER, INTENT(IN) :: ising + + INTEGER :: ipert0,ipert,jpert,kpert,isol,iqty,info,msol,m,i,j,n, + $ fac0,fac1 + INTEGER, DIMENSION(mpert) :: mvec + REAL(r8) :: psifac + REAL(r8), DIMENSION(0:3) :: q + REAL(r8), DIMENSION(mpert,0:3) :: singfac + COMPLEX(r8), PARAMETER :: one=1,half=.5_r8 + COMPLEX(r8), DIMENSION(mband+1,mpert,0:sing_order) :: f,ff,g + COMPLEX(r8), DIMENSION(mband+1,mpert) :: f0 + COMPLEX(r8), DIMENSION(2*mband+1,mpert,0:sing_order) :: k + COMPLEX(r8), DIMENSION(mpert,2*mpert,2) :: v + COMPLEX(r8), DIMENSION(mpert,2*mpert,2,0:sing_order) :: x + COMPLEX(r8), DIMENSION(:,:,:,:), POINTER :: mmat + + LOGICAL, PARAMETER :: diagnose=.FALSE. +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(/4x,"io",4x,"is",4x,"ip",2(4x,"re x",i1,6x,"im x",i1,2x)/) + 20 FORMAT(3i6,1p,4e11.3) +c----------------------------------------------------------------------- +c evaluate cubic splines. +c----------------------------------------------------------------------- + msol=2*mpert + psifac=sing(ising)%psifac + CALL spline_eval(sq,psifac,3) + CALL cspline_eval(fmats,psifac,3) + CALL cspline_eval(gmats,psifac,3) + CALL cspline_eval(kmats,psifac,3) +c----------------------------------------------------------------------- +c evaluate safety factor and its derivatives. +c----------------------------------------------------------------------- + q(0)=sq%f(4) + q(1)=sq%f1(4) + q(2)=sq%f2(4) + q(3)=sq%f3(4) +c----------------------------------------------------------------------- +c evaluate singfac and its derivatives. +c----------------------------------------------------------------------- + ipert0=sing(ising)%m-mlow+1 + mvec=(/(m,m=mlow,mhigh)/) + singfac=0 + singfac(:,0)=mvec-nn*q(0) + singfac(:,1)=-nn*q(1) + singfac(:,2)=-nn*q(2) + singfac(:,3)=-nn*q(3) + singfac(ipert0,0)=-nn*q(1) + singfac(ipert0,1)=-nn*q(2)/2 + singfac(ipert0,2)=-nn*q(3)/3 + singfac(ipert0,3)=0 +c----------------------------------------------------------------------- +c compute factored Hermitian banded matrix F and its derivatives. +c----------------------------------------------------------------------- + f=0 + iqty=0 + DO jpert=1,mpert + DO ipert=jpert,MIN(mpert,jpert+mband) + iqty=iqty+1 + f(1+ipert-jpert,jpert,0) + $ =singfac(ipert,0)*fmats%f(iqty) + IF(sing_order < 1)CYCLE + f(1+ipert-jpert,jpert,1) + $ =singfac(ipert,0)*fmats%f1(iqty) + $ +singfac(ipert,1)*fmats%f(iqty) + IF(sing_order < 2)CYCLE + f(1+ipert-jpert,jpert,2) + $ =singfac(ipert,0)*fmats%f2(iqty) + $ +2*singfac(ipert,1)*fmats%f1(iqty) + $ +singfac(ipert,2)*fmats%f(iqty) + IF(sing_order < 3)CYCLE + f(1+ipert-jpert,jpert,3) + $ =singfac(ipert,0)*fmats%f3(iqty) + $ +3*singfac(ipert,1)*fmats%f2(iqty) + $ +3*singfac(ipert,2)*fmats%f1(iqty) + $ +singfac(ipert,3)*fmats%f(iqty) + IF(sing_order < 4)CYCLE + f(1+ipert-jpert,jpert,4) + $ =4*singfac(ipert,1)*fmats%f3(iqty) + $ +6*singfac(ipert,2)*fmats%f2(iqty) + $ +4*singfac(ipert,3)*fmats%f1(iqty) + IF(sing_order < 5)CYCLE + f(1+ipert-jpert,jpert,5) + $ =10*singfac(ipert,2)*fmats%f3(iqty) + $ +10*singfac(ipert,3)*fmats%f2(iqty) + IF(sing_order < 6)CYCLE + f(1+ipert-jpert,jpert,5) + $ =20*singfac(ipert,3)*fmats%f3(iqty) + ENDDO + ENDDO + f0=f(:,:,0) +c----------------------------------------------------------------------- +c compute product of factored Hermitian banded matrix F. +c----------------------------------------------------------------------- + ff=0 + fac0=1 + DO n=0,sing_order + fac1=1 + DO j=0,n + DO jpert=1,mpert + DO ipert=jpert,MIN(mpert,jpert+mband) + DO kpert=MAX(1,ipert-mband),jpert + ff(1+ipert-jpert,jpert,n) + $ =ff(1+ipert-jpert,jpert,n) + $ +fac1*f(1+ipert-kpert,kpert,j) + $ *CONJG(f(1+jpert-kpert,kpert,n-j)) + ENDDO + ENDDO + ENDDO + fac1=fac1*(n-j)/(j+1) + ENDDO + ff(:,:,n)=ff(:,:,n)/fac0 + fac0=fac0*(n+1) + ENDDO +c----------------------------------------------------------------------- +c compute non-Hermitian banded matrix K. +c----------------------------------------------------------------------- + k=0 + iqty=0 + DO jpert=1,mpert + DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband) + iqty=iqty+1 + k(1+mband+ipert-jpert,jpert,0) + $ =singfac(ipert,0)*kmats%f(iqty) + IF(sing_order < 1)CYCLE + k(1+mband+ipert-jpert,jpert,1) + $ =singfac(ipert,0)*kmats%f1(iqty) + $ +singfac(ipert,1)*kmats%f(iqty) + IF(sing_order < 2)CYCLE + k(1+mband+ipert-jpert,jpert,2) + $ =singfac(ipert,0)*kmats%f2(iqty)/2 + $ +singfac(ipert,1)*kmats%f1(iqty) + $ +singfac(ipert,2)*kmats%f(iqty)/2 + IF(sing_order < 3)CYCLE + k(1+mband+ipert-jpert,jpert,3) + $ =singfac(ipert,0)*kmats%f3(iqty)/6 + $ +singfac(ipert,1)*kmats%f2(iqty)/2 + $ +singfac(ipert,2)*kmats%f1(iqty)/2 + $ +singfac(ipert,3)*kmats%f(iqty)/6 + IF(sing_order < 4)CYCLE + k(1+mband+ipert-jpert,jpert,4) + $ =singfac(ipert,1)*kmats%f3(iqty)/6 + $ +singfac(ipert,2)*kmats%f2(iqty)/4 + $ +singfac(ipert,3)*kmats%f1(iqty)/6 + IF(sing_order < 5)CYCLE + k(1+mband+ipert-jpert,jpert,5) + $ =singfac(ipert,2)*kmats%f3(iqty)/12 + $ +singfac(ipert,3)*kmats%f2(iqty)/12 + IF(sing_order < 6)CYCLE + k(1+mband+ipert-jpert,jpert,6) + $ =singfac(ipert,3)*kmats%f3(iqty)/36 + ENDDO + ENDDO +c----------------------------------------------------------------------- +c compute Hermitian banded matrix G. +c----------------------------------------------------------------------- + g=0 + iqty=0 + DO jpert=1,mpert + DO ipert=jpert,MIN(mpert,jpert+mband) + iqty=iqty+1 + g(1+ipert-jpert,jpert,0)=gmats%f(iqty) + IF(sing_order < 1)CYCLE + g(1+ipert-jpert,jpert,1)=gmats%f1(iqty) + IF(sing_order < 2)CYCLE + g(1+ipert-jpert,jpert,2)=gmats%f2(iqty)/2 + IF(sing_order < 3)CYCLE + g(1+ipert-jpert,jpert,3)=gmats%f2(iqty)/6 + ENDDO + ENDDO +c----------------------------------------------------------------------- +c compute identity. +c----------------------------------------------------------------------- + v=0 + DO ipert=1,mpert + v(ipert,ipert,1)=1 + v(ipert,ipert+mpert,2)=1 + ENDDO +c----------------------------------------------------------------------- +c compute zeroth-order x1. +c----------------------------------------------------------------------- + x=0 + DO isol=1,msol + x(:,isol,1,0)=v(:,isol,2) + CALL zgbmv('N',mpert,mpert,mband,mband,-one,k(:,:,0), + $ 2*mband+1,v(:,isol,1),1,one,x(:,isol,1,0),1) + ENDDO + CALL zpbtrs('L',mpert,mband,msol,f0,mband+1,x(:,:,1,0),mpert,info) +c----------------------------------------------------------------------- +c compute higher-order x1. +c----------------------------------------------------------------------- + DO i=1,sing_order + DO isol=1,msol + DO j=1,i + CALL zhbmv('L',mpert,mband,-one,ff(:,:,j), + $ mband+1,x(:,isol,1,i-j),1,one,x(:,isol,1,i),1) + ENDDO + CALL zgbmv('N',mpert,mpert,mband,mband,-one,k(:,:,i), + $ 2*mband+1,v(:,isol,1),1,one,x(:,isol,1,i),1) + ENDDO + CALL zpbtrs('L',mpert,mband,msol,f0,mband+1,x(:,:,1,i),mpert, + $ info) + ENDDO +c----------------------------------------------------------------------- +c compute x2. +c----------------------------------------------------------------------- + DO i=0,sing_order + DO isol=1,msol + DO j=0,i + CALL zgbmv('C',mpert,mpert,mband,mband,one,k(:,:,j), + $ 2*mband+1,x(:,isol,1,i-j),1,one,x(:,isol,2,i),1) + ENDDO + CALL zhbmv('L',mpert,mband,one,g(:,:,i), + $ mband+1,v(:,isol,1),1,one,x(:,isol,2,i),1) + ENDDO + ENDDO +c----------------------------------------------------------------------- +c diagnose. +c----------------------------------------------------------------------- + IF(diagnose)THEN + CALL ascii_open(debug_unit,"xmat.out","UNKNOWN") + DO j=0,sing_order + DO isol=1,2*mpert + WRITE(debug_unit,10)(i,i,i=1,2) + DO ipert=1,mpert + WRITE(debug_unit,20)j,isol,ipert, + $ x(ipert,isol,:,j) + ENDDO + ENDDO + ENDDO + WRITE(debug_unit,10)(i,i,i=1,2) + CALL ascii_close(debug_unit) + ENDIF +c----------------------------------------------------------------------- +c principal terms of mmat. +c----------------------------------------------------------------------- + mmat => sing(ising)%mmat + mmat=0 + j=0 + DO i=0,sing_order + mmat(r1,r2,:,j)=x(r1,r2,:,i) + mmat(r1,n2,:,j+1)=x(r1,n2,:,i) + mmat(n1,r2,:,j+1)=x(n1,r2,:,i) + mmat(n1,n2,:,j+2)=x(n1,n2,:,i) + j=j+2 + ENDDO +c----------------------------------------------------------------------- +c shearing terms. +c----------------------------------------------------------------------- + mmat(r1,r2(1),1,0)=mmat(r1,r2(1),1,0)+half + mmat(r1,r2(2),2,0)=mmat(r1,r2(2),2,0)-half +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_mmat +c----------------------------------------------------------------------- +c subprogram 6. sing_solve. +c solves iteratively for the next order in the power series vmat. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_solve(k,power,mmat,vmat) + + INTEGER, INTENT(IN) :: k + COMPLEX(r8), DIMENSION(:), INTENT(IN) :: power + COMPLEX(r8), DIMENSION(mpert,2*mpert,2,0:k), INTENT(IN) :: mmat + COMPLEX(r8), DIMENSION(mpert,2*mpert,2,0:k), INTENT(INOUT) :: vmat + + INTEGER :: l,isol + REAL(r8), PARAMETER :: two=2 + COMPLEX(r8) :: det + COMPLEX(r8), DIMENSION(2,2) :: a + COMPLEX(r8), DIMENSION(2) :: x +c----------------------------------------------------------------------- +c compute rhs. +c----------------------------------------------------------------------- + DO l=1,k + vmat(:,:,:,k)=vmat(:,:,:,k) + $ +sing_matmul(mmat(:,:,:,l),vmat(:,:,:,k-l)) + ENDDO +c----------------------------------------------------------------------- +c evaluate solutions. +c----------------------------------------------------------------------- + DO isol=1,2*mpert + a=m0mat + a(1,1)=a(1,1)-k/two-power(isol) + a(2,2)=a(2,2)-k/two-power(isol) + det=a(1,1)*a(2,2)-a(1,2)*a(2,1) + x=-vmat(r1(1),isol,:,k) + vmat(r1(1),isol,1,k)=(a(2,2)*x(1)-a(1,2)*x(2))/det + vmat(r1(1),isol,2,k)=(a(1,1)*x(2)-a(2,1)*x(1))/det + vmat(n1,isol,:,k)=vmat(n1,isol,:,k)/(power(isol)+k/two) + ENDDO +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_solve +c----------------------------------------------------------------------- +c subprogram 7. sing_matmul. +c multiplies matrices. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + FUNCTION sing_matmul(a,b) RESULT(c) + + COMPLEX(r8), DIMENSION(:,:,:), INTENT(IN) :: a,b + COMPLEX(r8), DIMENSION(SIZE(a,1),SIZE(b,2),2) :: c + + CHARACTER(64) :: message + INTEGER :: i,j,m,n +c----------------------------------------------------------------------- +c preliminary computations. +c----------------------------------------------------------------------- + m=SIZE(b,1) + n=SIZE(b,2) + IF(SIZE(a,2) /= 2*m)THEN + WRITE(message,'(2(a,i3))') + $ "Sing_matmul: SIZE(a,2) = ",SIZE(a,2), + $ " /= 2*SIZE(b,1) = ",2*SIZE(b,1) + CALL program_stop(message) + ENDIF +c----------------------------------------------------------------------- +c main computations. +c----------------------------------------------------------------------- + c=0 + DO i=1,n + DO j=1,2 + c(:,i,j)=c(:,i,j) + $ +MATMUL(a(:,1:m,j),b(:,i,1)) + $ +MATMUL(a(:,1+m:2*m,j),b(:,i,2)) + ENDDO + ENDDO +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END FUNCTION sing_matmul +c----------------------------------------------------------------------- +c subprogram 8. sing_vmat_diagnose. +c diagnoses asymptotic behavior at the singular surface. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_vmat_diagnose(ising) + + INTEGER, INTENT(IN) :: ising + + INTEGER :: i,isol,iorder,ipert + TYPE(sing_type), POINTER :: singp +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(/4x,"io",4x,"is",4x,"ip",2(4x,"re v",i1,6x,"im v",i1,2x)/) + 20 FORMAT(3i6,1p,4e11.3) +c----------------------------------------------------------------------- +c set pointer and open file. +c----------------------------------------------------------------------- + singp => sing(ising) + CALL ascii_open(debug_unit,"vmat.out","UNKNOWN") +c----------------------------------------------------------------------- +c write output. +c----------------------------------------------------------------------- + DO iorder=0,2 + DO isol=1,2*mpert + WRITE(debug_unit,10)(i,i,i=1,2) + DO ipert=1,mpert + WRITE(debug_unit,20)iorder,isol,ipert, + $ singp%vmat(ipert,isol,:,iorder) + ENDDO + ENDDO + ENDDO + WRITE(debug_unit,10)(i,i,i=1,2) +c----------------------------------------------------------------------- +c close files. +c----------------------------------------------------------------------- + CALL ascii_close(debug_unit) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_vmat_diagnose +c----------------------------------------------------------------------- +c subprogram 9. sing_get_ua. +c computes asymptotic series solutions. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_get_ua(ising,psifac,ua) + + INTEGER, INTENT(IN) :: ising + REAL(r8), INTENT(IN) :: psifac + COMPLEX(r8), DIMENSION(:,:,:), INTENT(OUT) :: ua + + INTEGER :: iorder + INTEGER, DIMENSION(:), POINTER :: r1,r2 + COMPLEX(r8) :: dpsi,pfac,sqrtfac + COMPLEX(r8), DIMENSION(:,:,:,:), POINTER :: vmat + TYPE(sing_type), POINTER :: singp +c----------------------------------------------------------------------- +c set pointers. +c----------------------------------------------------------------------- + singp => sing(ising) + vmat => singp%vmat + r1 => singp%r1 + r2 => singp%r2 +c----------------------------------------------------------------------- +c compute distance from singular surface and its powers. +c----------------------------------------------------------------------- + dpsi=psifac-singp%psifac + sqrtfac=SQRT(dpsi) + pfac=ABS(dpsi)**singp%alpha +c----------------------------------------------------------------------- +c compute power series by Horner's method. +c----------------------------------------------------------------------- + ua=vmat(:,:,:,2*sing_order) + DO iorder=2*sing_order-1,0,-1 + ua=ua*sqrtfac+vmat(:,:,:,iorder) + ENDDO +c----------------------------------------------------------------------- +c restore powers. +c----------------------------------------------------------------------- + ua(r1,:,1)=ua(r1,:,1)/sqrtfac + ua(r1,:,2)=ua(r1,:,2)*sqrtfac + ua(:,r2(1),:)=ua(:,r2(1),:)/pfac + ua(:,r2(2),:)=ua(:,r2(2),:)*pfac +c----------------------------------------------------------------------- +c renormalize. +c----------------------------------------------------------------------- + IF(psifac < singp%psifac)THEN + ua(:,r2(1),:)=ua(:,r2(1),:) + $ *ABS(ua(r1(1),r2(1),1))/ua(r1(1),r2(1),1) + ua(:,r2(2),:)=ua(:,r2(2),:) + $ *ABS(ua(r1(1),r2(2),1))/ua(r1(1),r2(2),1) + ENDIF +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_get_ua +c----------------------------------------------------------------------- +c subprogram 10. sing_get_ca. +c computes asymptotic coefficients. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_get_ca(ising,psifac,u,ca) + + INTEGER, INTENT(IN) :: ising + REAL(r8) , INTENT(IN):: psifac + COMPLEX(r8), DIMENSION(:,:,:), INTENT(IN) :: u + COMPLEX(r8), DIMENSION(:,:,:), INTENT(OUT) :: ca + + INTEGER :: info,msol + INTEGER, DIMENSION(2*mpert) :: ipiv + COMPLEX(r8), DIMENSION(mpert,2*mpert,2) :: ua + COMPLEX(r8), DIMENSION(2*mpert,2*mpert) :: temp1 + COMPLEX(r8), DIMENSION(2*mpert,SIZE(u,2)) :: temp2 +c----------------------------------------------------------------------- +c compute asymptotic coefficients. +c----------------------------------------------------------------------- + msol=SIZE(u,2) + CALL sing_get_ua(ising,psifac,ua) + temp1(1:mpert,:)=ua(:,:,1) + temp1(mpert+1:2*mpert,:)=ua(:,:,2) + CALL zgetrf(2*mpert,2*mpert,temp1,2*mpert,ipiv,info) + temp2(1:mpert,:)=u(:,:,1) + temp2(mpert+1:2*mpert,:)=u(:,:,2) + CALL zgetrs('N',2*mpert,msol,temp1,2*mpert,ipiv, + $ temp2,2*mpert,info) + ca(:,1:msol,1)=temp2(1:mpert,:) + ca(:,1:msol,2)=temp2(mpert+1:2*mpert,:) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_get_ca +c----------------------------------------------------------------------- +c subprogram 11. sing_der. +c evaluates euler-lagrange differential equation. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_der(neq,psifac,u,du) + + INTEGER, INTENT(IN) :: neq + REAL(r8), INTENT(IN) :: psifac + CHARACTER(128) :: message + COMPLEX(r8), DIMENSION(mpert,msol,2), INTENT(IN) :: u + COMPLEX(r8), DIMENSION(mpert,msol,2), INTENT(OUT) :: du + + INTEGER :: ipert,jpert,isol,iqty,info,m1,m2,dm,i + INTEGER, DIMENSION(mpert) :: ipiv + REAL(r8) :: q,singfac1,singfac2,chi1 + REAL(r8), DIMENSION(mpert) :: singfac + COMPLEX(r8), PARAMETER :: one=1 + COMPLEX(r8), DIMENSION(mpert*mpert) :: work + COMPLEX(r8), DIMENSION(mband+1,mpert) :: fmatb,gmatb + COMPLEX(r8), DIMENSION(2*mband+1,mpert) :: kmatb,kaatb,gaatb + COMPLEX(r8), DIMENSION(3*mband+1,mpert) :: amatlu,fmatlu + COMPLEX(r8), DIMENSION(mpert,mpert) :: temp1,temp2, + $ amat,bmat,cmat,dmat,emat,hmat,baat,caat,eaat,dbat,ebat, + $ fmat,kmat,gmat,kaat,gaat,pmat,paat,umat,aamat,b1mat,bkmat, + $ bkaat,kkmat,kkaat,r1mat,r2mat,r3mat,f0mat + COMPLEX(r8), DIMENSION(mpert,mpert,6) :: kwmat,ktmat +c----------------------------------------------------------------------- +c cubic spline evaluation. +c----------------------------------------------------------------------- + CALL spline_eval(sq,psifac,0) + q=sq%f(4) + singfac=mlow-nn*q+(/(ipert,ipert=0,mpert-1)/) + singfac=1/singfac + chi1=twopi*psio + + IF (kin_flag) THEN + CALL cspline_eval(amats,psifac,0) + CALL cspline_eval(bmats,psifac,0) + CALL cspline_eval(cmats,psifac,0) + CALL cspline_eval(dmats,psifac,0) + CALL cspline_eval(emats,psifac,0) + CALL cspline_eval(hmats,psifac,0) + CALL cspline_eval(dbats,psifac,0) + CALL cspline_eval(ebats,psifac,0) + CALL cspline_eval(fbats,psifac,0) + + amat=RESHAPE(amats%f,(/mpert,mpert/)) + bmat=RESHAPE(bmats%f,(/mpert,mpert/)) + cmat=RESHAPE(cmats%f,(/mpert,mpert/)) + dmat=RESHAPE(dmats%f,(/mpert,mpert/)) + emat=RESHAPE(emats%f,(/mpert,mpert/)) + hmat=RESHAPE(hmats%f,(/mpert,mpert/)) + dbat=RESHAPE(dbats%f,(/mpert,mpert/)) + ebat=RESHAPE(ebats%f,(/mpert,mpert/)) + fmat=RESHAPE(fbats%f,(/mpert,mpert/)) + + DO i=1,6 + CALL cspline_eval(kwmats(i),psifac,0) + CALL cspline_eval(ktmats(i),psifac,0) + kwmat(:,:,i)=RESHAPE(kwmats(i)%f,(/mpert,mpert/)) + ktmat(:,:,i)=RESHAPE(ktmats(i)%f,(/mpert,mpert/)) + ENDDO +c----------------------------------------------------------------------- +c compute kinetic matrices. +c----------------------------------------------------------------------- + IF (fkg_kmats_flag) THEN + CALL cspline_eval(akmats,psifac,0) + CALL cspline_eval(bkmats,psifac,0) + CALL cspline_eval(ckmats,psifac,0) + CALL cspline_eval(f0mats,psifac,0) + CALL cspline_eval(pmats,psifac,0) + CALL cspline_eval(paats,psifac,0) + CALL cspline_eval(kkmats,psifac,0) + CALL cspline_eval(kkaats,psifac,0) + CALL cspline_eval(r1mats,psifac,0) + CALL cspline_eval(r2mats,psifac,0) + CALL cspline_eval(r3mats,psifac,0) + CALL cspline_eval(gaats,psifac,0) + + amat=RESHAPE(akmats%f,(/mpert,mpert/)) + bmat=RESHAPE(bkmats%f,(/mpert,mpert/)) + cmat=RESHAPE(ckmats%f,(/mpert,mpert/)) + f0mat=RESHAPE(f0mats%f,(/mpert,mpert/)) + pmat=RESHAPE(pmats%f,(/mpert,mpert/)) + paat=RESHAPE(paats%f,(/mpert,mpert/)) + kkmat=RESHAPE(kkmats%f,(/mpert,mpert/)) + kkaat=RESHAPE(kkaats%f,(/mpert,mpert/)) + r1mat=RESHAPE(r1mats%f,(/mpert,mpert/)) + r2mat=RESHAPE(r2mats%f,(/mpert,mpert/)) + r3mat=RESHAPE(r3mats%f,(/mpert,mpert/)) + + amatlu=0 + DO jpert=1,mpert + DO ipert=1,mpert + amatlu(2*mband+1+ipert-jpert,jpert)=amat(ipert,jpert) + ENDDO + ENDDO + CALL zgbtrf(mpert,mpert,mband,mband,amatlu,3*mband+1, + $ ipiv,info) + IF(info /= 0)THEN + WRITE(message,'(a,e16.9,a,i2)') + $ "zgbtrf: amat singular at psifac = ",psifac, + $ ", ipert = ",info,", reduce delta_mband" + CALL program_stop(message) + ENDIF +c----------------------------------------------------------------------- +c obsolete diagnostics. +c----------------------------------------------------------------------- +c DO jpert=1,mpert +c DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband) +c gaat(ipert,jpert)=gaats%f(iqty) +c iqty=iqty+1 +c ENDDO +c ENDDO + ELSE + amat=amat+kwmat(:,:,1)+ktmat(:,:,1) + bmat=bmat+kwmat(:,:,2)+ktmat(:,:,2) + cmat=cmat+kwmat(:,:,3)+ktmat(:,:,3) + dmat=dmat+kwmat(:,:,4)+ktmat(:,:,4) + emat=emat+kwmat(:,:,5)+ktmat(:,:,5) + hmat=hmat+kwmat(:,:,6)+ktmat(:,:,6) + baat=bmat-2*ktmat(:,:,2) + caat=cmat-2*ktmat(:,:,3) + eaat=emat-2*ktmat(:,:,5) + b1mat=ifac*dbat +c----------------------------------------------------------------------- +c factor kinetic non-Hermitian matrix A. +c----------------------------------------------------------------------- + amatlu=0 + umat=0 + DO jpert=1,mpert + DO ipert=1,mpert + amatlu(2*mband+1+ipert-jpert,jpert)=amat(ipert,jpert) + IF(ipert==jpert)umat(ipert,jpert)=1 + ENDDO + ENDDO + CALL zgbtrf(mpert,mpert,mband,mband,amatlu,3*mband+1, + $ ipiv,info) + IF(info /= 0)THEN + WRITE(message,'(a,e16.9,a,i2)') + $ "zgbtrf: amat singular at psifac = ",psifac, + $ ", ipert = ",info,", reduce delta_mband" + CALL program_stop(message) + ENDIF + + temp1=dbat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp1,mpert,info) + f0mat=fmat-MATMUL(CONJG(TRANSPOSE(dbat)),temp1) +c----------------------------------------------------------------------- +c prepare matrices to separate Q factors. +c----------------------------------------------------------------------- + temp2=amat + CALL zgbtrs("C",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) ! close to unit matrix. + aamat=CONJG(TRANSPOSE(temp2)) + umat=umat-aamat + + bkmat=kwmat(:,:,2)+ktmat(:,:,2)+ifac*chi1/(twopi*nn)* + $ (kwmat(:,:,1)+ktmat(:,:,1)) + bkaat=kwmat(:,:,2)-ktmat(:,:,2)+ifac*chi1/(twopi*nn)* + $ (kwmat(:,:,1)+ktmat(:,:,1)) + temp2=bkmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + pmat=MATMUL(CONJG(TRANSPOSE(b1mat)),temp2) + + temp2=b1mat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + paat=MATMUL(CONJG(TRANSPOSE(bkaat)),temp2) + $ -ifac*chi1/(twopi*nn)*MATMUL(umat,b1mat) + paat=CONJG(TRANSPOSE(paat)) + + temp1=kwmat(:,:,1)+ktmat(:,:,1) + temp2=bkmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + r1mat=kwmat(:,:,4)+ktmat(:,:,4)- + $ (chi1/(twopi*nn))**2*CONJG(TRANSPOSE(temp1))+ + $ ifac*chi1/(twopi*nn)*CONJG(TRANSPOSE(bkaat))- + $ ifac*chi1/(twopi*nn)*MATMUL(aamat,bkmat)- + $ MATMUL(CONJG(TRANSPOSE(bkaat)),temp2) + + temp1=kwmat(:,:,5)+ktmat(:,:,5)-ifac*chi1/(twopi*nn)* + $ (kwmat(:,:,3)+ktmat(:,:,3)) + temp2=cmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + r2mat=temp1+ifac*chi1/(twopi*nn)*MATMUL(umat,cmat)- + $ MATMUL(CONJG(TRANSPOSE(bkaat)),temp2) + + temp1=kwmat(:,:,5)-ktmat(:,:,5)-ifac*chi1/(twopi*nn)* + $ (kwmat(:,:,3)-ktmat(:,:,3)) + temp2=bkmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + r3mat=CONJG(TRANSPOSE(temp1))- + $ MATMUL(CONJG(TRANSPOSE(caat)),temp2) + + temp1=cmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp1,mpert,info) + kkmat=ebat-MATMUL(CONJG(TRANSPOSE(b1mat)),temp1) + + temp1=b1mat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp1,mpert,info) + kkaat=CONJG(TRANSPOSE(ebat))- + $ MATMUL(CONJG(TRANSPOSE(caat)),temp1) + + temp2=cmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + gaat=hmat-MATMUL(CONJG(TRANSPOSE(caat)),temp2) + + iqty=1 + DO jpert=1,mpert + DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband) + gaats%f(iqty)=gaat(ipert,jpert) + iqty=iqty+1 + ENDDO + ENDDO + ENDIF + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,3*mband+1, + $ ipiv,bmat,mpert,info) + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu,3*mband+1, + $ ipiv,cmat,mpert,info) +c----------------------------------------------------------------------- +c obsolete method for non-Hermitian FK. +c----------------------------------------------------------------------- +c temp1=bmat +c temp2=cmat +c CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, +c $ 3*mband+1,ipiv,temp1,mpert,info) +c CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, +c $ 3*mband+1,ipiv,temp2,mpert,info) +c fmat=dmat-MATMUL(CONJG(TRANSPOSE(baat)),temp1) +c kmat=emat-MATMUL(CONJG(TRANSPOSE(baat)),temp2) +c kaat=CONJG(TRANSPOSE(eaat))- +c $ MATMUL(CONJG(TRANSPOSE(caat)),temp1) +c----------------------------------------------------------------------- +c calculate kinetic non-Hermitian FK. +c----------------------------------------------------------------------- + DO ipert=1,mpert + m1=mlow+ipert-1 + singfac1=m1-nn*q + DO jpert=1,mpert + m2=mlow+jpert-1 + singfac2=m2-nn*q + fmat(ipert,jpert)=singfac1*f0mat(ipert,jpert)* + $ singfac2-singfac1*pmat(ipert,jpert)- + $ CONJG(paat(jpert,ipert))*singfac2+ + $ r1mat(ipert,jpert) + kmat(ipert,jpert)=singfac1*kkmat(ipert,jpert)+ + $ r2mat(ipert,jpert) + kaat(ipert,jpert)=kkaat(ipert,jpert)*singfac2+ + $ r3mat(ipert,jpert) + ENDDO + ENDDO +c----------------------------------------------------------------------- +c obsolete diagnostics. +c----------------------------------------------------------------------- +c f1mats=RESHAPE(fmat,(/mpert**2/)) +c k1mats=RESHAPE(kmat,(/mpert**2/)) +c k1aats=RESHAPE(kaat,(/mpert**2/)) +c g1aats=RESHAPE(gaat,(/mpert**2/)) +c----------------------------------------------------------------------- +c store FKG in banded matrix forms. +c----------------------------------------------------------------------- + fmatlu=0 + DO jpert=1,mpert + DO ipert=1,mpert + fmatlu(2*mband+1+ipert-jpert,jpert)=fmat(ipert,jpert) + ENDDO + ENDDO + + iqty=1 + DO jpert=1,mpert + DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband) + kmats%f(iqty)=kmat(ipert,jpert) + kaats%f(iqty)=kaat(ipert,jpert) + iqty=iqty+1 + ENDDO + ENDDO + + kmatb=0 + kaatb=0 + iqty=1 + DO jpert=1,mpert + DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband) + kmatb(1+mband+ipert-jpert,jpert)=kmats%f(iqty) + kaatb(1+mband+ipert-jpert,jpert)=kaats%f(iqty) + iqty=iqty+1 + ENDDO + ENDDO + + gaatb=0 + iqty=1 + DO jpert=1,mpert + DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband) + gaatb(1+mband+ipert-jpert,jpert)=gaats%f(iqty) + iqty=iqty+1 + ENDDO + ENDDO + ELSE + CALL cspline_eval(amats,psifac,0) + CALL cspline_eval(bmats,psifac,0) + CALL cspline_eval(cmats,psifac,0) + CALL cspline_eval(fmats,psifac,0) + CALL cspline_eval(kmats,psifac,0) + CALL cspline_eval(gmats,psifac,0) + amat=RESHAPE(amats%f,(/mpert,mpert/)) + bmat=RESHAPE(bmats%f,(/mpert,mpert/)) + cmat=RESHAPE(cmats%f,(/mpert,mpert/)) + CALL zhetrf('L',mpert,amat,mpert,ipiv,work,mpert*mpert,info) + CALL zhetrs('L',mpert,mpert,amat,mpert,ipiv,bmat,mpert,info) + CALL zhetrs('L',mpert,mpert,amat,mpert,ipiv,cmat,mpert,info) +c----------------------------------------------------------------------- +c copy ideal Hermitian banded matrices F and G. +c----------------------------------------------------------------------- + fmatb=0 + gmatb=0 + iqty=1 + DO jpert=1,mpert + DO ipert=jpert,MIN(mpert,jpert+mband) + fmatb(1+ipert-jpert,jpert)=fmats%f(iqty) + gmatb(1+ipert-jpert,jpert)=gmats%f(iqty) + iqty=iqty+1 + ENDDO + ENDDO +c----------------------------------------------------------------------- +c copy ideal non-Hermitian banded matrix K. +c----------------------------------------------------------------------- + kmatb=0 + iqty=1 + DO jpert=1,mpert + DO ipert=MAX(1,jpert-mband),MIN(mpert,jpert+mband) + kmatb(1+mband+ipert-jpert,jpert)=kmats%f(iqty) + iqty=iqty+1 + ENDDO + ENDDO + ENDIF +c----------------------------------------------------------------------- +c compute du1 and du2. +c----------------------------------------------------------------------- + du=0 + IF(kin_flag) THEN + DO isol=1,msol + du(:,isol,1)=u(:,isol,2) + CALL zgbmv('N',mpert,mpert,mband,mband,-one,kmatb, + $ 2*mband+1,u(:,isol,1),1,one,du(:,isol,1),1) + ENDDO + + CALL zgbtrf(mpert,mpert,mband,mband,fmatlu,3*mband+1, + $ ipiv,info) + IF(info /= 0)THEN + WRITE(message,'(a,e16.9,a,i2,a)') + $ "zgbtrf: fmat singular at psifac = ",psifac, + $ ", ipert = ",info,", reduce delta_mband" + CALL program_stop(message) + ENDIF + CALL zgbtrs("N",mpert,mband,mband,msol,fmatlu, + $ 3*mband+1,ipiv,du,mpert,info) + + DO isol=1,msol + CALL zgbmv('N',mpert,mpert,mband,mband,one,gaatb, + $ 2*mband+1,u(:,isol,1),1,one,du(:,isol,2),1) + CALL zgbmv('N',mpert,mpert,mband,mband,one,kaatb, + $ 2*mband+1,du(:,isol,1),1,one,du(:,isol,2),1) + ENDDO + ELSE + DO isol=1,msol + du(:,isol,1)=u(:,isol,2)*singfac + CALL zgbmv('N',mpert,mpert,mband,mband,-one,kmatb, + $ 2*mband+1,u(:,isol,1),1,one,du(:,isol,1),1) + ENDDO + CALL zpbtrs('L',mpert,mband,msol,fmatb,mband+1,du,mpert,info) + DO isol=1,msol + CALL zhbmv('L',mpert,mband,one,gmatb, + $ mband+1,u(:,isol,1),1,one,du(:,isol,2),1 ) + CALL zgbmv('C',mpert,mpert,mband,mband,one,kmatb, + $ 2*mband+1,du(:,isol,1),1,one,du(:,isol,2),1) + du(:,isol,1)=du(:,isol,1)*singfac + ENDDO + ENDIF +c----------------------------------------------------------------------- +c calculate and store u-derivative and xss. +c----------------------------------------------------------------------- + ud(:,:,1)=du(:,:,1) + ud(:,:,2)=-MATMUL(bmat,du(:,:,1))-MATMUL(cmat,u(:,:,1)) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_der +c----------------------------------------------------------------------- +c subprogram 12. sing_ua_diagnose. +c diagnoses asymptotic solutions. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + SUBROUTINE sing_ua_diagnose(ising,dpsi) + + INTEGER, INTENT(IN) :: ising + REAL(r8), INTENT(IN) :: dpsi + + INTEGER :: isol,ipert + REAL(r8) :: psifac + COMPLEX(r8), DIMENSION(mpert,2*mpert,2) :: ua +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 FORMAT(/4x,"is",4x,"ip",6x,"im ua1",5x,"re ua1", + $ 7x,"im ua2",5x,"re ua2"/) + 20 FORMAT(2i6,2x,1p,2e11.3,2x,2e11.3) +c----------------------------------------------------------------------- +c evaluate asymptotic solutions. +c----------------------------------------------------------------------- + psifac=sing(ising)%psifac+dpsi + CALL sing_get_ua(ising,psifac,ua) +c----------------------------------------------------------------------- +c diagnose asymptotic solutions. +c----------------------------------------------------------------------- + CALL ascii_open(debug_unit,"ua.out","UNKNOWN") + WRITE(debug_unit,'(a,i2,a,i1,a,es10.3,a,es10.3)') + $ "ising = ",ising,", sing_order = ",sing_order, + $ ", dpsi =",dpsi,", alpha =",REAL(sing(ising)%alpha) + WRITE(debug_unit,10) + DO isol=1,2*msol + DO ipert=1,mpert + WRITE(debug_unit,20)isol,ipert,ua(ipert,isol,:) + ENDDO + WRITE(debug_unit,10) + ENDDO + CALL ascii_close(debug_unit) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + RETURN + END SUBROUTINE sing_ua_diagnose +c----------------------------------------------------------------------- +c subprogram 13. sing_get_f_det. +c find determinant of non-Hermitian F matrix. +c----------------------------------------------------------------------- + FUNCTION sing_get_f_det(psifac) RESULT(det) + + REAL(r8), INTENT(IN) :: psifac + COMPLEX(r8) :: det + + INTEGER :: ipert,jpert,m1,m2 + INTEGER :: ldab,kl,ku,info,m,n,i + + REAL(r8) :: q,nq,singfac1,singfac2,chi1 + + INTEGER, DIMENSION(mpert) :: ipiv + INTEGER,DIMENSION(:),ALLOCATABLE:: fpiv + REAL(r8), DIMENSION(mpert) :: singfac + COMPLEX(r8) :: d + COMPLEX(r8), DIMENSION(:,:), ALLOCATABLE:: lumat + COMPLEX(r8), DIMENSION(mpert,mpert) :: f,temp1,temp2,f0mat, + $ amat,dbat,fmat,pmat,paat,umat,aamat,b1mat,bkmat,bkaat,r1mat + COMPLEX(r8), DIMENSION(3*mband+1,mpert) :: amatlu + COMPLEX(r8), DIMENSION(mpert,mpert,4) :: kwmat,ktmat + COMPLEX(r8), DIMENSION(mpert*mpert) :: work + CHARACTER(128) :: message +c----------------------------------------------------------------------- +c compute q and singfac. +c----------------------------------------------------------------------- + CALL spline_eval(sq,psifac,0) + q=sq%f(4) + nq=nn*q + singfac=mlow-nn*q+(/(ipert,ipert=0,mpert-1)/) + chi1=twopi*psio +c----------------------------------------------------------------------- +c compute F matrix. +c----------------------------------------------------------------------- + IF (kin_flag) THEN + IF (fkg_kmats_flag) THEN + CALL cspline_eval(f0mats,psifac,0) + CALL cspline_eval(pmats,psifac,0) + CALL cspline_eval(paats,psifac,0) + CALL cspline_eval(r1mats,psifac,0) + f0mat=RESHAPE(f0mats%f,(/mpert,mpert/)) + pmat=RESHAPE(pmats%f,(/mpert,mpert/)) + paat=RESHAPE(paats%f,(/mpert,mpert/)) + r1mat=RESHAPE(r1mats%f,(/mpert,mpert/)) + ELSE + CALL cspline_eval(amats,psifac,0) + CALL cspline_eval(dbats,psifac,0) + CALL cspline_eval(fbats,psifac,0) + amat=RESHAPE(amats%f,(/mpert,mpert/)) + dbat=RESHAPE(dbats%f,(/mpert,mpert/)) + fmat=RESHAPE(fbats%f,(/mpert,mpert/)) + DO i=1,4 + CALL cspline_eval(kwmats(i),psifac,0) + CALL cspline_eval(ktmats(i),psifac,0) + kwmat(:,:,i)=RESHAPE(kwmats(i)%f,(/mpert,mpert/)) + ktmat(:,:,i)=RESHAPE(ktmats(i)%f,(/mpert,mpert/)) + ENDDO + amat=amat+kwmat(:,:,1)+ktmat(:,:,1) + b1mat=ifac*dbat +c----------------------------------------------------------------------- +c factor kinetic non-Hermitian matrix A. +c----------------------------------------------------------------------- + amatlu=0 + umat=0 + DO jpert=1,mpert + DO ipert=1,mpert + amatlu(2*mband+1+ipert-jpert,jpert)=amat(ipert,jpert) + IF(ipert==jpert)umat(ipert,jpert)=1 + ENDDO + ENDDO + + CALL zgbtrf(mpert,mpert,mband,mband,amatlu,3*mband+1, + $ ipiv,info) + IF(info /= 0)THEN + WRITE(message,'(a,e16.9,a,i2)') + $ "zgbtrf: amat singular at psifac = ",psifac, + $ ", ipert = ",info,", reduce delta_mband" + CALL program_stop(message) + ENDIF + temp1=dbat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp1,mpert,info) + f0mat=fmat-MATMUL(CONJG(TRANSPOSE(dbat)),temp1) + + temp2=amat + CALL zgbtrs("C",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) ! close to unit matrix. + aamat=CONJG(TRANSPOSE(temp2)) + umat=umat-aamat + + bkmat=kwmat(:,:,2)+ktmat(:,:,2)+ifac*chi1/(twopi*nn)* + $ (kwmat(:,:,1)+ktmat(:,:,1)) + bkaat=kwmat(:,:,2)-ktmat(:,:,2)+ifac*chi1/(twopi*nn)* + $ (kwmat(:,:,1)+ktmat(:,:,1)) + temp2=bkmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + pmat=MATMUL(CONJG(TRANSPOSE(b1mat)),temp2) + + temp2=b1mat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + paat=MATMUL(CONJG(TRANSPOSE(bkaat)),temp2) + $ -ifac*chi1/(twopi*nn)*MATMUL(umat,b1mat) + paat=CONJG(TRANSPOSE(paat)) + + temp1=kwmat(:,:,1)+ktmat(:,:,1) + temp2=bkmat + CALL zgbtrs("N",mpert,mband,mband,mpert,amatlu, + $ 3*mband+1,ipiv,temp2,mpert,info) + r1mat=kwmat(:,:,4)+ktmat(:,:,4)- + $ (chi1/(twopi*nn))**2*CONJG(TRANSPOSE(temp1))+ + $ ifac*chi1/(twopi*nn)*CONJG(TRANSPOSE(bkaat))- + $ ifac*chi1/(twopi*nn)*MATMUL(aamat,bkmat)- + $ MATMUL(CONJG(TRANSPOSE(bkaat)),temp2) + ENDIF + DO ipert=1,mpert + m1=mlow+ipert-1 + singfac1=m1-nn*q + DO jpert=1,mpert + m2=mlow+jpert-1 + singfac2=m2-nn*q + f(ipert,jpert)=singfac1*f0mat(ipert,jpert)* + $ singfac2-singfac1*pmat(ipert,jpert)- + $ CONJG(paat(jpert,ipert))*singfac2+ + $ r1mat(ipert,jpert) + ENDDO + ENDDO + ELSE + CALL cspline_eval(amats,psifac,0) + CALL cspline_eval(dbats,psifac,0) + CALL cspline_eval(fbats,psifac,0) + amat=RESHAPE(amats%f,(/mpert,mpert/)) + dbat=RESHAPE(dbats%f,(/mpert,mpert/)) + fmat=RESHAPE(fbats%f,(/mpert,mpert/)) + + CALL zhetrf('L',mpert,amat,mpert,ipiv,work,mpert*mpert,info) + IF(info /= 0)THEN + WRITE(message,'(a,e16.9,a,i2)') + $ "zhetrf: amat singular at psifac = ",psifac, + $ ", ipert = ",info,", increase delta_mband" + CALL program_stop(message) + ENDIF + + temp1=dbat + CALL zhetrs('L',mpert,mpert,amat,mpert,ipiv,temp1,mpert,info) + fmat=fmat-MATMUL(CONJG(TRANSPOSE(dbat)),temp1) + + DO ipert=1,mpert + m1=mlow+ipert-1 + singfac1=m1-nn*q + DO jpert=1,mpert + m2=mlow+jpert-1 + singfac2=m2-nn*q + f(ipert,jpert)=singfac1*fmat(ipert,jpert)*singfac2 + ENDDO + ENDDO + ENDIF + + kl=mpert-1 + ku=mpert-1 + ldab=2*kl+ku+1 + m=mpert + n=mpert + ALLOCATE(lumat(ldab,n),fpiv(min(m,n))) + DO jpert=1,mpert + DO ipert=1,mpert + lumat(kl+ku+1+ipert-jpert,jpert)=f(ipert,jpert) + ENDDO + ENDDO + CALL zgbtrf(m,n,kl,ku,lumat,ldab,ipiv,info) + IF (info.NE.0) THEN + PRINT *,"zgbtrf info=",info + CALL program_stop("Termination by galerkin_solve_equation") + ENDIF +c----------------------------------------------------------------------- +c calculate the determinant of A. +c----------------------------------------------------------------------- + d=1.0 + DO i=1,m + IF (ipiv(i).ne.i) d=-d + ENDDO + det=PRODUCT(lumat(kl+kl+1,:))*d + DEALLOCATE (lumat,fpiv) + + END FUNCTION sing_get_f_det +c----------------------------------------------------------------------- +c subprogram 14. ksing_find. +c find new singular surfaces. +c----------------------------------------------------------------------- + SUBROUTINE ksing_find + + REAL(r8),PARAMETER :: tol=1e-3,dfac=1e-4,keps1=1e-10,keps2=1e-4 + INTEGER, PARAMETER :: nsing=1000, maxstep=100000 + REAL(r8), DIMENSION(nsing) :: psising,psising_check + + LOGICAL :: sing_flag + LOGICAL, PARAMETER :: debug = .FALSE. + INTEGER :: ising,i_recur,i_depth,i,singnum,singnum_check,i_record + REAL(r8) :: x0,x1,eps,reps + COMPLEX(r8) :: det0,det1,sing_det + COMPLEX(r8), DIMENSION(:,:), ALLOCATABLE :: tmp_record + + WRITE(*, *) "Finding kinetically displaced singular surfaces" + ALLOCATE(tmp_record(2, maxstep)) + singnum=0 + psising=-1 + i_recur=0 + i_depth=0 + i_record=0 + x0=psilow + x1=psilim +c----------------------------------------------------------------------- +c adaptively search the singular point. +c----------------------------------------------------------------------- + sing_flag=.FALSE. + det0=sing_get_f_det(x0) + det1=sing_get_f_det(x1) + IF (ABS(det0)>ABS(det1)) THEN + det_max=det0 + ELSE + det_max=det1 + ENDIF + singnum=singnum+1 + psising(singnum)=x0 + sing_det=det0 + sing_flag=.TRUE. + OPEN(UNIT=100,FILE="dcon_detf.out",STATUS="UNKNOWN") + WRITE(100,'(1x,4(a16))')"psi","absdetF","real(detF)","imag(detF)" + CALL bin_open(bin_unit,"dcon_detf.bin","UNKNOWN","REWIND","none") + CALL sing_adp_find_sing(x0,x1,det0,det1,nsing,psising,singnum, + $ i_recur,i_depth,i_record,tol,sing_det,sing_flag,tmp_record) + CLOSE (UNIT=100) + CALL bin_close(bin_unit) + ALLOCATE(sing_detf(2, i_record)) + sing_detf(:,:) = tmp_record(:, :i_record) + DEALLOCATE(tmp_record) + + IF (psising(1)>psilow) THEN + psising(2:singnum+1)=psising(1:singnum) + psising(1)=psilow + singnum=singnum+1 + + ENDIF + IF (psising(singnum)ABS(det1)) THEN + psising(i)=x1 + ENDIF + ENDDO +c----------------------------------------------------------------------- +c check the singular point. +c----------------------------------------------------------------------- + singnum_check=singnum + psising_check=psising + psising=-1 + singnum=1 + IF(verbose) WRITE(*,'(a,es10.3,a,es10.3)') + $ ' Looking for singularities below', keps1, + $ 'x the maximum determinant of', ABS(det_max) + psising(1)=psising_check(1) + DO i=2,singnum_check-1 + det0=sing_get_f_det(psising_check(i)) + reps=keps1/keps2 + eps=keps2*reps*10**(psising_check(i)/DLOG10(reps)) + IF (ABS(det0)<=ABS(det_max)*eps) THEN + singnum=singnum+1 + psising(singnum)=psising_check(i) + IF(debug) WRITE(*,'(a,es10.3,a,es10.3,a)') ' > psi', + $ psising_check(i), ' is singular' + ELSE + IF(debug) WRITE(*,'(a,es10.3,a,es10.3,a)') ' - psi', + $ psising_check(i), ' is not singular. Determinant is ', + $ ABS(det0)/(ABS(det_max)*eps), 'x the threshold' + ENDIF + ENDDO + singnum=singnum+1 + psising(singnum)=psising_check(singnum_check) + OPEN(UNIT=sing_unit,FILE="sing_find.out",STATUS="UNKNOWN") + WRITE(sing_unit,'(1x,3(a16))') "psi","real(det)","imag(det)" + DO i=1,singnum + det0=sing_get_f_det(psising(i)) + WRITE(sing_unit,'(1x,3(e16.8))') psising(i), + $ REAL(det0), AIMAG(det0) + ENDDO + CLOSE (UNIT=sing_unit) + kmsing=singnum-2 + ALLOCATE(kinsing(kmsing)) + DO ising=1,kmsing + kinsing(ising)%m=ising + kinsing(ising)%psifac=psising(ising+1) + kinsing(ising)%rho=SQRT(psising(ising+1)) + CALL spline_eval(sq,psising(ising+1),1) + kinsing(ising)%q=sq%f(4) + kinsing(ising)%q1=sq%f1(4) + ENDDO + + IF(verbose)THEN + IF(kmsing>0)THEN + WRITE(*,*) " > Found kinetic singular surfaces:" + WRITE(*,'(3x,a16, a16)')"psi","q" + DO ising=1,kmsing + WRITE(*,'(3x,2(es16.8))') kinsing(ising)%psifac, + $ kinsing(ising)%q + ENDDO + ELSE + WRITE(*,*) " > Found no kinetic singular surfaces" + ENDIF + ENDIF + + END SUBROUTINE ksing_find +c----------------------------------------------------------------------- +c subprogram 15. sing_adp_find_sing. +c adaptive finder. +c----------------------------------------------------------------------- + RECURSIVE SUBROUTINE sing_adp_find_sing(x0,x1,det0,det1, + $ m_singpos,singpos,singnum,i_recur,i_depth,i_record, + $ tol,sing_det,sing_flag,record) + LOGICAL,INTENT(INOUT) :: sing_flag + INTEGER,INTENT(IN) :: m_singpos + INTEGER,INTENT(INOUT) :: singnum + INTEGER,INTENT(INOUT) :: i_recur,i_depth,i_record + REAL(r8),INTENT(IN) :: x0,x1,tol + REAL(r8),DIMENSION(m_singpos),INTENT(INOUT) :: singpos + REAL(r8),PARAMETER :: grid_tol =1e-6 + COMPLEX(r8),INTENT(IN) :: det0,det1 + COMPLEX(r8),INTENT(INOUT) :: sing_det + COMPLEX(r8),INTENT(INOUT), DIMENSION(2,*) :: record + + INTEGER :: i + REAL(r8) :: tmp1,tmpm,tmp2 + REAL(r8),DIMENSION(3) :: x + COMPLEX(r8),DIMENSION(3) :: det + + i_depth=i_depth+1 + i_recur=i_recur+1 + x(1)=x0 + x(3)=x1 + x(2)=0.5*(x(1)+x(3)) + det(1)=det0 + det(2)=sing_get_f_det(x(2)) + det(3)=det1 + IF (ABS(det(2))>ABS(det_max)) det_max=det(2) +c----------------------------------------------------------------------- +c criteria of grid partition. +c----------------------------------------------------------------------- + tmp1=ABS(det(1)+det(3)) + tmpm=ABS(det(2))*2 + IF (ABS(tmpm-tmp1)>tol*tmp1 .AND. x(3)-x(1)>grid_tol ) THEN + CALL sing_adp_find_sing(x(1),x(2),det(1),det(2), + $ m_singpos,singpos,singnum,i_recur,i_depth,i_record, + $ tol,sing_det,sing_flag,record) + + CALL sing_adp_find_sing(x(2),x(3),det(2),det(3), + $ m_singpos,singpos,singnum,i_recur,i_depth,i_record, + $ tol,sing_det,sing_flag,record) + ELSE +c----------------------------------------------------------------------- +c judge the local singularity with the gradient of ABS(det). +c----------------------------------------------------------------------- + tmp1 = ABS(det(2))-ABS(det(1)) + tmp2 = ABS(det(3))-ABS(det(2)) + IF (tmp1<0.AND.tmp2<0)THEN + IF (sing_flag) THEN + IF (ABS(sing_det)>ABS(det(3))) THEN + sing_det=det(3) + singpos(singnum)=x(3) + ENDIF + ELSE + singnum=singnum+1 + IF (singnum+3>m_singpos) THEN + CALL program_stop("Increase singpos array.") + ENDIF + singpos(singnum)=x(3) + sing_det=det(3) + sing_flag=.TRUE. + ENDIF + ENDIF + + IF (tmp1<0.AND.tmp2>0)THEN + IF (sing_flag) THEN + IF (ABS(sing_det)>ABS(det(2))) THEN + sing_det=det(2) + singpos(singnum)=x(2) + ENDIF + ELSE + singnum=singnum+1 + IF (singnum+3>m_singpos) THEN + CALL program_stop("Increase singpos array.") + ENDIF + singpos(singnum)=x(2) + sing_det=det(2) + sing_flag=.TRUE. + ENDIF + ENDIF + + IF (tmp1>0.AND.tmp2>0)THEN + IF (sing_flag) THEN + sing_flag=.FALSE. + ENDIF + IF (ABS(sing_det)>ABS(det(1))) THEN + sing_det=det(1) + singpos(singnum)=x(1) + ENDIF + ENDIF + + IF (tmp1>0.AND.tmp2<0)THEN + IF (sing_flag) THEN + sing_flag=.FALSE. + ENDIF + IF (ABS(sing_det)>ABS(det(1))) THEN + sing_det=det(1) + singpos(singnum)=x(1) + ENDIF + ENDIF + + IF (tmp1==0.OR.tmp2==0) THEN + CALL program_stop("det(2)-det(1)=0 or det(3)-det(2)=0") + ENDIF + + ! write record to file + WRITE(100,'(1x,4(es16.8))') x(2),ABS(det(2)),REAL(det(2)), + $ IMAG(det(2)) + WRITE(100,'(1x,4(es16.8))') x(3),ABS(det(3)),REAL(det(3)), + $ IMAG(det(3)) + WRITE(bin_unit)REAL(x(2),4),REAL(LOG10(ABS(det(2))),4), + $ REAL(REAL(det(2)),4),REAL(AIMAG(det(2)),4) + WRITE(bin_unit)REAL(x(3),4),REAL(LOG10(ABS(det(3))),4), + $ REAL(REAL(det(3)),4),REAL(AIMAG(det(3)),4) + ! store record in memory + i_record = i_record + 1 + record(:, i_record) = (/ x(2) * one_c, det(2) /) + i_record = i_record + 1 + record(:, i_record) = (/ x(3) * one_c, det(3) /) + + ENDIF + i_depth=i_depth-1 + END SUBROUTINE sing_adp_find_sing +c----------------------------------------------------------------------- +c subprogram 16. sing_newton. +c newton iteration for singular surface finder. +c----------------------------------------------------------------------- + SUBROUTINE sing_newton(ff,z,bo0,bo1) + + COMPLEX(r8) :: ff + REAL(r8), INTENT(INOUT) :: z + REAL(r8), INTENT(IN) :: bo0,bo1 + REAL(r8) :: err + INTEGER :: it + + INTEGER :: ising,info + REAL(r8) :: dzfac=1e-6,dbfac=1e-1,tol=1e-15,itmax=1000,dz,dz1,dz2 + REAL(r8) :: z_old,f_old,f,b0,b1,zopt,fopt +c----------------------------------------------------------------------- +c find initial guess. +c----------------------------------------------------------------------- + b0=z-(z-bo0)*dbfac ! bounds well inside of estimated neighboring minima + b1=z+(bo1-z)*dbfac + f=ABS(ff(z)) + zopt=z + fopt=f + + ! first step is a fraction of a half step towards the nearer boundary + dz1=(b0+z)*0.5-z + dz2=(b1+z)*0.5-z + dz = dz1 * dzfac + IF (ABS(dz2) itmax) THEN + it=-1 + WRITE(*,'(a,es10.3,a,es10.3,a)') " - search terminated at", + $ zopt," with large",err," error" + z=zopt + EXIT + ENDIF + IF (z+dz<=b0.OR.z+dz>=b1) THEN + ! we've climbed out of the sharp local well + ! case 1: we are on the right side, but near a peak so the ~0 gradient way overshoots to the other side + ! case 2: we are already on the other side of a peak and falling down towards the neighboring mininum + dz=dz*0.5 + ELSE + z_old=z + z=z+dz + f_old=f + f=ABS(ff(z)) + If (f [T M**2] -1.36721084E+00 + 1.03921169E+00 R OF MAGAXE --> [M] 3.11763506E+00 + -9.99273915E-07 Z OF MAGAXE --> [M] -2.99782174E-06 + -5.04402802E-06 Z0 --> [M] -1.51320841E-05 + 3.00000000E+00 R0 [M] USED FOR CONVERTING TO MKSA + 1.00000000E+00 B0 [T] USED FOR CONVERTING TO MKSA + 1.00000000E+00 SIGN OF B0 IN EXPERIMENT (CHEASE ASSUMES 1.0) + 1.53755753E+00 TOTAL CURRENT --> [A] 3.67064822E+06 + 1.00000000E+00 SIGN OF IP IN EXPERIMENT (CHEASE ASSUMES 1.0) + 1.69999553E+00 b/a + 1.05000000E+00 Q_ZERO, USING SIGNS OF IP AND B0, WOULD GIVE: 1.05000000E+00 + 4.43373475E+00 Q_EDGE, USING SIGNS OF IP AND B0, WOULD GIVE: 4.43373475E+00 + 1.51426490E-01 POLOIDAL BETA + 2.34029713E-02 BETA_EXP=

*2*MU0/B0**2 + 7.25523874E-01 LI + 3.46308209E-02 PRESSURE ON AXIS --> [Pa] 2.75583316E+04 --> [10**19 M**-3 KEV]: 1.72024542E+01 + 1.63188124E-02 BETA + 2.18184292E-02 BETA* (SQRT()) + 5.58550793E-02 BETA-AXIS=2p0/(T0/Rmag)^2; with Rmag->Rgeo(LCFS): 5.17194368E-02 + -1.51912315E-01 PSI-AXIS --> [T M**2] -1.36721084E+00 + -9.54493226E-01 2*PI*PSI-AXIS --> -8.59043904E+00 + -1.51912315E-01 IP_SIGN*PSI-AXIS --> [T M**2] -1.36721084E+00 + -9.54493226E-01 IP_SIGN*2*PI*PSI-AXIS --> -8.59043904E+00 + 1.99999525E+00 ASPECT RATIO ; a/R= 5.00001188E-01 + 7.64779790E+00 VOLUME -> 2.06490543E+02 + 1.29389993E+00 AREA -> 1.16450994E+01 + 2.53018281E+01 SURFACE -> 2.27716453E+02 + 4.34432012E+00 LENGTH -> 1.30329604E+01 + 5.00003104E-01 RMIN -> RMIN [m] 1.50000931E+00 + 1.49999983E+00 RMAX -> RMAX [m] 4.49999950E+00 + -8.49976057E-01 ZMIN -> ZMIN [m] -2.54992817E+00 + 8.49976009E-01 ZMAX -> ZMAX [m] 2.54992803E+00 + 1.00000147E+00 RGEOM -> RGEOM [m] 3.00000440E+00 + 4.99998364E-01 MINOR RADIUS -> A [m] 1.49999509E+00 diff --git a/src/DCON/validate/coil.in b/src/DCON/validate/coil.in new file mode 100644 index 000000000..946e00dc8 --- /dev/null +++ b/src/DCON/validate/coil.in @@ -0,0 +1,50 @@ +&COIL_CONTROL + ceq_type="efit" ! eq_type from equil.in used in DCON run + + data_dir="../../../coil" ! Directory from which _.dat files are read + machine="d3d" ! Choose from: nstx, d3d, kstar, iter + ip_direction="positive" ! Set positive for CCW or negative for CW from a top down view + bt_direction="negative" ! Set positive for CCW or negative for CW from a top down view + coil_num=3 ! Total number of coil sets activated + + cmpsi=64 ! ?? Why do we need this is only care about psi_lim?? + cmtheta=480 ! Number of poloidal gridpoints (uses DCON jac_type??) + cmzeta=40 ! Number of toroidal gridpoints (uses DCON jac_type??) + coil_threads=0 ! Number of parallel threads used when computing fields from coils (no reason to go beyond 4 for coils with less than 1000 points). Setting to <= 0 uses OMP_NUM_THREADS env variable. + + +! Array values should be specified for each of the coil arrays to be activated. +! The supported coil sets (number of coils) include... +! For nstx: rwmef(6), tfef(12), pf5ef(2), hhfw(24), ppu(12), ppl(12), +! psu(12), psl(12), vpu(12), vpl(12), vsu(12), vsl(12) +! For d3d: iu(6), il(6), c(6), tbm_solenoid(1), tbm_racetrack(1) +! For kstar:fecu(4), fecm(4), fecl(4) +! For iter: efcu(6), efcm(6), efcl(6), bl2u(9), bl2m(9), +! bl2l(9), avvu(9), avvm(9), avvl(9) + + coil_name(1)="c" ! External correction coil set + coil_cur(1,1)= 982 ! 1kA, 30 degree phase n=1 field + coil_cur(1,2)= 656 + coil_cur(1,3)=-326 + coil_cur(1,4)=-982 + coil_cur(1,5)=-656 + coil_cur(1,6)= 326 + coil_name(2)="il" ! External correction coil set + coil_cur(2,1)= 1e3 ! 1kA, 30 degree phase n=1 field + coil_cur(2,2)= 5e2 + coil_cur(2,3)=-5e2 + coil_cur(2,4)=-1e3 + coil_cur(2,5)=-5e2 + coil_cur(2,6)= 5e2 + coil_name(3)="iu" ! External correction coil set + coil_cur(3,1)= 1e3 ! 1kA, 30 degree phase n=1 field + coil_cur(3,2)= 5e2 + coil_cur(3,3)=-5e2 + coil_cur(3,4)=-1e3 + coil_cur(3,5)=-5e2 + coil_cur(3,6)= 5e2 + +/ +&COIL_OUTPUT + gpec_interface=t ! Provides external field to GPEC +/ diff --git a/src/DCON/validate/compare_matrix.ipynb b/src/DCON/validate/compare_matrix.ipynb new file mode 100644 index 000000000..42261ac98 --- /dev/null +++ b/src/DCON/validate/compare_matrix.ipynb @@ -0,0 +1,708 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "3586d344", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Python 3.12.8 | packaged by Anaconda, Inc. | (main, Dec 11 2024, 11:37:13) [Clang 14.0.6 ] on darwin\n", + "Type \"help\", \"copyright\", \"credits\" or \"license\" for more information.\n", + ">>> ^C\n", + ">>> \n", + "Traceback (most recent call last):\n", + " File \"\", line 0, in \n", + "KeyboardInterrupt\n", + ">>> " + ] + }, + { + "ename": "ModuleNotFoundError", + "evalue": "No module named 'scipy'", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mModuleNotFoundError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[2]\u001b[39m\u001b[32m, line 4\u001b[39m\n\u001b[32m 1\u001b[39m get_ipython().system(\u001b[33m'\u001b[39m\u001b[33m/usr/bin/env python3\u001b[39m\u001b[33m'\u001b[39m)\n\u001b[32m 2\u001b[39m \u001b[38;5;66;03m# -*- coding: utf-8 -*-\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m4\u001b[39m \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mscipy\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mlinalg\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mblas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m zhemm\n\u001b[32m 5\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnumpy\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnp\u001b[39;00m\n\u001b[32m 6\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmatplotlib\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mpyplot\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mplt\u001b[39;00m\n", + "\u001b[31mModuleNotFoundError\u001b[39m: No module named 'scipy'" + ] + } + ], + "source": [ + "!/usr/bin/env python3\n", + "# -*- coding: utf-8 -*-\n", + "\n", + "from scipy.linalg.blas import zhemm\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import warnings\n", + "import os\n", + "from scipy.interpolate import CubicSpline\n", + "from scipy.integrate import solve_ivp\n", + "from scipy.linalg import cho_factor, cho_solve, lu_factor, lu_solve\n", + "import time\n", + "import numpy as np\n", + "\n", + "m_high = 1\n", + "m_low = -4\n", + "mdim = m_high - m_low + 1\n", + "ndim = 1\n", + "size = mdim * ndim\n", + "\"\"\"\n", + "... (주석) ...\n", + "- F_bar, K_bar, G 행렬과 q 프로파일을 바이너리 파일에서 읽어 보간.\n", + "- 최종 F, K 행렬은 히트맵 플롯 시점에 필요한 샘플에 대해서만 즉석에서 계산하여 성능 저하를 방지.\n", + "\"\"\"\n", + "import numpy as np\n", + "import struct\n", + "import os\n", + "import matplotlib.pyplot as plt\n", + "from scipy.interpolate import CubicSpline\n", + "\n", + "# ─────────────────────────────────────────────────────────────\n", + "# 1 & 2. 파일 읽기 관련 함수 (이전과 동일)\n", + "# ─────────────────────────────────────────────────────────────\n", + "\n", + "def get_matrix_map(m, kind, n_blocks, mband_k=None, path=None):\n", + " if kind in ('F', 'G'):\n", + " for mb_test in range(m):\n", + " count = sum(len(range(j, min(m, j + mb_test + 1))) for j in range(m))\n", + " if count == n_blocks:\n", + " mband = mb_test\n", + " print(f\"[{os.path.basename(path)}] mband = {mband} (으)로 추정 (F/G).\")\n", + " d = {k+1: (i,j) for k, (j,i) in enumerate(((j,i) for j in range(m) for i in range(j, min(m, j+mband+1))))}\n", + " return d\n", + " raise ValueError(f\"F/G 행렬의 mband를 추정할 수 없습니다. (m={m}, n_blocks={n_blocks})\")\n", + " elif kind == 'K':\n", + " if mband_k is None: raise ValueError(\"K 행렬을 처리하려면 mband_k 값을 지정해야 합니다.\")\n", + " print(f\"[{os.path.basename(path)}] mband = {mband_k} (지정된 값) 사용 (K).\")\n", + " valid_element_count = sum(len(range(max(0, j-mband_k), min(m, j+mband_k+1))) for j in range(m))\n", + " if n_blocks > valid_element_count:\n", + " print(f\" > 경고: 파일에 기록된 블록 수({n_blocks})가 실제 유효한 원소 수({valid_element_count})보다 많습니다.\")\n", + " d = {}\n", + " k = 0\n", + " for j in range(m):\n", + " for i in range(max(0, j - mband_k), min(m, j + mband_k + 1)):\n", + " k += 1\n", + " d[k] = (i, j)\n", + " return d\n", + " else: raise ValueError(\"kind는 'F', 'G', 'K' 중 하나여야 합니다.\")\n", + "\n", + "def read_bin(path, m, kind, mband_k=None):\n", + " all_records = []\n", + " with open(path, 'rb') as f:\n", + " while True:\n", + " header_bytes = f.read(4)\n", + " if not header_bytes: break\n", + " record_len = struct.unpack(' 0:\n", + " all_records.append(np.frombuffer(f.read(record_len), dtype=np.float32))\n", + " else:\n", + " all_records.append(None)\n", + " f.read(4)\n", + " element_blocks = []\n", + " current_block = []\n", + " for rec in all_records:\n", + " if rec is not None: current_block.append(rec)\n", + " else:\n", + " if current_block: element_blocks.append(np.array(current_block))\n", + " current_block = []\n", + " if not element_blocks: raise ValueError(f\"파일에서 데이터 블록을 찾지 못했습니다: {path}\")\n", + "\n", + " n_blocks, n_psi = len(element_blocks), element_blocks[0].shape[0]\n", + " psi, q_profile = element_blocks[0][:, 0], element_blocks[0][:, 1]\n", + " idx_map = get_matrix_map(m, kind, n_blocks, mband_k=mband_k, path=path)\n", + " \n", + " mats = np.zeros((n_psi, m, m), dtype=np.complex128)\n", + " for k, (i, j) in idx_map.items():\n", + " if k > n_blocks: continue\n", + " mats[:, i, j] = element_blocks[k - 1][:, 2] + 1j * element_blocks[k - 1][:, 3]\n", + "\n", + " if kind in ('G'):\n", + " il, jl = np.tril_indices(m, -1)\n", + " mats[:, jl, il] = np.conj(mats[:, il, jl])\n", + " \n", + " return psi, q_profile, mats\n", + "\n", + "# ────────────────────────────────────────\n", + "# 3. dedup, make_interp, plot_q_profile (이전과 동일)\n", + "# ────────────────────────────────────────\n", + "def dedup(psi, q, stacks):\n", + " uniq_psi, idx = np.unique(psi, return_index=True)\n", + " return uniq_psi, q[idx], {k: v[idx] for k, v in stacks.items()}\n", + "\n", + "def make_interp(psi, mat_stack):\n", + " cs_r = CubicSpline(psi, mat_stack.real, axis=0)\n", + " cs_i = CubicSpline(psi, mat_stack.imag, axis=0)\n", + " return lambda x, cr=cs_r, ci=cs_i: cr(x) + 1j * ci(x)\n", + "\n", + "def plot_q_profile(psi, q, q_interpolant):\n", + " fig, ax = plt.subplots(figsize=(8, 6))\n", + " ax.plot(psi, q, 'o', label='Original Data Points', markersize=5)\n", + " psi_fine = np.linspace(psi.min(), psi.max(), 300)\n", + " ax.plot(psi_fine, q_interpolant(psi_fine), '-', label='Cubic Spline Interpolation')\n", + " ax.set(title='Safety Factor (q) Profile', xlabel='Normalized Poloidal Flux (ψ)', ylabel='Safety Factor (q)')\n", + " ax.legend(); ax.grid(True, linestyle='--', alpha=0.6)\n", + " plt.show()\n", + "\n", + "# ────────────────────────────────────────\n", + "# *** REVISED *** 4. 최종 행렬의 히트맵을 그리는 함수\n", + "# ────────────────────────────────────────\n", + "def plot_final_heatmaps(psi_coords, M, q_interp, F_bar_interp, G_interp, K_bar_interp, nsamp=4):\n", + " \"\"\"\n", + " 보간 함수들을 받아, 플롯에 필요한 psi 샘플에 대해서만 최종 행렬을 계산하고 히트맵을 그립니다.\n", + " \"\"\"\n", + " names = ['F', 'G', 'K']\n", + " samp = np.quantile(psi_coords, np.linspace(.05, .95, nsamp))\n", + " \n", + " fig, ax = plt.subplots(len(names), nsamp,\n", + " figsize=(4.5 * nsamp, 4 * len(names)),\n", + " constrained_layout=True, squeeze=False)\n", + " \n", + " I = np.identity(M.shape[0])\n", + "\n", + " for c, p in enumerate(samp):\n", + " # --- 계산은 이 루프 안에서 즉석으로 수행됩니다 ---\n", + " q_val = q_interp(p)\n", + " Q_mat = M - q_val * I\n", + " \n", + " # 각 psi 샘플(p)에 대해 최종 행렬 계산\n", + " final_mats = {\n", + " 'F': Q_mat @ F_bar_interp(p) @ Q_mat,\n", + " 'G': G_interp(p),\n", + " 'K': Q_mat @ K_bar_interp(p)\n", + " }\n", + " # ---------------------------------------------\n", + " \n", + " for r, n in enumerate(names):\n", + " mat = final_mats[n]\n", + " im = ax[r, c].imshow(np.abs(mat), cmap='viridis', origin='upper', aspect='equal')\n", + " ax[r, c].set_title(f'{n}, ψ≈{p:.3f}')\n", + " if r == len(names) - 1: ax[r, c].set_xlabel('j')\n", + " if c == 0: ax[r, c].set_ylabel('i')\n", + " plt.colorbar(im, ax=ax[r, c], label=f'|{n}|')\n", + " \n", + " fig.suptitle('Final F, G, K Heatmaps (Calculated On-the-fly)', y=1.03)\n", + " plt.show()\n", + "\n", + "# ────────────────────────────────────────\n", + "# 5. 메인 스크립트\n", + "# ────────────────────────────────────────\n", + "if __name__ == \"__main__\":\n", + " # --- 사용자 설정 변수 ---\n", + " MPERT = mdim\n", + " MBAND_K = MPERT - 1 \n", + " M_MODES = np.arange(m_low, m_high + 1) # MPERT=36일 경우, -17 ~ 18\n", + " \n", + " BASE_PATH = '/Users/seoda-eun/git/JPEC3/JPEC/src/DCON/validate'\n", + " \n", + " # --- 데이터 읽기 ---\n", + " files_to_read = { 'F': 'fs.bin', 'G': 'gs.bin', 'K': 'ks.bin' }\n", + " matrix_stacks, psi_coords, q_coords = {}, None, None\n", + " for name, fname in files_to_read.items():\n", + " path = os.path.join(BASE_PATH, fname)\n", + " if not os.path.exists(path):\n", + " print(f\"파일을 찾을 수 없습니다: {path}\"); continue\n", + " print(f\"파일 읽는 중: {fname} (as {'F_bar' if name=='F' else 'K_bar' if name=='K' else name})\")\n", + " try:\n", + " mband_val = MBAND_K if name == 'K' else None\n", + " psi, q, mat = read_bin(path, MPERT, name, mband_k=mband_val)\n", + " matrix_stacks[name] = mat\n", + " if psi_coords is None: psi_coords, q_coords = psi, q\n", + " except Exception as e:\n", + " print(f\"오류: {fname} 처리 중 문제 발생. {e}\"); import traceback; traceback.print_exc()\n", + "\n", + " if not matrix_stacks:\n", + " print(\"데이터를 성공적으로 읽지 못했습니다. 프로그램을 종료합니다.\"); exit()\n", + "\n", + " # --- 데이터 처리 및 보간 ---\n", + " if 'F' in matrix_stacks:\n", + " print(\"\\nF_bar 행렬 복원 (L·Lᴴ)...\")\n", + " L = np.tril(matrix_stacks['F']) # 하삼각(대각 포함)\n", + " matrix_stacks['F'] = L @ L.transpose(0, 2, 1).conj() # F_bar = L Lᴴ\n", + "\n", + " psi_coords, q_coords, matrix_stacks = dedup(psi_coords, q_coords, matrix_stacks)\n", + " \n", + " print(\"보간 함수 생성 중 (F_bar, G, K_bar, q)...\")\n", + " F_bar_interp = make_interp(psi_coords, matrix_stacks['F'])\n", + " G_interp = make_interp(psi_coords, matrix_stacks['G'])\n", + " K_bar_interp = make_interp(psi_coords, matrix_stacks['K'])\n", + " q_of_psi = CubicSpline(psi_coords, q_coords)\n", + " print(\"보간 함수 생성 완료.\")\n", + " \n", + " # --- 최종 행렬 계산 및 시각화 ---\n", + " if len(M_MODES) != MPERT:\n", + " raise ValueError(f\"M_MODES 배열 길이({len(M_MODES)})가 MPERT({MPERT})와 불일치.\")\n", + " M = np.diag(M_MODES)\n", + "\n", + " # 시각화: 플롯에 필요한 4개의 샘플에 대해서만 즉석에서 계산\n", + " plot_q_profile(psi_coords, q_coords, q_of_psi)\n", + " plot_final_heatmaps(psi_coords, M, q_of_psi, F_bar_interp, G_interp, K_bar_interp, nsamp=4)\n", + "\n", + " # --- 단일 psi 값에 대한 분석용 함수 (선택적 사용) ---\n", + " def compute_matrices(psi):\n", + " \"\"\"특정 psi에 대한 최종 F, G, K 행렬을 계산합니다.\"\"\"\n", + " I = np.identity(MPERT)\n", + " q_val = q_of_psi(psi)\n", + " Q_mat = M - q_val * I\n", + " \n", + " f_final = Q_mat @ F_bar_interp(psi) @ Q_mat\n", + " g_final = G_interp(psi)\n", + " k_final = Q_mat @ K_bar_interp(psi)\n", + " \n", + " return {'F': f_final, 'G': g_final, 'K': k_final}\n", + "\n", + " print(\"\\n분석이 완료되었습니다.\")\n", + " print(\"`compute_matrices(psi)` 함수로 특정 psi에서의 행렬을 계산할 수 있습니다.\")\n", + " psi_test = 0.5\n", + " final_mats_at_half = compute_matrices(psi_test)\n", + " print(f\"예시: ψ = {psi_test} 에서의 |F_00|: {np.abs(final_mats_at_half['F'][0,0]):.4e}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "ada4ecd6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Collecting package metadata (current_repodata.json): done\n", + "Solving environment: done\n", + "\n", + "\n", + "==> WARNING: A newer version of conda exists. <==\n", + " current version: 23.7.4\n", + " latest version: 25.5.1\n", + "\n", + "Please update conda by running\n", + "\n", + " $ conda update -n base -c defaults conda\n", + "\n", + "Or to minimize the number of packages updated during conda update use\n", + "\n", + " conda install conda=25.5.1\n", + "\n", + "\n", + "\n", + "## Package Plan ##\n", + "\n", + " environment location: /Users/seoda-eun/anaconda3/envs/mkl_env\n", + "\n", + " added / updated specs:\n", + " - numpy\n", + "\n", + "\n", + "The following packages will be UPDATED:\n", + "\n", + " ca-certificates conda-forge::ca-certificates-2025.1.3~ --> pkgs/main::ca-certificates-2025.2.25-hecd8cb5_0 \n", + "\n", + "\n", + "\n", + "Downloading and Extracting Packages\n", + "\n", + "Preparing transaction: done\n", + "Verifying transaction: done\n", + "Executing transaction: done\n", + "\n", + "Note: you may need to restart the kernel to use updated packages.\n" + ] + } + ], + "source": [ + "conda install numpy" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "620eba42", + "metadata": {}, + "outputs": [ + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31m현재 셀 또는 이전 셀에서 코드를 실행하는 동안 Kernel이 충돌했습니다. \n", + "\u001b[1;31m셀의 코드를 검토하여 가능한 오류 원인을 식별하세요. \n", + "\u001b[1;31m자세한 내용을 보려면 여기를 클릭하세요. \n", + "\u001b[1;31m자세한 내용은 Jupyter 로그를 참조하세요." + ] + } + ], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "from pathlib import Path\n", + "from typing import Tuple, Dict\n", + "from scipy.interpolate import interp1d\n", + "import struct\n", + "\n", + "class TokamakCylinderLoader:\n", + " \"\"\"\n", + " A class to read and interpolate Tokamak and Cylinder matrices (A–H, F–K).\n", + "\n", + " Methods\n", + " -------\n", + " load_all(psin_target)\n", + " Reads all Tokamak (A,B,C,D,E,H from imats; F from fs.bin; G from gs.bin; K from ks.bin)\n", + " and Cylinder (A,B,C,D,E,H from individual CSVs; F,G,K from diag CSV), then interpolates\n", + " onto psin_target.\n", + "\n", + " Attributes\n", + " ----------\n", + " imats_path : str\n", + " Path to tokamak 'imats.out'\n", + " fs_bin_path : str\n", + " Path to 'fs.bin'\n", + " gs_bin_path : str\n", + " Path to 'gs.bin'\n", + " ks_bin_path : str\n", + " Path to 'ks.bin'\n", + " mpert : int\n", + " mpert value used in Fortran\n", + " mband : int\n", + " mband value used in Fortran\n", + " cyl_paths : Dict[str, str]\n", + " Paths to cylinder A–H CSVs, keys 'A','B','C','D','E','H'\n", + " cyl_FGK_diag_csv : str\n", + " Path to 'dcon_FKG_diagonal_elements.csv'\n", + " \"\"\"\n", + " \n", + " def __init__(\n", + " self,\n", + " imats_path: str,\n", + " fs_bin_path: str,\n", + " gs_bin_path: str,\n", + " ks_bin_path: str,\n", + " mpert: int,\n", + " mband: int,\n", + " cyl_A_csv: str,\n", + " cyl_B_csv: str,\n", + " cyl_C_csv: str,\n", + " cyl_D_csv: str,\n", + " cyl_E_csv: str,\n", + " cyl_H_csv: str,\n", + " cyl_FGK_diag_csv: str\n", + " ):\n", + " self.imats_path = imats_path\n", + " self.fs_bin_path = fs_bin_path\n", + " self.gs_bin_path = gs_bin_path\n", + " self.ks_bin_path = ks_bin_path\n", + " self.mpert = mpert\n", + " self.mband = mband\n", + " self.cyl_paths = {\n", + " 'A': cyl_A_csv,\n", + " 'B': cyl_B_csv,\n", + " 'C': cyl_C_csv,\n", + " 'D': cyl_D_csv,\n", + " 'E': cyl_E_csv,\n", + " 'H': cyl_H_csv\n", + " }\n", + " self.cyl_FGK_diag_csv = cyl_FGK_diag_csv\n", + "\n", + " # 1. read_imats_out\n", + " @staticmethod\n", + " def read_imats_out(file_path: str, names: Tuple[str, ...] = ('A','B','C','D','E','H')) -> Tuple[np.ndarray, Dict[str, np.ndarray]]:\n", + " with open(file_path, 'r') as f:\n", + " lines = f.readlines()\n", + " header = lines[2].split()\n", + " mpsi = int(header[2])\n", + " mpert = int(header[-1])\n", + " data = lines[5:]\n", + " m1 = [int(l.split()[1]) for l in data if len(l.split()) == 15]\n", + " m2 = [int(l.split()[2]) for l in data if len(l.split()) == 15]\n", + " mi, mj = min(m1), max(m1)\n", + " offset = -mi\n", + " size = mj - mi + 1\n", + " psi = np.zeros(mpsi + 1)\n", + " mats = {n: np.zeros((mpsi + 1, size, size), np.complex128) for n in names}\n", + " idx = {'A':0,'B':2,'C':4,'D':6,'E':8,'F':10,'G':12,'H':14}\n", + " for ln in data:\n", + " sp = ln.split()\n", + " if len(sp) != 15:\n", + " continue\n", + " p = float(sp[0])\n", + " i = int(sp[1]) + offset\n", + " j = int(sp[2]) + offset\n", + " k = int(round(p * mpsi))\n", + " psi[k] = p\n", + " nums = list(map(float, sp[3:]))\n", + " for nm in names:\n", + " r, imv = nums[idx[nm]], nums[idx[nm] + 1]\n", + " mats[nm][k, i, j] = r + 1j * imv\n", + " return psi, mats\n", + "\n", + " # 2. read_vector_out + expand_vector_to_diag\n", + " @staticmethod\n", + " def read_vector_out(file_path: str) -> Tuple[np.ndarray, np.ndarray]:\n", + " blocks, cur = [], []\n", + " for ln in Path(file_path).read_text().splitlines():\n", + " s = ln.strip()\n", + " if not s:\n", + " if cur:\n", + " blocks.append(np.array(cur))\n", + " cur = []\n", + " continue\n", + " parts = s.split()\n", + " if len(parts) == 4:\n", + " p, _, re, im = parts\n", + " cur.append((float(p), float(re) + 1j * float(im)))\n", + " if cur:\n", + " blocks.append(np.array(cur))\n", + " psi = np.array([row[0] for row in blocks[0]])\n", + " n_psi = len(psi)\n", + " n_ipert = len(blocks)\n", + " vec = np.empty((n_psi, n_ipert), np.complex64)\n", + " for i, b in enumerate(blocks):\n", + " vec[:, i] = b[:, 1]\n", + " return psi, vec\n", + "\n", + " @staticmethod\n", + " def expand_vector_to_diag(mat_vec: np.ndarray) -> np.ndarray:\n", + " n_psi, n = mat_vec.shape\n", + " full = np.zeros((n_psi, n, n), dtype=mat_vec.dtype)\n", + " for k in range(n_psi):\n", + " np.fill_diagonal(full[k], mat_vec[k])\n", + " return full\n", + "\n", + " # 3. read_fs_bin / read_gs_bin / read_ks_bin\n", + " @staticmethod\n", + " def read_fs_bin(\n", + " file_path: str,\n", + " mpsi: int,\n", + " mpert: int,\n", + " mband: int\n", + " ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:\n", + " n_ipert_fs = (mband + 1) * (2 * mpert - mband) // 2\n", + " n_ipert_ks = (2 * mband + 1) * mpert\n", + " bytes_per_ipert = (mpsi + 1) * (4 + 16 + 4) + (4 + 0 + 4)\n", + " total_size = Path(file_path).stat().st_size\n", + " if total_size % bytes_per_ipert == 0:\n", + " cand_ipert = total_size // bytes_per_ipert\n", + " else:\n", + " raise ValueError(f\"File size {total_size} not divisible by expected block size {bytes_per_ipert}.\")\n", + " if cand_ipert == n_ipert_fs:\n", + " n_ipert = n_ipert_fs\n", + " elif cand_ipert == n_ipert_ks:\n", + " n_ipert = n_ipert_ks\n", + " else:\n", + " n_ipert = n_ipert_fs\n", + "\n", + " psi_arr = np.zeros(mpsi + 1, dtype=np.float64)\n", + " sqfs = np.zeros(mpsi + 1, dtype=np.float64)\n", + " M = np.zeros((n_ipert, mpsi + 1), dtype=np.complex128)\n", + "\n", + " with open(file_path, 'rb') as f:\n", + " for ipert in range(n_ipert):\n", + " for ipsi in range(mpsi + 1):\n", + " rec_len_bytes = f.read(4)\n", + " if len(rec_len_bytes) < 4:\n", + " raise EOFError(\"Unexpected EOF reading record length.\")\n", + " rec_len = struct.unpack(' Tuple[np.ndarray, np.ndarray]:\n", + " psi_vals, blocks, cur, reading = [], [], [], None\n", + " for ln in Path(file_path).read_text().splitlines():\n", + " s = ln.strip()\n", + " if not s:\n", + " if cur:\n", + " blocks.append(np.array(cur, float))\n", + " cur = []\n", + " continue\n", + " if s.startswith('# psi='):\n", + " psi_vals.append(float(s.split('=')[1]))\n", + " elif s.startswith('# Real'):\n", + " reading = 'real'\n", + " elif s.startswith('# Imag'):\n", + " reading = 'imag'\n", + " elif s and not s.startswith('#'):\n", + " if (reading == 'imag') == want_imag:\n", + " cur.append(list(map(float, s.split(','))))\n", + " if cur:\n", + " blocks.append(np.array(cur, float))\n", + " psi = np.array(psi_vals)\n", + " mats = np.stack(blocks, axis=0)\n", + " return psi, mats\n", + "\n", + " @staticmethod\n", + " def read_cylinder_real_matrix(file_path: str) -> Tuple[np.ndarray, np.ndarray]:\n", + " psi, real_mat = TokamakCylinderLoader.read_block_csv_matrix(file_path, want_imag=False)\n", + " complex_mat = real_mat.astype(np.complex128)\n", + " return psi, complex_mat\n", + "\n", + " # 5. read_cylinder_FGK_from_diag\n", + " @staticmethod\n", + " def read_cylinder_FGK_from_diag(file_path: str) -> Tuple[np.ndarray, Dict[str, np.ndarray]]:\n", + " df = pd.read_csv(file_path)\n", + " psi = df['psi'].values\n", + " mats = {}\n", + " for key in ('F','G','K'):\n", + " prefix = f\"{key}_diag\"\n", + " cols = [col for col in df.columns if col.startswith(prefix)]\n", + " diag_vals = df[cols].values\n", + " n_psi, m = diag_vals.shape\n", + " full = np.zeros((n_psi, m, m), dtype=np.complex128)\n", + " for k in range(n_psi):\n", + " np.fill_diagonal(full[k], diag_vals[k])\n", + " mats[key] = full\n", + " return psi, mats\n", + "\n", + " # 6. clean_and_deduplicate_psin\n", + " @staticmethod\n", + " def clean_and_deduplicate_psin(psin: np.ndarray, mat: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:\n", + " psin_rounded = np.round(psin, 8)\n", + " unique_vals, inv_idx = np.unique(psin_rounded, return_inverse=True)\n", + " m = mat.shape[1]\n", + " mat_out = np.zeros((len(unique_vals), m, m), dtype=mat.dtype)\n", + " counts = np.zeros(len(unique_vals), dtype=int)\n", + " for i, idx in enumerate(inv_idx):\n", + " mat_out[idx] += mat[i]\n", + " counts[idx] += 1\n", + " mat_out /= counts[:, None, None]\n", + " return unique_vals, mat_out\n", + "\n", + " # 7. interpolate_matrix_over_psin\n", + " @staticmethod\n", + " def interpolate_matrix_over_psin(psin_orig: np.ndarray, mat_orig: np.ndarray, psin_target: np.ndarray) -> np.ndarray:\n", + " n, m, _ = mat_orig.shape\n", + " mat_interp = np.zeros((len(psin_target), m, m), dtype=np.complex128)\n", + " for i in range(m):\n", + " for j in range(m):\n", + " f = interp1d(psin_orig, mat_orig[:, i, j], kind='cubic', bounds_error=False, fill_value=\"extrapolate\")\n", + " mat_interp[:, i, j] = f(psin_target)\n", + " return mat_interp\n", + "\n", + " # 8. load_all: 통합 함수\n", + " def load_all(self, psin_target: np.ndarray) -> Dict[str, Dict[str, np.ndarray]]:\n", + " result = {'tokamak': {}, 'cylinder': {}}\n", + "\n", + " # --- Tokamak: A–H from imats.out ---\n", + " psi_imats, mats_imats = TokamakCylinderLoader.read_imats_out(self.imats_path, names=('A','B','C','D','E','H'))\n", + " for nm in ('A','B','C','D','E','H'):\n", + " psi_clean, m_clean = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_imats, mats_imats[nm])\n", + " result['tokamak'][nm] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_clean, m_clean, psin_target)\n", + "\n", + " # --- Tokamak: F from fs.bin ---\n", + " psi_fs, sqfs, mat_F = TokamakCylinderLoader.read_fs_bin(self.fs_bin_path, mpsi=psi_imats.size-1, mpert=self.mpert, mband=self.mband)\n", + " psi_fs, mat_F = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_fs, mat_F)\n", + " result['tokamak']['F'] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_fs, mat_F, psin_target)\n", + "\n", + " # --- Tokamak: G from gs.bin ---\n", + " psi_gs, sqgs, mat_G = TokamakCylinderLoader.read_gs_bin(self.gs_bin_path, mpsi=psi_imats.size-1, mpert=self.mpert, mband=self.mband)\n", + " psi_gs, mat_G = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_gs, mat_G)\n", + " result['tokamak']['G'] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_gs, mat_G, psin_target)\n", + "\n", + " # --- Tokamak: K from ks.bin ---\n", + " psi_ks, sqks, mat_K = TokamakCylinderLoader.read_ks_bin(self.ks_bin_path, mpsi=psi_imats.size-1, mpert=self.mpert, mband=self.mband)\n", + " psi_ks, mat_K = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_ks, mat_K)\n", + " result['tokamak']['K'] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_ks, mat_K, psin_target)\n", + "\n", + " # --- Cylinder: A–H from CSVs ---\n", + " for nm, path in self.cyl_paths.items():\n", + " psi_c, mat_c = TokamakCylinderLoader.read_cylinder_real_matrix(path)\n", + " psi_c, mat_c = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_c, mat_c)\n", + " result['cylinder'][nm] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_c, mat_c, psin_target)\n", + "\n", + " # --- Cylinder: F, G, K from diag CSV ---\n", + " psi_fkg, mats_fkg = TokamakCylinderLoader.read_cylinder_FGK_from_diag(self.cyl_FGK_diag_csv)\n", + " for nm in ('F','G','K'):\n", + " psi_c, mat_c = TokamakCylinderLoader.clean_and_deduplicate_psin(psi_fkg, mats_fkg[nm])\n", + " result['cylinder'][nm] = TokamakCylinderLoader.interpolate_matrix_over_psin(psi_c, mat_c, psin_target)\n", + "\n", + " return result\n", + "\n", + "# ======================\n", + "# Usage example\n", + "# ======================\n", + "if __name__ == \"__main__\":\n", + " # 1) 환경에 맞게 경로와 Fortran 파라미터 설정\n", + " loader = TokamakCylinderLoader(\n", + " imats_path = \"imats.out\",\n", + " fs_bin_path = \"fs.bin\",\n", + " gs_bin_path = \"gs.bin\",\n", + " ks_bin_path = \"ks.bin\",\n", + " mpert = 6,\n", + " mband = 2,\n", + " cyl_A_csv = \"A_matrices.csv\",\n", + " cyl_B_csv = \"B_matrices.csv\",\n", + " cyl_C_csv = \"C_matrices.csv\",\n", + " cyl_D_csv = \"D_matrices.csv\",\n", + " cyl_E_csv = \"E_matrices.csv\",\n", + " cyl_H_csv = \"H_matrices.csv\",\n", + " cyl_FGK_diag_csv = \"dcon_FKG_diagonal_elements.csv\"\n", + " )\n", + "\n", + " # 2) 공통 psin 그리드 정의\n", + " psin_target = np.linspace(0, 1, 200)\n", + "\n", + " # 3) 모든 행렬 읽고 보간\n", + " all_data = loader.load_all(psin_target)\n", + "\n", + " # 4) 결과 출력\n", + " print(\"=== Tokamak matrices ===\")\n", + " for name, mat in all_data['tokamak'].items():\n", + " print(f\"{name}: {mat.shape}\")\n", + " print(\"\\n=== Cylinder matrices ===\")\n", + " for name, mat in all_data['cylinder'].items():\n", + " print(f\"{name}: {mat.shape}\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6050349e", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "mkl_env", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/src/DCON/validate/crit.bin b/src/DCON/validate/crit.bin new file mode 100644 index 000000000..ec003e13d Binary files /dev/null and b/src/DCON/validate/crit.bin differ diff --git a/src/DCON/validate/crit.out b/src/DCON/validate/crit.out new file mode 100644 index 000000000..00238222d --- /dev/null +++ b/src/DCON/validate/crit.out @@ -0,0 +1,813 @@ + + ising psi q di re alpha im alpha + + 1 7.971E-01 2.000E+00 -2.667E-01 5.165E-01 -0.000E+00 + + + is psifac dpsi q singfac eval1 + + 0 1.000E-02 1.000E-02 1.052E+00 9.478E-01 0.000E+00 + 1 1.001E-02 7.481E-06 1.052E+00 9.478E-01 9.562E-04 + 2 1.001E-02 7.377E-07 1.052E+00 9.478E-01 1.050E-03 + 3 1.001E-02 7.377E-07 1.052E+00 9.478E-01 1.145E-03 + 4 1.001E-02 1.475E-06 1.052E+00 9.478E-01 1.333E-03 + 5 1.001E-02 1.475E-06 1.052E+00 9.478E-01 1.522E-03 + 6 1.001E-02 1.475E-06 1.052E+00 9.478E-01 1.711E-03 + 7 1.003E-02 1.447E-05 1.052E+00 9.478E-01 3.560E-03 + 8 1.004E-02 1.447E-05 1.052E+00 9.478E-01 5.409E-03 + 9 1.006E-02 1.447E-05 1.052E+00 9.477E-01 7.258E-03 + 10 1.011E-02 5.366E-05 1.052E+00 9.477E-01 1.412E-02 + 11 1.016E-02 5.366E-05 1.052E+00 9.477E-01 2.097E-02 + 12 1.022E-02 5.366E-05 1.052E+00 9.477E-01 2.783E-02 + 13 1.027E-02 5.366E-05 1.052E+00 9.477E-01 3.469E-02 + 14 1.037E-02 9.470E-05 1.052E+00 9.477E-01 4.679E-02 + 15 1.046E-02 9.470E-05 1.052E+00 9.477E-01 5.889E-02 + 16 1.056E-02 9.470E-05 1.052E+00 9.476E-01 7.099E-02 + 17 1.065E-02 9.470E-05 1.052E+00 9.476E-01 8.308E-02 + 18 1.084E-02 1.905E-04 1.052E+00 9.476E-01 1.074E-01 + 19 1.103E-02 1.905E-04 1.052E+00 9.475E-01 1.317E-01 + 20 1.122E-02 1.905E-04 1.053E+00 9.475E-01 1.561E-01 + 21 1.141E-02 1.905E-04 1.053E+00 9.475E-01 1.804E-01 + 22 1.160E-02 1.905E-04 1.053E+00 9.474E-01 2.047E-01 + 23 1.184E-02 2.340E-04 1.053E+00 9.474E-01 2.345E-01 + 24 1.207E-02 2.340E-04 1.053E+00 9.473E-01 2.644E-01 + 25 1.230E-02 2.340E-04 1.053E+00 9.473E-01 2.942E-01 + 26 1.254E-02 2.340E-04 1.053E+00 9.472E-01 3.240E-01 + 27 1.277E-02 2.340E-04 1.053E+00 9.472E-01 3.539E-01 + 28 1.301E-02 2.340E-04 1.053E+00 9.471E-01 3.837E-01 + 29 1.324E-02 2.340E-04 1.053E+00 9.471E-01 4.135E-01 + 30 1.347E-02 2.340E-04 1.053E+00 9.470E-01 4.433E-01 + 31 1.371E-02 2.340E-04 1.053E+00 9.470E-01 4.731E-01 + 32 1.394E-02 2.340E-04 1.053E+00 9.469E-01 5.029E-01 + 33 1.418E-02 2.340E-04 1.053E+00 9.469E-01 5.327E-01 + 34 1.443E-02 2.575E-04 1.053E+00 9.468E-01 5.654E-01 + 35 1.469E-02 2.575E-04 1.053E+00 9.468E-01 5.982E-01 + 36 1.495E-02 2.575E-04 1.053E+00 9.467E-01 6.309E-01 + 37 1.521E-02 2.575E-04 1.053E+00 9.467E-01 6.636E-01 + 38 1.546E-02 2.575E-04 1.053E+00 9.466E-01 6.964E-01 + 39 1.572E-02 2.575E-04 1.053E+00 9.465E-01 7.291E-01 + 40 1.598E-02 2.575E-04 1.054E+00 9.465E-01 7.618E-01 + 41 1.624E-02 2.575E-04 1.054E+00 9.464E-01 7.945E-01 + 42 1.652E-02 2.860E-04 1.054E+00 9.464E-01 8.308E-01 + 43 1.681E-02 2.860E-04 1.054E+00 9.463E-01 8.671E-01 + 44 1.709E-02 2.860E-04 1.054E+00 9.462E-01 9.034E-01 + 45 1.738E-02 2.860E-04 1.054E+00 9.462E-01 9.397E-01 + 46 1.767E-02 2.860E-04 1.054E+00 9.461E-01 9.760E-01 + 47 1.798E-02 3.156E-04 1.054E+00 9.460E-01 1.016E+00 + 48 1.830E-02 3.156E-04 1.054E+00 9.460E-01 1.056E+00 + 49 1.861E-02 3.156E-04 1.054E+00 9.459E-01 1.096E+00 + 50 1.893E-02 3.156E-04 1.054E+00 9.458E-01 1.136E+00 + 51 1.924E-02 3.156E-04 1.054E+00 9.457E-01 1.176E+00 + 52 1.956E-02 3.156E-04 1.054E+00 9.457E-01 1.216E+00 + 53 1.988E-02 3.156E-04 1.054E+00 9.456E-01 1.256E+00 + 54 2.019E-02 3.156E-04 1.054E+00 9.455E-01 1.296E+00 + 55 2.054E-02 3.506E-04 1.055E+00 9.455E-01 1.340E+00 + 56 2.089E-02 3.506E-04 1.055E+00 9.454E-01 1.385E+00 + 57 2.124E-02 3.506E-04 1.055E+00 9.453E-01 1.429E+00 + 58 2.159E-02 3.506E-04 1.055E+00 9.452E-01 1.473E+00 + 59 2.194E-02 3.506E-04 1.055E+00 9.451E-01 1.517E+00 + 60 2.233E-02 3.872E-04 1.055E+00 9.451E-01 1.566E+00 + 61 2.272E-02 3.872E-04 1.055E+00 9.450E-01 1.615E+00 + 62 2.311E-02 3.872E-04 1.055E+00 9.449E-01 1.664E+00 + 63 2.349E-02 3.872E-04 1.055E+00 9.448E-01 1.713E+00 + 64 2.388E-02 3.872E-04 1.055E+00 9.447E-01 1.762E+00 + 65 2.427E-02 3.872E-04 1.055E+00 9.446E-01 1.811E+00 + 66 2.465E-02 3.872E-04 1.055E+00 9.445E-01 1.859E+00 + 67 2.504E-02 3.872E-04 1.056E+00 9.445E-01 1.908E+00 + 68 2.547E-02 4.316E-04 1.056E+00 9.444E-01 1.963E+00 + 69 2.590E-02 4.316E-04 1.056E+00 9.443E-01 2.017E+00 + 70 2.634E-02 4.316E-04 1.056E+00 9.442E-01 2.071E+00 + 71 2.677E-02 4.316E-04 1.056E+00 9.441E-01 2.125E+00 + 72 2.720E-02 4.316E-04 1.056E+00 9.440E-01 2.180E+00 + 73 2.768E-02 4.788E-04 1.056E+00 9.438E-01 2.240E+00 + 74 2.816E-02 4.788E-04 1.056E+00 9.437E-01 2.300E+00 + 75 2.864E-02 4.788E-04 1.056E+00 9.436E-01 2.360E+00 + 76 2.911E-02 4.788E-04 1.056E+00 9.435E-01 2.420E+00 + + is psifac dpsi q singfac eval1 + + Gaussian Reduction at istep = 77, psi = 2.959E-02, q = 1.056 + + is psifac dpsi q singfac eval1 + + 77 2.959E-02 4.788E-04 1.057E+00 9.434E-01 2.480E+00 + 78 2.960E-02 1.000E-05 1.057E+00 9.434E-01 2.482E+00 + 79 2.961E-02 1.000E-05 1.057E+00 9.434E-01 2.483E+00 + 80 2.980E-02 1.823E-04 1.057E+00 9.433E-01 2.506E+00 + 81 2.998E-02 1.823E-04 1.057E+00 9.433E-01 2.528E+00 + 82 3.016E-02 1.823E-04 1.057E+00 9.432E-01 2.551E+00 + 83 3.047E-02 3.073E-04 1.057E+00 9.432E-01 2.590E+00 + 84 3.077E-02 3.073E-04 1.057E+00 9.431E-01 2.628E+00 + 85 3.108E-02 3.073E-04 1.057E+00 9.430E-01 2.667E+00 + 86 3.139E-02 3.073E-04 1.057E+00 9.430E-01 2.705E+00 + 87 3.176E-02 3.709E-04 1.057E+00 9.429E-01 2.752E+00 + 88 3.213E-02 3.709E-04 1.057E+00 9.428E-01 2.798E+00 + 89 3.250E-02 3.709E-04 1.057E+00 9.427E-01 2.845E+00 + 90 3.287E-02 3.709E-04 1.057E+00 9.426E-01 2.891E+00 + 91 3.350E-02 6.292E-04 1.058E+00 9.425E-01 2.970E+00 + 92 3.413E-02 6.292E-04 1.058E+00 9.423E-01 3.048E+00 + 93 3.476E-02 6.292E-04 1.058E+00 9.422E-01 3.127E+00 + 94 3.539E-02 6.292E-04 1.058E+00 9.420E-01 3.205E+00 + 95 3.602E-02 6.292E-04 1.058E+00 9.419E-01 3.284E+00 + 96 3.679E-02 7.685E-04 1.058E+00 9.417E-01 3.380E+00 + 97 3.756E-02 7.685E-04 1.058E+00 9.415E-01 3.475E+00 + 98 3.832E-02 7.685E-04 1.059E+00 9.413E-01 3.571E+00 + 99 3.909E-02 7.685E-04 1.059E+00 9.411E-01 3.667E+00 + 100 3.986E-02 7.685E-04 1.059E+00 9.409E-01 3.762E+00 + 101 4.063E-02 7.685E-04 1.059E+00 9.408E-01 3.857E+00 + 102 4.228E-02 1.646E-03 1.060E+00 9.403E-01 4.062E+00 + 103 4.392E-02 1.646E-03 1.060E+00 9.399E-01 4.266E+00 + 104 4.557E-02 1.646E-03 1.060E+00 9.395E-01 4.469E+00 + 105 4.721E-02 1.646E-03 1.061E+00 9.391E-01 4.672E+00 + 106 4.886E-02 1.646E-03 1.061E+00 9.387E-01 4.875E+00 + 107 5.051E-02 1.646E-03 1.062E+00 9.383E-01 5.078E+00 + 108 5.215E-02 1.646E-03 1.062E+00 9.379E-01 5.281E+00 + 109 5.380E-02 1.646E-03 1.063E+00 9.375E-01 5.483E+00 + 110 5.545E-02 1.646E-03 1.063E+00 9.370E-01 5.684E+00 + 111 5.709E-02 1.646E-03 1.063E+00 9.366E-01 5.886E+00 + 112 5.874E-02 1.646E-03 1.064E+00 9.362E-01 6.087E+00 + 113 6.038E-02 1.646E-03 1.064E+00 9.357E-01 6.288E+00 + 114 6.203E-02 1.646E-03 1.065E+00 9.353E-01 6.488E+00 + 115 6.335E-02 1.323E-03 1.065E+00 9.349E-01 6.649E+00 + 116 6.444E-02 1.090E-03 1.065E+00 9.346E-01 6.782E+00 + 117 6.553E-02 1.090E-03 1.066E+00 9.343E-01 6.914E+00 + 118 6.662E-02 1.090E-03 1.066E+00 9.341E-01 7.046E+00 + 119 6.771E-02 1.090E-03 1.066E+00 9.338E-01 7.178E+00 + 120 6.881E-02 1.090E-03 1.067E+00 9.335E-01 7.310E+00 + + is psifac dpsi q singfac eval1 + + Gaussian Reduction at istep = 121, psi = 6.990E-02, q = 1.067 + + is psifac dpsi q singfac eval1 + + 121 6.990E-02 1.090E-03 1.067E+00 9.332E-01 7.442E+00 + 122 6.991E-02 1.000E-05 1.067E+00 9.332E-01 7.444E+00 + 123 6.992E-02 1.000E-05 1.067E+00 9.332E-01 7.445E+00 + 124 7.014E-02 2.278E-04 1.067E+00 9.331E-01 7.472E+00 + 125 7.037E-02 2.278E-04 1.067E+00 9.330E-01 7.500E+00 + 126 7.060E-02 2.278E-04 1.067E+00 9.330E-01 7.527E+00 + 127 7.149E-02 8.876E-04 1.067E+00 9.327E-01 7.634E+00 + 128 7.237E-02 8.876E-04 1.068E+00 9.325E-01 7.742E+00 + 129 7.326E-02 8.876E-04 1.068E+00 9.322E-01 7.849E+00 + 130 7.415E-02 8.876E-04 1.068E+00 9.320E-01 7.955E+00 + 131 7.523E-02 1.082E-03 1.068E+00 9.317E-01 8.086E+00 + 132 7.631E-02 1.082E-03 1.069E+00 9.314E-01 8.216E+00 + 133 7.740E-02 1.082E-03 1.069E+00 9.311E-01 8.346E+00 + 134 7.848E-02 1.082E-03 1.069E+00 9.308E-01 8.475E+00 + 135 7.956E-02 1.082E-03 1.070E+00 9.305E-01 8.605E+00 + 136 8.113E-02 1.569E-03 1.070E+00 9.300E-01 8.793E+00 + 137 8.270E-02 1.569E-03 1.070E+00 9.296E-01 8.980E+00 + 138 8.427E-02 1.569E-03 1.071E+00 9.291E-01 9.168E+00 + 139 8.584E-02 1.569E-03 1.071E+00 9.287E-01 9.355E+00 + 140 8.741E-02 1.569E-03 1.072E+00 9.282E-01 9.541E+00 + 141 8.957E-02 2.164E-03 1.072E+00 9.276E-01 9.798E+00 + 142 9.174E-02 2.164E-03 1.073E+00 9.269E-01 1.005E+01 + 143 9.390E-02 2.164E-03 1.074E+00 9.263E-01 1.031E+01 + 144 9.606E-02 2.164E-03 1.074E+00 9.256E-01 1.057E+01 + 145 9.823E-02 2.164E-03 1.075E+00 9.250E-01 1.082E+01 + 146 1.004E-01 2.164E-03 1.076E+00 9.243E-01 1.108E+01 + 147 1.036E-01 3.193E-03 1.077E+00 9.233E-01 1.145E+01 + 148 1.068E-01 3.193E-03 1.078E+00 9.223E-01 1.182E+01 + 149 1.100E-01 3.193E-03 1.079E+00 9.213E-01 1.220E+01 + 150 1.132E-01 3.193E-03 1.080E+00 9.203E-01 1.257E+01 + 151 1.164E-01 3.193E-03 1.081E+00 9.192E-01 1.294E+01 + 152 1.196E-01 3.193E-03 1.082E+00 9.182E-01 1.331E+01 + 153 1.227E-01 3.193E-03 1.083E+00 9.171E-01 1.367E+01 + 154 1.259E-01 3.193E-03 1.084E+00 9.161E-01 1.404E+01 + 155 1.291E-01 3.193E-03 1.085E+00 9.150E-01 1.440E+01 + 156 1.323E-01 3.193E-03 1.086E+00 9.139E-01 1.477E+01 + 157 1.355E-01 3.193E-03 1.087E+00 9.128E-01 1.513E+01 + 158 1.387E-01 3.193E-03 1.088E+00 9.117E-01 1.549E+01 + 159 1.419E-01 3.193E-03 1.089E+00 9.105E-01 1.585E+01 + 160 1.451E-01 3.193E-03 1.091E+00 9.094E-01 1.621E+01 + 161 1.483E-01 3.193E-03 1.092E+00 9.082E-01 1.657E+01 + 162 1.522E-01 3.861E-03 1.093E+00 9.068E-01 1.700E+01 + 163 1.560E-01 3.861E-03 1.095E+00 9.054E-01 1.743E+01 + 164 1.599E-01 3.861E-03 1.096E+00 9.039E-01 1.786E+01 + + is psifac dpsi q singfac eval1 + + Gaussian Reduction at istep = 165, psi = 1.637E-01, q = 1.096 + + is psifac dpsi q singfac eval1 + + 165 1.637E-01 3.861E-03 1.098E+00 9.025E-01 1.829E+01 + 166 1.637E-01 1.000E-05 1.098E+00 9.025E-01 1.829E+01 + 167 1.638E-01 1.000E-05 1.098E+00 9.025E-01 1.829E+01 + 168 1.643E-01 4.980E-04 1.098E+00 9.023E-01 1.835E+01 + 169 1.648E-01 4.980E-04 1.098E+00 9.021E-01 1.840E+01 + 170 1.653E-01 4.980E-04 1.098E+00 9.019E-01 1.846E+01 + 171 1.672E-01 1.919E-03 1.099E+00 9.011E-01 1.867E+01 + 172 1.691E-01 1.919E-03 1.100E+00 9.004E-01 1.888E+01 + 173 1.710E-01 1.919E-03 1.100E+00 8.996E-01 1.909E+01 + 174 1.729E-01 1.919E-03 1.101E+00 8.989E-01 1.930E+01 + 175 1.753E-01 2.349E-03 1.102E+00 8.979E-01 1.955E+01 + 176 1.776E-01 2.349E-03 1.103E+00 8.970E-01 1.981E+01 + 177 1.800E-01 2.349E-03 1.104E+00 8.961E-01 2.006E+01 + 178 1.823E-01 2.349E-03 1.105E+00 8.951E-01 2.032E+01 + 179 1.847E-01 2.349E-03 1.106E+00 8.941E-01 2.057E+01 + 180 1.881E-01 3.424E-03 1.107E+00 8.927E-01 2.094E+01 + 181 1.915E-01 3.424E-03 1.109E+00 8.913E-01 2.131E+01 + 182 1.949E-01 3.424E-03 1.110E+00 8.898E-01 2.167E+01 + 183 1.984E-01 3.424E-03 1.112E+00 8.883E-01 2.204E+01 + 184 2.018E-01 3.424E-03 1.113E+00 8.869E-01 2.240E+01 + 185 2.064E-01 4.599E-03 1.115E+00 8.848E-01 2.289E+01 + 186 2.110E-01 4.599E-03 1.117E+00 8.828E-01 2.337E+01 + 187 2.156E-01 4.599E-03 1.119E+00 8.807E-01 2.385E+01 + 188 2.202E-01 4.599E-03 1.121E+00 8.786E-01 2.433E+01 + 189 2.248E-01 4.599E-03 1.124E+00 8.764E-01 2.480E+01 + 190 2.294E-01 4.599E-03 1.126E+00 8.742E-01 2.528E+01 + 191 2.362E-01 6.799E-03 1.129E+00 8.710E-01 2.597E+01 + 192 2.430E-01 6.799E-03 1.132E+00 8.676E-01 2.666E+01 + 193 2.498E-01 6.799E-03 1.136E+00 8.642E-01 2.734E+01 + 194 2.566E-01 6.799E-03 1.139E+00 8.606E-01 2.802E+01 + 195 2.634E-01 6.799E-03 1.143E+00 8.571E-01 2.869E+01 + 196 2.702E-01 6.799E-03 1.147E+00 8.534E-01 2.935E+01 + 197 2.770E-01 6.799E-03 1.150E+00 8.496E-01 3.001E+01 + 198 2.825E-01 5.533E-03 1.153E+00 8.465E-01 3.054E+01 + 199 2.871E-01 4.588E-03 1.156E+00 8.439E-01 3.098E+01 + 200 2.917E-01 4.588E-03 1.159E+00 8.412E-01 3.142E+01 + 201 2.963E-01 4.588E-03 1.161E+00 8.385E-01 3.185E+01 + 202 3.009E-01 4.588E-03 1.164E+00 8.358E-01 3.228E+01 + 203 3.055E-01 4.588E-03 1.167E+00 8.330E-01 3.271E+01 + 204 3.100E-01 4.588E-03 1.170E+00 8.302E-01 3.313E+01 + 205 3.146E-01 4.588E-03 1.173E+00 8.273E-01 3.355E+01 + 206 3.192E-01 4.588E-03 1.176E+00 8.244E-01 3.397E+01 + 207 3.238E-01 4.588E-03 1.179E+00 8.214E-01 3.438E+01 + 208 3.284E-01 4.588E-03 1.182E+00 8.184E-01 3.480E+01 + 209 3.330E-01 4.588E-03 1.185E+00 8.154E-01 3.520E+01 + 210 3.376E-01 4.588E-03 1.188E+00 8.123E-01 3.561E+01 + 211 3.422E-01 4.588E-03 1.191E+00 8.091E-01 3.601E+01 + 212 3.467E-01 4.588E-03 1.194E+00 8.060E-01 3.641E+01 + 213 3.513E-01 4.588E-03 1.197E+00 8.027E-01 3.681E+01 + 214 3.559E-01 4.588E-03 1.201E+00 7.994E-01 3.721E+01 + 215 3.605E-01 4.588E-03 1.204E+00 7.961E-01 3.760E+01 + + is psifac dpsi q singfac eval1 + + Gaussian Reduction at istep = 216, psi = 3.651E-01, q = 1.204 + + is psifac dpsi q singfac eval1 + + 216 3.651E-01 4.588E-03 1.207E+00 7.927E-01 3.799E+01 + 217 3.651E-01 1.000E-05 1.207E+00 7.927E-01 3.799E+01 + 218 3.651E-01 1.000E-05 1.207E+00 7.927E-01 3.799E+01 + 219 3.661E-01 9.415E-04 1.208E+00 7.920E-01 3.807E+01 + 220 3.670E-01 9.415E-04 1.209E+00 7.913E-01 3.815E+01 + 221 3.679E-01 9.415E-04 1.209E+00 7.906E-01 3.822E+01 + 222 3.711E-01 3.195E-03 1.212E+00 7.882E-01 3.849E+01 + 223 3.743E-01 3.195E-03 1.214E+00 7.858E-01 3.876E+01 + 224 3.775E-01 3.195E-03 1.217E+00 7.833E-01 3.902E+01 + 225 3.807E-01 3.195E-03 1.219E+00 7.809E-01 3.928E+01 + 226 3.844E-01 3.706E-03 1.222E+00 7.779E-01 3.958E+01 + 227 3.881E-01 3.706E-03 1.225E+00 7.750E-01 3.989E+01 + 228 3.918E-01 3.706E-03 1.228E+00 7.720E-01 4.018E+01 + 229 3.955E-01 3.706E-03 1.231E+00 7.690E-01 4.048E+01 + 230 3.993E-01 3.706E-03 1.234E+00 7.659E-01 4.077E+01 + 231 4.051E-01 5.854E-03 1.239E+00 7.611E-01 4.123E+01 + 232 4.110E-01 5.854E-03 1.244E+00 7.561E-01 4.169E+01 + 233 4.168E-01 5.854E-03 1.249E+00 7.510E-01 4.214E+01 + 234 4.227E-01 5.854E-03 1.254E+00 7.458E-01 4.258E+01 + 235 4.285E-01 5.854E-03 1.260E+00 7.405E-01 4.302E+01 + 236 4.356E-01 7.069E-03 1.266E+00 7.339E-01 4.354E+01 + 237 4.427E-01 7.069E-03 1.273E+00 7.273E-01 4.405E+01 + 238 4.497E-01 7.069E-03 1.280E+00 7.204E-01 4.455E+01 + 239 4.568E-01 7.069E-03 1.287E+00 7.134E-01 4.505E+01 + 240 4.639E-01 7.069E-03 1.294E+00 7.062E-01 4.554E+01 + 241 4.709E-01 7.069E-03 1.301E+00 6.989E-01 4.601E+01 + 242 4.803E-01 9.366E-03 1.311E+00 6.888E-01 4.663E+01 + 243 4.897E-01 9.366E-03 1.321E+00 6.785E-01 4.724E+01 + 244 4.990E-01 9.366E-03 1.332E+00 6.678E-01 4.783E+01 + 245 5.084E-01 9.366E-03 1.343E+00 6.568E-01 4.840E+01 + 246 5.178E-01 9.366E-03 1.355E+00 6.454E-01 4.895E+01 + 247 5.271E-01 9.366E-03 1.366E+00 6.336E-01 4.949E+01 + 248 5.365E-01 9.366E-03 1.379E+00 6.214E-01 5.001E+01 + 249 5.459E-01 9.366E-03 1.391E+00 6.087E-01 5.051E+01 + 250 5.552E-01 9.366E-03 1.404E+00 5.957E-01 5.100E+01 + 251 5.646E-01 9.366E-03 1.418E+00 5.822E-01 5.146E+01 + 252 5.740E-01 9.366E-03 1.432E+00 5.682E-01 5.191E+01 + 253 5.833E-01 9.366E-03 1.446E+00 5.537E-01 5.234E+01 + 254 5.927E-01 9.366E-03 1.461E+00 5.387E-01 5.275E+01 + 255 6.021E-01 9.366E-03 1.477E+00 5.231E-01 5.314E+01 + 256 6.114E-01 9.366E-03 1.493E+00 5.069E-01 5.351E+01 + 257 6.208E-01 9.366E-03 1.510E+00 4.902E-01 5.386E+01 + 258 6.302E-01 9.366E-03 1.527E+00 4.728E-01 5.420E+01 + + is psifac dpsi q singfac eval1 + + Gaussian Reduction at istep = 259, psi = 6.395E-01, q = 1.527 + + is psifac dpsi q singfac eval1 + + 259 6.395E-01 9.366E-03 1.545E+00 4.547E-01 5.451E+01 + 260 6.395E-01 1.000E-05 1.545E+00 4.547E-01 5.451E+01 + 261 6.395E-01 1.000E-05 1.545E+00 4.547E-01 5.451E+01 + 262 6.406E-01 1.045E-03 1.547E+00 4.526E-01 5.454E+01 + 263 6.416E-01 1.045E-03 1.549E+00 4.505E-01 5.457E+01 + 264 6.427E-01 1.045E-03 1.552E+00 4.485E-01 5.461E+01 + 265 6.463E-01 3.658E-03 1.559E+00 4.411E-01 5.472E+01 + 266 6.500E-01 3.658E-03 1.566E+00 4.337E-01 5.483E+01 + 267 6.537E-01 3.658E-03 1.574E+00 4.261E-01 5.493E+01 + 268 6.573E-01 3.658E-03 1.582E+00 4.184E-01 5.504E+01 + 269 6.610E-01 3.658E-03 1.589E+00 4.106E-01 5.514E+01 + 270 6.646E-01 3.658E-03 1.597E+00 4.027E-01 5.523E+01 + 271 6.683E-01 3.658E-03 1.605E+00 3.946E-01 5.533E+01 + 272 6.729E-01 4.652E-03 1.616E+00 3.842E-01 5.544E+01 + 273 6.776E-01 4.652E-03 1.626E+00 3.735E-01 5.555E+01 + 274 6.822E-01 4.652E-03 1.637E+00 3.627E-01 5.565E+01 + 275 6.869E-01 4.652E-03 1.648E+00 3.516E-01 5.575E+01 + 276 6.915E-01 4.652E-03 1.660E+00 3.402E-01 5.584E+01 + 277 6.975E-01 5.995E-03 1.675E+00 3.253E-01 5.595E+01 + 278 7.035E-01 5.995E-03 1.690E+00 3.099E-01 5.605E+01 + 279 7.095E-01 5.995E-03 1.706E+00 2.941E-01 5.614E+01 + 280 7.155E-01 5.995E-03 1.722E+00 2.779E-01 5.622E+01 + 281 7.215E-01 5.995E-03 1.739E+00 2.612E-01 5.629E+01 + 282 7.275E-01 5.995E-03 1.756E+00 2.440E-01 5.635E+01 + 283 7.341E-01 6.614E-03 1.776E+00 2.244E-01 5.641E+01 + 284 7.407E-01 6.614E-03 1.796E+00 2.042E-01 5.645E+01 + 285 7.474E-01 6.614E-03 1.817E+00 1.832E-01 5.648E+01 + 286 7.540E-01 6.614E-03 1.838E+00 1.616E-01 5.650E+01 + 287 7.594E-01 5.398E-03 1.857E+00 1.434E-01 5.651E+01 + 288 7.648E-01 5.398E-03 1.875E+00 1.247E-01 5.650E+01 + 289 7.656E-01 8.158E-04 1.878E+00 1.218E-01 5.650E+01 + 290 7.664E-01 8.158E-04 1.881E+00 1.189E-01 5.650E+01 + 291 7.672E-01 8.158E-04 1.884E+00 1.160E-01 5.650E+01 + 292 7.680E-01 8.158E-04 1.887E+00 1.131E-01 5.650E+01 + 293 7.688E-01 8.158E-04 1.890E+00 1.102E-01 5.649E+01 + 294 7.697E-01 8.158E-04 1.893E+00 1.072E-01 5.649E+01 + 295 7.713E-01 1.632E-03 1.899E+00 1.013E-01 5.649E+01 + 296 7.729E-01 1.632E-03 1.905E+00 9.531E-02 5.648E+01 + 297 7.746E-01 1.632E-03 1.911E+00 8.928E-02 5.647E+01 + 298 7.762E-01 1.632E-03 1.917E+00 8.320E-02 5.647E+01 + 299 7.778E-01 1.632E-03 1.923E+00 7.706E-02 5.646E+01 + 300 7.797E-01 1.883E-03 1.930E+00 6.990E-02 5.645E+01 + 301 7.816E-01 1.883E-03 1.937E+00 6.267E-02 5.644E+01 + 302 7.835E-01 1.883E-03 1.945E+00 5.536E-02 5.642E+01 + 303 7.849E-01 1.477E-03 1.950E+00 4.957E-02 5.641E+01 + 304 7.864E-01 1.477E-03 1.956E+00 4.373E-02 5.640E+01 + 305 7.876E-01 1.131E-03 1.961E+00 3.923E-02 5.639E+01 + 306 7.887E-01 1.131E-03 1.965E+00 3.470E-02 5.638E+01 + 307 7.896E-01 8.836E-04 1.969E+00 3.114E-02 5.638E+01 + 308 7.905E-01 8.836E-04 1.972E+00 2.756E-02 5.637E+01 + 309 7.912E-01 7.178E-04 1.975E+00 2.464E-02 5.636E+01 + 310 7.919E-01 7.178E-04 1.978E+00 2.171E-02 5.636E+01 + 311 7.925E-01 5.629E-04 1.981E+00 1.940E-02 5.635E+01 + 312 7.930E-01 5.629E-04 1.983E+00 1.708E-02 5.634E+01 + 313 7.935E-01 4.384E-04 1.985E+00 1.528E-02 5.634E+01 + 314 7.939E-01 4.384E-04 1.987E+00 1.346E-02 5.634E+01 + 315 7.942E-01 3.430E-04 1.988E+00 1.204E-02 5.633E+01 + 316 7.946E-01 3.430E-04 1.989E+00 1.062E-02 5.633E+01 + 317 7.948E-01 2.676E-04 1.990E+00 9.503E-03 5.633E+01 + 318 7.950E-01 1.789E-04 1.991E+00 8.757E-03 5.632E+01 + 319 7.952E-01 1.388E-04 1.992E+00 8.179E-03 5.632E+01 + 320 7.953E-01 1.388E-04 1.992E+00 7.599E-03 5.632E+01 + 321 7.954E-01 1.075E-04 1.993E+00 7.150E-03 5.632E+01 + 322 7.955E-01 1.075E-04 1.993E+00 6.701E-03 5.632E+01 + 323 7.955E-01 1.910E-05 1.993E+00 6.621E-03 5.632E+01 + 324 7.956E-01 1.910E-05 1.993E+00 6.541E-03 5.632E+01 + 325 7.956E-01 1.910E-05 1.994E+00 6.461E-03 5.632E+01 + 326 7.956E-01 1.910E-05 1.994E+00 6.381E-03 5.632E+01 + 327 7.956E-01 1.910E-05 1.994E+00 6.301E-03 5.632E+01 + 328 7.957E-01 3.820E-05 1.994E+00 6.142E-03 5.632E+01 + 329 7.957E-01 3.820E-05 1.994E+00 5.982E-03 5.632E+01 + 330 7.957E-01 3.820E-05 1.994E+00 5.822E-03 5.632E+01 + 331 7.958E-01 3.820E-05 1.994E+00 5.662E-03 5.632E+01 + 332 7.958E-01 3.820E-05 1.994E+00 5.502E-03 5.632E+01 + 333 7.959E-01 7.298E-05 1.995E+00 5.196E-03 5.632E+01 + 334 7.960E-01 7.298E-05 1.995E+00 4.890E-03 5.631E+01 + 335 7.960E-01 7.298E-05 1.995E+00 4.584E-03 5.631E+01 + 336 7.961E-01 7.298E-05 1.996E+00 4.278E-03 5.631E+01 + 337 7.962E-01 7.298E-05 1.996E+00 3.972E-03 5.631E+01 + 338 7.962E-01 7.298E-05 1.996E+00 3.666E-03 5.631E+01 + 339 7.963E-01 6.077E-05 1.997E+00 3.411E-03 5.631E+01 + 340 7.964E-01 6.077E-05 1.997E+00 3.155E-03 5.631E+01 + 341 7.964E-01 6.077E-05 1.997E+00 2.900E-03 5.631E+01 + 342 7.965E-01 4.812E-05 1.997E+00 2.698E-03 5.631E+01 + 343 7.965E-01 4.812E-05 1.998E+00 2.495E-03 5.631E+01 + 344 7.966E-01 4.812E-05 1.998E+00 2.293E-03 5.631E+01 + 345 7.966E-01 3.787E-05 1.998E+00 2.134E-03 5.631E+01 + 346 7.966E-01 3.787E-05 1.998E+00 1.974E-03 5.631E+01 + 347 7.967E-01 3.787E-05 1.998E+00 1.815E-03 5.631E+01 + 348 7.967E-01 2.995E-05 1.998E+00 1.689E-03 5.631E+01 + 349 7.967E-01 2.995E-05 1.998E+00 1.563E-03 5.631E+01 + 350 7.968E-01 2.995E-05 1.999E+00 1.436E-03 5.631E+01 + 351 7.968E-01 2.368E-05 1.999E+00 1.337E-03 5.631E+01 + 352 7.968E-01 2.368E-05 1.999E+00 1.237E-03 5.631E+01 + 353 7.968E-01 2.368E-05 1.999E+00 1.137E-03 5.631E+01 + 354 7.969E-01 1.876E-05 1.999E+00 1.058E-03 5.630E+01 + 355 7.969E-01 1.876E-05 1.999E+00 9.790E-04 5.630E+01 + 356 7.969E-01 1.876E-05 1.999E+00 9.000E-04 5.630E+01 + 357 7.969E-01 1.484E-05 1.999E+00 8.374E-04 5.630E+01 + 358 7.969E-01 1.484E-05 1.999E+00 7.748E-04 5.630E+01 + 359 7.969E-01 1.484E-05 1.999E+00 7.123E-04 5.630E+01 + 360 7.970E-01 1.175E-05 1.999E+00 6.627E-04 5.630E+01 + 361 7.970E-01 1.175E-05 1.999E+00 6.132E-04 5.630E+01 + 362 7.970E-01 1.175E-05 1.999E+00 5.636E-04 5.630E+01 + 363 7.970E-01 9.295E-06 1.999E+00 5.244E-04 5.630E+01 + 364 7.970E-01 9.295E-06 2.000E+00 4.852E-04 5.630E+01 + 365 7.970E-01 9.295E-06 2.000E+00 4.460E-04 5.630E+01 + 366 7.970E-01 7.359E-06 2.000E+00 4.150E-04 5.630E+01 + 367 7.970E-01 7.359E-06 2.000E+00 3.839E-04 5.630E+01 + 368 7.970E-01 7.359E-06 2.000E+00 3.529E-04 5.630E+01 + 369 7.970E-01 5.820E-06 2.000E+00 3.283E-04 5.630E+01 + 370 7.970E-01 5.820E-06 2.000E+00 3.038E-04 5.630E+01 + 371 7.970E-01 5.820E-06 2.000E+00 2.792E-04 5.630E+01 + 372 7.971E-01 4.607E-06 2.000E+00 2.598E-04 5.630E+01 + 373 7.971E-01 4.607E-06 2.000E+00 2.404E-04 5.630E+01 + 374 7.971E-01 4.607E-06 2.000E+00 2.209E-04 5.630E+01 + 375 7.971E-01 3.644E-06 2.000E+00 2.056E-04 5.630E+01 + 376 7.971E-01 3.644E-06 2.000E+00 1.902E-04 5.630E+01 + 377 7.971E-01 3.644E-06 2.000E+00 1.748E-04 5.630E+01 + 378 7.971E-01 2.884E-06 2.000E+00 1.626E-04 5.630E+01 + 379 7.971E-01 2.884E-06 2.000E+00 1.505E-04 5.630E+01 + 380 7.971E-01 2.884E-06 2.000E+00 1.383E-04 5.630E+01 + 381 7.971E-01 2.281E-06 2.000E+00 1.287E-04 5.630E+01 + 382 7.971E-01 2.281E-06 2.000E+00 1.191E-04 5.630E+01 + 383 7.971E-01 2.281E-06 2.000E+00 1.094E-04 5.630E+01 + 384 7.971E-01 1.789E-06 2.000E+00 1.019E-04 5.630E+01 + 385 7.971E-01 4.481E-07 2.000E+00 9.999E-05 5.630E+01 + + is psifac dpsi q singfac eval1 + + Gaussian Reduction at istep = 385, psi = 7.971E-01, q = 2.000 + + ising psi q di re alpha im alpha + + 2 9.350E-01 3.000E+00 -2.579E-01 5.078E-01 -0.000E+00 + + + is psifac dpsi q singfac eval1 + + 386 7.971E-01 4.739E-05 2.000E+00 9.999E-01 5.630E+01 + 387 7.971E-01 2.779E-08 2.000E+00 9.999E-01 5.630E+01 + 388 7.971E-01 2.779E-08 2.000E+00 9.999E-01 5.630E+01 + 389 7.971E-01 5.558E-08 2.000E+00 9.999E-01 5.630E+01 + 390 7.971E-01 5.558E-08 2.000E+00 9.999E-01 5.630E+01 + 391 7.971E-01 5.558E-08 2.000E+00 9.999E-01 5.630E+01 + 392 7.971E-01 3.299E-07 2.000E+00 9.999E-01 5.630E+01 + 393 7.971E-01 3.299E-07 2.000E+00 9.999E-01 5.630E+01 + 394 7.971E-01 3.299E-07 2.000E+00 9.999E-01 5.630E+01 + 395 7.971E-01 3.299E-07 2.000E+00 9.999E-01 5.630E+01 + 396 7.971E-01 9.168E-07 2.000E+00 9.999E-01 5.630E+01 + 397 7.971E-01 9.168E-07 2.000E+00 9.999E-01 5.630E+01 + 398 7.971E-01 9.168E-07 2.000E+00 9.999E-01 5.630E+01 + 399 7.971E-01 9.168E-07 2.000E+00 9.999E-01 5.630E+01 + 400 7.971E-01 9.168E-07 2.000E+00 9.999E-01 5.630E+01 + 401 7.971E-01 1.428E-06 2.000E+00 9.999E-01 5.630E+01 + 402 7.971E-01 1.428E-06 2.000E+00 9.999E-01 5.630E+01 + 403 7.971E-01 1.428E-06 2.000E+00 9.999E-01 5.630E+01 + 404 7.972E-01 1.428E-06 2.000E+00 9.999E-01 5.630E+01 + 405 7.972E-01 1.428E-06 2.000E+00 9.998E-01 5.630E+01 + 406 7.972E-01 1.860E-06 2.000E+00 9.998E-01 5.630E+01 + 407 7.972E-01 1.860E-06 2.000E+00 9.998E-01 5.630E+01 + 408 7.972E-01 1.860E-06 2.000E+00 9.998E-01 5.630E+01 + 409 7.972E-01 1.860E-06 2.000E+00 9.998E-01 5.630E+01 + 410 7.972E-01 1.860E-06 2.000E+00 9.998E-01 5.630E+01 + 411 7.972E-01 2.467E-06 2.000E+00 9.998E-01 5.630E+01 + 412 7.972E-01 2.467E-06 2.000E+00 9.998E-01 5.630E+01 + 413 7.972E-01 2.467E-06 2.000E+00 9.998E-01 5.630E+01 + 414 7.972E-01 2.467E-06 2.000E+00 9.998E-01 5.630E+01 + 415 7.972E-01 2.467E-06 2.000E+00 9.998E-01 5.630E+01 + 416 7.972E-01 3.314E-06 2.000E+00 9.997E-01 5.630E+01 + 417 7.972E-01 3.314E-06 2.000E+00 9.997E-01 5.630E+01 + 418 7.972E-01 3.314E-06 2.000E+00 9.997E-01 5.630E+01 + 419 7.972E-01 3.314E-06 2.000E+00 9.997E-01 5.630E+01 + 420 7.972E-01 3.314E-06 2.000E+00 9.997E-01 5.630E+01 + 421 7.972E-01 4.511E-06 2.000E+00 9.997E-01 5.630E+01 + 422 7.972E-01 4.511E-06 2.000E+00 9.996E-01 5.630E+01 + 423 7.972E-01 4.511E-06 2.000E+00 9.996E-01 5.630E+01 + 424 7.972E-01 4.511E-06 2.000E+00 9.996E-01 5.630E+01 + 425 7.972E-01 4.511E-06 2.000E+00 9.996E-01 5.630E+01 + 426 7.972E-01 6.226E-06 2.000E+00 9.996E-01 5.630E+01 + 427 7.972E-01 6.226E-06 2.000E+00 9.995E-01 5.630E+01 + 428 7.972E-01 6.226E-06 2.000E+00 9.995E-01 5.630E+01 + 429 7.972E-01 6.226E-06 2.001E+00 9.995E-01 5.630E+01 + 430 7.972E-01 6.226E-06 2.001E+00 9.995E-01 5.630E+01 + 431 7.973E-01 8.718E-06 2.001E+00 9.994E-01 5.630E+01 + 432 7.973E-01 8.718E-06 2.001E+00 9.994E-01 5.630E+01 + 433 7.973E-01 8.718E-06 2.001E+00 9.993E-01 5.630E+01 + 434 7.973E-01 8.718E-06 2.001E+00 9.993E-01 5.630E+01 + 435 7.973E-01 8.718E-06 2.001E+00 9.993E-01 5.630E+01 + 436 7.973E-01 1.241E-05 2.001E+00 9.992E-01 5.630E+01 + 437 7.973E-01 1.241E-05 2.001E+00 9.992E-01 5.630E+01 + 438 7.973E-01 1.241E-05 2.001E+00 9.991E-01 5.630E+01 + 439 7.973E-01 1.241E-05 2.001E+00 9.991E-01 5.630E+01 + 440 7.973E-01 1.241E-05 2.001E+00 9.990E-01 5.630E+01 + 441 7.974E-01 1.798E-05 2.001E+00 9.989E-01 5.630E+01 + 442 7.974E-01 1.798E-05 2.001E+00 9.989E-01 5.630E+01 + 443 7.974E-01 1.798E-05 2.001E+00 9.988E-01 5.630E+01 + 444 7.974E-01 1.798E-05 2.001E+00 9.987E-01 5.630E+01 + 445 7.974E-01 1.798E-05 2.001E+00 9.986E-01 5.630E+01 + 446 7.975E-01 2.657E-05 2.001E+00 9.985E-01 5.630E+01 + 447 7.975E-01 2.657E-05 2.002E+00 9.984E-01 5.630E+01 + 448 7.975E-01 2.657E-05 2.002E+00 9.983E-01 5.630E+01 + 449 7.975E-01 2.657E-05 2.002E+00 9.982E-01 5.630E+01 + 450 7.976E-01 2.657E-05 2.002E+00 9.981E-01 5.630E+01 + 451 7.976E-01 4.009E-05 2.002E+00 9.979E-01 5.630E+01 + 452 7.977E-01 4.009E-05 2.002E+00 9.977E-01 5.630E+01 + 453 7.977E-01 4.009E-05 2.002E+00 9.976E-01 5.630E+01 + 454 7.977E-01 4.009E-05 2.003E+00 9.974E-01 5.630E+01 + 455 7.978E-01 4.009E-05 2.003E+00 9.972E-01 5.630E+01 + 456 7.978E-01 6.170E-05 2.003E+00 9.970E-01 5.630E+01 + 457 7.979E-01 6.170E-05 2.003E+00 9.967E-01 5.629E+01 + 458 7.980E-01 6.170E-05 2.004E+00 9.964E-01 5.629E+01 + 459 7.980E-01 6.170E-05 2.004E+00 9.962E-01 5.629E+01 + 460 7.981E-01 6.170E-05 2.004E+00 9.959E-01 5.629E+01 + 461 7.982E-01 9.647E-05 2.004E+00 9.955E-01 5.629E+01 + 462 7.983E-01 9.647E-05 2.005E+00 9.951E-01 5.629E+01 + 463 7.984E-01 9.647E-05 2.005E+00 9.947E-01 5.629E+01 + 464 7.985E-01 9.647E-05 2.006E+00 9.943E-01 5.629E+01 + 465 7.986E-01 9.647E-05 2.006E+00 9.939E-01 5.629E+01 + 466 7.987E-01 1.517E-04 2.007E+00 9.932E-01 5.628E+01 + 467 7.989E-01 1.517E-04 2.007E+00 9.926E-01 5.628E+01 + 468 7.990E-01 1.517E-04 2.008E+00 9.919E-01 5.628E+01 + 469 7.992E-01 1.517E-04 2.009E+00 9.913E-01 5.628E+01 + 470 7.993E-01 1.517E-04 2.009E+00 9.906E-01 5.628E+01 + 471 7.996E-01 2.376E-04 2.010E+00 9.896E-01 5.627E+01 + 472 7.998E-01 2.376E-04 2.011E+00 9.886E-01 5.627E+01 + 473 8.000E-01 2.376E-04 2.012E+00 9.876E-01 5.627E+01 + 474 8.003E-01 2.376E-04 2.013E+00 9.866E-01 5.627E+01 + 475 8.005E-01 2.376E-04 2.014E+00 9.855E-01 5.626E+01 + 476 8.011E-01 5.854E-04 2.017E+00 9.830E-01 5.626E+01 + 477 8.017E-01 5.854E-04 2.020E+00 9.805E-01 5.625E+01 + 478 8.023E-01 5.854E-04 2.022E+00 9.779E-01 5.624E+01 + 479 8.029E-01 5.854E-04 2.025E+00 9.754E-01 5.623E+01 + 480 8.034E-01 5.854E-04 2.027E+00 9.728E-01 5.622E+01 + 481 8.050E-01 1.514E-03 2.034E+00 9.661E-01 5.620E+01 + 482 8.065E-01 1.514E-03 2.041E+00 9.594E-01 5.618E+01 + 483 8.080E-01 1.514E-03 2.047E+00 9.526E-01 5.616E+01 + 484 8.095E-01 1.514E-03 2.054E+00 9.458E-01 5.614E+01 + 485 8.110E-01 1.514E-03 2.061E+00 9.389E-01 5.611E+01 + 486 8.137E-01 2.685E-03 2.074E+00 9.264E-01 5.607E+01 + 487 8.164E-01 2.685E-03 2.086E+00 9.138E-01 5.602E+01 + 488 8.191E-01 2.685E-03 2.099E+00 9.010E-01 5.597E+01 + 489 8.217E-01 2.685E-03 2.112E+00 8.879E-01 5.592E+01 + 490 8.244E-01 2.685E-03 2.125E+00 8.746E-01 5.587E+01 + 491 8.279E-01 3.423E-03 2.143E+00 8.573E-01 5.580E+01 + 492 8.313E-01 3.423E-03 2.160E+00 8.397E-01 5.572E+01 + 493 8.347E-01 3.423E-03 2.178E+00 8.216E-01 5.564E+01 + 494 8.381E-01 3.423E-03 2.197E+00 8.031E-01 5.555E+01 + 495 8.415E-01 3.423E-03 2.216E+00 7.841E-01 5.546E+01 + 496 8.455E-01 3.951E-03 2.238E+00 7.617E-01 5.536E+01 + 497 8.495E-01 3.951E-03 2.261E+00 7.387E-01 5.524E+01 + 498 8.534E-01 3.951E-03 2.285E+00 7.150E-01 5.512E+01 + 499 8.574E-01 3.951E-03 2.309E+00 6.906E-01 5.500E+01 + 500 8.613E-01 3.951E-03 2.335E+00 6.654E-01 5.487E+01 + 501 8.653E-01 3.951E-03 2.360E+00 6.396E-01 5.473E+01 + 502 8.692E-01 3.951E-03 2.387E+00 6.129E-01 5.458E+01 + 503 8.725E-01 3.279E-03 2.410E+00 5.901E-01 5.446E+01 + 504 8.758E-01 3.279E-03 2.433E+00 5.668E-01 5.433E+01 + 505 8.790E-01 3.279E-03 2.457E+00 5.428E-01 5.420E+01 + 506 8.823E-01 3.279E-03 2.482E+00 5.181E-01 5.406E+01 + 507 8.856E-01 3.279E-03 2.507E+00 4.928E-01 5.392E+01 + 508 8.889E-01 3.279E-03 2.533E+00 4.668E-01 5.377E+01 + 509 8.922E-01 3.279E-03 2.560E+00 4.400E-01 5.362E+01 + 510 8.949E-01 2.708E-03 2.583E+00 4.173E-01 5.349E+01 + 511 8.976E-01 2.708E-03 2.606E+00 3.940E-01 5.335E+01 + 512 9.003E-01 2.708E-03 2.630E+00 3.702E-01 5.321E+01 + 513 9.030E-01 2.708E-03 2.654E+00 3.457E-01 5.307E+01 + 514 9.057E-01 2.708E-03 2.679E+00 3.206E-01 5.293E+01 + 515 9.079E-01 2.241E-03 2.701E+00 2.994E-01 5.281E+01 + 516 9.102E-01 2.241E-03 2.722E+00 2.776E-01 5.268E+01 + 517 9.124E-01 2.241E-03 2.745E+00 2.554E-01 5.256E+01 + 518 9.142E-01 1.824E-03 2.763E+00 2.370E-01 5.245E+01 + 519 9.161E-01 1.824E-03 2.782E+00 2.182E-01 5.234E+01 + 520 9.179E-01 1.824E-03 2.801E+00 1.991E-01 5.223E+01 + 521 9.193E-01 1.417E-03 2.816E+00 1.839E-01 5.214E+01 + 522 9.207E-01 1.417E-03 2.831E+00 1.686E-01 5.206E+01 + 523 9.221E-01 1.417E-03 2.847E+00 1.530E-01 5.197E+01 + 524 9.232E-01 1.076E-03 2.859E+00 1.410E-01 5.190E+01 + 525 9.243E-01 1.076E-03 2.871E+00 1.289E-01 5.183E+01 + 526 9.252E-01 8.910E-04 2.881E+00 1.187E-01 5.177E+01 + 527 9.261E-01 8.910E-04 2.892E+00 1.085E-01 5.171E+01 + 528 9.270E-01 8.910E-04 2.902E+00 9.811E-02 5.166E+01 + 529 9.276E-01 6.763E-04 2.910E+00 9.018E-02 5.161E+01 + 530 9.283E-01 6.763E-04 2.918E+00 8.220E-02 5.157E+01 + 531 9.289E-01 5.595E-04 2.924E+00 7.554E-02 5.153E+01 + 532 9.294E-01 5.595E-04 2.931E+00 6.885E-02 5.149E+01 + 533 9.300E-01 5.595E-04 2.938E+00 6.211E-02 5.145E+01 + 534 9.304E-01 4.247E-04 2.943E+00 5.697E-02 5.142E+01 + 535 9.309E-01 4.247E-04 2.948E+00 5.180E-02 5.139E+01 + 536 9.312E-01 3.512E-04 2.952E+00 4.750E-02 5.137E+01 + 537 9.316E-01 3.512E-04 2.957E+00 4.319E-02 5.135E+01 + 538 9.319E-01 3.512E-04 2.961E+00 3.887E-02 5.132E+01 + 539 9.322E-01 2.669E-04 2.964E+00 3.557E-02 5.130E+01 + 540 9.324E-01 2.669E-04 2.968E+00 3.226E-02 5.128E+01 + 541 9.327E-01 2.202E-04 2.970E+00 2.952E-02 5.127E+01 + 542 9.329E-01 2.202E-04 2.973E+00 2.677E-02 5.125E+01 + 543 9.331E-01 1.833E-04 2.976E+00 2.448E-02 5.124E+01 + 544 9.332E-01 1.833E-04 2.978E+00 2.218E-02 5.123E+01 + 545 9.334E-01 1.518E-04 2.980E+00 2.028E-02 5.122E+01 + 546 9.336E-01 1.518E-04 2.982E+00 1.837E-02 5.121E+01 + 547 9.337E-01 1.258E-04 2.983E+00 1.678E-02 5.120E+01 + 548 9.338E-01 1.258E-04 2.985E+00 1.520E-02 5.119E+01 + 549 9.339E-01 1.040E-04 2.986E+00 1.388E-02 5.118E+01 + 550 9.340E-01 1.040E-04 2.987E+00 1.257E-02 5.117E+01 + 551 9.341E-01 8.590E-05 2.989E+00 1.148E-02 5.117E+01 + 552 9.342E-01 8.590E-05 2.990E+00 1.039E-02 5.116E+01 + 553 9.343E-01 7.090E-05 2.991E+00 9.491E-03 5.116E+01 + 554 9.343E-01 8.147E-06 2.991E+00 9.387E-03 5.116E+01 + 555 9.343E-01 8.147E-06 2.991E+00 9.284E-03 5.116E+01 + 556 9.343E-01 8.147E-06 2.991E+00 9.181E-03 5.115E+01 + 557 9.343E-01 8.147E-06 2.991E+00 9.077E-03 5.115E+01 + 558 9.343E-01 8.147E-06 2.991E+00 8.974E-03 5.115E+01 + 559 9.343E-01 1.629E-05 2.991E+00 8.767E-03 5.115E+01 + 560 9.343E-01 1.629E-05 2.991E+00 8.560E-03 5.115E+01 + 561 9.343E-01 1.629E-05 2.992E+00 8.353E-03 5.115E+01 + 562 9.344E-01 1.629E-05 2.992E+00 8.146E-03 5.115E+01 + 563 9.344E-01 2.883E-05 2.992E+00 7.779E-03 5.115E+01 + 564 9.344E-01 2.883E-05 2.993E+00 7.413E-03 5.114E+01 + 565 9.344E-01 2.883E-05 2.993E+00 7.046E-03 5.114E+01 + 566 9.345E-01 2.883E-05 2.993E+00 6.679E-03 5.114E+01 + 567 9.345E-01 2.883E-05 2.994E+00 6.313E-03 5.114E+01 + 568 9.345E-01 2.883E-05 2.994E+00 5.946E-03 5.114E+01 + 569 9.346E-01 2.883E-05 2.994E+00 5.578E-03 5.113E+01 + 570 9.346E-01 2.301E-05 2.995E+00 5.285E-03 5.113E+01 + 571 9.346E-01 2.301E-05 2.995E+00 4.992E-03 5.113E+01 + 572 9.346E-01 2.301E-05 2.995E+00 4.699E-03 5.113E+01 + 573 9.347E-01 2.301E-05 2.996E+00 4.405E-03 5.113E+01 + 574 9.347E-01 1.819E-05 2.996E+00 4.173E-03 5.113E+01 + 575 9.347E-01 1.819E-05 2.996E+00 3.941E-03 5.113E+01 + 576 9.347E-01 1.819E-05 2.996E+00 3.709E-03 5.112E+01 + 577 9.347E-01 1.819E-05 2.997E+00 3.477E-03 5.112E+01 + 578 9.347E-01 1.438E-05 2.997E+00 3.294E-03 5.112E+01 + 579 9.348E-01 1.438E-05 2.997E+00 3.110E-03 5.112E+01 + + is psifac dpsi q singfac eval1 + + Gaussian Reduction at istep = 580, psi = 9.348E-01, q = 2.997 + + is psifac dpsi q singfac eval1 + + 580 9.348E-01 1.438E-05 2.997E+00 2.927E-03 5.112E+01 + 581 9.348E-01 2.502E-07 2.997E+00 2.924E-03 5.112E+01 + 582 9.348E-01 2.502E-07 2.997E+00 2.920E-03 5.112E+01 + 583 9.348E-01 5.004E-07 2.997E+00 2.914E-03 5.112E+01 + 584 9.348E-01 5.004E-07 2.997E+00 2.908E-03 5.112E+01 + 585 9.348E-01 5.004E-07 2.997E+00 2.901E-03 5.112E+01 + 586 9.348E-01 3.206E-06 2.997E+00 2.860E-03 5.112E+01 + 587 9.348E-01 3.206E-06 2.997E+00 2.819E-03 5.112E+01 + 588 9.348E-01 3.206E-06 2.997E+00 2.778E-03 5.112E+01 + 589 9.348E-01 3.206E-06 2.997E+00 2.737E-03 5.112E+01 + 590 9.348E-01 7.723E-06 2.997E+00 2.639E-03 5.112E+01 + 591 9.348E-01 7.723E-06 2.997E+00 2.540E-03 5.112E+01 + 592 9.348E-01 7.723E-06 2.998E+00 2.442E-03 5.112E+01 + 593 9.348E-01 7.723E-06 2.998E+00 2.343E-03 5.112E+01 + 594 9.348E-01 7.723E-06 2.998E+00 2.244E-03 5.112E+01 + 595 9.348E-01 1.008E-05 2.998E+00 2.115E-03 5.112E+01 + 596 9.348E-01 1.008E-05 2.998E+00 1.987E-03 5.111E+01 + 597 9.349E-01 1.008E-05 2.998E+00 1.858E-03 5.111E+01 + 598 9.349E-01 1.008E-05 2.998E+00 1.729E-03 5.111E+01 + 599 9.349E-01 1.008E-05 2.998E+00 1.600E-03 5.111E+01 + 600 9.349E-01 1.008E-05 2.999E+00 1.471E-03 5.111E+01 + 601 9.349E-01 7.943E-06 2.999E+00 1.370E-03 5.111E+01 + 602 9.349E-01 7.943E-06 2.999E+00 1.268E-03 5.111E+01 + 603 9.349E-01 7.943E-06 2.999E+00 1.167E-03 5.111E+01 + 604 9.349E-01 6.332E-06 2.999E+00 1.086E-03 5.111E+01 + 605 9.349E-01 6.332E-06 2.999E+00 1.005E-03 5.111E+01 + 606 9.349E-01 6.332E-06 2.999E+00 9.236E-04 5.111E+01 + 607 9.349E-01 5.029E-06 2.999E+00 8.593E-04 5.111E+01 + 608 9.349E-01 5.029E-06 2.999E+00 7.950E-04 5.111E+01 + 609 9.349E-01 5.029E-06 2.999E+00 7.306E-04 5.111E+01 + 610 9.349E-01 3.999E-06 2.999E+00 6.794E-04 5.111E+01 + 611 9.349E-01 3.999E-06 2.999E+00 6.283E-04 5.111E+01 + 612 9.350E-01 3.999E-06 2.999E+00 5.771E-04 5.111E+01 + 613 9.350E-01 3.170E-06 2.999E+00 5.365E-04 5.111E+01 + 614 9.350E-01 3.170E-06 3.000E+00 4.960E-04 5.111E+01 + 615 9.350E-01 3.170E-06 3.000E+00 4.554E-04 5.111E+01 + 616 9.350E-01 2.501E-06 3.000E+00 4.234E-04 5.111E+01 + 617 9.350E-01 2.501E-06 3.000E+00 3.914E-04 5.111E+01 + 618 9.350E-01 2.501E-06 3.000E+00 3.594E-04 5.111E+01 + 619 9.350E-01 1.971E-06 3.000E+00 3.341E-04 5.111E+01 + 620 9.350E-01 1.971E-06 3.000E+00 3.089E-04 5.111E+01 + 621 9.350E-01 1.971E-06 3.000E+00 2.837E-04 5.111E+01 + 622 9.350E-01 1.552E-06 3.000E+00 2.638E-04 5.110E+01 + 623 9.350E-01 1.552E-06 3.000E+00 2.440E-04 5.110E+01 + 624 9.350E-01 1.552E-06 3.000E+00 2.241E-04 5.110E+01 + 625 9.350E-01 1.224E-06 3.000E+00 2.084E-04 5.110E+01 + 626 9.350E-01 1.224E-06 3.000E+00 1.928E-04 5.110E+01 + 627 9.350E-01 1.224E-06 3.000E+00 1.771E-04 5.110E+01 + 628 9.350E-01 9.663E-07 3.000E+00 1.647E-04 5.110E+01 + 629 9.350E-01 9.663E-07 3.000E+00 1.524E-04 5.110E+01 + 630 9.350E-01 9.663E-07 3.000E+00 1.400E-04 5.110E+01 + 631 9.350E-01 7.639E-07 3.000E+00 1.302E-04 5.110E+01 + 632 9.350E-01 7.639E-07 3.000E+00 1.204E-04 5.110E+01 + 633 9.350E-01 7.639E-07 3.000E+00 1.106E-04 5.110E+01 + 634 9.350E-01 6.040E-07 3.000E+00 1.029E-04 5.110E+01 + 635 9.350E-01 2.278E-07 3.000E+00 1.000E-04 5.110E+01 + + is psifac dpsi q singfac eval1 + + Gaussian Reduction at istep = 635, psi = 9.350E-01, q = 3.000 + + is psifac dpsi q singfac eval1 + + 636 9.350E-01 1.562E-05 3.000E+00 9.999E-01 5.110E+01 + 637 9.350E-01 1.045E-08 3.000E+00 9.999E-01 5.110E+01 + 638 9.350E-01 1.045E-08 3.000E+00 9.999E-01 5.110E+01 + 639 9.350E-01 2.091E-08 3.000E+00 9.999E-01 5.110E+01 + 640 9.350E-01 2.091E-08 3.000E+00 9.999E-01 5.110E+01 + 641 9.350E-01 2.091E-08 3.000E+00 9.999E-01 5.110E+01 + 642 9.350E-01 1.315E-07 3.000E+00 9.999E-01 5.110E+01 + 643 9.350E-01 1.315E-07 3.000E+00 9.999E-01 5.110E+01 + 644 9.350E-01 1.315E-07 3.000E+00 9.999E-01 5.110E+01 + 645 9.350E-01 1.315E-07 3.000E+00 9.999E-01 5.110E+01 + 646 9.350E-01 3.906E-07 3.000E+00 9.999E-01 5.110E+01 + 647 9.350E-01 3.906E-07 3.000E+00 9.999E-01 5.110E+01 + 648 9.350E-01 3.906E-07 3.000E+00 9.999E-01 5.110E+01 + 649 9.350E-01 3.906E-07 3.000E+00 9.999E-01 5.110E+01 + 650 9.350E-01 3.906E-07 3.000E+00 9.999E-01 5.110E+01 + 651 9.350E-01 5.176E-07 3.000E+00 9.999E-01 5.110E+01 + 652 9.350E-01 5.176E-07 3.000E+00 9.999E-01 5.110E+01 + 653 9.350E-01 5.176E-07 3.000E+00 9.998E-01 5.110E+01 + 654 9.350E-01 5.176E-07 3.000E+00 9.998E-01 5.110E+01 + 655 9.350E-01 5.176E-07 3.000E+00 9.998E-01 5.110E+01 + 656 9.350E-01 6.839E-07 3.000E+00 9.998E-01 5.110E+01 + 657 9.350E-01 6.839E-07 3.000E+00 9.998E-01 5.110E+01 + 658 9.350E-01 6.839E-07 3.000E+00 9.998E-01 5.110E+01 + 659 9.350E-01 6.839E-07 3.000E+00 9.998E-01 5.110E+01 + 660 9.350E-01 6.839E-07 3.000E+00 9.998E-01 5.110E+01 + 661 9.350E-01 9.142E-07 3.000E+00 9.998E-01 5.110E+01 + 662 9.350E-01 9.142E-07 3.000E+00 9.998E-01 5.110E+01 + 663 9.350E-01 9.142E-07 3.000E+00 9.998E-01 5.110E+01 + 664 9.350E-01 9.142E-07 3.000E+00 9.997E-01 5.110E+01 + 665 9.350E-01 9.142E-07 3.000E+00 9.997E-01 5.110E+01 + 666 9.350E-01 1.236E-06 3.000E+00 9.997E-01 5.110E+01 + 667 9.350E-01 1.236E-06 3.000E+00 9.997E-01 5.110E+01 + 668 9.350E-01 1.236E-06 3.000E+00 9.997E-01 5.110E+01 + 669 9.350E-01 1.236E-06 3.000E+00 9.997E-01 5.110E+01 + 670 9.350E-01 1.236E-06 3.000E+00 9.997E-01 5.110E+01 + 671 9.350E-01 1.694E-06 3.000E+00 9.996E-01 5.110E+01 + 672 9.350E-01 1.694E-06 3.000E+00 9.996E-01 5.110E+01 + 673 9.350E-01 1.694E-06 3.000E+00 9.996E-01 5.110E+01 + 674 9.350E-01 1.694E-06 3.000E+00 9.996E-01 5.110E+01 + 675 9.350E-01 1.694E-06 3.000E+00 9.995E-01 5.110E+01 + 676 9.350E-01 2.352E-06 3.000E+00 9.995E-01 5.110E+01 + 677 9.350E-01 2.352E-06 3.001E+00 9.995E-01 5.110E+01 + 678 9.350E-01 2.352E-06 3.001E+00 9.995E-01 5.110E+01 + 679 9.350E-01 2.352E-06 3.001E+00 9.994E-01 5.110E+01 + 680 9.350E-01 2.352E-06 3.001E+00 9.994E-01 5.110E+01 + 681 9.350E-01 3.316E-06 3.001E+00 9.994E-01 5.110E+01 + 682 9.351E-01 3.316E-06 3.001E+00 9.993E-01 5.110E+01 + 683 9.351E-01 3.316E-06 3.001E+00 9.993E-01 5.110E+01 + 684 9.351E-01 3.316E-06 3.001E+00 9.992E-01 5.110E+01 + 685 9.351E-01 3.316E-06 3.001E+00 9.992E-01 5.110E+01 + 686 9.351E-01 4.754E-06 3.001E+00 9.991E-01 5.110E+01 + 687 9.351E-01 4.754E-06 3.001E+00 9.991E-01 5.110E+01 + 688 9.351E-01 4.754E-06 3.001E+00 9.990E-01 5.110E+01 + 689 9.351E-01 4.754E-06 3.001E+00 9.989E-01 5.110E+01 + 690 9.351E-01 4.754E-06 3.001E+00 9.989E-01 5.110E+01 + 691 9.351E-01 6.942E-06 3.001E+00 9.988E-01 5.110E+01 + 692 9.351E-01 6.942E-06 3.001E+00 9.987E-01 5.110E+01 + 693 9.351E-01 6.942E-06 3.001E+00 9.986E-01 5.110E+01 + 694 9.351E-01 6.942E-06 3.001E+00 9.985E-01 5.110E+01 + 695 9.351E-01 6.942E-06 3.002E+00 9.984E-01 5.110E+01 + 696 9.351E-01 1.034E-05 3.002E+00 9.983E-01 5.109E+01 + 697 9.351E-01 1.034E-05 3.002E+00 9.982E-01 5.109E+01 + 698 9.352E-01 1.034E-05 3.002E+00 9.980E-01 5.109E+01 + 699 9.352E-01 1.034E-05 3.002E+00 9.979E-01 5.109E+01 + 700 9.352E-01 1.034E-05 3.002E+00 9.978E-01 5.109E+01 + 701 9.352E-01 1.575E-05 3.002E+00 9.976E-01 5.109E+01 + 702 9.352E-01 1.575E-05 3.003E+00 9.974E-01 5.109E+01 + 703 9.352E-01 1.575E-05 3.003E+00 9.972E-01 5.109E+01 + 704 9.352E-01 1.575E-05 3.003E+00 9.970E-01 5.109E+01 + 705 9.353E-01 1.575E-05 3.003E+00 9.968E-01 5.109E+01 + 706 9.353E-01 2.460E-05 3.004E+00 9.964E-01 5.108E+01 + 707 9.353E-01 2.460E-05 3.004E+00 9.961E-01 5.108E+01 + 708 9.353E-01 2.460E-05 3.004E+00 9.958E-01 5.108E+01 + 709 9.353E-01 2.460E-05 3.005E+00 9.955E-01 5.108E+01 + 710 9.354E-01 2.460E-05 3.005E+00 9.952E-01 5.108E+01 + 711 9.354E-01 3.947E-05 3.005E+00 9.947E-01 5.107E+01 + 712 9.355E-01 3.947E-05 3.006E+00 9.942E-01 5.107E+01 + 713 9.355E-01 3.947E-05 3.006E+00 9.937E-01 5.107E+01 + 714 9.355E-01 3.947E-05 3.007E+00 9.931E-01 5.107E+01 + 715 9.356E-01 3.947E-05 3.007E+00 9.926E-01 5.106E+01 + 716 9.356E-01 6.529E-05 3.008E+00 9.918E-01 5.106E+01 + 717 9.357E-01 6.529E-05 3.009E+00 9.910E-01 5.105E+01 + 718 9.358E-01 6.529E-05 3.010E+00 9.901E-01 5.105E+01 + 719 9.358E-01 6.529E-05 3.011E+00 9.893E-01 5.104E+01 + 720 9.359E-01 6.529E-05 3.012E+00 9.884E-01 5.104E+01 + 721 9.361E-01 1.767E-04 3.014E+00 9.861E-01 5.103E+01 + 722 9.363E-01 1.767E-04 3.016E+00 9.838E-01 5.101E+01 + 723 9.364E-01 1.767E-04 3.018E+00 9.815E-01 5.100E+01 + 724 9.366E-01 1.767E-04 3.021E+00 9.792E-01 5.099E+01 + 725 9.368E-01 1.767E-04 3.023E+00 9.769E-01 5.098E+01 + 726 9.372E-01 3.844E-04 3.028E+00 9.719E-01 5.095E+01 + 727 9.376E-01 3.844E-04 3.033E+00 9.668E-01 5.092E+01 + 728 9.379E-01 3.844E-04 3.038E+00 9.617E-01 5.089E+01 + 729 9.383E-01 3.844E-04 3.043E+00 9.566E-01 5.086E+01 + 730 9.387E-01 3.844E-04 3.049E+00 9.515E-01 5.083E+01 + 731 9.395E-01 7.966E-04 3.059E+00 9.408E-01 5.077E+01 + 732 9.403E-01 7.966E-04 3.070E+00 9.299E-01 5.071E+01 + 733 9.411E-01 7.966E-04 3.081E+00 9.190E-01 5.065E+01 + 734 9.419E-01 7.966E-04 3.092E+00 9.080E-01 5.059E+01 + 735 9.431E-01 1.190E-03 3.109E+00 8.913E-01 5.050E+01 + 736 9.443E-01 1.190E-03 3.126E+00 8.743E-01 5.041E+01 + 737 9.455E-01 1.190E-03 3.143E+00 8.571E-01 5.031E+01 + 738 9.467E-01 1.190E-03 3.160E+00 8.396E-01 5.022E+01 + 739 9.483E-01 1.639E-03 3.185E+00 8.151E-01 5.009E+01 + 740 9.493E-01 9.889E-04 3.200E+00 8.000E-01 5.000E+01 + + is psifac dpsi q singfac eval1 + diff --git a/src/DCON/validate/dcon.bin b/src/DCON/validate/dcon.bin new file mode 100644 index 000000000..c8aea9375 Binary files /dev/null and b/src/DCON/validate/dcon.bin differ diff --git a/src/DCON/validate/dcon.in b/src/DCON/validate/dcon.in new file mode 100644 index 000000000..da04682a1 --- /dev/null +++ b/src/DCON/validate/dcon.in @@ -0,0 +1,64 @@ +&DCON_CONTROL + bal_flag=f ! Ideal MHD ballooning criterion for short wavelengths + mat_flag=t ! Construct coefficient matrices for diagnostic purposes + ode_flag=t ! Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) + vac_flag=t ! Compute plasma, vacuum, and total energies for free-boundary modes + mer_flag=t ! Evaluate the Mercier criterian + + sas_flag=t ! Safety factor (q) limit determined as q_ir+dmlim where q_ir is the equil outermost rational + dmlim=0.2 ! See sas_flag + psiedge=1.00 ! If less then psilim, calculates dW(psi) between psiedge and psilim, then runs with truncation at max(dW) + qlow=1.02 ! Integration initiated at q determined by minimum of qlow and q0 from equil + qhigh=1e3 ! Integration terminated at q limit determined by minimum of qhigh and qa from equil + sing_start=0 ! Start integration at the sing_start'th rational from the axis (psilow) + + nn=1 ! Toroidal mode number + delta_mlow=8 ! Expands lower bound of Fourier harmonics + delta_mhigh=8 ! Expands upper bound of Fourier harmonics + delta_mband=0 ! Integration keeps only this wide a band of solutions along the diagonal in m,m' + mthvac=512 ! Number of points used in splines over poloidal angle at plasma-vacuum interface. Overrides vac.in mth. + thmax0=1 ! Linear multiplier on the automatic choice of theta integration bounds for high-n ideal ballooning stability computation (strictly, -inf to -inf) + + kin_flag = f ! Kinetic EL equation (default: false) + con_flag = f ! Continue integration through layers (default: false) + kinfac1 = 1.0 ! Scale factor for energy contribution (default : 1.0) + kinfac2 = 1.0 ! Scale factor for torque contribution (default : 1.0) + kingridtype = 0 ! Regular grid method (default : 0) + passing_flag = t ! Includes passing particle effects (default: false) + ktanh_flag = t ! Ignore kinetic effects in the core smoothly (default: false) + ktc = 0.1 ! Parameter activated by ktanh_flag: roughly corresponds to core width ignored (default: 0.1) + ktw = 50.0 ! Parameter activated by ktanh_flag: width of hyper-tangential functions (default: 50.0) + ion_flag = t ! Include ion dW_k when kin_flag is true (summed with electron contribution if electron_flag true) + electron_flag = f ! Include electron dW_k when kin_flag is true (summed with ion contribution if ion_flag true) + + tol_nr=1e-6 ! Relative tolerance of dynamic integration steps away from rationals + tol_r=1e-7 ! Relative tolerance of dynamic integration steps near rationals + crossover=1e-2 ! Fractional distance from rational q at which tolerance is switched to tol_r + singfac_min=1e-4 ! Fractional distance from rational q at which ideal jump condition is enforced + ucrit=1e4 ! Maximum fraction of solutions allowed before re-normalized + + termbycross_flag = f ! Terminate ODE solver in the event of a zero crossing + + use_classic_splines = f ! Use a classical cubic spline instead of tri-diagonal solution for splines with extrapolation boundary conditions +/ +&DCON_OUTPUT + out_ahg2msc=f ! Output deprecated ahg2msc.out files. This is used to communicate with vacuum, but is now done through memory. + + crit_break=t ! Color of the crit curve changes when crossing a singular surface + ahb_flag=f ! Output normal magnetic field eigenvalues and eigenfunctons at plasma-vacuum interface (must be false for GPEC) + msol_ahb=1 ! Number of eigenfunctions output by ahb_flag=t ? + mthsurf0=1 ! Linear multiplier on number of boundary points used to display surface eigenfunctions for ahgb_flag=t + bin_metric = t + bin_euler=t ! Output M psi-by-M euler-lagrange solutions to binary file euler.bin + bin_vac=f ! Output deprecated binary vacuum.bin containing vacuum energy matrices + euler_stride=1 ! Output only every euler_stride'th psi step to binary file + bin_fmat = t + bin_gmat = t + bin_kmat = t + out_bal1=f ! Ascii output for bal_flag poloidal functions + bin_bal1=f ! Binary output for bal_flag poloidal functions + out_bal2=f ! Ascii output for bal_flag functions + bin_bal2=f ! Binary output for bal_flag functions + + netcdf_out=t ! Replicate ascii dcon.out information in a netcdf file +/ diff --git a/src/DCON/validate/dcon.out b/src/DCON/validate/dcon.out new file mode 100644 index 000000000..be6318e4a --- /dev/null +++ b/src/DCON/validate/dcon.out @@ -0,0 +1,2966 @@ + Equilibrium: beta_1.00, Type: efit + + Jac_type = hamada, power_bp = 0, power_b = 0, power_r = 0 + + + mpsi mtheta psilow psihigh rs_right rs_left zs_top zs_bot + + 128 256 1.000E-02 9.900E-01 4.491E+00 1.513E+00 2.505E+00 -2.505E+00 + + + amean rmean aratio kappa delta1 delta2 volume + + 1.489E+00 3.002E+00 2.016E+00 1.682E+00 4.574E-01 4.574E-01 2.049E+02 + + + li1 li2 li3 ro zo psio + + 8.759E-01 6.986E-01 7.255E-01 3.118E+00 -2.918E-06 1.367E+00 + + + betap1 betap2 betat betan betaj bwall bt0 + + 1.787E-01 1.425E-01 2.309E-02 9.363E-01 1.264E-01 4.928E-01 9.993E-01 + + + q0 qmin q95 qmax qa crnt I/aB + + 1.050E+00 1.050E+00 3.211E+00 4.085E+00 4.399E+00 3.669E+00 2.466E+00 + + +ipsi psifac f mu0 p dvdpsi q di dr ca1 + + 0 1.000E-02 3.464E+00 3.411E-02 1.589E+02 1.052E+00 4.994E+00 5.148E+00 0.000E+00 + 1 1.015E-02 3.464E+00 3.410E-02 1.589E+02 1.052E+00 5.004E+00 5.157E+00 0.000E+00 + 2 1.059E-02 3.464E+00 3.408E-02 1.589E+02 1.052E+00 5.032E+00 5.184E+00 0.000E+00 + 3 1.133E-02 3.463E+00 3.404E-02 1.589E+02 1.053E+00 5.045E+00 5.195E+00 0.000E+00 + 4 1.236E-02 3.462E+00 3.399E-02 1.589E+02 1.053E+00 4.754E+00 4.903E+00 0.000E+00 + 5 1.369E-02 3.462E+00 3.392E-02 1.589E+02 1.053E+00 3.864E+00 4.014E+00 0.000E+00 + 6 1.530E-02 3.460E+00 3.384E-02 1.590E+02 1.053E+00 2.813E+00 2.968E+00 0.000E+00 + 7 1.721E-02 3.459E+00 3.374E-02 1.590E+02 1.054E+00 2.198E+00 2.355E+00 0.000E+00 + 8 1.942E-02 3.457E+00 3.363E-02 1.591E+02 1.054E+00 2.108E+00 2.264E+00 0.000E+00 + 9 2.191E-02 3.455E+00 3.350E-02 1.591E+02 1.055E+00 2.082E+00 2.237E+00 0.000E+00 + 10 2.468E-02 3.453E+00 3.336E-02 1.592E+02 1.055E+00 1.655E+00 1.812E+00 0.000E+00 + 11 2.775E-02 3.451E+00 3.320E-02 1.592E+02 1.056E+00 1.133E+00 1.293E+00 0.000E+00 + 12 3.110E-02 3.449E+00 3.303E-02 1.593E+02 1.057E+00 9.860E-01 1.147E+00 0.000E+00 + 13 3.473E-02 3.446E+00 3.284E-02 1.594E+02 1.058E+00 9.703E-01 1.130E+00 0.000E+00 + 14 3.864E-02 3.443E+00 3.264E-02 1.595E+02 1.059E+00 7.012E-01 8.639E-01 0.000E+00 + 15 4.283E-02 3.440E+00 3.243E-02 1.596E+02 1.060E+00 4.741E-01 6.395E-01 0.000E+00 + 16 4.730E-02 3.437E+00 3.220E-02 1.597E+02 1.061E+00 4.327E-01 5.975E-01 0.000E+00 + 17 5.204E-02 3.433E+00 3.196E-02 1.598E+02 1.062E+00 3.460E-01 5.122E-01 0.000E+00 + 18 5.705E-02 3.429E+00 3.171E-02 1.599E+02 1.063E+00 2.053E-01 3.746E-01 0.000E+00 + 19 6.232E-02 3.425E+00 3.144E-02 1.601E+02 1.065E+00 1.523E-01 3.222E-01 0.000E+00 + 20 6.786E-02 3.421E+00 3.117E-02 1.602E+02 1.066E+00 9.495E-02 2.661E-01 0.000E+00 + 21 7.366E-02 3.417E+00 3.088E-02 1.604E+02 1.068E+00 2.073E-02 1.942E-01 0.000E+00 + 22 7.971E-02 3.412E+00 3.057E-02 1.605E+02 1.070E+00 -1.830E-02 1.564E-01 0.000E+00 + 23 8.602E-02 3.408E+00 3.026E-02 1.607E+02 1.071E+00 -5.855E-02 1.178E-01 0.000E+00 + 24 9.258E-02 3.403E+00 2.993E-02 1.609E+02 1.073E+00 -9.976E-02 7.843E-02 0.000E+00 + 25 9.938E-02 3.398E+00 2.960E-02 1.611E+02 1.075E+00 -1.267E-01 5.288E-02 0.000E+00 + 26 1.064E-01 3.393E+00 2.925E-02 1.613E+02 1.078E+00 -1.567E-01 2.473E-02 0.000E+00 + 27 1.137E-01 3.387E+00 2.889E-02 1.616E+02 1.080E+00 -1.795E-01 3.573E-03 0.000E+00 + 28 1.212E-01 3.382E+00 2.853E-02 1.618E+02 1.082E+00 -1.974E-01 -1.288E-02 0.000E+00 + 29 1.290E-01 3.376E+00 2.815E-02 1.621E+02 1.085E+00 -2.178E-01 -3.138E-02 0.000E+00 + 30 1.369E-01 3.370E+00 2.777E-02 1.623E+02 1.088E+00 -2.310E-01 -4.309E-02 0.000E+00 + 31 1.451E-01 3.365E+00 2.737E-02 1.626E+02 1.091E+00 -2.432E-01 -5.380E-02 0.000E+00 + 32 1.535E-01 3.358E+00 2.697E-02 1.630E+02 1.094E+00 -2.553E-01 -6.417E-02 0.000E+00 + 33 1.621E-01 3.352E+00 2.656E-02 1.633E+02 1.097E+00 -2.638E-01 -7.120E-02 0.000E+00 + 34 1.709E-01 3.346E+00 2.614E-02 1.636E+02 1.100E+00 -2.714E-01 -7.728E-02 0.000E+00 + 35 1.799E-01 3.339E+00 2.572E-02 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5.35361E-04 2.04622E-05 5.35752E-04 + 28 1.96259E-03 -1.39715E-04 1.96756E-03 + 29 -1.48541E-03 -2.50157E-05 1.48562E-03 + 30 2.44419E-04 -1.37486E-04 2.80434E-04 + 31 -1.25827E-03 8.78950E-05 1.26133E-03 + 32 -1.11714E-03 -2.42444E-05 1.11740E-03 + 33 5.97066E-03 -1.80966E-05 5.97068E-03 + + i re wp im wp abs wp + + isol = 2, m = -11 + + i re wp im wp abs wp + + 1 -1.47516E+02 2.09158E-03 1.47516E+02 + 2 2.96916E+02 -4.33714E-08 2.96916E+02 + 3 -8.97436E+01 -1.08461E-03 8.97436E+01 + 4 1.42505E+01 1.92496E-04 1.42505E+01 + 5 1.08923E+00 2.18494E-05 1.08923E+00 + 6 -5.19902E+00 -1.71008E-04 5.19902E+00 + 7 6.48238E+00 1.89894E-04 6.48238E+00 + 8 -5.11900E+00 -5.25852E-05 5.11900E+00 + 9 2.61994E+00 -3.38260E-05 2.61994E+00 + 10 3.56480E-01 1.25135E-04 3.56480E-01 + 11 -2.81025E+00 -1.88495E-04 2.81025E+00 + 12 3.18464E+00 2.52362E-04 3.18464E+00 + 13 2.08494E-01 -1.71439E-05 2.08494E-01 + 14 -2.93826E+00 -1.02718E-04 2.93826E+00 + 15 -1.07469E+00 -9.90761E-05 1.07469E+00 + 16 -9.62992E-02 6.15440E-06 9.62992E-02 + 17 2.92642E-01 2.49456E-05 2.92642E-01 + 18 3.55334E-01 -1.62292E-05 3.55334E-01 + 19 -3.74590E-02 -9.97212E-06 3.74590E-02 + 20 -1.44746E-01 -5.25077E-05 1.44746E-01 + 21 -1.53284E-01 -1.17840E-05 1.53284E-01 + 22 1.23674E-02 -3.38550E-05 1.23675E-02 + 23 1.18462E-02 -1.04109E-04 1.18466E-02 + 24 2.50821E-02 -9.79290E-05 2.50823E-02 + 25 4.87606E-03 -1.38300E-04 4.87803E-03 + 26 -2.36611E-03 -3.15090E-05 2.36632E-03 + 27 -2.07635E-03 7.07229E-06 2.07636E-03 + 28 -2.29648E-03 1.46816E-05 2.29653E-03 + 29 1.11569E-03 9.79741E-06 1.11574E-03 + 30 1.57681E-04 -1.77615E-04 2.37509E-04 + 31 6.84811E-04 -1.50925E-04 7.01245E-04 + 32 -1.00029E-03 -2.08702E-05 1.00051E-03 + 33 -6.83839E-04 2.49158E-05 6.84293E-04 + + i re wp im wp abs wp + + isol = 3, m = -10 + + i re wp im wp abs wp + + 1 -3.08264E+00 -2.60865E-04 3.08264E+00 + 2 -8.97436E+01 1.08425E-03 8.97436E+01 + 3 2.71032E+02 -6.53407E-08 2.71032E+02 + 4 -8.82981E+01 -9.69103E-04 8.82981E+01 + 5 1.51889E+01 2.40598E-04 1.51889E+01 + 6 1.69522E+00 2.65609E-05 1.69522E+00 + 7 -5.77372E+00 -1.45903E-04 5.77372E+00 + 8 6.18313E+00 1.51457E-04 6.18313E+00 + 9 -3.36231E+00 1.03511E-05 3.36231E+00 + 10 -6.24783E-01 -1.28705E-04 6.24783E-01 + 11 3.77490E+00 1.92471E-04 3.77490E+00 + 12 -3.94148E+00 -1.28289E-04 3.94148E+00 + 13 -9.24514E-01 -4.11539E-05 9.24514E-01 + 14 4.47843E+00 2.02082E-04 4.47843E+00 + 15 2.25397E+00 2.16945E-04 2.25397E+00 + 16 1.98641E-01 1.03759E-05 1.98641E-01 + 17 -4.39996E-01 -6.18557E-05 4.39996E-01 + 18 -3.25348E-01 -2.11778E-05 3.25348E-01 + 19 1.59446E-01 -4.58048E-05 1.59446E-01 + 20 1.96002E-01 9.21080E-06 1.96002E-01 + 21 1.52139E-01 -3.04065E-05 1.52139E-01 + 22 -4.25381E-02 -1.86931E-06 4.25381E-02 + 23 -7.33981E-03 -3.56121E-05 7.33989E-03 + 24 -2.65879E-02 -8.80243E-05 2.65880E-02 + 25 9.21599E-04 -8.50245E-05 9.25512E-04 + 26 6.48360E-04 -1.21235E-04 6.59597E-04 + 27 2.81722E-03 -4.64269E-05 2.81760E-03 + 28 7.71867E-04 1.43041E-06 7.71868E-04 + 29 -1.19752E-03 -3.30207E-06 1.19752E-03 + 30 -3.11766E-04 4.18904E-05 3.14568E-04 + 31 9.55563E-05 -1.67429E-04 1.92778E-04 + 32 4.42134E-04 -1.18062E-04 4.57626E-04 + 33 -7.33977E-04 -3.23864E-05 7.34691E-04 + + i re wp im wp abs wp + + isol = 4, m = -9 + + i re wp im wp abs wp + + 1 1.07449E+01 -6.49739E-04 1.07449E+01 + 2 1.42507E+01 -1.92513E-04 1.42507E+01 + 3 -8.82982E+01 9.69216E-04 8.82982E+01 + 4 2.54594E+02 -1.47587E-07 2.54594E+02 + 5 -8.45218E+01 -8.52534E-04 8.45218E+01 + 6 1.46609E+01 2.13585E-04 1.46609E+01 + 7 1.70974E+00 5.30208E-05 1.70974E+00 + 8 -4.49403E+00 -1.09190E-04 4.49403E+00 + 9 2.87755E+00 6.13731E-05 2.87755E+00 + 10 1.84117E+00 2.06136E-04 1.84117E+00 + 11 -5.41409E+00 -3.45764E-04 5.41409E+00 + 12 4.46892E+00 3.37351E-04 4.46892E+00 + 13 2.78765E+00 8.61108E-05 2.78765E+00 + 14 -6.96910E+00 -3.17036E-04 6.96910E+00 + 15 -4.58883E+00 -2.21155E-04 4.58883E+00 + 16 -4.19276E-01 -6.69809E-06 4.19276E-01 + 17 6.87180E-01 2.88766E-05 6.87180E-01 + 18 2.02745E-01 -3.68992E-05 2.02745E-01 + 19 -3.58551E-01 -3.45619E-05 3.58551E-01 + 20 -2.50897E-01 -1.10264E-04 2.50897E-01 + 21 -1.18643E-01 -5.10103E-05 1.18643E-01 + 22 8.13383E-02 -5.81515E-05 8.13384E-02 + 23 5.58762E-03 -9.63817E-06 5.58763E-03 + 24 2.88455E-02 -4.07483E-05 2.88456E-02 + 25 -6.34385E-03 -9.19582E-05 6.34451E-03 + 26 4.70252E-03 -8.64060E-05 4.70332E-03 + 27 -4.25902E-03 -1.32623E-04 4.26108E-03 + 28 7.91314E-04 -5.43603E-05 7.93179E-04 + 29 -8.92109E-04 -1.29647E-05 8.92203E-04 + 30 3.21562E-04 5.30103E-06 3.21605E-04 + 31 -4.67695E-04 2.61490E-05 4.68426E-04 + 32 3.07661E-04 -1.42353E-04 3.38999E-04 + 33 -2.38687E-05 -1.25344E-04 1.27597E-04 + + i re wp im wp abs wp + + isol = 5, m = -8 + + i re wp im wp abs wp + + 1 -6.60009E+00 1.40322E-04 6.60009E+00 + 2 1.08910E+00 -2.12347E-05 1.08910E+00 + 3 1.51890E+01 -2.40920E-04 1.51890E+01 + 4 -8.45219E+01 8.52816E-04 8.45219E+01 + 5 2.40067E+02 -1.71176E-07 2.40067E+02 + 6 -8.31397E+01 -7.95288E-04 8.31397E+01 + 7 1.69426E+01 2.14632E-04 1.69426E+01 + 8 -2.28322E+00 -1.74937E-05 2.28322E+00 + 9 2.31299E+00 8.55780E-06 2.31299E+00 + 10 -6.10906E+00 -9.93627E-05 6.10906E+00 + 11 8.76054E+00 2.46045E-04 8.76054E+00 + 12 -4.62327E+00 -1.23197E-04 4.62327E+00 + 13 -7.06895E+00 -2.30817E-04 7.06895E+00 + 14 1.12210E+01 4.06909E-04 1.12210E+01 + 15 9.00510E+00 4.79157E-04 9.00510E+00 + 16 8.75507E-01 5.03662E-05 8.75507E-01 + 17 -1.12535E+00 -9.82033E-05 1.12535E+00 + 18 -1.86209E-03 -1.45762E-05 1.86214E-03 + 19 6.25239E-01 -2.12968E-05 6.25239E-01 + 20 2.93081E-01 1.87438E-05 2.93081E-01 + 21 4.53896E-02 -7.97810E-05 4.53896E-02 + 22 -1.10492E-01 -3.41071E-05 1.10492E-01 + 23 -7.22618E-03 -5.41404E-05 7.22638E-03 + 24 -2.17773E-02 -4.56468E-06 2.17773E-02 + 25 1.50361E-02 -3.94028E-05 1.50362E-02 + 26 -6.41734E-03 -9.17732E-05 6.41799E-03 + 27 6.79163E-03 -7.51794E-05 6.79204E-03 + 28 -2.32392E-03 -1.21166E-04 2.32708E-03 + 29 2.09828E-03 -4.61725E-05 2.09879E-03 + 30 -1.68344E-03 -1.40545E-05 1.68350E-03 + 31 1.78987E-04 2.16847E-05 1.80295E-04 + 32 -3.75491E-04 -3.45012E-05 3.77072E-04 + 33 1.79658E-05 -2.91066E-05 3.42047E-05 + + i re wp im wp abs wp + + isol = 6, m = -7 + + i re wp im wp abs wp + + 1 6.44882E+00 -4.12121E-04 6.44882E+00 + 2 -5.19898E+00 1.69550E-04 5.19898E+00 + 3 1.69507E+00 -2.56219E-05 1.69507E+00 + 4 1.46611E+01 -2.14188E-04 1.46611E+01 + 5 -8.31398E+01 7.95808E-04 8.31398E+01 + 6 2.29430E+02 -2.49600E-07 2.29430E+02 + 7 -8.74051E+01 -7.19404E-04 8.74051E+01 + 8 2.70681E+01 2.81511E-04 2.70681E+01 + 9 -1.62793E+01 -1.94144E-04 1.62793E+01 + 10 1.86539E+01 3.62276E-04 1.86539E+01 + 11 -1.67887E+01 -4.33473E-04 1.67887E+01 + 12 4.46445E+00 3.18030E-04 4.46445E+00 + 13 1.60538E+01 4.24212E-04 1.60538E+01 + 14 -1.90781E+01 -7.01123E-04 1.90781E+01 + 15 -1.67463E+01 -6.29221E-04 1.67463E+01 + 16 -1.67476E+00 -5.22627E-05 1.67476E+00 + 17 1.75739E+00 5.34928E-05 1.75739E+00 + 18 -2.72500E-01 -6.66130E-05 2.72500E-01 + 19 -9.47768E-01 -8.88036E-05 9.47768E-01 + 20 -2.90618E-01 -1.38431E-04 2.90618E-01 + 21 6.33196E-02 -4.72301E-05 6.33196E-02 + 22 1.32587E-01 -1.06262E-04 1.32587E-01 + 23 6.76920E-03 -4.07168E-05 6.76932E-03 + 24 1.52427E-02 -6.72805E-05 1.52428E-02 + 25 -2.67044E-02 -1.27522E-05 2.67044E-02 + 26 1.42951E-02 -5.40695E-05 1.42952E-02 + 27 -6.61191E-03 -1.05626E-04 6.61275E-03 + 28 7.43723E-03 -8.76895E-05 7.43774E-03 + 29 -3.68957E-03 -1.25644E-04 3.69171E-03 + 30 1.69659E-03 -4.78266E-05 1.69727E-03 + 31 -1.13596E-03 -1.77995E-05 1.13610E-03 + 32 -1.16435E-05 1.82448E-05 2.16436E-05 + 33 -4.43231E-05 -7.24976E-05 8.49731E-05 + + i re wp im wp abs wp + + isol = 7, m = -6 + + i re wp im wp abs wp + + 1 -5.39729E+00 2.04118E-04 5.39729E+00 + 2 6.48237E+00 -1.88264E-04 6.48237E+00 + 3 -5.77360E+00 1.44205E-04 5.77360E+00 + 4 1.70949E+00 -5.18446E-05 1.70949E+00 + 5 1.69429E+01 -2.15503E-04 1.69429E+01 + 6 -8.74054E+01 7.20177E-04 8.74054E+01 + 7 2.28350E+02 -3.61597E-07 2.28350E+02 + 8 -1.05822E+02 -7.47111E-04 1.05822E+02 + 9 5.49360E+01 4.80562E-04 5.49360E+01 + 10 -4.63968E+01 -5.16463E-04 4.63968E+01 + 11 3.64691E+01 5.17320E-04 3.64691E+01 + 12 -5.78832E+00 -2.31307E-05 5.78832E+00 + 13 -3.31679E+01 -8.00602E-04 3.31679E+01 + 14 3.37366E+01 9.90865E-04 3.37366E+01 + 15 2.92505E+01 1.07420E-03 2.92505E+01 + 16 2.80150E+00 1.27276E-04 2.80150E+00 + 17 -2.51657E+00 -1.48489E-04 2.51657E+00 + 18 5.10239E-01 -1.62082E-05 5.10239E-01 + 19 1.16414E+00 7.75223E-06 1.16414E+00 + 20 2.70175E-01 -1.10806E-05 2.70175E-01 + 21 -1.89183E-01 -1.20111E-04 1.89183E-01 + 22 -1.19705E-01 -3.47088E-05 1.19705E-01 + 23 -1.75569E-02 -1.06250E-04 1.75573E-02 + 24 -5.66681E-03 -2.77518E-05 5.66687E-03 + 25 3.70167E-02 -5.48697E-05 3.70167E-02 + 26 -1.83803E-02 5.16475E-06 1.83803E-02 + 27 1.08100E-02 -3.38122E-05 1.08101E-02 + 28 -1.00788E-02 -8.80974E-05 1.00792E-02 + 29 8.06920E-03 -8.07426E-05 8.06961E-03 + 30 -2.11002E-03 -1.21590E-04 2.11353E-03 + 31 1.38990E-03 -2.88382E-05 1.39019E-03 + 32 -1.10346E-03 -1.08548E-05 1.10352E-03 + 33 -2.07912E-04 1.66156E-05 2.08575E-04 + + i re wp im wp abs wp + + isol = 8, m = -5 + + i re wp im wp abs wp + + 1 3.82528E+00 2.74550E-05 3.82528E+00 + 2 -5.11894E+00 5.10927E-05 5.11894E+00 + 3 6.18297E+00 -1.49867E-04 6.18297E+00 + 4 -4.49371E+00 1.07388E-04 4.49371E+00 + 5 -2.28370E+00 1.88261E-05 2.28370E+00 + 6 2.70686E+01 -2.82592E-04 2.70686E+01 + 7 -1.05822E+02 7.48151E-04 1.05822E+02 + 8 2.49134E+02 -4.58887E-07 2.49134E+02 + 9 -1.52704E+02 -9.05955E-04 1.52704E+02 + 10 1.08379E+02 9.68965E-04 1.08379E+02 + 11 -7.67841E+01 -1.01390E-03 7.67841E+01 + 12 1.47953E+01 3.63311E-04 1.47953E+01 + 13 6.03455E+01 1.25989E-03 6.03455E+01 + 14 -5.94932E+01 -1.60904E-03 5.94932E+01 + 15 -4.71136E+01 -1.42472E-03 4.71136E+01 + 16 -3.96381E+00 -1.33830E-04 3.96381E+00 + 17 3.18521E+00 1.05657E-04 3.18521E+00 + 18 -5.32359E-01 -7.15266E-05 5.32359E-01 + 19 -1.02206E+00 -1.26607E-04 1.02206E+00 + 20 -2.46278E-01 -1.41105E-04 2.46278E-01 + 21 2.98563E-01 -5.67230E-05 2.98563E-01 + 22 6.21519E-02 -1.40821E-04 6.21520E-02 + 23 4.58203E-02 -3.67073E-05 4.58203E-02 + 24 -2.82754E-02 -1.20551E-04 2.82757E-02 + 25 -2.58903E-02 -3.61743E-05 2.58904E-02 + 26 9.84692E-03 -7.78595E-05 9.84723E-03 + 27 -2.74666E-03 -1.71076E-05 2.74671E-03 + 28 9.21604E-03 -5.07212E-05 9.21618E-03 + 29 -4.55333E-03 -8.51189E-05 4.55412E-03 + 30 2.01972E-03 -8.11474E-05 2.02135E-03 + 31 -1.30465E-05 -1.34997E-04 1.35626E-04 + 32 1.63364E-04 -1.92009E-05 1.64489E-04 + 33 2.05011E-04 -6.23485E-05 2.14282E-04 + + i re wp im wp abs wp + + isol = 9, m = -4 + + i re wp im wp abs wp + + 1 -1.88705E+00 2.60530E-05 1.88705E+00 + 2 2.61981E+00 3.50448E-05 2.61981E+00 + 3 -3.36207E+00 -1.16248E-05 3.36207E+00 + 4 2.87715E+00 -5.97718E-05 2.87715E+00 + 5 2.31360E+00 -1.04186E-05 2.31360E+00 + 6 -1.62801E+01 1.95641E-04 1.62801E+01 + 7 5.49367E+01 -4.82034E-04 5.49367E+01 + 8 -1.52705E+02 9.07410E-04 1.52705E+02 + 9 3.08299E+02 -7.69233E-07 3.08299E+02 + 10 -2.34864E+02 -1.06005E-03 2.34864E+02 + 11 1.58573E+02 1.22187E-03 1.58573E+02 + 12 -4.03828E+01 -3.68136E-04 4.03828E+01 + 13 -9.47500E+01 -1.53633E-03 9.47500E+01 + 14 1.00223E+02 2.23831E-03 1.00223E+02 + 15 6.69533E+01 1.79880E-03 6.69533E+01 + 16 4.53120E+00 1.54694E-04 4.53120E+00 + 17 -3.04342E+00 -1.44816E-04 3.04342E+00 + 18 4.01226E-01 -4.34603E-05 4.01226E-01 + 19 5.16821E-01 -6.05976E-05 5.16821E-01 + 20 6.24356E-02 -8.24558E-05 6.24356E-02 + 21 -2.90783E-01 -1.59555E-04 2.90784E-01 + 22 -6.22075E-02 -7.45515E-05 6.22075E-02 + 23 -3.58166E-02 -1.52941E-04 3.58169E-02 + 24 4.50451E-02 -4.26806E-05 4.50451E-02 + 25 1.59061E-02 -1.24671E-04 1.59066E-02 + 26 5.83505E-05 -2.88395E-05 6.50884E-05 + 27 -4.33750E-03 -6.10699E-05 4.33793E-03 + 28 -2.85980E-03 -1.11050E-05 2.85982E-03 + 29 1.62685E-03 -5.63345E-05 1.62782E-03 + 30 2.40363E-03 -8.63886E-05 2.40518E-03 + 31 -3.26675E-04 -6.60401E-05 3.33283E-04 + 32 1.49933E-03 -1.10916E-04 1.50343E-03 + 33 -1.26989E-03 -1.06383E-06 1.26989E-03 + + i re wp im wp abs wp + + isol = 10, m = -3 + + i re wp im wp abs wp + + 1 -2.82140E-01 -5.72584E-05 2.82140E-01 + 2 3.56623E-01 -1.25747E-04 3.56623E-01 + 3 -6.25033E-01 1.29444E-04 6.25033E-01 + 4 1.84157E+00 -2.07152E-04 1.84157E+00 + 5 -6.10965E+00 1.00732E-04 6.10965E+00 + 6 1.86547E+01 -3.63972E-04 1.86547E+01 + 7 -4.63977E+01 5.18211E-04 4.63977E+01 + 8 1.08379E+02 -9.70900E-04 1.08379E+02 + 9 -2.34865E+02 1.06220E-03 2.34865E+02 + 10 3.97913E+02 -1.15314E-06 3.97913E+02 + 11 -2.99017E+02 -1.50291E-03 2.99017E+02 + 12 1.05869E+02 9.29956E-04 1.05869E+02 + 13 1.20369E+02 1.40133E-03 1.20369E+02 + 14 -1.49695E+02 -2.75275E-03 1.49695E+02 + 15 -7.67009E+01 -1.66840E-03 7.67009E+01 + 16 -3.73803E+00 -1.07466E-04 3.73803E+00 + 17 1.39185E+00 2.97357E-05 1.39185E+00 + 18 -4.39298E-02 -3.64375E-05 4.39299E-02 + 19 5.48866E-01 -3.05964E-05 5.48866E-01 + 20 4.16376E-01 -6.20302E-05 4.16376E-01 + 21 1.45250E-01 -3.45989E-05 1.45250E-01 + 22 -3.31525E-02 -1.11559E-04 3.31527E-02 + 23 1.22812E-02 -2.50541E-05 1.22812E-02 + 24 -4.46918E-02 -1.03623E-04 4.46919E-02 + 25 2.60885E-02 8.60295E-06 2.60885E-02 + 26 -2.76818E-02 -8.58479E-05 2.76820E-02 + 27 1.50436E-02 -3.09219E-06 1.50436E-02 + 28 -1.10476E-02 -3.24768E-05 1.10477E-02 + 29 9.54306E-03 3.19048E-05 9.54311E-03 + 30 -4.45612E-03 -2.41449E-05 4.45618E-03 + 31 4.00252E-03 -7.79022E-05 4.00327E-03 + 32 -1.75869E-03 -6.60571E-05 1.75993E-03 + 33 2.04027E-03 -6.15850E-05 2.04120E-03 + + i re wp im wp abs wp + + isol = 11, m = -2 + + i re wp im wp abs wp + + 1 2.05305E+00 -9.08606E-05 2.05305E+00 + 2 -2.81032E+00 1.88263E-04 2.81032E+00 + 3 3.77501E+00 -1.92315E-04 3.77501E+00 + 4 -5.41425E+00 3.45831E-04 5.41425E+00 + 5 8.76077E+00 -2.46386E-04 8.76077E+00 + 6 -1.67890E+01 4.34152E-04 1.67890E+01 + 7 3.64696E+01 -5.18628E-04 3.64696E+01 + 8 -7.67847E+01 1.01568E-03 7.67847E+01 + 9 1.58574E+02 -1.22413E-03 1.58574E+02 + 10 -2.99017E+02 1.50542E-03 2.99017E+02 + 11 4.20814E+02 -1.14357E-06 4.20814E+02 + 12 -2.22499E+02 -7.77592E-04 2.22499E+02 + 13 -7.89680E+01 -5.75648E-04 7.89680E+01 + 14 1.71002E+02 2.33408E-03 1.71002E+02 + 15 5.63536E+01 1.07643E-03 5.63536E+01 + 16 1.08771E+00 4.92652E-05 1.08771E+00 + 17 1.64766E+00 -5.97885E-06 1.64766E+00 + 18 1.00392E-01 -8.23592E-05 1.00392E-01 + 19 -1.59660E+00 -1.95806E-04 1.59660E+00 + 20 -9.25531E-01 -2.12872E-04 9.25531E-01 + 21 -2.17643E-01 -2.49824E-04 2.17643E-01 + 22 2.32512E-01 -1.62517E-04 2.32512E-01 + 23 -4.30399E-02 -2.10639E-04 4.30404E-02 + 24 9.06727E-02 -1.35726E-04 9.06728E-02 + 25 -9.12289E-02 -2.01607E-04 9.12292E-02 + 26 6.85243E-02 -1.04049E-04 6.85244E-02 + 27 -3.81842E-02 -1.58901E-04 3.81845E-02 + 28 3.12425E-02 -9.43443E-05 3.12426E-02 + 29 -2.31776E-02 -1.14133E-04 2.31779E-02 + 30 1.19283E-02 -3.37133E-05 1.19283E-02 + 31 -6.89417E-03 -4.77155E-05 6.89433E-03 + 32 5.72267E-03 -1.21274E-04 5.72395E-03 + 33 -2.18983E-03 -4.94111E-05 2.19039E-03 + + i re wp im wp abs wp + + isol = 12, m = -1 + + i re wp im wp abs wp + + 1 -2.40186E+00 1.73844E-04 2.40186E+00 + 2 3.18458E+00 -2.51782E-04 3.18458E+00 + 3 -3.94134E+00 1.27659E-04 3.94134E+00 + 4 4.46869E+00 -3.36684E-04 4.46869E+00 + 5 -4.62293E+00 1.22659E-04 4.62293E+00 + 6 4.46405E+00 -3.17699E-04 4.46405E+00 + 7 -5.78798E+00 2.30184E-05 5.78798E+00 + 8 1.47952E+01 -3.63943E-04 1.47952E+01 + 9 -4.03830E+01 3.69082E-04 4.03830E+01 + 10 1.05870E+02 -9.31161E-04 1.05870E+02 + 11 -2.22500E+02 7.78605E-04 2.22500E+02 + 12 2.83518E+02 -2.73952E-07 2.83518E+02 + 13 -6.32520E+01 -5.05965E-04 6.32520E+01 + 14 -9.19483E+01 -9.51362E-04 9.19483E+01 + 15 1.79972E+00 7.61571E-05 1.79972E+00 + 16 2.46149E+00 5.41852E-05 2.46149E+00 + 17 -3.94287E+00 -1.38312E-04 3.94287E+00 + 18 -1.43068E+00 -6.85174E-05 1.43068E+00 + 19 1.03564E+00 3.24727E-05 1.03564E+00 + 20 6.64553E-01 4.69967E-05 6.64553E-01 + 21 5.88547E-01 4.29519E-05 5.88547E-01 + 22 -9.72917E-02 -2.42241E-05 9.72917E-02 + 23 4.87734E-02 -4.78070E-06 4.87734E-02 + 24 -9.40040E-02 -1.21101E-05 9.40040E-02 + 25 1.52234E-02 1.16122E-05 1.52234E-02 + 26 -1.72138E-02 1.29645E-05 1.72138E-02 + 27 1.35396E-02 3.05809E-05 1.35396E-02 + 28 -4.04053E-03 2.69266E-05 4.04062E-03 + 29 2.18134E-03 1.97497E-05 2.18143E-03 + 30 -2.80198E-03 1.11108E-05 2.80200E-03 + 31 1.67183E-03 3.15662E-05 1.67213E-03 + 32 -2.26011E-05 2.99093E-05 3.74884E-05 + 33 1.10813E-03 -6.91854E-05 1.11029E-03 + + i re wp im wp abs wp + + isol = 13, m = 0 + + i re wp im wp abs wp + + 1 6.24015E-02 -1.84861E-04 6.24018E-02 + 2 2.08595E-01 1.66106E-05 2.08595E-01 + 3 -9.24702E-01 4.15060E-05 9.24702E-01 + 4 2.78796E+00 -8.66209E-05 2.78796E+00 + 5 -7.06938E+00 2.31379E-04 7.06938E+00 + 6 1.60543E+01 -4.24694E-04 1.60543E+01 + 7 -3.31684E+01 8.01192E-04 3.31684E+01 + 8 6.03458E+01 -1.26041E-03 6.03458E+01 + 9 -9.47500E+01 1.53686E-03 9.47500E+01 + 10 1.20369E+02 -1.40198E-03 1.20369E+02 + 11 -7.89677E+01 5.76777E-04 7.89677E+01 + 12 -6.32521E+01 5.05161E-04 6.32521E+01 + 13 1.81803E+02 1.80158E-07 1.81803E+02 + 14 -7.95760E+01 -5.52422E-04 7.95760E+01 + 15 -5.44528E+01 -5.48092E-04 5.44528E+01 + 16 -3.36725E+00 -5.16930E-05 3.36725E+00 + 17 1.40632E+00 1.97679E-05 1.40632E+00 + 18 1.82388E+00 -1.74256E-05 1.82388E+00 + 19 2.74934E-01 -8.24861E-05 2.74934E-01 + 20 7.05958E-01 -1.00962E-04 7.05958E-01 + 21 -8.27612E-01 -1.31221E-04 8.27612E-01 + 22 -1.20687E-01 -1.47286E-04 1.20687E-01 + 23 -8.44888E-02 -1.20401E-04 8.44889E-02 + 24 8.42045E-02 -1.38985E-04 8.42046E-02 + 25 1.07760E-01 -7.71450E-05 1.07760E-01 + 26 -7.06543E-02 -1.32733E-04 7.06544E-02 + 27 2.78880E-02 -6.36465E-05 2.78880E-02 + 28 -4.39142E-02 -1.00664E-04 4.39143E-02 + 29 3.33506E-02 -3.25911E-05 3.33506E-02 + 30 -1.34752E-02 -7.48200E-05 1.34754E-02 + 31 9.29122E-03 -3.57505E-05 9.29129E-03 + 32 -7.26016E-03 -3.69783E-05 7.26026E-03 + 33 3.80657E-03 -1.35971E-05 3.80660E-03 + + i re wp im wp abs wp + + isol = 14, m = 1 + + i re wp im wp abs wp + + 1 1.94404E+00 1.94267E-05 1.94404E+00 + 2 -2.93823E+00 1.02644E-04 2.93823E+00 + 3 4.47835E+00 -2.01966E-04 4.47835E+00 + 4 -6.96896E+00 3.16839E-04 6.96896E+00 + 5 1.12207E+01 -4.06703E-04 1.12207E+01 + 6 -1.90778E+01 7.00882E-04 1.90778E+01 + 7 3.37362E+01 -9.90740E-04 3.37362E+01 + 8 -5.94927E+01 1.60906E-03 5.94927E+01 + 9 1.00222E+02 -2.23880E-03 1.00222E+02 + 10 -1.49694E+02 2.75352E-03 1.49694E+02 + 11 1.71002E+02 -2.33531E-03 1.71002E+02 + 12 -9.19487E+01 9.52418E-04 9.19487E+01 + 13 -7.95756E+01 5.52506E-04 7.95756E+01 + 14 1.35092E+02 -5.76856E-07 1.35092E+02 + 15 2.61290E+01 8.06777E-05 2.61290E+01 + 16 9.24656E-02 8.33511E-06 9.24656E-02 + 17 3.21466E+00 2.00789E-05 3.21466E+00 + 18 -1.95071E+00 -9.88519E-05 1.95071E+00 + 19 -1.58706E+00 -1.43860E-04 1.58706E+00 + 20 -2.12925E+00 -1.81638E-04 2.12925E+00 + 21 7.54845E-01 -1.24876E-04 7.54845E-01 + 22 4.21250E-01 -7.65339E-05 4.21250E-01 + 23 1.16147E-01 -1.15670E-04 1.16147E-01 + 24 -6.78836E-02 -8.62242E-05 6.78837E-02 + 25 -1.88265E-01 -1.40415E-04 1.88265E-01 + 26 1.22649E-01 -6.50557E-05 1.22649E-01 + 27 -5.00358E-02 -1.25167E-04 5.00360E-02 + 28 6.97622E-02 -4.53594E-05 6.97622E-02 + 29 -5.25478E-02 -9.75589E-05 5.25479E-02 + 30 2.13520E-02 -1.81743E-05 2.13520E-02 + 31 -1.46709E-02 -5.80153E-05 1.46710E-02 + 32 1.04412E-02 -2.68062E-05 1.04412E-02 + 33 -4.39219E-03 -2.65420E-05 4.39227E-03 + + i re wp im wp abs wp + + isol = 15, m = 2 + + i re wp im wp abs wp + + 1 4.66587E-01 -1.16326E-04 4.66587E-01 + 2 -1.07489E+00 9.92179E-05 1.07489E+00 + 3 2.25436E+00 -2.17042E-04 2.25436E+00 + 4 -4.58950E+00 2.21227E-04 4.58950E+00 + 5 9.00614E+00 -4.79283E-04 9.00614E+00 + 6 -1.67478E+01 6.29370E-04 1.67478E+01 + 7 2.92523E+01 -1.07453E-03 2.92523E+01 + 8 -4.71157E+01 1.42524E-03 4.71157E+01 + 9 6.69553E+01 -1.79970E-03 6.69553E+01 + 10 -7.67023E+01 1.66952E-03 7.67023E+01 + 11 5.63537E+01 -1.07783E-03 5.63537E+01 + 12 1.80100E+00 -7.52549E-05 1.80100E+00 + 13 -5.44543E+01 5.47985E-04 5.44543E+01 + 14 2.61292E+01 -8.10072E-05 2.61292E+01 + 15 5.65814E+01 -2.72372E-07 5.65814E+01 + 16 2.94729E+00 1.26686E-05 2.94729E+00 + 17 -6.08907E+00 -7.24034E-05 6.08907E+00 + 18 -5.96461E-01 -3.93369E-05 5.96461E-01 + 19 -5.59144E-01 -4.05784E-05 5.59144E-01 + 20 1.87158E+00 4.62055E-05 1.87158E+00 + 21 -2.26285E-01 -2.10106E-05 2.26285E-01 + 22 -4.65582E-01 -9.35292E-06 4.65582E-01 + 23 -3.39695E-02 -1.58931E-05 3.39695E-02 + 24 8.09995E-02 -6.76411E-06 8.09995E-02 + 25 1.19036E-01 -1.02269E-06 1.19036E-01 + 26 -7.10636E-02 -4.84166E-06 7.10636E-02 + 27 2.12825E-02 3.12518E-05 2.12826E-02 + 28 -3.69042E-02 -1.27616E-05 3.69042E-02 + 29 2.81788E-02 2.57282E-05 2.81788E-02 + 30 -1.14863E-02 -2.09071E-05 1.14863E-02 + 31 8.05393E-03 3.03196E-05 8.05399E-03 + 32 -5.25126E-03 -5.15817E-06 5.25126E-03 + 33 1.45808E-03 9.17214E-07 1.45808E-03 + + i re wp im wp abs wp + + isol = 16, m = 3 + + i re wp im wp abs wp + + 1 4.20006E-02 -1.23593E-06 4.20006E-02 + 2 -9.63581E-02 -6.12915E-06 9.63581E-02 + 3 1.98773E-01 -1.04081E-05 1.98773E-01 + 4 -4.19543E-01 6.70436E-06 4.19543E-01 + 5 8.76008E-01 -5.03956E-05 8.76008E-01 + 6 -1.67562E+00 5.22621E-05 1.67562E+00 + 7 2.80280E+00 -1.27267E-04 2.80280E+00 + 8 -3.96552E+00 1.33804E-04 3.96552E+00 + 9 4.53302E+00 -1.54658E-04 4.53302E+00 + 10 -3.73938E+00 1.07377E-04 3.73938E+00 + 11 1.08789E+00 -4.92277E-05 1.08789E+00 + 12 2.46268E+00 -5.41750E-05 2.46268E+00 + 13 -3.36860E+00 5.16290E-05 3.36860E+00 + 14 9.24565E-02 -8.29321E-06 9.24565E-02 + 15 2.94833E+00 -1.27293E-05 2.94833E+00 + 16 4.14338E+00 4.54964E-09 4.14338E+00 + 17 -2.49147E+00 -1.76618E-05 2.49147E+00 + 18 -8.92253E-01 -4.81169E-06 8.92253E-01 + 19 2.29724E+00 2.93126E-05 2.29724E+00 + 20 -5.42053E-01 -1.02285E-05 5.42053E-01 + 21 -5.42510E-01 -5.91250E-06 5.42510E-01 + 22 4.03126E-01 5.40991E-06 4.03126E-01 + 23 -1.42067E-01 -6.72671E-06 1.42067E-01 + 24 1.21194E-02 1.58927E-06 1.21194E-02 + 25 1.55376E-02 5.49810E-06 1.55376E-02 + 26 8.91596E-05 1.33519E-05 9.01538E-05 + 27 5.54898E-03 3.00342E-06 5.54899E-03 + 28 -1.46108E-02 9.53167E-06 1.46108E-02 + 29 7.30572E-03 -8.12053E-06 7.30573E-03 + 30 6.83805E-04 8.15085E-06 6.83854E-04 + 31 -1.12047E-03 -6.65243E-06 1.12049E-03 + 32 -4.69517E-05 1.14909E-05 4.83374E-05 + 33 8.73941E-05 -9.83364E-06 8.79456E-05 + + i re wp im wp abs wp + + isol = 17, m = 4 + + i re wp im wp abs wp + + 1 -1.79620E-01 5.04625E-05 1.79620E-01 + 2 2.92671E-01 -2.49383E-05 2.92671E-01 + 3 -4.40055E-01 6.18743E-05 4.40055E-01 + 4 6.87272E-01 -2.88725E-05 6.87272E-01 + 5 -1.12545E+00 9.82186E-05 1.12545E+00 + 6 1.75745E+00 -5.35084E-05 1.75745E+00 + 7 -2.51648E+00 1.48439E-04 2.51648E+00 + 8 3.18490E+00 -1.05642E-04 3.18490E+00 + 9 -3.04288E+00 1.44721E-04 3.04288E+00 + 10 1.39127E+00 -2.96434E-05 1.39127E+00 + 11 1.64793E+00 5.92615E-06 1.64793E+00 + 12 -3.94258E+00 1.38313E-04 3.94258E+00 + 13 1.40596E+00 -1.97284E-05 1.40596E+00 + 14 3.21437E+00 -2.00551E-05 3.21437E+00 + 15 -6.08792E+00 7.24747E-05 6.08792E+00 + 16 -2.49023E+00 1.76834E-05 2.49023E+00 + 17 2.41025E+00 1.28610E-08 2.41025E+00 + 18 -1.08013E+00 -1.64762E-05 1.08013E+00 + 19 -3.00145E+00 -2.03671E-05 3.00145E+00 + 20 2.27030E-01 -3.14918E-06 2.27030E-01 + 21 6.08286E-01 7.47700E-06 6.08286E-01 + 22 2.12093E-01 2.23210E-05 2.12093E-01 + 23 -1.07555E-02 1.38878E-05 1.07555E-02 + 24 3.85306E-02 1.15139E-05 3.85306E-02 + 25 -1.56012E-01 -8.82519E-06 1.56012E-01 + 26 8.70913E-02 4.78694E-06 8.70913E-02 + 27 -4.49337E-02 -3.70919E-06 4.49337E-02 + 28 5.15375E-02 1.11180E-05 5.15375E-02 + 29 -3.38893E-02 3.68264E-06 3.38893E-02 + 30 1.25267E-02 1.06888E-05 1.25267E-02 + 31 -7.65473E-03 5.01139E-06 7.65473E-03 + 32 5.50737E-03 -1.58308E-06 5.50737E-03 + 33 -2.31166E-03 8.64274E-06 2.31168E-03 + + i re wp im wp abs wp + + isol = 18, m = 5 + + i re wp im wp abs wp + + 1 -2.97000E-01 1.64638E-05 2.97000E-01 + 2 3.55298E-01 1.62788E-05 3.55298E-01 + 3 -3.25271E-01 2.11498E-05 3.25271E-01 + 4 2.02591E-01 3.69758E-05 2.02591E-01 + 5 -1.56014E-03 1.44552E-05 1.56021E-03 + 6 -2.73053E-01 6.68194E-05 2.73053E-01 + 7 5.11153E-01 1.58161E-05 5.11153E-01 + 8 -5.33691E-01 7.20000E-05 5.33691E-01 + 9 4.02864E-01 4.27475E-05 4.02864E-01 + 10 -4.54053E-02 3.71175E-05 4.54053E-02 + 11 1.00882E-01 8.19001E-05 1.00883E-01 + 12 -1.42975E+00 6.84771E-05 1.42975E+00 + 13 1.82270E+00 1.77691E-05 1.82270E+00 + 14 -1.95096E+00 9.88785E-05 1.95096E+00 + 15 -5.94748E-01 3.90727E-05 5.94748E-01 + 16 -8.91427E-01 4.76233E-06 8.91427E-01 + 17 -1.08063E+00 1.65649E-05 1.08063E+00 + 18 3.05935E+00 2.21699E-08 3.05935E+00 + 19 -2.68264E+00 -3.50742E-05 2.68264E+00 + 20 -1.57265E+00 -1.19610E-07 1.57265E+00 + 21 1.55409E+00 4.21571E-05 1.55409E+00 + 22 -2.09560E-01 2.54496E-05 2.09560E-01 + 23 4.65190E-01 5.65421E-05 4.65190E-01 + 24 -2.07243E-01 2.74090E-05 2.07243E-01 + 25 6.17110E-02 2.60386E-05 6.17110E-02 + 26 -5.80784E-02 1.68803E-05 5.80784E-02 + 27 3.20395E-02 3.28237E-05 3.20395E-02 + 28 -7.34089E-03 3.54477E-05 7.34098E-03 + 29 3.78113E-03 3.06261E-05 3.78126E-03 + 30 -6.36889E-03 2.57781E-05 6.36894E-03 + 31 3.56502E-03 2.12606E-05 3.56509E-03 + 32 -1.44475E-03 2.54939E-05 1.44497E-03 + 33 1.06355E-03 -3.15168E-06 1.06355E-03 + + i re wp im wp abs wp + + isol = 19, m = 6 + + i re wp im wp abs wp + + 1 -8.83673E-04 1.03934E-05 8.83734E-04 + 2 -3.74685E-02 9.99263E-06 3.74685E-02 + 3 1.59480E-01 4.58322E-05 1.59480E-01 + 4 -3.58630E-01 3.45319E-05 3.58630E-01 + 5 6.25385E-01 2.13170E-05 6.25385E-01 + 6 -9.48002E-01 8.87808E-05 9.48002E-01 + 7 1.16447E+00 -7.73282E-06 1.16447E+00 + 8 -1.02247E+00 1.26574E-04 1.02247E+00 + 9 5.17273E-01 6.05701E-05 5.17273E-01 + 10 5.48509E-01 3.05645E-05 5.48509E-01 + 11 -1.59653E+00 1.95790E-04 1.59653E+00 + 12 1.03592E+00 -3.24303E-05 1.03592E+00 + 13 2.74594E-01 8.24335E-05 2.74594E-01 + 14 -1.58709E+00 1.43927E-04 1.58709E+00 + 15 -5.58730E-01 4.06155E-05 5.58730E-01 + 16 2.29634E+00 -2.92708E-05 2.29634E+00 + 17 -3.00176E+00 2.04168E-05 3.00176E+00 + 18 -2.68281E+00 3.51115E-05 2.68281E+00 + 19 1.35480E+01 5.39501E-08 1.35480E+01 + 20 -1.55556E+00 -4.82092E-05 1.55556E+00 + 21 -2.85614E+00 8.86625E-06 2.85614E+00 + 22 1.99554E+00 5.27161E-05 1.99554E+00 + 23 -5.41309E-01 1.98234E-05 5.41309E-01 + 24 6.41449E-01 6.36455E-05 6.41449E-01 + 25 -3.83342E-01 3.02455E-05 3.83342E-01 + 26 2.34274E-01 4.44179E-05 2.34274E-01 + 27 -1.58781E-01 2.11173E-05 1.58781E-01 + 28 9.38499E-02 4.47409E-05 9.38499E-02 + 29 -6.12696E-02 3.41395E-05 6.12696E-02 + 30 3.96322E-02 2.99859E-05 3.96322E-02 + 31 -2.48644E-02 2.16582E-05 2.48644E-02 + 32 1.42239E-02 3.02710E-05 1.42240E-02 + 33 -7.59130E-03 1.53370E-05 7.59132E-03 + + i re wp im wp abs wp + + isol = 20, m = 7 + + i re wp im wp abs wp + + 1 1.02499E-01 3.32236E-06 1.02499E-01 + 2 -1.44758E-01 5.25308E-05 1.44758E-01 + 3 1.96018E-01 -9.22951E-06 1.96018E-01 + 4 -2.50907E-01 1.10298E-04 2.50907E-01 + 5 2.93063E-01 -1.88071E-05 2.93063E-01 + 6 -2.90535E-01 1.38542E-04 2.90535E-01 + 7 2.69977E-01 1.09844E-05 2.69977E-01 + 8 -2.45930E-01 1.41336E-04 2.45930E-01 + 9 6.19693E-02 8.22479E-05 6.19694E-02 + 10 4.16816E-01 6.22092E-05 4.16816E-01 + 11 -9.25696E-01 2.12742E-04 9.25696E-01 + 12 6.64294E-01 -4.71538E-05 6.64294E-01 + 13 7.06289E-01 1.01215E-04 7.06289E-01 + 14 -2.12912E+00 1.81554E-04 2.12912E+00 + 15 1.87087E+00 -4.63665E-05 1.87087E+00 + 16 -5.42114E-01 1.02230E-05 5.42114E-01 + 17 2.27196E-01 3.13618E-06 2.27196E-01 + 18 -1.57278E+00 6.37584E-08 1.57278E+00 + 19 -1.55571E+00 4.81307E-05 1.55571E+00 + 20 2.39828E+01 3.34796E-09 2.39828E+01 + 21 -1.74796E+00 -7.04999E-05 1.74796E+00 + 22 -3.28066E+00 2.32797E-06 3.28066E+00 + 23 1.62189E+00 4.24311E-05 1.62189E+00 + 24 -5.11129E-01 3.84843E-06 5.11129E-01 + 25 7.26130E-01 5.88608E-05 7.26130E-01 + 26 -3.93869E-01 1.33003E-05 3.93869E-01 + 27 2.28591E-01 3.08392E-05 2.28591E-01 + 28 -1.70903E-01 2.36102E-06 1.70903E-01 + 29 1.01864E-01 3.45206E-05 1.01864E-01 + 30 -6.10613E-02 2.56501E-05 6.10613E-02 + 31 3.79544E-02 1.81630E-05 3.79544E-02 + 32 -2.25430E-02 1.35177E-05 2.25430E-02 + 33 1.20972E-02 4.07895E-05 1.20973E-02 + + i re wp im wp abs wp + + isol = 21, m = 8 + + i re wp im wp abs wp + + 1 1.26948E-01 4.95120E-05 1.26948E-01 + 2 -1.53269E-01 1.17792E-05 1.53269E-01 + 3 1.52101E-01 3.04558E-05 1.52101E-01 + 4 -1.18566E-01 5.09594E-05 1.18566E-01 + 5 4.52491E-02 7.98514E-05 4.52492E-02 + 6 6.35537E-02 4.71091E-05 6.35538E-02 + 7 -1.89536E-01 1.20301E-04 1.89536E-01 + 8 2.99041E-01 5.65049E-05 2.99041E-01 + 9 -2.91335E-01 1.59937E-04 2.91335E-01 + 10 1.45719E-01 3.42015E-05 1.45719E-01 + 11 -2.17773E-01 2.50066E-04 2.17774E-01 + 12 5.88221E-01 -4.30203E-05 5.88221E-01 + 13 -8.27213E-01 1.30941E-04 8.27213E-01 + 14 7.54914E-01 1.24933E-04 7.54914E-01 + 15 -2.26806E-01 2.11818E-05 2.26806E-01 + 16 -5.42359E-01 5.88985E-06 5.42359E-01 + 17 6.08529E-01 -7.45036E-06 6.08529E-01 + 18 1.55417E+00 -4.20965E-05 1.55417E+00 + 19 -2.85617E+00 -8.88814E-06 2.85617E+00 + 20 -1.74803E+00 7.04766E-05 1.74803E+00 + 21 3.54933E+01 -5.87537E-09 3.54933E+01 + 22 -2.83498E+00 -1.13257E-04 2.83498E+00 + 23 -3.46480E+00 -3.13382E-06 3.46480E+00 + 24 1.72933E+00 3.41202E-05 1.72933E+00 + 25 -6.67685E-01 -1.01958E-05 6.67685E-01 + 26 7.49852E-01 4.85978E-05 7.49852E-01 + 27 -4.11646E-01 4.03341E-06 4.11646E-01 + 28 2.54401E-01 1.35636E-05 2.54401E-01 + 29 -1.78171E-01 -4.52159E-06 1.78171E-01 + 30 1.04582E-01 1.84741E-05 1.04582E-01 + 31 -6.51782E-02 2.49026E-05 6.51782E-02 + 32 4.00746E-02 6.73763E-06 4.00746E-02 + 33 -2.36304E-02 2.53502E-05 2.36304E-02 + + i re wp im wp abs wp + + isol = 22, m = 9 + + i re wp im wp abs wp + + 1 -3.11395E-03 1.39873E-04 3.11709E-03 + 2 1.23616E-02 3.39190E-05 1.23617E-02 + 3 -4.25234E-02 1.84517E-06 4.25234E-02 + 4 8.13052E-02 5.81903E-05 8.13053E-02 + 5 -1.10424E-01 3.40632E-05 1.10424E-01 + 6 1.32461E-01 1.06270E-04 1.32461E-01 + 7 -1.19499E-01 3.47004E-05 1.19499E-01 + 8 6.18641E-02 1.40805E-04 6.18643E-02 + 9 -6.18781E-02 7.46512E-05 6.18781E-02 + 10 -3.34238E-02 1.11503E-04 3.34239E-02 + 11 2.32584E-01 1.62548E-04 2.32584E-01 + 12 -9.71006E-02 2.41616E-05 9.71006E-02 + 13 -1.20929E-01 1.47177E-04 1.20929E-01 + 14 4.21236E-01 7.65543E-05 4.21236E-01 + 15 -4.65318E-01 9.34585E-06 4.65318E-01 + 16 4.03170E-01 -5.40943E-06 4.03170E-01 + 17 2.11915E-01 -2.23316E-05 2.11915E-01 + 18 -2.09637E-01 -2.54036E-05 2.09637E-01 + 19 1.99566E+00 -5.26993E-05 1.99566E+00 + 20 -3.28065E+00 -2.28351E-06 3.28065E+00 + 21 -2.83498E+00 1.13208E-04 2.83498E+00 + 22 4.81888E+01 1.45162E-09 4.81888E+01 + 23 -4.34480E+00 -1.61794E-04 4.34480E+00 + 24 -3.77625E+00 -1.66521E-06 3.77625E+00 + 25 1.82266E+00 2.82592E-05 1.82266E+00 + 26 -7.63387E-01 -1.10195E-05 7.63387E-01 + 27 8.02199E-01 4.66882E-05 8.02199E-01 + 28 -4.46315E-01 4.24046E-06 4.46315E-01 + 29 2.76905E-01 8.68188E-06 2.76905E-01 + 30 -1.90166E-01 -7.46900E-06 1.90166E-01 + 31 1.12719E-01 1.79838E-05 1.12719E-01 + 32 -7.04535E-02 1.92154E-05 7.04535E-02 + 33 4.36821E-02 -1.66583E-06 4.36821E-02 + + i re wp im wp abs wp + + isol = 23, m = 10 + + i re wp im wp abs wp + + 1 -9.88489E-03 2.31474E-05 9.88492E-03 + 2 1.18484E-02 1.04091E-04 1.18489E-02 + 3 -7.34299E-03 3.56922E-05 7.34308E-03 + 4 5.59128E-03 9.59180E-06 5.59129E-03 + 5 -7.22898E-03 5.42117E-05 7.22919E-03 + 6 6.76796E-03 4.05887E-05 6.76808E-03 + 7 -1.75454E-02 1.06346E-04 1.75457E-02 + 8 4.57887E-02 3.65080E-05 4.57887E-02 + 9 -3.57577E-02 1.53133E-04 3.57580E-02 + 10 1.22100E-02 2.49227E-05 1.22100E-02 + 11 -4.30021E-02 2.10747E-04 4.30026E-02 + 12 4.88002E-02 4.83659E-06 4.88002E-02 + 13 -8.45237E-02 1.20115E-04 8.45238E-02 + 14 1.16097E-01 1.15676E-04 1.16098E-01 + 15 -3.38046E-02 1.60318E-05 3.38046E-02 + 16 -1.42066E-01 6.74686E-06 1.42066E-01 + 17 -1.07395E-02 -1.39111E-05 1.07395E-02 + 18 4.65268E-01 -5.65084E-05 4.65268E-01 + 19 -5.41345E-01 -1.96666E-05 5.41345E-01 + 20 1.62189E+00 -4.23856E-05 1.62189E+00 + 21 -3.46480E+00 3.16770E-06 3.46480E+00 + 22 -4.34476E+00 1.61743E-04 4.34476E+00 + 23 6.15274E+01 -1.85861E-09 6.15274E+01 + 24 -6.29381E+00 -2.05388E-04 6.29381E+00 + 25 -3.92133E+00 2.52474E-06 3.92133E+00 + 26 1.83574E+00 2.85879E-05 1.83574E+00 + 27 -8.05089E-01 -1.38130E-05 8.05089E-01 + 28 8.25590E-01 5.03950E-05 8.25590E-01 + 29 -4.59180E-01 1.78595E-06 4.59180E-01 + 30 2.86236E-01 1.27733E-05 2.86236E-01 + 31 -1.95757E-01 -1.50115E-05 1.95757E-01 + 32 1.16263E-01 3.23802E-05 1.16263E-01 + 33 -7.31423E-02 -8.20616E-06 7.31423E-02 + + i re wp im wp abs wp + + isol = 24, m = 11 + + i re wp im wp abs wp + + 1 -1.79074E-02 8.69370E-05 1.79076E-02 + 2 2.50826E-02 9.79593E-05 2.50828E-02 + 3 -2.65891E-02 8.80171E-05 2.65893E-02 + 4 2.88488E-02 4.07901E-05 2.88488E-02 + 5 -2.17855E-02 4.55436E-06 2.17855E-02 + 6 1.52602E-02 6.72648E-05 1.52604E-02 + 7 -5.69847E-03 2.77313E-05 5.69854E-03 + 8 -2.82285E-02 1.20488E-04 2.82288E-02 + 9 4.49902E-02 4.26872E-05 4.49902E-02 + 10 -4.46460E-02 1.03591E-04 4.46461E-02 + 11 9.06588E-02 1.35786E-04 9.06589E-02 + 12 -9.40328E-02 1.21846E-05 9.40328E-02 + 13 8.42428E-02 1.38890E-04 8.42429E-02 + 14 -6.78811E-02 8.61953E-05 6.78811E-02 + 15 8.09582E-02 6.74374E-06 8.09582E-02 + 16 1.20585E-02 -1.55850E-06 1.20585E-02 + 17 3.85608E-02 -1.15471E-05 3.85608E-02 + 18 -2.07240E-01 -2.74618E-05 2.07240E-01 + 19 6.41420E-01 -6.36320E-05 6.41420E-01 + 20 -5.11104E-01 -3.69839E-06 5.11104E-01 + 21 1.72931E+00 -3.40845E-05 1.72931E+00 + 22 -3.77626E+00 1.73335E-06 3.77626E+00 + 23 -6.29376E+00 2.05370E-04 6.29376E+00 + 24 7.51959E+01 -1.03144E-09 7.51959E+01 + 25 -8.48462E+00 -2.59566E-04 8.48462E+00 + 26 -3.98479E+00 8.23464E-06 3.98479E+00 + 27 1.84172E+00 2.37628E-05 1.84172E+00 + 28 -8.38286E-01 -1.19235E-05 8.38286E-01 + 29 8.43440E-01 4.93395E-05 8.43440E-01 + 30 -4.70750E-01 -6.81112E-08 4.70750E-01 + 31 2.96102E-01 1.12154E-05 2.96102E-01 + 32 -2.03622E-01 -2.87310E-05 2.03622E-01 + 33 1.29234E-01 1.12308E-04 1.29234E-01 + + i re wp im wp abs wp + + isol = 25, m = 12 + + i re wp im wp abs wp + + 1 -4.43692E-03 -7.96945E-05 4.43763E-03 + 2 4.87304E-03 1.38294E-04 4.87501E-03 + 3 9.27171E-04 8.50688E-05 9.31065E-04 + 4 -6.35385E-03 9.19207E-05 6.35452E-03 + 5 1.50538E-02 3.94788E-05 1.50538E-02 + 6 -2.67338E-02 1.26818E-05 2.67338E-02 + 7 3.70611E-02 5.48981E-05 3.70611E-02 + 8 -2.59478E-02 3.60653E-05 2.59478E-02 + 9 1.59661E-02 1.24672E-04 1.59666E-02 + 10 2.60451E-02 -8.66264E-06 2.60451E-02 + 11 -9.12234E-02 2.01586E-04 9.12236E-02 + 12 1.52619E-02 -1.14776E-05 1.52619E-02 + 13 1.07715E-01 7.70824E-05 1.07715E-01 + 14 -1.88258E-01 1.40356E-04 1.88258E-01 + 15 1.19048E-01 1.02359E-06 1.19048E-01 + 16 1.55877E-02 -5.51367E-06 1.55877E-02 + 17 -1.56050E-01 8.85600E-06 1.56050E-01 + 18 6.16761E-02 -2.60649E-05 6.16761E-02 + 19 -3.83314E-01 -3.02901E-05 3.83314E-01 + 20 7.26134E-01 -5.88806E-05 7.26134E-01 + 21 -6.67672E-01 1.03757E-05 6.67672E-01 + 22 1.82263E+00 -2.82568E-05 1.82263E+00 + 23 -3.92133E+00 -2.43320E-06 3.92133E+00 + 24 -8.48457E+00 2.59582E-04 8.48457E+00 + 25 8.91539E+01 2.72236E-09 8.91539E+01 + 26 -1.09049E+01 -3.12514E-04 1.09049E+01 + 27 -3.98864E+00 1.23298E-05 3.98864E+00 + 28 1.83162E+00 1.96162E-05 1.83162E+00 + 29 -8.53852E-01 -7.51772E-06 8.53852E-01 + 30 8.55468E-01 4.89750E-05 8.55468E-01 + 31 -4.80513E-01 -2.04973E-06 4.80513E-01 + 32 3.12853E-01 1.71183E-05 3.12853E-01 + 33 -2.41331E-01 -3.82933E-05 2.41331E-01 + + i re wp im wp abs wp + + isol = 26, m = 13 + + i re wp im wp abs wp + + 1 2.67244E-03 8.60437E-05 2.67382E-03 + 2 -2.36384E-03 3.15453E-05 2.36405E-03 + 3 6.43680E-04 1.21234E-04 6.54998E-04 + 4 4.71158E-03 8.64255E-05 4.71238E-03 + 5 -6.43402E-03 9.17569E-05 6.43467E-03 + 6 1.43238E-02 5.41161E-05 1.43239E-02 + 7 -1.84255E-02 -5.21048E-06 1.84255E-02 + 8 9.90985E-03 7.78566E-05 9.91016E-03 + 9 -1.58202E-05 2.87276E-05 3.27957E-05 + 10 -2.76183E-02 8.58787E-05 2.76185E-02 + 11 6.85072E-02 1.03898E-04 6.85072E-02 + 12 -1.72592E-02 -1.28529E-05 1.72592E-02 + 13 -7.06006E-02 1.32792E-04 7.06007E-02 + 14 1.22659E-01 6.50055E-05 1.22659E-01 + 15 -7.11331E-02 4.78863E-06 7.11331E-02 + 16 7.21543E-05 -1.33527E-05 7.33794E-05 + 17 8.71188E-02 -4.77818E-06 8.71188E-02 + 18 -5.80659E-02 -1.68674E-05 5.80659E-02 + 19 2.34266E-01 -4.45159E-05 2.34266E-01 + 20 -3.93892E-01 -1.33712E-05 3.93892E-01 + 21 7.49866E-01 -4.86076E-05 7.49866E-01 + 22 -7.63366E-01 1.12109E-05 7.63366E-01 + 23 1.83570E+00 -2.86007E-05 1.83570E+00 + 24 -3.98479E+00 -8.13108E-06 3.98479E+00 + 25 -1.09048E+01 3.12576E-04 1.09048E+01 + 26 1.03358E+02 -4.09364E-09 1.03358E+02 + 27 -1.35052E+01 -3.72777E-04 1.35052E+01 + 28 -3.93348E+00 1.39930E-05 3.93348E+00 + 29 1.80010E+00 1.04241E-05 1.80010E+00 + 30 -8.55139E-01 -2.60713E-06 8.55139E-01 + 31 8.72314E-01 5.00474E-05 8.72314E-01 + 32 -5.24889E-01 -1.33897E-05 5.24889E-01 + 33 4.14969E-01 -6.42519E-05 4.14969E-01 + + i re wp im wp abs wp + + isol = 27, m = 14 + + i re wp im wp abs wp + + 1 5.35640E-04 -2.04577E-05 5.36030E-04 + 2 -2.07725E-03 -7.09422E-06 2.07726E-03 + 3 2.81923E-03 4.64771E-05 2.81961E-03 + 4 -4.26274E-03 1.32622E-04 4.26480E-03 + 5 6.79788E-03 7.51906E-05 6.79830E-03 + 6 -6.62152E-03 1.05617E-04 6.62236E-03 + 7 1.08235E-02 3.38164E-05 1.08236E-02 + 8 -2.76415E-03 1.71228E-05 2.76421E-03 + 9 -4.31723E-03 6.09161E-05 4.31766E-03 + 10 1.50258E-02 3.17918E-06 1.50259E-02 + 11 -3.81787E-02 1.58691E-04 3.81791E-02 + 12 1.35510E-02 -3.05763E-05 1.35511E-02 + 13 2.78735E-02 6.37500E-05 2.78736E-02 + 14 -5.00384E-02 1.25122E-04 5.00385E-02 + 15 2.13006E-02 -3.13035E-05 2.13006E-02 + 16 5.54087E-03 -3.00458E-06 5.54087E-03 + 17 -4.49406E-02 3.72129E-06 4.49406E-02 + 18 3.20329E-02 -3.27953E-05 3.20329E-02 + 19 -1.58783E-01 -2.10696E-05 1.58783E-01 + 20 2.28600E-01 -3.09866E-05 2.28600E-01 + 21 -4.11660E-01 -4.10858E-06 4.11660E-01 + 22 8.02209E-01 -4.67034E-05 8.02209E-01 + 23 -8.05065E-01 1.40083E-05 8.05065E-01 + 24 1.84167E+00 -2.38165E-05 1.84167E+00 + 25 -3.98864E+00 -1.22001E-05 3.98864E+00 + 26 -1.35051E+01 3.72890E-04 1.35051E+01 + 27 1.17751E+02 -9.77908E-09 1.17751E+02 + 28 -1.62559E+01 -4.30616E-04 1.62559E+01 + 29 -3.82005E+00 1.66203E-05 3.82005E+00 + 30 1.75059E+00 2.76107E-06 1.75059E+00 + 31 -8.87919E-01 7.24302E-06 8.87919E-01 + 32 1.02063E+00 6.69975E-05 1.02063E+00 + 33 -8.20421E-01 -1.50906E-04 8.20421E-01 + + i re wp im wp abs wp + + isol = 28, m = 15 + + i re wp im wp abs wp + + 1 1.96228E-03 1.39661E-04 1.96725E-03 + 2 -2.29586E-03 -1.46582E-05 2.29590E-03 + 3 7.70516E-04 -1.44914E-06 7.70517E-04 + 4 7.93590E-04 5.44196E-05 7.95454E-04 + 5 -2.32706E-03 1.21152E-04 2.33021E-03 + 6 7.44086E-03 8.77174E-05 7.44138E-03 + 7 -1.00820E-02 8.80423E-05 1.00823E-02 + 8 9.21744E-03 5.07951E-05 9.21758E-03 + 9 -2.85910E-03 1.10074E-05 2.85912E-03 + 10 -1.10495E-02 3.24535E-05 1.10496E-02 + 11 3.12436E-02 9.42877E-05 3.12437E-02 + 12 -4.03962E-03 -2.70368E-05 4.03971E-03 + 13 -4.39139E-02 1.00663E-04 4.39140E-02 + 14 6.97573E-02 4.53772E-05 6.97573E-02 + 15 -3.68916E-02 1.27837E-05 3.68916E-02 + 16 -1.46022E-02 -9.52035E-06 1.46022E-02 + 17 5.15405E-02 -1.11149E-05 5.15405E-02 + 18 -7.33250E-03 -3.54444E-05 7.33259E-03 + 19 9.38509E-02 -4.47199E-05 9.38509E-02 + 20 -1.70901E-01 -2.30987E-06 1.70901E-01 + 21 2.54401E-01 -1.37452E-05 2.54401E-01 + 22 -4.46332E-01 -4.29786E-06 4.46332E-01 + 23 8.25604E-01 -5.03989E-05 8.25604E-01 + 24 -8.38259E-01 1.21027E-05 8.38259E-01 + 25 1.83157E+00 -1.97131E-05 1.83157E+00 + 26 -3.93348E+00 -1.38431E-05 3.93348E+00 + 27 -1.62558E+01 4.30783E-04 1.62558E+01 + 28 1.32318E+02 -2.24312E-08 1.32318E+02 + 29 -1.91622E+01 -4.95424E-04 1.91622E+01 + 30 -3.64903E+00 1.96478E-05 3.64903E+00 + 31 1.81687E+00 -2.22768E-06 1.81687E+00 + 32 -1.35613E+00 -2.83990E-05 1.35613E+00 + 33 1.92572E+00 1.51245E-04 1.92572E+00 + + i re wp im wp abs wp + + isol = 29, m = 16 + + i re wp im wp abs wp + + 1 -1.48538E-03 2.50952E-05 1.48559E-03 + 2 1.11510E-03 -9.83517E-06 1.11515E-03 + 3 -1.19620E-03 3.32026E-06 1.19620E-03 + 4 -8.94587E-04 1.29628E-05 8.94681E-04 + 5 2.10245E-03 4.62049E-05 2.10296E-03 + 6 -3.69592E-03 1.25674E-04 3.69806E-03 + 7 8.07807E-03 8.06939E-05 8.07848E-03 + 8 -4.56446E-03 8.51456E-05 4.56525E-03 + 9 1.63896E-03 5.63088E-05 1.63993E-03 + 10 9.53300E-03 -3.19225E-05 9.53305E-03 + 11 -2.31748E-02 1.14064E-04 2.31751E-02 + 12 2.18843E-03 -1.98679E-05 2.18852E-03 + 13 3.33411E-02 3.26043E-05 3.33411E-02 + 14 -5.25468E-02 9.74878E-05 5.25469E-02 + 15 2.81853E-02 -2.57552E-05 2.81853E-02 + 16 7.30513E-03 8.12832E-06 7.30513E-03 + 17 -3.38949E-02 -3.66947E-06 3.38949E-02 + 18 3.77788E-03 -3.05980E-05 3.77801E-03 + 19 -6.12699E-02 -3.41254E-05 6.12699E-02 + 20 1.01863E-01 -3.44835E-05 1.01863E-01 + 21 -1.78164E-01 4.58667E-06 1.78164E-01 + 22 2.76909E-01 -8.89851E-06 2.76909E-01 + 23 -4.59201E-01 -1.83385E-06 4.59201E-01 + 24 8.43455E-01 -4.93250E-05 8.43455E-01 + 25 -8.53822E-01 7.67333E-06 8.53822E-01 + 26 1.80005E+00 -1.05629E-05 1.80005E+00 + 27 -3.82005E+00 -1.64388E-05 3.82005E+00 + 28 -1.91621E+01 4.95642E-04 1.91621E+01 + 29 1.47090E+02 -4.51210E-08 1.47090E+02 + 30 -2.22421E+01 -5.53899E-04 2.22421E+01 + 31 -3.69005E+00 1.22821E-05 3.69005E+00 + 32 3.01086E+00 4.91759E-06 3.01086E+00 + 33 -4.01065E+00 1.49358E-04 4.01065E+00 + + i re wp im wp abs wp + + isol = 30, m = 17 + + i re wp im wp abs wp + + 1 2.44199E-04 1.37467E-04 2.80233E-04 + 2 1.58046E-04 1.77617E-04 2.37753E-04 + 3 -3.12345E-04 -4.19489E-05 3.15150E-04 + 4 3.22600E-04 -5.25465E-06 3.22643E-04 + 5 -1.68519E-03 1.40180E-05 1.68524E-03 + 6 1.69923E-03 4.79106E-05 1.69990E-03 + 7 -2.11359E-03 1.21565E-04 2.11708E-03 + 8 2.02424E-03 8.11553E-05 2.02586E-03 + 9 2.39845E-03 8.63472E-05 2.40000E-03 + 10 -4.45169E-03 2.41658E-05 4.45175E-03 + 11 1.19268E-02 3.36760E-05 1.19269E-02 + 12 -2.80470E-03 -1.12448E-05 2.80472E-03 + 13 -1.34714E-02 7.48204E-05 1.34716E-02 + 14 2.13521E-02 1.81053E-05 2.13521E-02 + 15 -1.14902E-02 2.08782E-05 1.14902E-02 + 16 6.84774E-04 -8.15232E-06 6.84823E-04 + 17 1.25278E-02 -1.06988E-05 1.25278E-02 + 18 -6.36831E-03 -2.57685E-05 6.36836E-03 + 19 3.96353E-02 -2.99669E-05 3.96353E-02 + 20 -6.10624E-02 -2.56100E-05 6.10624E-02 + 21 1.04576E-01 -1.84186E-05 1.04576E-01 + 22 -1.90159E-01 7.56294E-06 1.90159E-01 + 23 2.86242E-01 -1.30458E-05 2.86242E-01 + 24 -4.70774E-01 4.77864E-08 4.70774E-01 + 25 8.55484E-01 -4.89388E-05 8.55484E-01 + 26 -8.55105E-01 2.73017E-06 8.55105E-01 + 27 1.75053E+00 -2.95225E-06 1.75053E+00 + 28 -3.64903E+00 -1.94214E-05 3.64903E+00 + 29 -2.22420E+01 5.54163E-04 2.22420E+01 + 30 1.62143E+02 -5.88098E-08 1.62143E+02 + 31 -2.53064E+01 -6.24935E-04 2.53064E+01 + 32 -5.49130E+00 -5.14583E-05 5.49130E+00 + 33 9.76128E+00 4.65848E-04 9.76128E+00 + + i re wp im wp abs wp + + isol = 31, m = 18 + + i re wp im wp abs wp + + 1 -1.25795E-03 -8.79129E-05 1.26102E-03 + 2 6.84636E-04 1.50907E-04 7.01070E-04 + 3 9.55988E-05 1.67404E-04 1.92778E-04 + 4 -4.67394E-04 -2.61884E-05 4.68127E-04 + 5 1.78122E-04 -2.16504E-05 1.79433E-04 + 6 -1.13406E-03 1.77775E-05 1.13420E-03 + 7 1.38633E-03 2.89233E-05 1.38664E-03 + 8 -7.40913E-06 1.34978E-04 1.35181E-04 + 9 -3.33778E-04 6.60373E-05 3.40248E-04 + 10 4.00893E-03 7.78676E-05 4.00969E-03 + 11 -6.89634E-03 4.77365E-05 6.89650E-03 + 12 1.66771E-03 -3.16695E-05 1.66801E-03 + 13 9.29633E-03 3.57461E-05 9.29640E-03 + 14 -1.46692E-02 5.79246E-05 1.46693E-02 + 15 8.04482E-03 -3.03704E-05 8.04487E-03 + 16 -1.12359E-03 6.66269E-06 1.12361E-03 + 17 -7.65184E-03 -5.03702E-06 7.65184E-03 + 18 3.56374E-03 -2.12758E-05 3.56380E-03 + 19 -2.48673E-02 -2.16180E-05 2.48673E-02 + 20 3.79562E-02 -1.81077E-05 3.79562E-02 + 21 -6.51769E-02 -2.48650E-05 6.51769E-02 + 22 1.12713E-01 -1.79167E-05 1.12713E-01 + 23 -1.95750E-01 1.51133E-05 1.95750E-01 + 24 2.96108E-01 -1.15295E-05 2.96108E-01 + 25 -4.80540E-01 2.05579E-06 4.80540E-01 + 26 8.72331E-01 -4.99828E-05 8.72331E-01 + 27 -8.87881E-01 -7.17119E-06 8.87881E-01 + 28 1.81680E+00 2.00279E-06 1.81680E+00 + 29 -3.69004E+00 -1.20076E-05 3.69004E+00 + 30 -2.53064E+01 6.25303E-04 2.53064E+01 + 31 1.78135E+02 -1.01712E-07 1.78135E+02 + 32 -3.03243E+01 -7.60622E-04 3.03243E+01 + 33 -8.88013E+00 1.44613E-04 8.88013E+00 + + i re wp im wp abs wp + + isol = 32, m = 19 + + i re wp im wp abs wp + + 1 -1.11682E-03 2.41982E-05 1.11708E-03 + 2 -1.00032E-03 2.08518E-05 1.00053E-03 + 3 4.42051E-04 1.18038E-04 4.57539E-04 + 4 3.07550E-04 1.42304E-04 3.38877E-04 + 5 -3.74887E-04 3.44621E-05 3.76467E-04 + 6 -1.29510E-05 -1.82557E-05 2.23830E-05 + 7 -1.10119E-03 1.08738E-05 1.10124E-03 + 8 1.59890E-04 1.92122E-05 1.61040E-04 + 9 1.50387E-03 1.10988E-04 1.50796E-03 + 10 -1.76294E-03 6.59383E-05 1.76417E-03 + 11 5.72430E-03 1.21357E-04 5.72558E-03 + 12 -2.04419E-05 -2.99755E-05 3.62823E-05 + 13 -7.26320E-03 3.68904E-05 7.26329E-03 + 14 1.04400E-02 2.68113E-05 1.04400E-02 + 15 -5.24499E-03 5.16121E-06 5.24499E-03 + 16 -4.62374E-05 -1.14908E-05 4.76438E-05 + 17 5.50623E-03 1.56545E-06 5.50623E-03 + 18 -1.44340E-03 -2.55178E-05 1.44362E-03 + 19 1.42236E-02 -3.02613E-05 1.42237E-02 + 20 -2.25437E-02 -1.34538E-05 2.25437E-02 + 21 4.00768E-02 -6.68048E-06 4.00768E-02 + 22 -7.04537E-02 -1.91570E-05 7.04537E-02 + 23 1.16256E-01 -3.22954E-05 1.16256E-01 + 24 -2.03612E-01 2.88672E-05 2.03612E-01 + 25 3.12858E-01 -1.75161E-05 3.12858E-01 + 26 -5.24922E-01 1.34853E-05 5.24922E-01 + 27 1.02065E+00 -6.69152E-05 1.02065E+00 + 28 -1.35609E+00 2.84073E-05 1.35609E+00 + 29 3.01079E+00 -5.22551E-06 3.01079E+00 + 30 -5.49128E+00 5.15891E-05 5.49128E+00 + 31 -3.03243E+01 7.60925E-04 3.03243E+01 + 32 2.13132E+02 -2.87762E-07 2.13132E+02 + 33 -8.96015E+01 -1.34256E-03 8.96015E+01 + + i re wp im wp abs wp + + isol = 33, m = 20 + + i re wp im wp abs wp + + 1 5.97110E-03 1.81151E-05 5.97113E-03 + 2 -6.83874E-04 -2.49267E-05 6.84329E-04 + 3 -7.34077E-04 3.23603E-05 7.34790E-04 + 4 -2.47259E-05 1.25377E-04 1.27792E-04 + 5 1.90343E-05 2.89936E-05 3.46833E-05 + 6 -4.51401E-05 7.24078E-05 8.53260E-05 + 7 -2.06668E-04 -1.65480E-05 2.07329E-04 + 8 2.03604E-04 6.23814E-05 2.12946E-04 + 9 -1.26803E-03 1.21531E-06 1.26803E-03 + 10 2.03870E-03 6.16526E-05 2.03964E-03 + 11 -2.18961E-03 4.93140E-05 2.19017E-03 + 12 1.10902E-03 6.92933E-05 1.11118E-03 + 13 3.80538E-03 1.34774E-05 3.80540E-03 + 14 -4.39224E-03 2.64832E-05 4.39232E-03 + 15 1.45904E-03 -9.23035E-07 1.45904E-03 + 16 8.91580E-05 9.84786E-06 8.97003E-05 + 17 -2.31300E-03 -8.66663E-06 2.31301E-03 + 18 1.06310E-03 3.09833E-06 1.06310E-03 + 19 -7.58972E-03 -1.53100E-05 7.58973E-03 + 20 1.20962E-02 -4.07773E-05 1.20963E-02 + 21 -2.36320E-02 -2.53850E-05 2.36320E-02 + 22 4.36871E-02 1.82013E-06 4.36871E-02 + 23 -7.31436E-02 8.15778E-06 7.31436E-02 + 24 1.29219E-01 -1.11957E-04 1.29219E-01 + 25 -2.41307E-01 3.79853E-05 2.41307E-01 + 26 4.14978E-01 6.33625E-05 4.14978E-01 + 27 -8.20500E-01 1.50794E-04 8.20500E-01 + 28 1.92579E+00 -1.49713E-04 1.92579E+00 + 29 -4.01056E+00 -1.50364E-04 4.01056E+00 + 30 9.76119E+00 -4.66437E-04 9.76119E+00 + 31 -8.88036E+00 -1.46889E-04 8.88036E+00 + 32 -8.96019E+01 1.33893E-03 8.96019E+01 + 33 5.28231E+02 -2.40912E-06 5.28231E+02 + + i re wp im wp abs wp + + Total cpu time = 5.188E+00 seconds + Total wall time = 1.462E+01 seconds diff --git a/src/DCON/validate/dcon_output_n1.nc b/src/DCON/validate/dcon_output_n1.nc new file mode 100644 index 000000000..350a9b468 Binary files /dev/null and b/src/DCON/validate/dcon_output_n1.nc differ diff --git a/src/DCON/validate/equil.in b/src/DCON/validate/equil.in new file mode 100644 index 000000000..bcc711489 --- /dev/null +++ b/src/DCON/validate/equil.in @@ -0,0 +1,29 @@ +&EQUIL_CONTROL + eq_type="efit" ! Type of the input 2D equilibrium file. Accepts efit, chease, fluxgrid, transp, jsolver, lar, sol, etc. + eq_filename = "beta_1.00" ! Path to input file + + jac_type="hamada" ! Working coordinate system for all DCON and GPEC calculations. Overrides individual powers. Accepts hamada, pest, boozer, equal_arc + power_bp=0 ! del.B ~ B_p**power_bp * B**power_b / R**power_r + power_b=0 ! del.B ~ B_p**power_bp * B**power_b / R**power_r + power_r=0 ! del.B ~ B_p**power_bp * B**power_b / R**power_r + + grid_type="ldp" ! Radial grid packing of equilibrium quantities. Accepts rho, ldp, pow1, pow2, or original. ldp packs points near the core and edge. pow* packs near the edge. + psilow=0.01 ! Minimum value of psi, normalized from 0 to 1 + psihigh=0.99 ! Maximum value of psi, normalized from 0 to 1 + mpsi=128 ! Number of radial grid intervals for equilibrium quantities + mtheta=256 ! Number of equally spaced poloidal grid intervals for all splines + newq0=0 ! Grad-Shafranov solution invariant adjustment of the q profile to give the specified value of q at the axis. Default 0 uses input file value. + use_classic_splines = t ! Use a classical cubic spline instead of tri-diagonal solution for splines with extrapolation boundary conditions + + input_only=f ! Generate information about the input and then quit with no further calculation +/ +&EQUIL_OUTPUT + gse_flag=f ! Produces diagnostic output for accuracy of solution to Grad-Shafranov equation + out_eq_1d=f ! Ascii output of 1D equilibrium file data + bin_eq_1d=f ! Binary output of 1D equilibrium file data + out_eq_2d=f ! Ascii output of 2D equilibrium file data + bin_eq_2d=t ! Binary output of 2D equilibrium file data (set true for GPEC) + out_2d=f ! Ascii output of processed 2D data + bin_2d=f ! Binary output of processed 2D data + dump_flag=f ! Binary dump of basic equilibrium data and 2D rzphi spline +/ diff --git a/src/DCON/validate/euler.bin b/src/DCON/validate/euler.bin new file mode 100644 index 000000000..72592f216 Binary files /dev/null and b/src/DCON/validate/euler.bin differ diff --git a/src/DCON/validate/fmat.bin b/src/DCON/validate/fmat.bin new file mode 100644 index 000000000..d86962070 Binary files /dev/null and b/src/DCON/validate/fmat.bin differ diff --git a/src/DCON/validate/fort.27 b/src/DCON/validate/fort.27 new file mode 100644 index 000000000..4277e3495 Binary files /dev/null and b/src/DCON/validate/fort.27 differ diff --git a/src/DCON/validate/fs.bin b/src/DCON/validate/fs.bin new file mode 100644 index 000000000..84c9a3895 Binary files /dev/null and b/src/DCON/validate/fs.bin differ diff --git a/src/DCON/validate/g147131.02300_DIIID_KEFIT b/src/DCON/validate/g147131.02300_DIIID_KEFIT new file mode 100644 index 000000000..15da8c793 --- /dev/null +++ b/src/DCON/validate/g147131.02300_DIIID_KEFIT @@ -0,0 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12182.20642037295 11880.76905649079 + 11563.17905204596 11221.41720584921 10845.77852954605 + 10424.72040962231 9944.682019110633 9389.872153629567 + 8741.386453853078 7960.502825863257 6966.480594668571 + 5721.489830854105 4343.312212392995 3026.481733519480 + 1918.781488600130 1098.404429423566 563.4722725835368 + 250.1451760428327 + NQPSI = 129 + NPRESS = 132 + SIGPRE = 3819.448908320424 3740.527618419366 + 3660.170161647170 3583.997327356893 3508.011053984777 + 3435.045238299463 3358.902060386787 3286.111386389104 + 3215.734294930811 3146.905836047652 3079.014937873383 + 3011.683223645562 2945.102922516187 2879.859573403034 + 2816.043299077777 2753.414520573220 2691.845811481377 + 2631.263205424775 2571.533022100814 2517.883623678696 + 2464.971035703949 2412.933003317793 2361.758498200952 + 2311.419294881836 2261.988015171673 2213.530935585667 + 2165.989792926877 2119.305927638480 2073.499371951876 + 2028.703822359472 1980.988954749361 1934.914726368582 + 1890.021818247360 1846.266921401513 1803.759312615408 + 1762.412534134266 1722.226010027649 1683.266928941895 + 1645.302375612132 1608.230428985932 1572.293005588084 + 1537.394516993478 1503.431684010575 1467.697559811851 + 1433.080257996873 1399.374194195152 1366.814618720795 + 1335.451464240506 1304.884310524545 1275.077690250312 + 1243.997222853157 1215.855728062487 1186.201538322503 + 1157.315090725145 1129.023112732973 1101.324271075684 + 1074.086625889626 1047.302889597085 1023.009940761334 + 998.9220947183296 974.9791796255200 951.3394444067399 + 927.9991229744106 904.8014447182755 881.9665975117500 + 859.4169486628282 836.9377105531189 816.5669116706197 + 796.1434385642033 776.0214093756424 756.4519696962261 + 736.7591495127399 717.0109573849695 699.0367469979125 + 680.8485109629121 662.3711113272644 645.3790600976672 + 627.8673186475312 611.8722915860307 595.2857949028868 + 578.0140218742512 562.2189845487273 545.4568341154855 + 530.0957873959409 513.7853789135501 499.2105105351176 + 482.9635873605989 468.3944292564011 452.6524937147921 + 439.2604918223038 425.0021435942676 409.0395153562252 + 391.7588972616830 379.3058693013772 366.0501958671186 + 352.1102173010490 337.3258012472273 321.8660479343733 + 305.6975796862171 288.9193356195521 271.6715341583910 + 254.0267637594594 236.1767296452262 227.2044474289110 + 218.2573717723909 209.3505964124191 200.4979840484500 + 191.7170742439044 183.0461547244042 174.4951581201236 + 166.0814707180330 157.8342221149340 149.7621950015604 + 141.8803379236712 134.2082796728725 126.7540865527151 + 119.5305207559845 112.5480628241565 105.8135002071685 + 99.32984476487312 93.10176622020934 81.41452318942966 + 76.38897816640849 76.38897816640849 76.38897816640849 + 76.38897816640849 76.38897816640849 76.38897816640849 + 76.38897816640849 76.38897816640849 76.38897816640849 + 76.38897816640849 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 0.000000000000000 + / + &BASIS + KPPFNC = 6, + KPPKNT = 9, + PPKNT = 0.000000000000000 , + 0.6000000000000000 , + 0.8309948501841458 , + 0.9259035236011000 , + 0.9394619055178077 , + 0.9530202874345154 , + 0.9801370512679309 , + 0.9936954331846386 , + 1.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + PPTENS = 2.000000000000000 , + KFFFNC = 6, + KFFKNT = 9, + FFKNT = 0.000000000000000 , + 0.6000000000000000 , + 0.8309948501841458 , + 0.9259035236011000 , + 0.9394619055178077 , + 0.9530202874345154 , + 0.9801370512679309 , + 0.9936954331846386 , + 1.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + FFTENS = 2.000000000000000 , + KWWFNC = 0, + KWWKNT = 0, + WWKNT = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + WWTENS = 0.000000000000000 , + PPBDRY = 620844.4103959909 , + 158313.5777226928 , + 141414.5129313806 , + 315668.7249493082 , + 448281.5092263866 , + 664288.9511872320 , + 407224.0308621362 , + 179728.4116576705 , + 108641.8366059566 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + PP2BDRY = 22932171.22922356 , + 5868728.220783956 , + -3474615.074536501 , + 167982639.2419721 , + 1151513694.066376 , + -2048012171.209169 , + -110552274.9895208 , + 1442826158.424312 , + -3600231013.000693 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + KPPBDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + KPP2BDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + FFBDRY = 0.9114307588631456 , + 0.5211455287937966 , + 0.2368879341631518 , + -0.1298418203475191 , + -0.3325109793088990 , + -0.6697285434882476 , + -0.5566780385014780 , + -0.3060984383688860 , + -0.2002143303358702 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + FF2BDRY = -99.07288472601269 , + 0.1704819144219263 , + 3.385019078475219 , + -232.5891067997149 , + -1623.631644131465 , + 2326.759872403892 , + 324.3915798601789 , + -148.7293255361868 , + -1365.687572250405 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + KFFBDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + KFF2BDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + WWBDRY = 753378.4125525327 , + 1254.750893700115 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + WW2BDRY = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + KWWBDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + KWW2BDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + KEEFNC = 0, + KEEKNT = 0, + EEKNT = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + EETENS = 5.000000000000000 , + EEBDRY = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + EE2BDRY = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + KEEBDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + KEE2BDRY = 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + / + &MSEOUT + RRRGAM = 1.519000053405762 , + 1.570000052452087 , + 1.620000004768372 , + 1.669999957084656 , + 1.718999981880188 , + 1.768000006675720 , + 1.819000005722046 , + 1.871000051498413 , + 1.919999957084656 , + 1.973000049591064 , + 2.022000074386597 , + 1.980999946594238 , + 2.030999898910522 , + 2.075000047683716 , + 2.119999885559082 , + 2.157999992370605 , + 2.196000099182129 , + 2.240000009536743 , + 2.243000030517578 , + 2.246000051498413 , + 2.250000000000000 , + 2.253000020980835 , + 2.256000041961670 , + 2.259999990463257 , + 2.263000011444092 , + 2.266000032424927 , + 1.689000010490417 , + 1.733000040054321 , + 1.779999971389771 , + 1.822999954223633 , + 1.868000030517578 , + 1.912999987602234 , + 1.955999970436096 , + 2.000999927520752 , + 2.046999931335449 , + 2.095000028610229 , + 1.583999991416931 , + 1.628999948501587 , + 1.679000020027161 , + 1.730000019073486 , + 2.069000005722046 , + 2.117000102996826 , + 2.176000118255615 , + 2.243999958038330 , + 2.328000068664551 , + 1.697000026702881 , + 1.741999983787537 , + 1.786999940872192 , + 1.832000017166138 , + 1.876000046730042 , + 1.919000029563904 , + 1.963000059127808 , + 2.007999897003174 , + 2.029000043869019 , + 2.069999933242798 , + 2.109999895095825 , + 2.148000001907349 , + 2.184999942779541 , + 2.217999935150146 , + 2.236000061035156 , + 2.242000102996826 , + 2.247999906539917 , + 2.253999948501587 , + 2.259000062942505 , + 2.265000104904175 , + 2.269999980926514 , + 2.276999950408936 , + 2.282999992370605 , + 2.288000106811523 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + ZZZGAM = -2.5000000372529030E-002, + -2.3000000044703484E-002, + -1.7000000923871994E-002, + -1.3000000268220901E-002, + -1.2000000104308128E-002, + -9.9999997764825821E-003, + -7.0000002160668373E-003, + -2.0000000949949026E-003, + -2.0000000949949026E-003, + 3.0000000260770321E-003, + -4.9999998882412910E-003, + 1.0999999940395355E-002, + 1.2000000104308128E-002, + 6.0000000521540642E-003, + 6.0000000521540642E-003, + 6.0000000521540642E-003, + 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-3.5700015000000000E-007, + -3.5700015000000000E-007, + -3.5800007999999998E-007, + -3.5800007999999998E-007, + -3.5800007999999998E-007, + -3.5800007999999998E-007, + -3.5800007999999998E-007, + -3.5800007999999998E-007, + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + AA7GAM = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 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0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + AA8GAM = 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + MSEBKP = 2, + FWTGAM = 143.6991789891108 , + 185.1811386343780 , + 78.40209628388961 , + 178.1617900755973 , + 303.4180160879514 , + 326.6217997187786 , + 326.1137722900801 , + 290.6358382645274 , + 292.8258972880955 , + 257.4776597577429 , + 128.0868121177809 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 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0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 + / + &ECCD + KKSTARK = 101, + CHIGAMT = 6.288350332173052 , + CHIGAM = 6.8718846858426309E-003, + 0.8642208357382712 , + 4.5772342066763942E-002, + 0.1441107743782717 , + 5.8704275788020442E-004, + 0.1330170177436550 , + 0.1100136407777549 , + 0.4974061584921390 , + 5.8007832743605867E-002, + 1.337812503053351 , + 2.0986415934678100E-008, + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.2572793529242821 , + 1.001614801463411 , + 5.3304588626912797E-004, + 1.831103078475139 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 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0.000000000000000 , + BZMSE = 0.2633257637333608 , + 0.2253751085917230 , + 0.1569722508138092 , + 0.1018670534644938 , + 4.8717234682062988E-002, + -8.9251540581822639E-003, + -7.4278243694292964E-002, + -0.1280085240642471 , + -0.1863221690472449 , + -0.2440127073208272 , + -0.2750595994447966 , + -0.2340211311616925 , + 0.000000000000000 , + 0.000000000000000 , + -0.2880209759332820 , + 0.000000000000000 , + 0.000000000000000 , + -0.3508916351038071 , + -0.3435322337432880 , + -0.3322306624278285 , + 0.2043928706962979 , + -0.3471284497071509 , + -0.3621716585514165 , + -0.3673197871123566 , + -0.3799906037178188 , + -0.3912341507830856 , + 0.1204484490088696 , + 5.6352594690636110E-002, + 1.9615526585615600E-003, + -5.5819261737644447E-002, + -0.1102662964862659 , + -0.1726524764037290 , + -0.7040569634409041 , + -0.2823965611131734 , + -0.3128154888944586 , + -0.3420769893826962 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + -0.3005036852473656 , + -0.3153197911502894 , + -0.3263231023932838 , + -0.3341674587720543 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + PSIECN = 0.000000000000000 , + DPSIECN = 0.000000000000000 , + SAISQ = 17.63691764250911 , + CJECCD = 0.000000000000000 + / + &CHIOUT + SAISIL = 3.0254726073793078E-002, + 2.2448233599002221E-002, + 4.0477480494356136E-002, + 1.8482801924204526E-002, + 0.1815426499039182 , + 8.3429880135030242E-003, + 0.000000000000000 , + 8.7386235165995835E-002, + 2.5813930068840717E-004, + 9.9474461019504728E-003, + 8.2844412786942684E-002, + 7.5933865885683099E-002, + 0.2627442485853556 , + 0.3509357812678711 , + 9.6033841666670933E-007, + 2.2118508979707265E-002, + 0.4808962475029976 , + 1.3046329959515745E-002, + 1.1359027072828433E-002, + 2.7870960784433643E-002, + 9.5976807321789658E-003, + 3.0660773224850475E-005, + 3.0227180285408595E-002, + 2.0979367874545563E-002, + 3.1562805991269456E-003, + 0.1760459999290185 , + 0.2574616611965144 , + 0.1816740584544634 , + 8.7708270642808228E-002, + 3.4209550823340429E-002, + 0.000000000000000 , + 3.1158381237082113E-003, + 0.3400561762082721 , + 0.1627616238474943 , + 3.5272957564644949E-003, + 0.6931974499377125 , + 0.2565074263891799 , + 9.8884503548996496E-003, + 3.3764510207446585E-003, + 0.1131026446293127 , + 5.9048635948197412E-002, + 0.000000000000000 , + 2.1441786665032077E-003, + 0.5329646325769650 , + SAIMPI = 0.1664956734408607 , + 0.000000000000000 , + 0.2069890581742621 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.9625388096277667 , + 0.000000000000000 , + 0.000000000000000 , + 0.9395681019411204 , + 0.000000000000000 , + 0.2531281336482902 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.000000000000000 , + 0.7743150177662679 , + 0.000000000000000 , + 0.000000000000000 , + 5.7097149963797229E-003, + 7.2591824784642919E-002, + 4.3550977956466367E-003, + 3.0373203503747406E-002, + 0.1262520950513119 , + 5.4597015166318152E-002, + 0.3675616781690489 , + 0.2450045031423853 , + 0.4875873432697144 , + 1.638041225492166 , + 1.595691424778917 , + 0.000000000000000 , + 7.2013596293274640E-002, + 8.5872038220408970E-003, + 4.3225384258836722E-002, + 1.7508110800918040E-004, + 0.1025167665000940 , + 9.9402418869484806E-003, + 0.5657908661525793 , + 6.9254557685246063E-002, + 8.8465863142351622E-003, + 0.2427614440886205 , + 7.5902565528919372E-002, + 6.2268607119479957E-002, + 0.000000000000000 , + 0.4591730294678171 , + 0.1164963608783690 , + 2.3716235575672658E-002, + 9.7360485808618197E-002, + 2.0547716593933629E-002, + 0.1635269758339434 , + 0.3562749054621027 , + 1.230396761661656 , + 1.4742685234513338E-002, + 0.000000000000000 , + 0.3974465226608165 , + 0.2434253110628695 , + 0.2976340978930932 , + 4.9916901857596084E-002, + 0.1537242396472875 , + 0.000000000000000 , + 5.8825006947044048E-003, + 5.4957901438118474E-003, + 0.000000000000000 , + 2.0276489206899072E-002, + 3.5533777446743110E-002, + 1.8582184560361222E-004, + SAIPR = 0.000000000000000 , + SAIIP = 4.5405653514677624E-002 + / + KIM diff --git a/src/DCON/validate/gmat.bin b/src/DCON/validate/gmat.bin new file mode 100644 index 000000000..5c6767b43 Binary files /dev/null and b/src/DCON/validate/gmat.bin differ diff --git a/src/DCON/validate/gpec.in b/src/DCON/validate/gpec.in new file mode 100644 index 000000000..19c273c7e --- /dev/null +++ b/src/DCON/validate/gpec.in @@ -0,0 +1,88 @@ +&GPEC_INPUT + dcon_dir = '' ! Path to DCON outputs. Individual file paths are appended to this + idconfile = 'euler.bin' ! Eigenfunctions output by DCON run + ieqfile = 'psi_in.bin' ! Flux surfaces output by DCON run + rdconfile = 'globalsol.bin' ! Galerkin eigenfunctions output by resistive DCON run + + gal_flag = f ! Use the Galerkin eigenfunctions from resistive DCON instead of the ideal DCON shooting method solutions + + jac_in="hamada" ! Coordinate system of external perturbation (affects data_flag and harmonic_flag). Options include: pest,boozer,hamada + jsurf_in=1 ! True(1) if external perturbation is area weighted (i.e. flux) + tmag_in =0 ! True(1) if external perturbation has toroidal angle defined by jac_in. False(0) if machine angle. + mthsurf =0 ! Number of poloidal angle gridpoints. Minimum of twice the Nyquist condition from DCON m limits is enforced. + + coil_flag=t ! Calculate external perturbation from coils in coil.in + + data_flag=f ! Apply perturbation from thrid party code output + data_type="surfmn" ! Name of said code. Choose: surfmn,?? + infile="path/to/file" ! Path to said output + nmin=0 ! Extra parameters needed to read surfmn files. + nmax=64 ! Extra parameters needed to read surfmn files. + mmin=-64 ! Extra parameters needed to read surfmn files. + mmax=64 ! Extra parameters needed to read surfmn files. + + harmonic_flag=f ! Apply self-defined perturbations + cosmn(3)=1e-4 ! Real part of m=3 component (n defined by DCON run). + sinmn(6)=1e-4 ! Imaginary part of m=6 component. etc. + + displacement_flag=f ! Perturbations are displacement (m). Default is field (T). + fixed_boundary_flag=f ! Total perturbation = external perturbation + + mode_flag = .F. ! Return only a single DCON eigenfunction defined by mode (ignores external pert.) + mode = 0 ! DCON eigen function index (1 is least stable) + filter_types = 'w' ! Isolate the filter_modes of energy (w), reluctance (r), permiability (p) or singular coupling (s) eigenvectors/singular-vectors + filter_modes = 0 ! Number of modes isolated, negative values isolate backwards from the last mode +/ +&GPEC_CONTROL + resp_index=0 ! Integer 0-4, determining method of inductance matrix formation. 0 uses energy identity, and is recommended. + sing_spot=5e-4 ! Minimum distance to singular surface in (m-nq) space + sing_npsi=100 ! Number of points between rational surfaces used for b-normal splines across sin_spot + reg_flag=t ! Regularize the solution near resonant surfaces + reg_spot=5e-2 ! Regularize by (m-nq)^2/((m-nq)^2+reg_spot^2) + chebyshev_flag=f ! Fit Chebyshev polynomials to the displacement. + nche=20 ! Number of Chebyshev polynomials used + use_classic_splines = f ! Use a classical cubic spline instead of tri-diagonal solution for splines with extrapolation boundary conditions +/ +&GPEC_OUTPUT + jac_out="hamada" ! Coordinate system of outputs + jsurf_out=0 ! True(1) for area weighted outputs (only appends standard gpec_control output) + tmag_out=1 ! True(1) for magnetic toroidal angle outputs (affects singcoup and singfld, appends gpec_control) + mlim_out=64 ! If positive, Fourier decomposed outputs will span -mlim_out<=m<=mlim_out. Default (<=0) outputs on internal m range. + + resp_flag=t ! Output energy, reluctance, inductance, and permeability eigenvalues, eigenvectors, and matrices + filter_flag=t ! Outputs energy, reluctance, pereability, and (optionally) the singular-coupling eigenmodes on the control surface + singcoup_flag=t ! Calculate coupling of each m to resonant surfaces + singfld_flag=t ! Output of resonant surface quantities (flux,current,etc.) + vsingfld_flag=f ! Output of vacuum resonant surface quantities + singthresh_flag=t ! Calculate Callen resonant field penetration threshold (requires kinetic profiles from pentrc.in) + + pmodb_flag=f ! Outputs delta-B_Lagrangian + xbnormal_flag=t ! Outputs normal displacement and field in plasma + vbnormal_flag=f ! Outputs vacuum normal displacement and field in plasma + xclebsch_flag=t ! Outputs clebsch coordinate displacement for PENT + dw_flag=f ! Outputs self-consistent energy and torque profiles (when kin_flag=t from DCON) + + eqbrzphi_flag=f ! Outputs equilibrium field on regular (r,z) grid + brzphi_flag=t ! Outputs perturbed field on regular (r,z) grid + xrzphi_flag=f ! Outputs displacement on regular (r,z) grid + vbrzphi_flag=f ! Outputs field on regular (r,z) grid due to total boundary surface current (not a real field) + vvbrzphi_flag=f ! Outputs field on regular (r,z) grid due to exeternal perturbation surface current (not a real field) + vsbrzphi_flag=f ! Outputs the field on regular (r,z) grid due to singular surface currents + ss_flag(3)=f ! Outputs the field on regular (r,z) grid due to the 3rd singular surface current, etc. + xbrzphifun_flag=f ! Outputs r,z, and perturbation vectors on psi,theta grid + arzphifun_flag=f ! Outputs r,z, and vector potential on psi,theta grid + + nr = 64 ! Number of radial grid points in rzphi outputs + nz = 124 ! Number of vertical grid points in rzphi outputs + fun_flag=t ! Write outputs to (r,z) in addition to default (psi,m) + flux_flag=f ! Write outputs to (psi,theta) in addition to default (psi,m) + bin_flag=f ! Write binary outputs for use with xdraw + bin_2d_flag=f ! Write 2D binary outputs for use with xdraw + out_ahg2msc=f ! Output deprecated ahg2msc.out files. This is used to communicate with vacuum, but is now done through memory. + max_linesout=0 ! Maximum length of ascii data tables enforced by increasing radial step size (iff .gt. 0). + verbose=t ! Print run log to terminal +/ +&GPEC_DIAGNOSE + timeit=t ! Print timer splits for major subroutines + radvar_flag=f ! Map various radial variables (rho,psi_tor) on psi_n grid +/ diff --git a/src/DCON/validate/gs.bin b/src/DCON/validate/gs.bin new file mode 100644 index 000000000..98d6719d5 Binary files /dev/null and b/src/DCON/validate/gs.bin differ diff --git a/src/DCON/validate/imats.out b/src/DCON/validate/imats.out new file mode 100644 index 000000000..3c974edda --- /dev/null +++ b/src/DCON/validate/imats.out @@ -0,0 +1,10451 @@ + psi m1 m2 real(Ai) imag(Ai) real(Bi) imag(Bi) real(Ci) imag(Ci) real(Di) imag(Di) real(Ei) imag(Ei) real(Hi) imag(Hi) + 9.99999978E-03 -4 -4 1.53034448E+03 0.00000000E+00 0.00000000E+00 5.46683289E+02 1.31073630E+00 2.68199585E+02 1.97254883E+02 0.00000000E+00 3.25231247E+01 -4.98163968E-01 7.94882031E+04 0.00000000E+00 + 9.99999978E-03 -4 -3 7.95266571E+01 8.21601774E-04 -1.79691793E-04 6.20876265E+00 -1.61386728E-01 -4.49731641E+03 -8.49028587E+00 3.04707210E-05 -2.15340771E+03 1.22419536E-01 -1.32670276E+03 -1.09824486E+01 + 9.99999978E-03 -4 -2 6.53283000E-01 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4.51522972E-03 -6.66718864E+00 -3.79097137E+01 -1.35003438E+05 6.04121045E+03 + 9.90000010E-01 4 3 -1.60067062E+02 1.86489951E-02 2.59487145E-02 2.21130951E+02 3.36232567E+01 2.07381714E+03 -3.02332489E+02 4.12194021E-02 5.76048462E+02 5.12726517E+01 7.38715156E+04 -4.83784814E+03 + 9.90000010E-01 4 4 3.59946136E+02 0.00000000E+00 -0.00000000E+00 -5.02725525E+02 -4.17905540E+01 -1.08198438E+04 7.02395203E+02 0.00000000E+00 1.53711797E+04 -5.76816750E+01 5.91554562E+05 0.00000000E+00 + diff --git a/src/DCON/validate/imats.xlsx b/src/DCON/validate/imats.xlsx new file mode 100644 index 000000000..90cd5f74c --- /dev/null +++ b/src/DCON/validate/imats.xlsx @@ -0,0 +1,10455 @@ + DCON ideal energy matrices + + mpsi = 128 mpert = 9 + + psi m1 m2 real(Ai) imag(Ai) real(Bi) imag(Bi) real(Ci) imag(Ci) real(Di) imag(Di) real(Ei) imag(Ei) real(Hi) imag(Hi) + 9.99999978E-03 -4 -4 1.53034448E+03 0.00000000E+00 0.00000000E+00 5.46683289E+02 1.31073630E+00 2.68199585E+02 1.97254883E+02 0.00000000E+00 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Ascii profiles. columns: psi_n, ni(m^-3), ne(m^-3), ti(eV), te(eV), omega_EXB(rad/s) + peq_file = "gpec_xclebsch_n1.out" ! Ascii displacement. columns: psi_n, m, real(xi^psi), imag(xi^psi), real(xi^alpha), imag(xi^alpha) + idconfile = "euler.bin" ! DCON output + data_dir = "" ! Location of pre-formed fnml matrix used in rlar and clar methods (check release package) + + mi = 2 ! Main ion mass (u) + zi = 1 ! Main ion charge (e) + mimp = 12 ! Impurity mass (u) + zimp = 6 ! Impurity charge (e) + nl = 4 ! Bounce harmonic range (-nl to nl) + electron = .false. ! Calculate all results for electrons INSTEAD OF ions (only one species per PENTRC run) + nutype = "harmonic" ! Collision operator: "zero", "krook", "harmonic" + f0type = "maxwellian" ! Distribution function: "maxwellian" + jac_in = "hamada" ! Jacobian of peq_file harmonic decomposition. 'default' uses jac_type of idconfile. + jsurf_in=0 ! True(1) if peq_file is area weighted + tmag_in=1 ! True(1) if peq_file has toroidal angle defined by jac_in. False(0) if machine angle. +/ +&PENT_CONTROL + wefac = 1 ! Artificial factor applied to omega_EXB + wdfac = 1 ! Artificial factor applied to omega_b + wpfac = 1 ! Artificial factor applied to omega_phi + nufac = 1 ! Artificial factor applied to collision operator + divxfac = 1 ! Artificial factor applied to div xi_perp + + force_xialpha = .false. ! Calculates tangential displacement from radial displacement and toroidal force balance (overwrites peq_file values) + + atol_xlmda = 1e-9 ! Absolute tolerance in energy and pitch integration + rtol_xlmda = 1e-6 ! Relative tolerance in energy and pitch integration + atol_psi = 1e-4 ! Absolute tolerance in psi_n integration + rtol_psi = 1e-4 ! Relative tolerance in psi_n integration + ntheta = 128 ! Poloidal angle grid for bounce integration + nlmda = 128 ! Pitch grid for omega_D, oemga_b, dJdJ + + xmax = 128 ! Upper bound of energy integral (x=E/T) + ximag = 0.0 ! Step off real energy axis (use to avoid zero collisionality singularities) + psilims = 0 1 ! Range in psi_n +/ +&PENT_OUTPUT + moment = "pressure" ! Use 'pressure' for torque and particle transport, 'heat' for heat transport + + fgar_flag = .true. ! Full general aspect ratio calculation + tgar_flag = .true. ! Trapped general aspect ratio calculation + pgar_flag = .false. ! Passing general aspect ratio calculation + clar_flag = .false. ! Circular large aspect ratio calculation + rlar_flag = .false. ! Reduced large aspect ratio calculation + fcgl_flag = .false. ! Fluid Chew-Goldberger-Low limit + wxyz_flag = .false. ! Euler-lagrange equation matrix output at psiout + fkmm_flag = .false. ! Full euler-lagrange matrix calculation (t,p also available) + ftmm_flag = .false. ! Full torque mxm matrix calculation (t,p also available) + fwmm_flag = .false. ! Full dW mxm matrix calculation (t,p also available) + + xlmda_out = .false. ! Output energy and pitch integrands on psi_out + theta_out = .false. ! Output bounce integrands on psi_out + psi_out = 0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0 ! 10 surfaces for energy, pitch, and poloidal outputs + + dynamic_grid = .true. ! Calculate each requested method using dynamic radial integration controlled by atol_psi and rtol_psi + equil_grid = .false. ! Recalculate each requested method on equilibrium grid from DCON + input_grid = .false. ! Recalculate each requested method on input displacements' grid + + verbose = .true. ! Print progress to terminal + clean = .false. ! Remove pentrc_*.out before running +/ +&PENT_ADMIN + fnml_flag = .false. ! Special function matrix [JKP PRL 2009] + ellip_flag = .false. ! Elliptic integral functions + diag_flag = .false. ! Diagnostic module + indebug = .false. ! Debug input file parsing and manipulations + tdebug = .false. ! Debug psi integration + lambdadebug = .false. ! Debug pitch integration + xdebug = .false. ! Debug energy integration +/ + diff --git a/src/DCON/validate/psi_in.bin b/src/DCON/validate/psi_in.bin new file mode 100644 index 000000000..abc793400 Binary files /dev/null and b/src/DCON/validate/psi_in.bin differ diff --git a/src/DCON/validate/read_matrix.ipynb b/src/DCON/validate/read_matrix.ipynb new file mode 100644 index 000000000..9f242a385 --- /dev/null +++ b/src/DCON/validate/read_matrix.ipynb @@ -0,0 +1,919 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "a96ad3ad", + "metadata": {}, + "outputs": [], + "source": [ + "conda install scipy" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4a435f5f", + "metadata": {}, + "outputs": [], + "source": [ + "#!/usr/bin/env python3\n", + "# -*- coding: utf-8 -*-\n", + "\n", + "from scipy.linalg.blas import zhemm\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import warnings\n", + "import os\n", + "from scipy.interpolate import CubicSpline\n", + "from scipy.integrate import solve_ivp\n", + "from scipy.linalg import cho_factor, cho_solve, lu_factor, lu_solve\n", + "import time\n", + "\n", + "m_high = 1\n", + "m_low = -4\n", + "mdim = m_high - m_low + 1\n", + "ndim = 1\n", + "matrix_size = mdim * ndim # 'size' 변수명 변경\n", + "\"\"\"\n", + "... (주석) ...\n", + "- F_bar, K_bar, G 행렬과 q 프로파일을 바이너리 파일에서 읽어 보간.\n", + "- 최종 F, K 행렬은 히트맵 플롯 시점에 필요한 샘플에 대해서만 즉석에서 계산하여 성능 저하를 방지.\n", + "\"\"\"\n", + "import numpy as np\n", + "import struct\n", + "import os\n", + "import matplotlib.pyplot as plt\n", + "from scipy.interpolate import CubicSpline\n", + "\n", + "# ─────────────────────────────────────────────────────────────\n", + "# 1 & 2. 파일 읽기 관련 함수 (이전과 동일)\n", + "# ─────────────────────────────────────────────────────────────\n", + "\n", + "def get_matrix_map(m, kind, n_blocks, mband_k=None, path=None):\n", + " if kind in ('F', 'G'):\n", + " for mb_test in range(m):\n", + " count = sum(len(range(j, min(m, j + mb_test + 1))) for j in range(m))\n", + " if count == n_blocks:\n", + " mband = mb_test\n", + " print(f\"[{os.path.basename(path)}] mband = {mband} (으)로 추정 (F/G).\")\n", + " d = {k+1: (i,j) for k, (j,i) in enumerate(((j,i) for j in range(m) for i in range(j, min(m, j+mband+1))))}\n", + " return d\n", + " raise ValueError(f\"F/G 행렬의 mband를 추정할 수 없습니다. (m={m}, n_blocks={n_blocks})\")\n", + " elif kind == 'K':\n", + " if mband_k is None: raise ValueError(\"K 행렬을 처리하려면 mband_k 값을 지정해야 합니다.\")\n", + " print(f\"[{os.path.basename(path)}] mband = {mband_k} (지정된 값) 사용 (K).\")\n", + " valid_element_count = sum(len(range(max(0, j-mband_k), min(m, j+mband_k+1))) for j in range(m))\n", + " if n_blocks > valid_element_count:\n", + " print(f\" > 경고: 파일에 기록된 블록 수({n_blocks})가 실제 유효한 원소 수({valid_element_count})보다 많습니다.\")\n", + " d = {}\n", + " k = 0\n", + " for j in range(m):\n", + " for i in range(max(0, j - mband_k), min(m, j + mband_k + 1)):\n", + " k += 1\n", + " d[k] = (i, j)\n", + " return d\n", + " else: raise ValueError(\"kind는 'F', 'G', 'K' 중 하나여야 합니다.\")\n", + "\n", + "def read_bin(path, m, kind, mband_k=None):\n", + " all_records = []\n", + " with open(path, 'rb') as f:\n", + " while True:\n", + " header_bytes = f.read(4)\n", + " if not header_bytes: break\n", + " record_len = struct.unpack(' 0:\n", + " all_records.append(np.frombuffer(f.read(record_len), dtype=np.float32))\n", + " else:\n", + " all_records.append(None)\n", + " f.read(4)\n", + " element_blocks = []\n", + " current_block = []\n", + " for rec in all_records:\n", + " if rec is not None: current_block.append(rec)\n", + " else:\n", + " if current_block: element_blocks.append(np.array(current_block))\n", + " current_block = []\n", + " if not element_blocks: raise ValueError(f\"파일에서 데이터 블록을 찾지 못했습니다: {path}\")\n", + "\n", + " n_blocks, n_psi = len(element_blocks), element_blocks[0].shape[0]\n", + " psi, q_profile = element_blocks[0][:, 0], element_blocks[0][:, 1]\n", + " idx_map = get_matrix_map(m, kind, n_blocks, mband_k=mband_k, path=path)\n", + " \n", + " mats = np.zeros((n_psi, m, m), dtype=np.complex128)\n", + " for k, (i, j) in idx_map.items():\n", + " if k > n_blocks: continue\n", + " mats[:, i, j] = element_blocks[k - 1][:, 2] + 1j * element_blocks[k - 1][:, 3]\n", + "\n", + " if kind in ('G'):\n", + " il, jl = np.tril_indices(m, -1)\n", + " mats[:, jl, il] = np.conj(mats[:, il, jl])\n", + " \n", + " return psi, q_profile, mats\n", + "\n", + "# ────────────────────────────────────────\n", + "# 3. dedup, make_interp, plot_q_profile (이전과 동일)\n", + "# ────────────────────────────────────────\n", + "def dedup(psi, q, stacks):\n", + " uniq_psi, idx = np.unique(psi, return_index=True)\n", + " return uniq_psi, q[idx], {k: v[idx] for k, v in stacks.items()}\n", + "\n", + "def make_interp(psi, mat_stack):\n", + " cs_r = CubicSpline(psi, mat_stack.real, axis=0)\n", + " cs_i = CubicSpline(psi, mat_stack.imag, axis=0)\n", + " return lambda x, cr=cs_r, ci=cs_i: cr(x) + 1j * ci(x)\n", + "\n", + "def plot_q_profile(psi, q, q_interpolant):\n", + " fig, ax = plt.subplots(figsize=(8, 6))\n", + " ax.plot(psi, q, 'o', label='Original Data Points', markersize=5)\n", + " psi_fine = np.linspace(psi.min(), psi.max(), 300)\n", + " ax.plot(psi_fine, q_interpolant(psi_fine), '-', label='Cubic Spline Interpolation')\n", + " ax.set(title='Safety Factor (q) Profile', xlabel='Normalized Poloidal Flux (ψ)', ylabel='Safety Factor (q)')\n", + " ax.legend(); ax.grid(True, linestyle='--', alpha=0.6)\n", + " plt.show()\n", + "\n", + "# ────────────────────────────────────────\n", + "# *** REVISED *** 4. 최종 행렬의 히트맵을 그리는 함수\n", + "# ────────────────────────────────────────\n", + "def plot_final_heatmaps(psi_coords, M, q_interp, F_bar_interp, G_interp, K_bar_interp, nsamp=4):\n", + " \"\"\"\n", + " 보간 함수들을 받아, 플롯에 필요한 psi 샘플에 대해서만 최종 행렬을 계산하고 히트맵을 그립니다.\n", + " \"\"\"\n", + " names = ['F', 'G', 'K']\n", + " samp = np.quantile(psi_coords, np.linspace(.05, .95, nsamp))\n", + " \n", + " fig, ax = plt.subplots(len(names), nsamp,\n", + " figsize=(4.5 * nsamp, 4 * len(names)),\n", + " constrained_layout=True, squeeze=False)\n", + " \n", + " I = np.identity(M.shape[0])\n", + "\n", + " for c, p in enumerate(samp):\n", + " # --- 계산은 이 루프 안에서 즉석으로 수행됩니다 ---\n", + " q_val = q_interp(p)\n", + " Q_mat = M - q_val * I\n", + " \n", + " # 각 psi 샘플(p)에 대해 최종 행렬 계산\n", + " final_mats = {\n", + " 'F': Q_mat @ F_bar_interp(p) @ Q_mat,\n", + " 'G': G_interp(p),\n", + " 'K': Q_mat @ K_bar_interp(p)\n", + " }\n", + " # ---------------------------------------------\n", + " \n", + " for r, n in enumerate(names):\n", + " mat = final_mats[n]\n", + " im = ax[r, c].imshow(np.abs(mat), cmap='viridis', origin='upper', aspect='equal')\n", + " ax[r, c].set_title(f'{n}, ψ≈{p:.3f}')\n", + " if r == len(names) - 1: ax[r, c].set_xlabel('j')\n", + " if c == 0: ax[r, c].set_ylabel('i')\n", + " plt.colorbar(im, ax=ax[r, c], label=f'|{n}|')\n", + " \n", + " fig.suptitle('Final F, G, K Heatmaps (Calculated On-the-fly)', y=1.03)\n", + " plt.show()\n", + "\n", + "# ────────────────────────────────────────\n", + "# 5. 메인 스크립트\n", + "# ────────────────────────────────────────" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a0e636b8", + "metadata": {}, + "outputs": [], + "source": [ + "println(\"Starting matrix reading and processing...\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "740e0928", + "metadata": {}, + "outputs": [], + "source": [ + "using LinearAlgebra\n", + "using Plots\n", + "using Interpolations\n", + "using Printf\n", + "\n", + "# Global parameters\n", + "m_high = 1\n", + "m_low = -4\n", + "mdim = m_high - m_low + 1\n", + "ndim = 1\n", + "matrix_size = mdim * ndim # 'size' 변수명 변경\n", + "\n", + "\"\"\"\n", + "DCON matrix binary file reader and analyzer for Julia\n", + "- Reads F_bar, K_bar, G matrices and q profile from binary files\n", + "- Provides interpolation and visualization capabilities\n", + "- Calculates final F, K matrices on-demand for performance\n", + "\"\"\"\n", + "\n", + "# ─────────────────────────────────────────────────────────────\n", + "# 1. Matrix mapping functions\n", + "# ─────────────────────────────────────────────────────────────\n", + "\n", + "\"\"\"\n", + " get_matrix_map(m::Int, kind::String, n_blocks::Int; mband_k=nothing, path=\"\")\n", + "\n", + "Determine matrix element mapping for band storage format\n", + "\"\"\"\n", + "function get_matrix_map(m::Int, kind::String, n_blocks::Int; mband_k=nothing, path=\"\")\n", + " if kind in [\"F\", \"G\"]\n", + " for mb_test in 0:(m-1)\n", + " count = sum(length(j:min(m, j + mb_test)) for j in 1:m)\n", + " if count == n_blocks\n", + " mband = mb_test\n", + " println(\"[$path] mband = $mband (estimated for $kind)\")\n", + " \n", + " # Create index mapping (1-based indexing)\n", + " d = Dict{Int, Tuple{Int,Int}}()\n", + " k = 1\n", + " for j in 1:m\n", + " for i in j:min(m, j + mband)\n", + " d[k] = (i, j)\n", + " k += 1\n", + " end\n", + " end\n", + " return d\n", + " end\n", + " end\n", + " error(\"Cannot estimate mband for $kind matrix (m=$m, n_blocks=$n_blocks)\")\n", + " \n", + " elseif kind == \"K\"\n", + " if mband_k === nothing\n", + " error(\"mband_k must be specified for K matrix\")\n", + " end\n", + " \n", + " println(\"[$path] mband = $mband_k (specified value for K)\")\n", + " \n", + " valid_element_count = sum(length(max(1, j-mband_k):min(m, j+mband_k)) for j in 1:m)\n", + " if n_blocks > valid_element_count\n", + " println(\" Warning: File blocks ($n_blocks) > valid elements ($valid_element_count)\")\n", + " end\n", + " \n", + " d = Dict{Int, Tuple{Int,Int}}()\n", + " k = 1\n", + " for j in 1:m\n", + " for i in max(1, j - mband_k):min(m, j + mband_k)\n", + " d[k] = (i, j)\n", + " k += 1\n", + " end\n", + " end\n", + " return d\n", + " else\n", + " error(\"kind must be 'F', 'G', or 'K'\")\n", + " end\n", + "end\n", + "\n", + "# ─────────────────────────────────────────────────────────────\n", + "# 2. Binary file reading functions\n", + "# ─────────────────────────────────────────────────────────────\n", + "\n", + "\"\"\"\n", + " read_bin(path::String, m::Int, kind::String; mband_k=nothing)\n", + "\n", + "Read DCON matrix binary files with Fortran unformatted structure\n", + "\"\"\"\n", + "function read_bin(path::String, m::Int, kind::String; mband_k=nothing)\n", + " println(\"📖 Reading $kind matrix from: $(basename(path))\")\n", + " \n", + " all_records = []\n", + " \n", + " try\n", + " open(path, \"r\") do f\n", + " while !eof(f)\n", + " # Read Fortran record header (4 bytes)\n", + " if eof(f) break end\n", + " header_bytes = read(f, 4)\n", + " if length(header_bytes) < 4 break end\n", + " \n", + " record_len = reinterpret(Int32, header_bytes)[1]\n", + " \n", + " if record_len > 0\n", + " # Read data\n", + " data_bytes = read(f, record_len)\n", + " if length(data_bytes) == record_len\n", + " # Convert to Float32 array\n", + " data = reinterpret(Float32, data_bytes)\n", + " push!(all_records, data)\n", + " else\n", + " push!(all_records, nothing)\n", + " end\n", + " else\n", + " push!(all_records, nothing)\n", + " end\n", + " \n", + " # Read Fortran record footer (4 bytes)\n", + " if !eof(f)\n", + " read(f, 4)\n", + " end\n", + " end\n", + " end\n", + " catch e\n", + " println(\"❌ Error reading file: $e\")\n", + " return nothing, nothing, nothing\n", + " end\n", + " \n", + " # Process records into blocks\n", + " element_blocks = []\n", + " current_block = []\n", + " \n", + " for rec in all_records\n", + " if rec !== nothing\n", + " push!(current_block, rec)\n", + " else\n", + " if !isempty(current_block)\n", + " # 🔧 FIX: deprecated .' 연산자를 transpose()로 변경\n", + " push!(element_blocks, transpose(hcat(current_block...)))\n", + " current_block = []\n", + " end\n", + " end\n", + " end\n", + " \n", + " # 🔧 FIX: 마지막 블록 처리\n", + " if !isempty(current_block)\n", + " push!(element_blocks, transpose(hcat(current_block...)))\n", + " end\n", + " \n", + " if isempty(element_blocks)\n", + " error(\"No data blocks found in file: $path\")\n", + " end\n", + " \n", + " n_blocks = length(element_blocks)\n", + " n_psi = size(element_blocks[1], 1)\n", + " \n", + " println(\" Found $n_blocks data blocks with $n_psi psi points each\")\n", + " \n", + " # Extract psi and q profile from first block\n", + " psi = element_blocks[1][:, 1]\n", + " q_profile = element_blocks[1][:, 2]\n", + " \n", + " # Get matrix mapping\n", + " idx_map = get_matrix_map(m, kind, n_blocks; mband_k=mband_k, path=basename(path))\n", + " \n", + " # Initialize matrix array\n", + " mats = zeros(ComplexF64, n_psi, m, m)\n", + " \n", + " # Fill matrix elements\n", + " for (k, (i, j)) in idx_map\n", + " if k <= n_blocks && k <= length(element_blocks)\n", + " # FIX: 안전한 배열 인덱싱\n", + " block = element_blocks[k]\n", + " if size(block, 2) >= 4\n", + " real_part = block[:, 3]\n", + " imag_part = block[:, 4]\n", + " mats[:, i, j] = complex.(real_part, imag_part)\n", + " end\n", + " end\n", + " end\n", + " \n", + " # Apply symmetry for Hermitian matrices\n", + " if kind == \"G\"\n", + " println(\" Applying Hermitian symmetry\")\n", + " for ipsi in 1:n_psi\n", + " for i in 1:m\n", + " for j in 1:(i-1)\n", + " mats[ipsi, j, i] = conj(mats[ipsi, i, j])\n", + " end\n", + " end\n", + " end\n", + " end\n", + " \n", + " println(\"✅ Successfully read $kind matrix ($(size(mats)))\")\n", + " \n", + " return psi, q_profile, mats\n", + "end\n", + "\n", + "# ─────────────────────────────────────────────────────────────\n", + "# 3. Data processing functions\n", + "# ─────────────────────────────────────────────────────────────\n", + "\n", + "\"\"\"\n", + " dedup(psi, q, stacks)\n", + "\n", + "Remove duplicate psi values and corresponding data\n", + "\"\"\"\n", + "function dedup(psi, q, stacks)\n", + " # Find unique psi values\n", + " unique_psi = unique(psi)\n", + " unique_indices = [findfirst(==(p), psi) for p in unique_psi]\n", + " \n", + " deduped_q = q[unique_indices]\n", + " deduped_stacks = Dict(k => v[unique_indices, :, :] for (k, v) in stacks)\n", + " \n", + " return unique_psi, deduped_q, deduped_stacks\n", + "end\n", + "\n", + "\"\"\"\n", + " make_interp(psi, mat_stack)\n", + "\n", + "Create interpolation functions for complex matrix data\n", + "\"\"\"\n", + "function make_interp(psi, mat_stack)\n", + " # Separate real and imaginary parts\n", + " real_parts = real.(mat_stack)\n", + " imag_parts = imag.(mat_stack)\n", + " \n", + " # Create interpolation objects for each matrix element\n", + " m1, m2 = size(mat_stack)[2:3]\n", + " \n", + " interp_real = [linear_interpolation(psi, real_parts[:, i, j]) for i in 1:m1, j in 1:m2]\n", + " interp_imag = [linear_interpolation(psi, imag_parts[:, i, j]) for i in 1:m1, j in 1:m2]\n", + " \n", + " # Return function that evaluates at given psi\n", + " function interpolated_matrix(psi_val)\n", + " result = zeros(ComplexF64, m1, m2)\n", + " for i in 1:m1, j in 1:m2\n", + " real_val = interp_real[i, j](psi_val)\n", + " imag_val = interp_imag[i, j](psi_val)\n", + " result[i, j] = complex(real_val, imag_val)\n", + " end\n", + " return result\n", + " end\n", + " \n", + " return interpolated_matrix\n", + "end\n", + "\n", + "\"\"\"\n", + " plot_q_profile(psi, q, q_interpolant)\n", + "\n", + "Plot safety factor profile with interpolation\n", + "\"\"\"\n", + "function plot_q_profile(psi, q, q_interpolant)\n", + " psi_fine = range(minimum(psi), maximum(psi), length=300)\n", + " q_fine = [q_interpolant(p) for p in psi_fine]\n", + " \n", + " p = plot(psi, q, seriestype=:scatter, label=\"Original Data Points\", \n", + " markersize=5, xlabel=\"Normalized Poloidal Flux (ψ)\", \n", + " ylabel=\"Safety Factor (q)\", title=\"Safety Factor (q) Profile\")\n", + " \n", + " plot!(p, psi_fine, q_fine, label=\"Linear Interpolation\", linewidth=2)\n", + " plot!(p, grid=true, gridwidth=1, gridstyle=:dash, gridalpha=0.6)\n", + " \n", + " display(p)\n", + " return p\n", + "end\n", + "\n", + "# ─────────────────────────────────────────────────────────────\n", + "# 4. Final matrix calculation and visualization\n", + "# ─────────────────────────────────────────────────────────────\n", + "\n", + "\"\"\"\n", + " plot_final_heatmaps(psi_coords, M, q_interp, F_bar_interp, G_interp, K_bar_interp; nsamp=4)\n", + "\n", + "Plot heatmaps of final F, G, K matrices calculated on-demand\n", + "\"\"\"\n", + "function plot_final_heatmaps(psi_coords, M, q_interp, F_bar_interp, G_interp, K_bar_interp; nsamp=4)\n", + " println(\"🎨 Plotting final matrix heatmaps...\")\n", + " \n", + " names = [\"F\", \"G\", \"K\"]\n", + " \n", + " # Sample psi values\n", + " quantiles = range(0.05, 0.95, length=nsamp)\n", + " samp = [quantile(psi_coords, q) for q in quantiles]\n", + " \n", + " # Create identity matrix\n", + " I_mat = Matrix{Float64}(LinearAlgebra.I, size(M)) # 🔧 FIX: 변수명 변경\n", + " \n", + " # Create subplot array\n", + " plots_array = []\n", + " \n", + " for (c, p) in enumerate(samp)\n", + " println(\" Computing matrices for ψ ≈ $(round(p, digits=3))\")\n", + " \n", + " # Calculate Q matrix\n", + " q_val = q_interp(p)\n", + " Q_mat = M - q_val * I_mat\n", + " \n", + " # Calculate final matrices on-demand\n", + " final_mats = Dict(\n", + " \"F\" => Q_mat * F_bar_interp(p) * Q_mat,\n", + " \"G\" => G_interp(p),\n", + " \"K\" => Q_mat * K_bar_interp(p)\n", + " )\n", + " \n", + " # Create heatmaps for each matrix\n", + " for (r, name) in enumerate(names)\n", + " mat = final_mats[name]\n", + " \n", + " p_heat = heatmap(abs.(mat), \n", + " title=\"$name, ψ≈$(round(p, digits=3))\",\n", + " color=:viridis,\n", + " aspect_ratio=:equal,\n", + " xlabel=\"j\", ylabel=\"i\")\n", + " \n", + " push!(plots_array, p_heat)\n", + " end\n", + " end\n", + " \n", + " # Combine plots\n", + " layout = (length(names), nsamp)\n", + " combined_plot = plot(plots_array..., layout=layout, size=(300*nsamp, 250*length(names)))\n", + " plot!(combined_plot, plot_title=\"Final F, G, K Heatmaps (Calculated On-the-fly)\")\n", + " \n", + " display(combined_plot)\n", + " return combined_plot\n", + "end\n", + "\n", + "# ─────────────────────────────────────────────────────────────\n", + "# 5. Main analysis function\n", + "# ─────────────────────────────────────────────────────────────\n", + "\n", + "\"\"\"\n", + " analyze_dcon_matrices(; m=6, mband_k=2, files=[\"fmat.bin\", \"gmat.bin\", \"kmat.bin\"])\n", + "\n", + "Main function to read and analyze DCON matrix files\n", + "\"\"\"\n", + "function analyze_dcon_matrices(; m=6, mband_k=2, files=[\"fmat.bin\", \"gmat.bin\", \"kmat.bin\"])\n", + " println(\"🔍 DCON Matrix Analysis\")\n", + " println(\"=\"^50)\n", + " \n", + " # Read matrix files\n", + " data = Dict()\n", + " kinds = [\"F\", \"G\", \"K\"]\n", + " \n", + " for (file, kind) in zip(files, kinds)\n", + " if isfile(file)\n", + " if kind == \"K\"\n", + " psi, q, mats = read_bin(file, m, kind; mband_k=mband_k)\n", + " else\n", + " psi, q, mats = read_bin(file, m, kind)\n", + " end\n", + " \n", + " if psi !== nothing\n", + " data[kind] = Dict(\"psi\" => psi, \"q\" => q, \"matrices\" => mats)\n", + " end\n", + " else\n", + " println(\"⚠️ File $file not found\")\n", + " end\n", + " end\n", + " \n", + " if isempty(data)\n", + " println(\"❌ No valid data files found\")\n", + " return nothing\n", + " end\n", + " \n", + " # Use first available dataset for psi coordinates\n", + " first_key = first(keys(data))\n", + " psi_coords = data[first_key][\"psi\"]\n", + " q_profile = data[first_key][\"q\"]\n", + " \n", + " println(\"\\n📊 Data Summary:\")\n", + " println(\" Psi range: [$(minimum(psi_coords)), $(maximum(psi_coords))]\")\n", + " println(\" Number of psi points: $(length(psi_coords))\")\n", + " println(\" Available matrices: $(collect(keys(data)))\")\n", + " \n", + " # Remove duplicates\n", + " matrix_stacks = Dict(k => v[\"matrices\"] for (k, v) in data)\n", + " psi_unique, q_unique, stacks_unique = dedup(psi_coords, q_profile, matrix_stacks)\n", + " \n", + " println(\" After deduplication: $(length(psi_unique)) unique psi points\")\n", + " \n", + " # Create interpolation functions\n", + " interpolants = Dict()\n", + " for (k, mats) in stacks_unique\n", + " interpolants[k] = make_interp(psi_unique, mats)\n", + " println(\" ✅ Created interpolant for $k matrix\")\n", + " end\n", + " \n", + " # Create q profile interpolation\n", + " q_interp = linear_interpolation(psi_unique, q_unique)\n", + " \n", + " # Plot q profile\n", + " plot_q_profile(psi_unique, q_unique, q_interp)\n", + " \n", + " # Create mode number matrix M\n", + " mode_numbers = collect(m_low:m_high)\n", + " M = diagm(mode_numbers)\n", + " println(\"\\n🔢 Mode number matrix M:\")\n", + " println(\" Mode range: $m_low to $m_high\")\n", + " println(\" Matrix size: $(size(M))\")\n", + " \n", + " # Plot final matrices if we have the required data\n", + " if haskey(interpolants, \"F\") && haskey(interpolants, \"G\") && haskey(interpolants, \"K\")\n", + " plot_final_heatmaps(psi_unique, M, q_interp, \n", + " interpolants[\"F\"], interpolants[\"G\"], interpolants[\"K\"])\n", + " else\n", + " println(\"⚠️ Cannot create final plots - missing some matrix types\")\n", + " println(\" Available: $(collect(keys(interpolants)))\")\n", + " end\n", + " \n", + " # Return results\n", + " return Dict(\n", + " \"psi\" => psi_unique,\n", + " \"q\" => q_unique,\n", + " \"interpolants\" => interpolants,\n", + " \"q_interp\" => q_interp,\n", + " \"M\" => M,\n", + " \"raw_data\" => data\n", + " )\n", + "end\n", + "\n", + "\"\"\"\n", + " test_matrix_reading()\n", + "\n", + "Quick test function for matrix reading\n", + "\"\"\"\n", + "function test_matrix_reading()\n", + " println(\"🧪 Testing DCON matrix reading...\")\n", + " \n", + " # Test with common parameters\n", + " results = analyze_dcon_matrices(m=6, mband_k=2)\n", + " \n", + " if results !== nothing\n", + " println(\"✅ Test completed successfully!\")\n", + " return results\n", + " else\n", + " println(\"❌ Test failed - check file availability\")\n", + " return nothing\n", + " end\n", + "end\n", + "\n", + "# Export main functions\n", + "export analyze_dcon_matrices, test_matrix_reading, read_bin, plot_q_profile\n", + "export get_matrix_map, dedup, make_interp, plot_final_heatmaps\n", + "\n", + "println(\"📦 DCON Matrix Analysis Module Loaded\")\n", + "println(\"Usage: results = analyze_dcon_matrices() or test_matrix_reading()\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "84a61707", + "metadata": {}, + "outputs": [], + "source": [ + "# ═══════════════════════════════════════════════════════════════\n", + "# 📖 DCON Matrix Reader 사용방법 (Usage Guide)\n", + "# ═══════════════════════════════════════════════════════════════\n", + "\n", + "println(\"🚀 DCON Matrix Reader 사용방법\")\n", + "println(\"=\"^60)\n", + "\n", + "println(\"\\n1️⃣ 기본 사용법 (Basic Usage):\")\n", + "println(\" # 모든 행렬 파일 자동 분석\")\n", + "println(\" results = analyze_dcon_matrices()\")\n", + "println(\" \")\n", + "println(\" # 파라미터 조정\")\n", + "println(\" results = analyze_dcon_matrices(m=6, mband_k=2)\")\n", + "\n", + "println(\"\\n2️⃣ 단일 파일 읽기 (Single File Reading):\")\n", + "println(\" # F 행렬 읽기\")\n", + "println(\" psi, q, F_matrices = read_bin(\\\"fmat.bin\\\", 6, \\\"F\\\")\")\n", + "println(\" \")\n", + "println(\" # K 행렬 읽기 (mband_k 필수)\")\n", + "println(\" psi, q, K_matrices = read_bin(\\\"kmat.bin\\\", 6, \\\"K\\\"; mband_k=2)\")\n", + "\n", + "println(\"\\n3️⃣ 개별 기능 사용 (Individual Functions):\")\n", + "println(\" # q 프로파일 플롯\")\n", + "println(\" plot_q_profile(psi, q, q_interpolant)\")\n", + "println(\" \")\n", + "println(\" # 히트맵 플롯\")\n", + "println(\" plot_final_heatmaps(psi, M, q_interp, F_interp, G_interp, K_interp)\")\n", + "\n", + "println(\"\\n4️⃣ 커스터마이징 (Customization):\")\n", + "println(\" # 특정 파일들만 분석\")\n", + "println(\" files = [\\\"fmat.bin\\\", \\\"gmat.bin\\\"]\")\n", + "println(\" results = analyze_dcon_matrices(files=files)\")\n", + "println(\" \")\n", + "println(\" # 샘플링 수 조정\")\n", + "println(\" plot_final_heatmaps(...; nsamp=6)\")\n", + "\n", + "println(\"\\n5️⃣ 반환값 활용 (Using Results):\")\n", + "println(\" results = analyze_dcon_matrices()\")\n", + "println(\" psi = results[\\\"psi\\\"] # ψ 좌표\")\n", + "println(\" q = results[\\\"q\\\"] # q 프로파일\")\n", + "println(\" interpolants = results[\\\"interpolants\\\"] # 보간 함수들\")\n", + "println(\" q_interp = results[\\\"q_interp\\\"] # q 보간 함수\")\n", + "println(\" M = results[\\\"M\\\"] # 모드 번호 행렬\")\n", + "\n", + "println(\"\\n6️⃣ 빠른 테스트 (Quick Test):\")\n", + "println(\" test_matrix_reading()\")\n", + "\n", + "println(\"\\n📋 파일 요구사항 (File Requirements):\")\n", + "println(\" • fmat.bin, gmat.bin, kmat.bin\")\n", + "println(\" • Fortran unformatted binary format\")\n", + "println(\" • 현재 작업 디렉토리에 위치\")\n", + "\n", + "println(\"\\n⚙️ 파라미터 설명 (Parameters):\")\n", + "println(\" • m: 행렬 크기 (기본값: 6)\")\n", + "println(\" • mband_k: K 행렬의 밴드폭 (기본값: 2)\")\n", + "println(\" • nsamp: 히트맵 샘플 수 (기본값: 4)\")\n", + "\n", + "println(\"\\n🎯 예제 실행 (Example Execution):\")\n", + "println(\" # 현재 디렉토리에 바이너리 파일이 있다면:\")\n", + "println(\" results = test_matrix_reading()\")\n", + "println(\" \")\n", + "println(\" # 결과 확인:\")\n", + "println(\" if results !== nothing\")\n", + "println(\" println(\\\"성공! 데이터 포인트 수: \\\", length(results[\\\"psi\\\"]))\")\n", + "println(\" end\")\n", + "\n", + "println(\"\\n\" * \"=\"^60)\n", + "println(\"🏁 Ready to analyze DCON matrices!\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9179d53b", + "metadata": {}, + "outputs": [], + "source": [ + "# ═══════════════════════════════════════════════════════════════\n", + "# 🚀 실제 실행 예제 (Actual Execution Examples)\n", + "# ═══════════════════════════════════════════════════════════════\n", + "\n", + "println(\"🔥 DCON Matrix Reader - 실제 실행 예제\")\n", + "println(\"=\"^60)\n", + "\n", + "# 1. 기본 테스트 실행\n", + "println(\"\\n1️⃣ 기본 테스트 실행 중...\")\n", + "try\n", + " results = test_matrix_reading()\n", + " \n", + " if results !== nothing\n", + " println(\"✅ 성공! 다음 데이터를 읽었습니다:\")\n", + " println(\" - Psi 포인트 수: \", length(results[\"psi\"]))\n", + " println(\" - 사용 가능한 행렬들: \", collect(keys(results[\"interpolants\"])))\n", + " println(\" - Psi 범위: [\", minimum(results[\"psi\"]), \", \", maximum(results[\"psi\"]), \"]\")\n", + " else\n", + " println(\"❌ 테스트 실패 - 바이너리 파일을 확인하세요\")\n", + " end\n", + "catch e\n", + " println(\"❌ 오류 발생: \", e)\n", + " println(\"💡 해결 방법:\")\n", + " println(\" 1. fmat.bin, gmat.bin, kmat.bin 파일이 현재 디렉토리에 있는지 확인\")\n", + " println(\" 2. 파일들이 올바른 Fortran 바이너리 형식인지 확인\")\n", + " println(\" 3. 파일 접근 권한 확인\")\n", + "end\n", + "\n", + "println(\"\\n\" * \"=\"^60)\n", + "\n", + "# 2. 개별 파일 읽기 예제\n", + "println(\"\\n2️⃣ 개별 파일 읽기 예제:\")\n", + "\n", + "# F 행렬 읽기 시도\n", + "if isfile(\"fmat.bin\")\n", + " println(\"📖 F 행렬 읽기 중...\")\n", + " try\n", + " psi_f, q_f, mats_f = read_bin(\"fmat.bin\", 6, \"F\")\n", + " if psi_f !== nothing\n", + " println(\"✅ F 행렬 성공적으로 읽음 - 크기: \", size(mats_f))\n", + " end\n", + " catch e\n", + " println(\"❌ F 행렬 읽기 실패: \", e)\n", + " end\n", + "else\n", + " println(\"⚠️ fmat.bin 파일이 없습니다\")\n", + "end\n", + "\n", + "# G 행렬 읽기 시도\n", + "if isfile(\"gmat.bin\")\n", + " println(\"📖 G 행렬 읽기 중...\")\n", + " try\n", + " psi_g, q_g, mats_g = read_bin(\"gmat.bin\", 6, \"G\")\n", + " if psi_g !== nothing\n", + " println(\"✅ G 행렬 성공적으로 읽음 - 크기: \", size(mats_g))\n", + " end\n", + " catch e\n", + " println(\"❌ G 행렬 읽기 실패: \", e)\n", + " end\n", + "else\n", + " println(\"⚠️ gmat.bin 파일이 없습니다\")\n", + "end\n", + "\n", + "# K 행렬 읽기 시도\n", + "if isfile(\"kmat.bin\")\n", + " println(\"📖 K 행렬 읽기 중...\")\n", + " try\n", + " psi_k, q_k, mats_k = read_bin(\"kmat.bin\", 6, \"K\"; mband_k=2)\n", + " if psi_k !== nothing\n", + " println(\"✅ K 행렬 성공적으로 읽음 - 크기: \", size(mats_k))\n", + " end\n", + " catch e\n", + " println(\"❌ K 행렬 읽기 실패: \", e)\n", + " end\n", + "else\n", + " println(\"⚠️ kmat.bin 파일이 없습니다\")\n", + "end\n", + "\n", + "println(\"\\n\" * \"=\"^60)\n", + "\n", + "# 3. 파라미터 조정 예제\n", + "println(\"\\n3️⃣ 파라미터 조정 예제:\")\n", + "\n", + "# 다른 행렬 크기로 시도\n", + "println(\"📊 다른 파라미터로 분석 시도...\")\n", + "try\n", + " # 더 작은 행렬 크기로 시도\n", + " results_small = analyze_dcon_matrices(m=4, mband_k=1)\n", + " if results_small !== nothing\n", + " println(\"✅ m=4, mband_k=1로 성공\")\n", + " end\n", + "catch e\n", + " println(\"❌ 파라미터 조정 실패: \", e)\n", + "end\n", + "\n", + "try\n", + " # 더 큰 행렬 크기로 시도\n", + " results_large = analyze_dcon_matrices(m=8, mband_k=3)\n", + " if results_large !== nothing\n", + " println(\"✅ m=8, mband_k=3으로 성공\")\n", + " end\n", + "catch e\n", + " println(\"❌ 파라미터 조정 실패: \", e)\n", + "end\n", + "\n", + "println(\"\\n\" * \"=\"^60)\n", + "\n", + "# 4. 결과 활용 예제\n", + "println(\"\\n4️⃣ 결과 활용 예제:\")\n", + "\n", + "try\n", + " # 전체 분석 실행\n", + " full_results = analyze_dcon_matrices()\n", + " \n", + " if full_results !== nothing\n", + " println(\"🎯 분석 완료! 결과 활용 예제:\")\n", + " \n", + " # 특정 psi 값에서 q 계산\n", + " psi_test = 0.5\n", + " if haskey(full_results, \"q_interp\")\n", + " q_at_test = full_results[\"q_interp\"](psi_test)\n", + " println(\" ψ = $psi_test 에서 q = $q_at_test\")\n", + " end\n", + " \n", + " # 특정 psi에서 행렬 계산\n", + " if haskey(full_results[\"interpolants\"], \"F\")\n", + " F_at_test = full_results[\"interpolants\"][\"F\"](psi_test)\n", + " println(\" ψ = $psi_test 에서 F 행렬 크기: \", size(F_at_test))\n", + " println(\" F 행렬 최대값: \", maximum(abs.(F_at_test)))\n", + " end\n", + " \n", + " # 모드 번호 정보\n", + " if haskey(full_results, \"M\")\n", + " M = full_results[\"M\"]\n", + " println(\" 모드 번호 행렬 대각선: \", diag(M))\n", + " end\n", + " \n", + " println(\"✅ 모든 분석이 성공적으로 완료되었습니다!\")\n", + " \n", + " else\n", + " println(\"❌ 전체 분석 실패\")\n", + " end\n", + " \n", + "catch e\n", + " println(\"❌ 결과 활용 중 오류: \", e)\n", + "end\n", + "\n", + "println(\"\\n\" * \"=\"^60)\n", + "\n", + "# 5. 파일 상태 체크\n", + "println(\"\\n5️⃣ 파일 상태 체크:\")\n", + "files_to_check = [\"fmat.bin\", \"gmat.bin\", \"kmat.bin\"]\n", + "\n", + "for file in files_to_check\n", + " if isfile(file)\n", + " filesize = stat(file).size\n", + " println(\"✅ $file: $(filesize) bytes\")\n", + " else\n", + " println(\"❌ $file: 파일 없음\")\n", + " end\n", + "end\n", + "\n", + "println(\"\\n🎉 실행 완료! 위 결과를 참고하여 필요한 수정을 진행하세요.\")\n", + "println(\"💡 팁: 바이너리 파일이 없다면 DCON 시뮬레이션을 먼저 실행하세요.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3074b173", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.11.6", + "language": "julia", + "name": "julia-1.11" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.11.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/src/DCON/validate/sol.in b/src/DCON/validate/sol.in new file mode 100644 index 000000000..e7aba88fe --- /dev/null +++ b/src/DCON/validate/sol.in @@ -0,0 +1,14 @@ +! Construct Soloviev equilibrium +&SOL_INPUT + mr = 128 ! number of radial grid zones + mz = 128 ! number of axial grid zones + ma = 128 ! number of flux grid zones + e = 1.6 ! elongation + a = 0.33 ! minor radius + r0 = 1.0 ! major radius + q0 = 1.9 ! safety factor at the o-point + p0fac=1 ! scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) + b0fac=1 ! scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) + f0fac=1 ! scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +/ + diff --git a/src/DCON/validate/stride.in b/src/DCON/validate/stride.in new file mode 100755 index 000000000..1a0e240a0 --- /dev/null +++ b/src/DCON/validate/stride.in @@ -0,0 +1,75 @@ +&stride_control + bal_flag=t ! Ideal MHD ballooning criterion for short wavelengths + mat_flag=t ! Construct coefficient matrices for diagnostic purposes + ode_flag=t ! Integrate ODE's for determining stability of internal long-wavelength mode (must be true for GPEC) + vac_flag=t ! Compute plasma, vacuum, and total energies for free-boundary modes + mer_flag=t ! Evaluate the Mercier criterian + + sas_flag=t ! Safety factor (q) limit determined as q_ir+dmlim where q_ir is the equil outermost rational + dmlim=0.2 ! See sas_flag + qlow=1.02 ! Integration initiated at q determined by minimum of qlow and q0 from equil + qhigh=1e3 ! Integration terminated at q limit determined by minimum of qhigh and qa from equil + sing_start=0 ! Start integration at the sing_start'th rational from the axis (psilow) + + nn=1 ! Toroidal mode number + delta_mlow=8 ! Expands lower bound of Fourier harmonics + delta_mhigh=8 ! Expands upper bound of Fourier harmonics + delta_mband=0 ! Integration keeps only this wide a band of solutions along the diagonal in m,m' + mthvac=512 ! Number of points used in splines over poloidal angle at plasma-vacuum interface. Overrides vac.in mth. + thmax0=1 ! Linear multiplier on the automatic choice of theta integration bounds for high-n ideal ballooning stability computation (strictly, -inf to -inf) + + tol_nr=1e-8 ! Relative tolerance of dynamic integration steps away from rationals. + tol_r=1e-8 ! Relative tolerance of dynamic integration steps near rationals + crossover=1e-2 ! Fractional distance from rational q at which tolerance is switched to tol_r + singfac_min=1e-4 ! Fractional distance from rational q at which ideal jump condition is enforced + ucrit=1e4 ! Maximum fraction of solutions allowed before re-normalized + sing_order=6 ! The highest order of power series to be retained near singular surfaces + + use_classic_splines=f ! Use a classical cubic spline instead of tri-diagonal solution for splines with extrapolation boundary conditions + use_notaknot_splines=f ! Use not-a-knot boundary instead of either "extrap" spline extrapolation +/ + +&stride_output + out_ahg2msc=f ! Output deprecated ahg2msc.out files. This is used to communicate with vacuum, but is now done through memory. + + crit_break=t ! Color of the crit curve changes when crossing a singular surface + + ahb_flag=f ! Output normal magnetic field eigenvalues and eigenfunctons at plasma-vacuum interface (must be false for GPEC) + msol_ahb=1 ! Number of eigenfunctions output by ahb_flag=t ? + mthsurf0=1 ! Linear multiplier on number of boundary points used to display surface eigenfunctions for ahgb_flag=t + + bin_euler=f ! **DUMMY VARIABLE** Currently does nothing + euler_stride=1 ! **DUMMY VARIABLE** Currently does nothing + + out_bal1=f ! Ascii output for bal_flag poloidal functions + bin_bal1=f ! Binary output for bal_flag poloidal functions + out_bal2=f ! Ascii output for bal_flag functions + bin_bal2=f ! Binary output for bal_flag functions + + netcdf_out=t ! Replicate ascii stride.out and delta_prime.out information in a netcdf file +/ + +&stride_params + nThreads=32 ! Number of threads used to calculate intervals in parallel + fourfit_metric_parallel=f ! Compute equilibrium metric tensor components in parallel + vac_parallel=t ! Doubles the number of main level threads, creating more threads than processors + + nIntervalsTot=33 ! Number of radial intervals calculated in separately and recombined at end + grid_packing="singularities" ! Choose from "singularities" and "naive" + axis_mid_pt_skew=12.0 ! Skews the distribution of intervals between psilow and psihigh + asymp_at_sing=t ! Use asymptotic expansions at singular surfaces + kill_big_soln_for_ideal_dW=f ! Explicitly remove the big solution + + calc_delta_prime=t ! When false, sing_order=2 is better for speed, (with less accuracy). + calc_dp_with_vac=t ! When vac_flag=t, this will use vacuum edge conditions to calculate delta prime. + big_soln_err_tol=1e-7 ! Threshold error for correct solution to the delta prime bvp. + + integrate_riccati=f ! Use Riccati integration for dW. Cannot calculate delta_prime. + riccati_bounce=t ! Toggle integration mode to control growth of matrix + riccati_match_hamiltonian_evals=f ! + verbose_riccati_output=t ! Creates peig and Psize output files + ric_dt=1e-8 ! Initial step size of Riccati integration + ric_tol=1e-6 ! Relative tolerance of Riccati integration + + verbose_performance_output=f ! Print detailed timing information to terminal +/ diff --git a/src/DCON/validate/sum1.bin b/src/DCON/validate/sum1.bin new file mode 100644 index 000000000..1ce96212c Binary files /dev/null and b/src/DCON/validate/sum1.bin differ diff --git a/src/DCON/validate/vac.in b/src/DCON/validate/vac.in new file mode 100644 index 000000000..68e91e03e --- /dev/null +++ b/src/DCON/validate/vac.in @@ -0,0 +1,99 @@ +! **** Running DCON's input *** +&MODES + mth = 480 + xiin(1:9) = 0 0 0 0 0 0 0 1 0 + lsymz = .TRUE. + leqarcw = 1 + lzio = 0 + lgato = 0 + lrgato = 0 +/ +&DEBUGS + checkd = .FALSE. + check1 = .FALSE. + check2 = .FALSE. + checke = .FALSE. + checks = .FALSE. + wall = .FALSE. + lkplt = 0 + verbose_timer_output = f +/ +&VACDAT + ishape = 6 + aw = 0.05 + bw = 1.5 + cw = 0 + dw = 0.5 + tw = 0.05 + nsing = 500 + epsq = 1e-05 + noutv = 37 + idgt = 6 + idot = 0 + idsk = 0 + delg = 15.01 + delfac = 0.001 + cn0 = 1 +/ +&SHAPE + ipshp = 0 + xpl = 100 + apl = 1 + a = 20 + b = 170 + bpl = 1 + dpl = 0 + r = 1 + abulg = 0.932 + bbulg = 17.0 + tbulg = 0.02 + qain = 2.5 +/ +&DIAGNS + lkdis = .FALSE. + ieig = 0 + iloop = 0 + lpsub = 1 + nloop = 128 + nloopr = 0 + nphil = 3 + nphse = 1 + xofsl = 0 + ntloop = 32 + aloop = 0.01 + bloop = 1.6 + dloop = 0.5 + rloop = 1.0 + deloop = 0.001 + mx = 21 + mz = 21 + nph = 0 + nxlpin = 6 + nzlpin = 11 + epslp = 0.02 + xlpmin = 0.7 + xlpmax = 2.7 + zlpmin = -1.5 + zlpmax = 1.5 + linterior = 2 +/ +&SPRK + nminus = 0 + nplus = 0 + mphi = 16 + lwrt11 = 0 + civ = 0.0 + sp2sgn1 = 1 + sp2sgn2 = 1 + sp2sgn3 = 1 + sp2sgn4 = 1 + sp2sgn5 = 1 + sp3sgn1 = -1 + sp3sgn2 = -1 + sp3sgn3 = -1 + sp3sgn4 = 1 + sp3sgn5 = 1 + lff = 0 + ff = 1.6 + fv = 1.6 1.6 1.6 1.6 1.6 1.0 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 +/ diff --git a/src/Equilibrium/AnalyticEquilibrium.jl b/src/Equilibrium/AnalyticEquilibrium.jl new file mode 100644 index 000000000..fa7a9ad58 --- /dev/null +++ b/src/Equilibrium/AnalyticEquilibrium.jl @@ -0,0 +1,324 @@ +#= +Analytic equilibrium functions that prepare all the necessary equilibrium +input information for a direct or inverse equilibrium construction +=# + +""" + lar_init_conditions(rmin, sigma_type, params) + +Initializes the starting radius and state vector for solving the LAR ODE system. +Also evaluates the initial derivative using the analytic model. + +## Arguments: +- `rmin`: Normalized starting radius (as a fraction of `lar_a`). +- `lar_input`: A `LargeAspectRatioConfig` object containing equilibrium parameters. + +## Returns: +- `r`: Physical radius corresponding to `rmin * lar_a`. +- `y`: Initial state vector of length 5. +""" +function lar_init_conditions(rmin::Float64, lar_input::LargeAspectRatioConfig) + lar_a = lar_input.lar_a + lar_r0 = lar_input.lar_r0 + q0 = lar_input.q0 + + r = rmin * lar_a + y = zeros(5) + + y[1] = r^2 / (lar_r0 * q0) + y[2] = 1.0 + y[3] = y[1] * lar_r0 / 2 + + dy = zeros(5) + lar_der(dy, r, y, lar_input) + + y[5] = dy[5] * r / 4 + + q = r^2 * y[2] / (lar_r0 * y[1]) + y[4] = (q / r)^2 * y[5] / 2 + + return r, y +end + +""" + lar_der(dy, r, y, lar_input) + +Evaluates the spatial derivatives of the LAR (Large Aspect Ratio) equilibrium ODE system +at a given radius `r`, using the current state vector `y` and equilibrium parameters. + +## Arguments: +- `dy`: A preallocated vector where the computed derivatives will be stored (in-place). +- `r`: The radial position at which the derivative is evaluated. +- `y`: The current state vector. +- `lar_input`: A `LargeAspectRatioConfig` object containing equilibrium shaping parameters. + +## Returns: +- 0. The result is stored in-place in `dy`. +""" + +function lar_der(dy::Vector{Float64}, r::Float64, y::Vector{Float64}, lar_input::LargeAspectRatioConfig) + lar_a = lar_input.lar_a + lar_r0 = lar_input.lar_r0 + + q0 = lar_input.q0 + + beta0 = lar_input.beta0 + p00 = beta0 / 2.0 + p_pres = lar_input.p_pres + p_sig = lar_input.p_sig + + sigma_type = lar_input.sigma_type + x = r / lar_a + xfac = 1 - x^2 + pp = -2 * p_pres * p00 * x * xfac^(p_pres - 1) # p' + sigma0 = 2.0 / (q0 * lar_r0) + + sigma = if sigma_type == "wesson" + sigma0 * xfac^p_sig + else + sigma0 / (1 + x^(2 * p_sig))^(1 + 1 / p_sig) + end + + bsq = (y[1] / max(r, eps()))^2 + y[2]^2 # B² + q = r^2 * y[2] / (lar_r0 * max(y[1], eps())) + + dy[1] = -pp/bsq*y[1] + sigma*y[2]*r + dy[2] = -pp/bsq*y[2] - sigma*y[1]/max(r, eps()) + dy[3] = y[1] * lar_r0 / max(r, eps()) + dy[4] = ((q / max(r, eps()))^2) * y[5] / max(r, eps()) + dy[5] = y[2] * (r / max(q, eps()))^2 * (r / lar_r0) * (1 - 2 * (lar_r0 * q / max(y[2], eps()))^2 * pp) + + return 0 +end + +""" + lar_run(lar_input) + +Solves the LAR (Large Aspect Ratio) plasma equilibrium ODE system using analytic profiles +defined by `lar_input`, and returns the full solution table including derived quantities. + +## Arguments: +- `lar_input`: A `LargeAspectRatioConfig` object containing profile and geometric parameters. + +## Returns: + - working on it not yet implemented +""" + +function lar_run(equil_input::EquilibriumConfig, lar_input::LargeAspectRatioConfig) + rmin = 1e-4 + lar_a = lar_input.lar_a + lar_r0 = lar_input.lar_r0 + q0 = lar_input.q0 + beta0 = lar_input.beta0 + sigma_type = lar_input.sigma_type + + p00 = beta0 / 2.0 + lar_input.p_pres = max(lar_input.p_pres, 1.001) + + sigma0 = 2.0 / (q0 * lar_r0) + + ma = lar_input.ma + mtau = lar_input.mtau + + function dydr(du, u, p, r) + lar_input = p + lar_der(du, r, u, lar_input) + end + + r0, y0 = lar_init_conditions(rmin, lar_input) + tspan = (r0, lar_a) + p = lar_input + + prob = ODEProblem(dydr, y0, tspan, p) + sol = solve(prob, Rosenbrock23(autodiff=AutoFiniteDiff()); reltol=1e-6, abstol=1e-8, maxiters=10000) + + r_arr = sol.t + y_mat = hcat(sol.u...)' + steps = length(r_arr) + + temp = zeros(steps, 9) + for i in 1:steps + r = r_arr[i] + y = y_mat[i, :] + x = r / lar_a + xfac = 1 - x^2 + pval = p00 * xfac^lar_input.p_pres + sigma = (sigma_type == "wesson") ? + sigma0 * xfac^lar_input.p_sig : + sigma0 / (1 + x^(2 * lar_input.p_sig))^(1 + 1 / lar_input.p_sig) + q = r^2 * y[2] / (lar_r0 * y[1]) + temp[i, :] = [r; y; pval; sigma; q] + end + + xs_r = temp[:, 1] + fs_r = temp[:, 2:9] + spl = Spl.CubicSpline(xs_r, fs_r, bctype=4) + + dr = lar_a / (ma + 1) + r = 0.0 + psio = temp[end, 4] # ψ_edge + + sq_xs = zeros(ma + 1) + sq_fs = zeros(ma + 1, 3) + r_nodes = zeros(ma + 1) + + for ia in 1:(ma + 1) + r += dr + r_nodes[ia] = r + f, f1 = Spl.spline_eval(spl, r,1) + ψ = f[3] + Bphi = f[2] + pval = f[6] + qval = f[8] + dψdr = f1[3] + r2 = -(f[4] * r / f[8]) / dψdr + sq_xs[ia] = ψ / psio + sq_fs[ia, 1] = lar_r0 * Bphi + sq_fs[ia, 2] = pval + sq_fs[ia, 3] = qval + end + + sq_in = Spl.CubicSpline(sq_xs, sq_fs, bctype=4) + + rzphi_y_nodes = range(0.0, 2π, length=mtau + 1) + rzphi_fs_nodes = zeros(ma + 1, mtau + 1, 2) + + for ia in 1:(ma + 1) + r = r_nodes[ia] + f, f1 = Spl.spline_eval(spl, r, 1) + y4 = f[4] + q = f[8] + dψdr = f1[3] + r2 = -(y4 * r / q) / dψdr + if lar_input.zeroth + r2 = 0.0 + end + + for itau in 1:(mtau + 1) + θ = 2π * (itau - 1) / mtau + cosθ, sinθ = cos(θ), sin(θ) + rfac = r + r2 * cosθ + rzphi_fs_nodes[ia, itau, 1] = lar_r0 + rfac * cosθ + rzphi_fs_nodes[ia, itau, 2] = rfac * sinθ + end + end + + rz_in = Spl.BicubicSpline(r_nodes, collect(rzphi_y_nodes), rzphi_fs_nodes, bctypex=4, bctypey=2) + + return InverseRunInput(equil_input, sq_in, rz_in, lar_r0, 0.0, psio) + +end + + +""" +This is a Julia version of the Fortran code in sol.f, implementing Soloviev's analytical equilibrium. + +## Arguments: +- `mr`: Number of radial grid zones +- `mz`: Number of axial grid zones +- `ma`: Number of flux grid zones +- `e`: Elongation +- `a`: Minor radius +- `r0`: Major radius +- `q0`: Safety factor at the o-point +- `p0fac`: Scales on axis pressure (s*P. beta changes. Phi,q constant) +- `b0fac`: Scales on toroidal field (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) +- `f0fac`: Scales on toroidal field (s*f. bt,q changes. Phi,p,bp constant) + +## Returns: +- `plasma_eq`: PlasmaEquilibrium object +""" +function sol_run( + equil_inputs::EquilibriumConfig, + sol_inputs::SolevevConfig + ) + + mr = sol_inputs.mr + mz = sol_inputs.mz + ma = sol_inputs.ma + e = sol_inputs.e + a = sol_inputs.a + r0 = sol_inputs.r0 + q0 = sol_inputs.q0 + p0fac = sol_inputs.p0fac + b0fac = sol_inputs.b0fac + f0fac = sol_inputs.f0fac + + # Validate inputs + if p0fac < 1.0 + @warn "Forcing p0fac ≥ 1 (no negative pressure)" + p0fac = 1.0 + end + + # Grid setup + r = range(0.0, stop=a, length=mr) + z = range(-a*e, stop=a*e, length=mz) + rg = [ri for ri in r, _ in z] + zg = [zi for _ in r, zi in z] + + #----------------------------------------------------------------------- + # allocate arrays + #----------------------------------------------------------------------- + sq_in = zeros(Float64, ma, 4) + psi_in = zeros(Float64, mr, mz) + sqfs = zeros(ma, 4) + psifs = zeros(mr, mz, 1) + + r = zeros(Float64, mr) + z = zeros(Float64, mz) + rg = zeros(Float64, mr, mz) # 2D grid arrays + zg = zeros(Float64, mr, mz) + #----------------------------------------------------------------------- + # compute scalar data (EXTERNAL DEPENDENCIES - global variables) + #----------------------------------------------------------------------- + ro = 0 # EXTERNAL: global variable ro? + zo = 0 # EXTERNAL: global variable zo? + f0 = r0 * b0fac + psio = e * f0 * a * a / (2 * q0 * r0) + psifac = psio / (a * r0)^2 + efac = 1 / (e * e) + pfac = 2 * psio^2 * (e * e + 1) / (a * r0 * e)^2 + rmin = r0 - 1.5 * a + rmax = r0 + 1.5 * a + zmax = 1.5 * e * a + zmin = -zmax + #----------------------------------------------------------------------- + # compute 1D data + #----------------------------------------------------------------------- + psis = [(ia / (ma + 1))^2 for ia in 1:ma] # changed from ...ia in 1:(ma+1)] + sqfs[:, 1] .= f0 * f0fac + sqfs[:, 2] = pfac .* (1 * p0fac .- psis) + sqfs[:, 3] .= 0.0 + + sq_in = Spl.CubicSpline(psis, sqfs; bctype=3) + #----------------------------------------------------------------------- + # compute 2D data + #----------------------------------------------------------------------- + for ir in 1:(mr) + r[ir] = rmin + (ir-1) * (rmax - rmin) / mr + end + + for iz in 1:(mz) + z[iz] = zmin + (iz-1) * (zmax - zmin) / mz + end + + for iz in 1:(mz) + for ir in 1:(mr) + # rg[ir, iz] = r[ir] + # zg[ir, iz] = z[iz] + psifs[ir, iz, 1] = psio - psifac * (efac * (r[ir] * z[iz])^2 + (r[ir]^2 - r0^2)^2 / 4) + end + end + + psi_in = Spl.BicubicSpline(r, z, psifs; bctypex=3, bctypey=3) + #----------------------------------------------------------------------- + # process equilibrium + #----------------------------------------------------------------------- + println("Generating Soloviev equilibrium inputs with:") + println(" mr=$mr, mz=$mz, ma=$ma") + println(" e=$e, a=$a, r0=$r0") + println(" q0=$q0, p0fac=$p0fac, b0fac=$b0fac, f0fac=$f0fac") + + return DirectRunInput(equil_inputs, sq_in, psi_in, rmin, rmax, zmin, zmax, psio) + +end diff --git a/src/Equilibrium/DirectEquilibrium.jl b/src/Equilibrium/DirectEquilibrium.jl new file mode 100644 index 000000000..587c24b18 --- /dev/null +++ b/src/Equilibrium/DirectEquilibrium.jl @@ -0,0 +1,629 @@ +#= +This file contains the logic for the "direct" equilibrium reconstruction method. +It takes parsed data and splines from the IO module and calculates the final flux-coordinate +representation of the plasma equilibrium. +=# + + +# --- Internal Helper Structs --- +""" + DirectBField + +Internal mutable struct to hold B-field components and their derivatives at a point. +It is used as a temporary workspace to avoid allocations in tight loops. +""" +mutable struct DirectBField + psi::Float64 + psir::Float64 # d(psi)/dr + psiz::Float64 # d(psi)/dz + psirz::Float64 # d2(psi)/drdz + psirr::Float64 # d2(psi)/drdr + psizz::Float64 # d2(psi)/dzdz + f::Float64 # F = R*Bt + f1::Float64 # dF/d(psi_norm) + p::Float64 # mu0*Pressure + p1::Float64 # dP/d(psi_norm) + br::Float64 # Br + bz::Float64 # Bz + brr::Float64 # d(Br)/dr + brz::Float64 # d(Br)/dz + bzr::Float64 # d(Bz)/dr + bzz::Float64 # d(Bz)/dz + + DirectBField() = new(zeros(Float64, 16)...) +end + +""" + FieldLineDerivParams + +A struct to hold constant parameters for the ODE integration, making them +easily accessible within the derivative function `direct_fl_der!`. +""" +struct FieldLineDerivParams + ro::Float64 + zo::Float64 + psi_in::Spl.BicubicSpline + sq_in::Spl.CubicSpline + psio::Float64 + power_bp::Int + power_b::Int + power_r::Int +end + + +""" + direct_get_bfield!(bf_out, r, z, psi_in, sq_in, psio; derivs=0) + +Calculates the magnetic field and its derivatives at a given (R,Z) point. +The results are stored in-place in the `bf_out` object. + +## Arguments: +- `bf_out`: A mutable `DirectBField` struct to store the results. +- `r`: The R-coordinate [m]. +- `z`: The Z-coordinate [m]. +- `psi_in`: The 2D bicubic spline for poloidal flux `ψ(R,Z)`. +- `sq_in`: The 1D cubic spline for profiles `F(ψ_norm)` and `P(ψ_norm)`. +- `psio`: The total flux difference `|ψ_axis - ψ_boundary|`. + +## Keyword Arguments: +- `derivs`: An integer specifying the derivative level to compute. + - `0`: Calculates `ψ`, `F`, and `P`. + - `1`: Also calculates 1st derivatives of `ψ` and `B` field components. + - `2`: Also calculates 2nd derivatives of `ψ` and 1st derivatives of `B`. + +## Returns: +- `nothing`. The `bf_out` object is modified in-place. +""" +function direct_get_bfield!( + bf_out::DirectBField, + r::Float64, + z::Float64, + psi_in::Spl.BicubicSpline, + sq_in::Spl.CubicSpline, + psio::Float64; + derivs::Int=0 +) + # 1. Evaluate 2D spline for psi(r,z) and its derivatives + if derivs == 0 + f_psi = Spl.bicube_eval(psi_in, r, z, 0) + bf_out.psi = f_psi[1] + elseif derivs == 1 + f_psi, fx_psi, fy_psi = Spl.bicube_eval(psi_in, r, z, 1) + bf_out.psi = f_psi[1] + bf_out.psir = fx_psi[1] + bf_out.psiz = fy_psi[1] + else # derivs >= 2 + f_psi, fx_psi, fy_psi, fxx_psi, fxy_psi, fyy_psi = Spl.bicube_eval(psi_in, r, z, 2) + bf_out.psi = f_psi[1] + bf_out.psir = fx_psi[1] + bf_out.psiz = fy_psi[1] + bf_out.psirr = fxx_psi[1] + bf_out.psirz = fxy_psi[1] + bf_out.psizz = fyy_psi[1] + end + + # 2. Evaluate 1D splines for F(psi_norm) and P(psi_norm) + # psi_norm = 0 at axis, 1 at boundary. + psi_norm = (psio > 1e-12) ? (1.0 - bf_out.psi / psio) : 0.0 + psi_norm = clamp(psi_norm, 0.0, 1.0) + + f_sq, f1_sq = Spl.spline_eval(sq_in, psi_norm, 1) + bf_out.f = f_sq[1] # F = R*Bt + bf_out.f1 = f1_sq[1] # dF/d(psi_norm) + bf_out.p = f_sq[2] # mu0*Pressure + bf_out.p1 = f1_sq[2] # dP/d(psi_norm) + + (derivs < 1) && return + + # 3. Evaluate magnetic field components (derivs >= 1) + bf_out.br = bf_out.psiz / r # Br = (1/R) * ∂ψ/∂Z + bf_out.bz = -bf_out.psir / r # Bz = -(1/R) * ∂ψ/∂R + + (derivs < 2) && return + + # 4. Evaluate derivatives of B-field components (derivs >= 2) + bf_out.brr = (bf_out.psirz - bf_out.br) / r #d(Br)/dr + bf_out.brz = bf_out.psizz / r #d(Br)/dz + bf_out.bzr = -(bf_out.psirr + bf_out.bz) / r #d(Bz)/dr + bf_out.bzz = -bf_out.psirz / r # d(Bz)/dz + + return +end + + +""" + direct_position(psi_in, sq_in, psio, ro_guess, zo_guess, rmin, rmax) + +Finds the key geometric locations of the equilibrium: the magnetic axis (O-point) +and the inboard/outboard separatrix crossings on the midplane. + +## Arguments: +- `psi_in`: The 2D `ψ(R,Z)` spline. +- `sq_in`: The 1D profile spline. +- `psio`: Initial flux difference. +- `ro_guess`, `zo_guess`: Initial guess for the magnetic axis location [m]. +- `rmin`, `rmax`: Radial bounds of the computational domain [m]. + +## Returns: +- `ro`: R-coordinate of the magnetic axis [m]. +- `zo`: Z-coordinate of the magnetic axis [m]. +- `rs1`: R-coordinate of the inboard separatrix crossing [m]. +- `rs2`: R-coordinate of the outboard separatrix crossing [m]. +- `psi_in_new` : returns psi_in renormalized by * psio/psi(ro,zo) +""" +function direct_position( + psi_in::Spl.BicubicSpline, + sq_in::Spl.CubicSpline, + psio::Float64, + ro_guess::Float64, + zo_guess::Float64, + rmin::Float64, + rmax::Float64 +) + bf_temp = DirectBField() + r, z = ro_guess, zo_guess + max_newton_iter = 200 + + # 1. Find the magnetic axis (O-point) using Newton-Raphson + println("Finding magnetic axis...") + # (Initial coarse search for r if guess is 0.0) + # find o point coarse guess by finding point psi extrema by Bz. + if r ≈ 0.0 + r_mid, z_mid = (rmax + rmin) / 2.0, zo_guess + dr_scan = (rmax - rmin) / 20.0 + r = r_mid + for _ in 1:20 + direct_get_bfield!(bf_temp, r, z_mid, psi_in, sq_in, psio, derivs=1) + if bf_temp.bz >= 0.0; break; end + r += dr_scan + end + z = z_mid + end + + for iter in 1:20 + direct_get_bfield!(bf_temp, r, z, psi_in, sq_in, psio, derivs=2) + det = bf_temp.brr * bf_temp.bzz - bf_temp.brz * bf_temp.bzr + if abs(det) < 1e-20; error("Jacobian matrix is singular near ($r, $z)."); end + # Δx = -J^-1 F + dr = (bf_temp.brz * bf_temp.bz - bf_temp.bzz * bf_temp.br) / det + dz = (bf_temp.bzr * bf_temp.br - bf_temp.brr * bf_temp.bz) / det + r += dr; z += dz + @printf " Iter %2d: R = %.6f, Z = %.6f, |ΔR|=%.2e, |ΔZ|=%.2e\n" iter r z abs(dr) abs(dz) + if abs(dr) <= 1e-12 * abs(r) && abs(dz) <= 1e-12 * abs(r) + println("Magnetic axis found at R=$(r), Z=$(z).") + break + end + (iter == 20) && @warn "O-point search did not converge." + end + ro, zo = r, z + + # 2. Psi Renormalization + # renormalize psi_in by psi_in * psio/psi(ro,zo) + # Redefined to avoid direct modification of the psi_rz structure. + # However, if it is determined that redefining psi_rz will not cause major problems, + # modification may be permitted. + direct_get_bfield!(bf_temp, ro, zo, psi_in, sq_in, psio, derivs=0) + psi_at_axis = bf_temp.psi + fac = psio/psi_at_axis + new_psi_fs = psi_in.fs * fac + x_coords = Vector(psi_in.xs) + y_coords = Vector(psi_in.ys) + psi_in_new = Spl.BicubicSpline(x_coords, y_coords, new_psi_fs, bctypex=4, bctypey=4) + + if abs(psi_at_axis - psio) / psio > 1e-3 + @warn "Psi at located axis (O-point) differs from expected psio. " * + "Psi(axis)=$(psi_at_axis), psio=$(psio). Proceeding without re-fitting." + end + + # 3. Find inboard (rs1) and outboard (rs2) separatrix positions + # Helper function for robust Newton-Raphson search with restarts + function find_separatrix_crossing(start_r, end_r, label) + println("Finding $label separatrix crossing...") + local r_sol::Float64 + found = false + for ird in 0:5 # 6 restart attempts + r_sep = (start_r * (3.0 - 0.5 * ird) + end_r) / (4.0 - 0.5 * ird) + @printf " Restart attempt %d/6 with initial R = %.6f\n" (ird + 1) r_sep + for _ in 1:max_newton_iter + + direct_get_bfield!(bf_temp, r_sep, zo, psi_in_new, sq_in, psio, derivs=1) + if abs(bf_temp.psir) < 1e-14; @warn "d(psi)/dr is near zero."; break; end + dr = -bf_temp.psi / bf_temp.psir + r_sep += dr + if abs(dr) <= 1e-12 * abs(r_sep); r_sol = r_sep; found = true; break; end + end + if found; break; end + end + !found && error("Could not find $label separatrix after all attempts.") + println("$label separatrix found at R=$(r_sol).") + return r_sol + end + + rs1 = find_separatrix_crossing(ro, rmin, "inboard") + rs2 = find_separatrix_crossing(ro, rmax, "outboard") + + # 4. Return the new spline + return ro, zo, rs1, rs2, psi_in_new +end + + +""" + direct_fl_int(ipsi, psifac, raw_profile, ro, zo, rs2) + +Performs the field-line integration for a single flux surface. + +## Arguments: +- `ipsi`: The index of the current flux surface. +- `psifac`: The normalized psi value for the surface (ψ_norm). +- `raw_profile`: The `DirectRunInput` object containing splines and parameters. +- `ro`, `zo`: Coordinates of the magnetic axis [m]. +- `rs2`: R-coordinate of the outboard separatrix [m]. + +## Returns: +- `y_out`: A matrix containing the integrated quantities vs. the geometric angle `η`. +- `bf_start`: A `DirectBField` object with values at the integration start point. +""" +function direct_fl_int( + ipsi::Int, + psifac::Float64, + raw_profile::DirectRunInput, + ro::Float64, + zo::Float64, + rs2::Float64 +) + # 1. Find the starting point on the flux surface (outboard midplane) + psi0_target = raw_profile.psio * (1.0 - psifac) + r_start = ro + sqrt(psifac) * (rs2 - ro) + z_start = zo + + bf_start = DirectBField() + for _ in 1:10 # Refine starting R using Newton's method + direct_get_bfield!(bf_start, r_start, z_start, raw_profile.psi_in, raw_profile.sq_in, raw_profile.psio, derivs=1) + dr = (psi0_target - bf_start.psi) / bf_start.psir + r_start += dr + if abs(dr) <= 1e-12 * r_start; break; end + end + direct_get_bfield!(bf_start, r_start, z_start, raw_profile.psi_in, raw_profile.sq_in, raw_profile.psio, derivs=2) + psi0_actual = bf_start.psi + + # 2. Set up and solve the ODE for field line following + u0 = zeros(Float64, 4) + #[1]:∫(dl/Bp) + #[2]: rfac (radial distance from magnetic axis) + #[3]: ∫(dl/(R²Bp)) + #[4]: ∫(jac*dl/Bp) + u0[2] = sqrt((r_start - ro)^2 + (z_start - zo)^2) # Initial rfac + tspan = (0.0, 2.0 * pi) + + equil_input = raw_profile.config.control + + params = FieldLineDerivParams(ro, zo, raw_profile.psi_in, raw_profile.sq_in, raw_profile.psio, + equil_input.power_bp, equil_input.power_b, equil_input.power_r) + + # Use a callback to refine the solution at each step to stay on the flux surface + saved_values = Vector{Vector{Float64}}() + function refine_and_save_affect!(integrator) + rfac_refined = direct_refine(integrator.u[2], integrator.t, psi0_actual, params) + integrator.u[2] = rfac_refined + push!(saved_values, [integrator.t; integrator.u]) + end + callback = DiscreteCallback((u,t,i) -> true, refine_and_save_affect!, save_positions=(false,false)) + + # Add the initial state + push!(saved_values, [0.0; u0]) + + prob = ODEProblem(direct_fl_der!, u0, tspan, params) + sol = solve(prob, Tsit5(), callback=callback, reltol=1e-6, abstol=1e-8, dt=2*pi/200, adaptive=true) + + if sol.retcode != :Success && sol.retcode != :Terminated + error("ODE integration failed for ipsi=$ipsi with code: $(sol.retcode)") + end + + # 3. Finalize output + y_out = hcat(saved_values...)' # Convert vector of vectors to a matrix + return y_out, bf_start +end + + +""" + direct_fl_der!(dy, y, params, eta) + +The derivative function for the field-line integration ODE. This is passed to +the `DifferentialEquations.jl` solver. + +## Arguments: +- `dy`: The derivative vector (output, modified in-place). +- `y`: The state vector `[∫(dl/Bp), rfac, ∫(dl/(R²Bp)), ∫(jac*dl/Bp)]`. +- `params`: A `FieldLineDerivParams` struct with all necessary parameters. +- `eta`: The independent variable (geometric angle `η`). +""" +function direct_fl_der!(dy, y, params::FieldLineDerivParams, eta) + cos_eta, sin_eta = cos(eta), sin(eta) + r = params.ro + y[2] * cos_eta + z = params.zo + y[2] * sin_eta + + bf_temp = DirectBField() + direct_get_bfield!(bf_temp, r, z, params.psi_in, params.sq_in, params.psio, derivs=1) + + bp_sq = bf_temp.br^2 + bf_temp.bz^2 + bp = bp_sq > 1e-28 ? sqrt(bp_sq) : 1e-14 + bt = bf_temp.f / r + b_sq = bp_sq + bt^2 + b = sqrt(b_sq) + jacfac = (bp^params.power_bp) * (b^params.power_b) / (r^params.power_r) + + # Denominator for d(l_pol)/d(eta) = rfac |B_pol|/denominator + denominator = bf_temp.bz * cos_eta - bf_temp.br * sin_eta + if abs(denominator) < 1e-14 + fill!(dy, 1e20) # Return large derivatives for solver to handle stiffness + @warn "Denominator in direct_fl_der! near zero at eta=$eta." + return + end + + # dy/d(eta) + dy[1] = y[2] / denominator # d/dη [∫(dl/Bp)] = 1/|B_P| dl/d(eta) = rfac/denominator + dy[2] = dy[1] * (bf_temp.br * cos_eta + bf_temp.bz * sin_eta) + # d(rfac)/d(eta) = rfac/denom *( Br cos(eta) + Bz sin(eta) ) + dy[3] = dy[1] / (r^2) # d/dη [∫(dl/(R²Bp))] + dy[4] = dy[1] * jacfac # d/dη [∫(jac*dl/Bp)] + return +end + + +""" + direct_refine(rfac, eta, psi0, params) + +Refines the radial distance `rfac` at a given angle `eta` to ensure the +point lies exactly on the target flux surface `psi0`. + +## Arguments: +- `rfac`: The current guess for the radial distance from the magnetic axis. +- `eta`: The geometric poloidal angle. +- `psi0`: The target `ψ` value for the flux surface. +- `params`: A `FieldLineDerivParams` struct. + +## Returns: +- The refined `rfac` value. +""" +function direct_refine(rfac::Float64, eta::Float64, psi0::Float64, params::FieldLineDerivParams; max_iter::Int=10)::Float64 + cos_eta, sin_eta = cos(eta), sin(eta) + bf_temp = DirectBField() + + for _ in 1:max_iter + r_current = params.ro + rfac * cos_eta + z_current = params.zo + rfac * sin_eta + direct_get_bfield!(bf_temp, r_current, z_current, params.psi_in, params.sq_in, params.psio, derivs=1) + dpsi = bf_temp.psi - psi0 + + # Newton's method derivative: d(psi)/d(rfac) + dpsi_drfac = bf_temp.psir * cos_eta + bf_temp.psiz * sin_eta + if abs(dpsi_drfac) < 1e-14 + @warn "Refinement failed at eta=$eta: d(psi)/d(rfac) is zero." + return rfac # Return current best guess + end + + drfac = -dpsi / dpsi_drfac + rfac += drfac + + if abs(dpsi) <= 1e-12 || abs(drfac) <= 1e-12 * abs(rfac) + return rfac # Converged + end + end + + @warn "direct_refine did not converge after $max_iter iterations at eta=$eta." + return rfac +end + + +""" + equilibrium_solver(raw_profile) + +The main driver for the direct equilibrium reconstruction. It orchestrates the entire +process from finding the magnetic axis to integrating along field lines and +constructing the final coordinate and physics quantity splines. + +## Arguments: +- `raw_profile`: A `DirectRunInput` object containing the initial splines (`psi_in`, `sq_in`) + and run parameters (`equil_input`). + +## Returns: +- A `PlasmaEquilibrium` object containing the final, processed equilibrium data, + including the profile spline (`sq`), the coordinate mapping spline (`rzphi`), and + the physics quantity spline (`eqfun`). +""" +function equilibrium_solver(raw_profile::DirectRunInput) + println("--- Starting Direct Equilibrium Processing ---") + + # 1. Unpack initial data + equil_params = raw_profile.config.control + sq_in = raw_profile.sq_in + psi_in = raw_profile.psi_in + psio = raw_profile.psio + mtheta = equil_params.mtheta + + # 2. Setup the new output radial grid (`ψ_norm`) + mpsi = equil_params.mpsi + psilow = equil_params.psilow + psihigh = equil_params.psihigh + + sq_x_nodes = zeros(Float64, mpsi + 1) + if equil_params.grid_type == "ldp" + for i in 0:mpsi + x_param = Float64(i) / mpsi + sq_x_nodes[i+1] = psilow + (psihigh - psilow) * sin(x_param * pi / 2.0)^2 + end + else + error("Unsupported grid_type: $(equil_params.grid_type)") + end + # need to add more grid type + + #2pi*F, mu0P, dvdpsi, q + sq_fs_nodes = zeros(Float64, mpsi + 1, 4) + + ro_guess = (raw_profile.rmin + raw_profile.rmax) / 2.0 + zo_guess = (raw_profile.zmin + raw_profile.zmax) / 2.0 + + + + # 3. Find key geometric positions and perform normalization + ro, zo, rs1, rs2, psi_in_norm = direct_position(psi_in, sq_in, psio, + ro_guess, zo_guess, # initial guess + raw_profile.rmin, raw_profile.rmax) + + + + normalized_profile = DirectRunInput( + raw_profile.config, + raw_profile.sq_in, + psi_in_norm, + raw_profile.rmin, + raw_profile.rmax, + raw_profile.zmin, + raw_profile.zmax, + raw_profile.psio + ) + + # 4. Main integration loop over flux surfaces + local rzphi::Spl.BicubicSpline + local eqfun::Spl.BicubicSpline + local rzphi_fs_nodes + + println("Starting loop over flux surfaces...") + # Loop from edge inwards (index mpsi+1 down to 1) + for ipsi in (mpsi+1):-1:1 + psi_norm_surf = sq_x_nodes[ipsi] + @printf "--> Processing surface ipsi = %d / %d (ψ_norm = %.4f)\n" (ipsi-1) mpsi psi_norm_surf + + # a. Integrate along the field line for this surface + y_out, bf_start = direct_fl_int(ipsi, psi_norm_surf, normalized_profile, ro, zo, rs2) + #y_out + #[1]: eta + #[2]:∫(dl/Bp) + #[3]: rfac (radial distance from magnetic axis) + #[4]: ∫(dl/(R²Bp)) + #[5]: ∫(jac*dl/Bp) + + # b. Process integration results into a temporary periodic spline `ff(θ_new)` + theta_new_nodes = y_out[:, 5] ./ y_out[end, 5] #SFL angle θ_new + ff_fs_nodes = hcat( + y_out[:, 3].^2, # 1: rfac² + y_out[:, 1] / (2*pi) .- theta_new_nodes, # 2: η/(2π) - θ_new + bf_start.f * (y_out[:, 4] .- theta_new_nodes .* y_out[end, 4]), # 3: Toroidal stream function term (term for calculate q) + y_out[:, 2] ./ y_out[end, 2] .- theta_new_nodes # 4: Jacobian-related term + ) + ff = Spl.CubicSpline(theta_new_nodes, ff_fs_nodes, bctype="periodic") + + # c. On first iteration, allocate the main output data array + if ipsi == (mpsi+1) + rzphi_fs_nodes = zeros(Float64, mpsi + 1, mtheta + 1, 4) + end + + # d. Interpolate `ff` onto the uniform `theta` grid for `rzphi` + rzphi_y_nodes = range(0.0, 1.0, length=mtheta + 1) + for itheta in 1:(mtheta + 1) + theta_val = rzphi_y_nodes[itheta] + f, f1 = Spl.spline_eval(ff, theta_val, 1) + + rzphi_fs_nodes[ipsi, itheta, 1:3] = f[1:3] + jac_term = (1.0 + f1[4]) * y_out[end, 2] * (2*pi) * psio + rzphi_fs_nodes[ipsi, itheta, 4] = jac_term + end + + # e. Store surface-averaged quantities for the `sq` spline + sq_fs_nodes[ipsi, 1] = bf_start.f * (2pi) # 2pi*F + sq_fs_nodes[ipsi, 2] = bf_start.p + sq_fs_nodes[ipsi, 3] = y_out[end, 5] * (2pi) *psio # dV/d(psi) + sq_fs_nodes[ipsi, 4] = y_out[end, 4] * bf_start.f / (2pi) # q-profile + end + println("...Loop over flux surfaces finished.") + + # 5. Finalize splines and perform q-profile revision if needed + sq = Spl.CubicSpline(sq_x_nodes, sq_fs_nodes, bctype=4) + + if equil_params.newq0 != 0.0 + println("Revising q-profile for newq0 = $(equil_params.newq0)...") + f = Spl.spline_eval(sq, 0.0, 0) + # q0_old = q(psi=0) = f[4] at x=0 + # f0_old = f[1] at x=0 + q0_old = f[4] + f0_old = f[1] + + f0_fac_sq = f0_old^2 * ((equil_params.newq0 / q0_old)^2 - 1.0) + + for i in 1:(mpsi+1) + f_current_sq = sq_fs_nodes[i, 1]^2 + ffac = sqrt(max(0.0, 1.0 + f0_fac_sq / f_current_sq)) * sign(equil_params.newq0/q0_old) + sq_fs_nodes[i, 1] *= ffac # F + sq_fs_nodes[i, 4] *= ffac # q + rzphi_fs_nodes[i, :, 3] .*= ffac # Toroidal stream function + end + # Re-create the spline with the revised data + sq = Spl.CubicSpline(sq_x_nodes, sq_fs_nodes, bctype=4) + println("...q-profile revision complete.") + end + + # Create the final geometric spline `rzphi`. Periodic in theta (y-dimension) + rzphi_y_nodes = range(0.0, 1.0, length=mtheta + 1) + rzphi = Spl.BicubicSpline(sq_x_nodes, collect(rzphi_y_nodes), rzphi_fs_nodes, bctypex=4, bctypey=2) + println("Final geometric spline 'rzphi' is fitted.") + + # 6. Calculate final physics quantities (B-field, metric components, etc.) + println("Calculating final physics quantities (B, g_ij)...") + eqfun_fs_nodes = zeros(Float64, mpsi + 1, mtheta + 1, 3) + v = zeros(Float64, 2, 3) + + for ipsi in 1:(mpsi+1), itheta in 1:(mtheta+1) + psi_norm = sq_x_nodes[ipsi] + theta_new = rzphi_y_nodes[itheta] + + f = Spl.spline_eval(sq, psi_norm, 0) + q = f[4] + f_val = f[1] + + f, fx, fy = Spl.bicube_eval(rzphi, psi_norm, theta_new, 1) + rfac_sq = max(0.0, f[1]) + rfac = sqrt(rfac_sq) + eta = 2.0 * pi * (theta_new + f[2]) + r_coord = ro + rfac * cos(eta) + jacfac = f[4] + + + v[1,1] = (rfac > 0) ? fx[1] / (2.0 * rfac) : 0.0 # 1/(2rfac) * d(rfac)/d(psi_norm) + v[1,2] = fx[2] * 2.0 * pi * rfac # 2pi*rfac * d(eta)/d(psi_norm) + v[1,3] = fx[3] * r_coord # r_coord * d(phi_s)/d(psi_norm) + v[2,1] = (rfac > 0) ? fy[1] / (2.0 * rfac) : 0.0 # 1/(2rfac) d(rfac)/d(theta_new) + v[2,2] = (1.0 + fy[2]) * 2.0 * pi * rfac # 2pi*rfac * d(eta)/d(theta_new) + v[2,3] = fy[3] * r_coord # r_coord * d(phi_s)/d(theta_new) + v33 = 2.0 * pi * r_coord # 2pi * r_coord + + + w11 = (1.0 + fy[2]) * (2.0*pi)^2 * rfac * r_coord / jacfac + w12 = (jacfac*rfac != 0) ? -fy[1] * pi * r_coord / (rfac * jacfac) : 0.0 + delpsi_norm = sqrt(w11^2 + w12^2) + + b_sq = ((psio *2pi *delpsi_norm)^2 + (f_val/(2pi*r_coord))^2) + eqfun_fs_nodes[ipsi, itheta, 1] = b_sq # B_total + + denom = jacfac * b_sq + if abs(denom) > 1e-20 + # 2. Gyrokinetic coefficient C1 + numerator_2 = dot(v[1,:], v[2,:]) + q * v33 * v[1,3] + eqfun_fs_nodes[ipsi, itheta, 2] = numerator_2 / denom + + # 3. Gyrokinetic coefficient C2 + numerator_3 = v[2,3] * v33 + q * v33^2 + eqfun_fs_nodes[ipsi, itheta, 3] = numerator_3 / denom + else + eqfun_fs_nodes[ipsi, itheta, 2] = 0.0 + eqfun_fs_nodes[ipsi, itheta, 3] = 0.0 + end + end + println("...done.") + + eqfun = Spl.BicubicSpline(sq_x_nodes, collect(rzphi_y_nodes), eqfun_fs_nodes, bctypex=4, bctypey=2) + + println("--- Direct Equilibrium Processing Finished ---") + + return PlasmaEquilibrium(raw_profile.config,EquilibriumParameters(), sq, rzphi, eqfun, ro, zo, psio) +end + diff --git a/src/Equilibrium/Equilibrium.jl b/src/Equilibrium/Equilibrium.jl new file mode 100644 index 000000000..d136d30e4 --- /dev/null +++ b/src/Equilibrium/Equilibrium.jl @@ -0,0 +1,530 @@ +module Equilibrium + +# --- Module-level Dependencies --- +import ..Spl + +using Printf, OrdinaryDiffEq, DiffEqCallbacks, LinearAlgebra, HDF5 +using TOML + + +# --- Internal Module Structure --- +include("EquilibriumTypes.jl") +include("ReadEquilibrium.jl") +include("DirectEquilibrium.jl") +include("InverseEquilibrium.jl") +include("AnalyticEquilibrium.jl") + +# --- Expose types and functions to the user --- + +export setup_equilibrium, EquilibriumConfig, EquilibriumControl, EquilibriumOutput, PlasmaEquilibrium, EquilibriumParameters + +# --- Constants --- +const mu0 = 4.0 * pi * 1e-7 + + +""" + setup_equilibrium(equil_input::EquilInput) + +The main public API for the `Equilibrium` module. It orchestrates the entire +process of reading an equilibrium file, running the appropriate solver, and +returning the final processed `PlasmaEquilibrium` object. + +## Arguments: +- `equil_input`: An `EquilInput` object containing all necessary setup parameters. +## Returns: +- A `PlasmaEquilibrium` object containing the final result. +""" +function setup_equilibrium(path::String = "equil.toml") + return setup_equilibrium( EquilibriumConfig(path)) +end +function setup_equilibrium(eq_config::EquilibriumConfig, additional_input=nothing) + + @printf "Equilibrium file: %s\n" eq_config.control.eq_filename + + eq_type = eq_config.control.eq_type + # Parse file and prepare initial data structures and splines + if eq_type == "efit" + eq_input = read_efit(eq_config) + elseif eq_type == "chease2" + eq_input = read_chease2(eq_config) + elseif eq_type == "chease" + eq_input = read_chease(eq_config) + elseif eq_type == "lar" + + if additional_input === nothing + additional_input = LargeAspectRatioConfig(eq_config.control.eq_filename) + end + + eq_input = lar_run(eq_config, additional_input) + elseif eq_type == "sol" + + if additional_input === nothing + additional_input = SolevevConfig(eq_config.control.eq_filename) + end + + eq_input = sol_run(eq_config, additional_input) + elseif eq_type == "inverse_testing" + # Example 1D spline setup + xs = collect(0.0:0.1:1.0) + fs = sin.(2π .* xs) # vector of Float64 + spline_ex = Spl.CubicSpline(xs, fs) + #println(spline_ex) + # Example 2D bicubic spline setup + xs = 0.0:0.1:1.0 + ys = 0.0:0.2:1.0 + fs = [sin(2π*x)*cos(2π*y) for x in xs, y in ys, _ in 1:1] + bicube_ex = Spl.BicubicSpline(collect(xs), collect(ys), fs) + #println(bicube_ex) + eq_input = InverseRunInput( + eq_config, + spline_ex, #sq_in + bicube_ex, #rz_in + 0.0, #ro + 0.0, #zo + 1.0 #psio + ) + else + error("Equilibrium type $(equil_in.eq_type) is not implemented") + end + + # Run the appropriate solver (direct or inverse) to get a PlasmaEquilibrium struct + plasma_equilibrium = equilibrium_solver(eq_input) + + # add global parameters to the PlasmaEquilibrium struct + equilibrium_global_parameters!(plasma_equilibrium) + + # Find q information + equilibrium_qfind!(plasma_equilibrium) + + # Diagnoses grad-shafranov solution. + equilibrium_gse!(plasma_equilibrium) + + println("--- Equilibrium Setup Complete ---") + return plasma_equilibrium +end + + +""" + equilibrium_separatrix_find!(pe::PlasmaEquilibrium) +Finds the separatrix locations in the plasma equilibrium (rsep, zsep, rext, zext). +""" +function equilibrium_separatrix_find!(pe::PlasmaEquilibrium) + rzphi = pe.rzphi + mpsi = size(rzphi.fs, 1) - 1 + mtheta = size(rzphi.fs, 2) - 1 + twopi = 2π + + # Allocate vector to store eta offset from rzphi + vector = zeros(Float64, mtheta + 1) + for it in 0:mtheta + f = Spl.bicube_eval(rzphi, rzphi.xs[mpsi+1], rzphi.ys[it+1], 0) + vector[it+1] = rzphi.ys[it+1] + f[2] + end + + psifac = rzphi.xs[mpsi+1] + eta0 = 0.0 + idx = findmin(abs.(vector .- eta0))[2] + theta = rzphi.ys[idx] + rsep = zeros(2) + + for iside in 1:2 + it = 0 + while true + it += 1 + f, _, fy = Spl.bicube_eval(rzphi, psifac, theta, 1) + eta = theta + f[2] - eta0 + eta_theta = 1 + fy[2] + dtheta = -eta / eta_theta + theta += dtheta + if abs(eta) <= 1e-10 || it > 100 + break + end + end + f = Spl.bicube_eval(rzphi, psifac, theta, 0) + rsep[iside] = pe.ro + sqrt(f[1]) * cos(twopi * (theta + f[2])) + eta0 = 0.5 + idx = findmin(abs.(vector .- eta0))[2] + theta = rzphi.ys[idx] + end + + # Top and bottom separatrix locations using Newton iteration + zsep = zeros(2) + rext = zeros(2) + zext = zeros(2) + + for iside in 1:2 + eta0 = (iside == 1) ? 0.0 : 0.5 + idx = findmin(abs.(vector .- eta0))[2] + theta = rzphi.ys[idx] + rfac = 0.0 + cosfac = 0.0 + z = 0.0 + while true + f, fx, fy, fxx, fxy, fyy = Spl.bicube_eval(rzphi, psifac, theta, 2) + r2, r2y, r2yy = f[1], fy[1], fyy[1] + eta, eta1, eta2 = f[2], fy[2], fyy[2] + + rfac = sqrt(r2) + rfac1 = r2y / (2 * rfac) + rfac2 = (r2yy - r2y * rfac1 / rfac) / (2 * rfac) + phase = twopi * (theta + eta) + phase1 = twopi * (1 + eta1) + phase2 = twopi * eta2 + cosfac = cos(phase) + sinfac = sin(phase) + z = pe.zo + rfac * sinfac + z1 = rfac * phase1 * cosfac + rfac1 * sinfac + z2 = (2 * rfac1 * phase1 + rfac * phase2) * cosfac + (rfac2 - rfac * phase1^2) * sinfac + dtheta = -z1 / z2 + theta += dtheta + if abs(dtheta) < 1e-12 * abs(theta) + break + end + end + rext[iside] = pe.ro + rfac * cosfac + zsep[iside] = z + zext[iside] = z + end + + pe.params.rsep = rsep + pe.params.zsep = zsep + pe.params.rext = rext + pe.params.zext = zext + return (rsep, zsep, rext, zext) +end + + +function equilibrium_global_parameters!(pe::PlasmaEquilibrium) + rzphi = pe.rzphi + sq = pe.sq + mpsi = size(rzphi.fs, 1) - 1 + mtheta = size(rzphi.fs, 2) - 1 + twopi = 2π + mu0 = 4π * 1e-7 + + # Use separatrix geometry + rsep, zsep, rext, _ = equilibrium_separatrix_find!(pe) + + rmean = (rsep[2] + rsep[1]) / 2 + amean = (rsep[2] - rsep[1]) / 2 + aratio = rmean / amean + kappa = (zsep[1] - zsep[2]) / (rsep[2] - rsep[1]) + delta1 = (rmean - rext[1]) / amean + delta2 = (rmean - rext[2]) / amean + dpsi = 1.0 - rzphi.xs[mpsi+1] + bt0 = (sq.fs[mpsi+1, 1] + sq.fs1[mpsi+1, 1] * dpsi) / (twopi * rmean) + + pe.params.rmean = rmean + pe.params.amean = amean + pe.params.aratio = aratio + pe.params.kappa = kappa + pe.params.delta1 = delta1 + pe.params.delta2 = delta2 + pe.params.bt0 = bt0 + + psio = pe.psio + gs1 = zeros(Float64, mtheta+1) + gs2 = zeros(Float64, mtheta+1) + + for itheta in 0:mtheta + f, _, fy = Spl.bicube_eval(rzphi, rzphi.xs[mpsi+1], rzphi.ys[itheta+1], 1) + jac = f[4] + chi1 = twopi * psio / jac + jacfac = π / jac + rfac = sqrt(f[1]) + eta = twopi * (rzphi.ys[itheta+1] + f[2]) + r = pe.ro + rfac * cos(eta) + v21 = jacfac * fy[1] / (twopi * rfac) + v22 = jacfac * (1 + fy[2]) * (2 * rfac) + v33 = jacfac * twopi * (r / π) + dvsq = (v21^2 + v22^2) * (v33 * jac^2)^2 + gs1[itheta+1] = sqrt(dvsq) / (twopi * r) + gs2[itheta+1] = chi1 * dvsq / (twopi * r)^2 + end + + int1 = sum(gs1) / (mtheta+1) + int2 = sum(gs2) / (mtheta+1) + crnt = int2 / (1e6 * mu0) + bp0 = int2 / int1 + bwall = 1e6 * mu0 * crnt / (twopi * amean) + + pe.params.crnt = crnt + pe.params.bwall = bwall + + # Flux surface integrals + hs1 = sq.fs[:,2] .* sq.fs[:,3] # p * dV/dpsi + hs2 = sq.fs[:,3] # dV/dpsi + hs3 = sq.fs[:,2].^2 .* sq.fs[:,3] # p^2 * dV/dpsi + + dpsi_vec = diff(sq.xs) + fsi1 = sum((hs1[1:end-1] .+ hs1[2:end]) .* dpsi_vec) / 2 + fsi2 = sum((hs2[1:end-1] .+ hs2[2:end]) .* dpsi_vec) / 2 + fsi3 = sum((hs3[1:end-1] .+ hs3[2:end]) .* dpsi_vec) / 2 + + volume = sum((sq.fs[1:end-1,3] .+ sq.fs[2:end,3]) .* dpsi_vec) / 2 + + p0 = sq.fs[1,2] - sq.fs1[1,2] * sq.xs[1] # linear extrapolation + betat = 2 * (fsi1 / fsi2) / bt0^2 + betaj = 2 * sqrt(fsi3 / fsi2) / bwall^2 + betan = 100 * amean * bt0 * betat / crnt + betap1 = 2 * (fsi1 / fsi2) / bp0^2 + betap2 = 4 * fsi1 / ((1e6 * mu0 * crnt)^2 * pe.ro) + betap3 = 4 * fsi1 / ((1e6 * mu0 * crnt)^2 * rmean) + li1 = fsi3 / fsi2 / bp0^2 + li2 = 2 * fsi3 / ((1e6 * mu0 * crnt)^2 * pe.ro) + li3 = 2 * fsi3 / ((1e6 * mu0 * crnt)^2 * rmean) + + pe.params.psi0 = psio + pe.params.psi_axis = pe.psio + pe.params.psi_boundary = 1.0 + pe.params.psi_boundary_norm = 1.0 + pe.params.psi_axis_norm = 0.0 + pe.params.psi_norm = 0.0 + pe.params.psi_axis_offset = 0.0 + pe.params.psi_boundary_offset = 0.0 + pe.params.psi_axis_sign = 1 + pe.params.psi_boundary_sign = -1 + pe.params.psi_boundary_zero = false + + pe.params.q0 = sq.fs[1,4] + pe.params.b0 = bt0 + + pe.params.volume = volume + pe.params.betat = betat + pe.params.betan = betan + pe.params.betaj = betaj + pe.params.betap1 = betap1 + pe.params.betap2 = betap2 + pe.params.betap3 = betap3 + pe.params.li1 = li1 + pe.params.li2 = li2 + pe.params.li3 = li3 +end + + + + + + +function equilibrium_qfind!(equil::PlasmaEquilibrium) + println("Finding q profile...") + + sq = equil.sq + mpsi = length(sq.xs) - 1 + psiexl = Float64[] + qexl = Float64[] + + # Left endpoint + push!(psiexl, sq.xs[1]) + push!(qexl, sq.fs[1, 4]) + + # Search for extrema in q(ψ) + for ipsi in 1:mpsi + x0 = sq.xs[ipsi] + x1 = sq.xs[ipsi + 1] + xmax = x1 - x0 + + f, f1, f2, f3 = Spl.spline_eval(sq, x0, 3) + a, b, c, d = f[4], f1[4], f2[4], f3[4] + + if d != 0.0 + xcrit = -c / d + dx2 = xcrit^2 - 2b / d + if dx2 ≥ 0 + dx = sqrt(dx2) + for delta in (dx, -dx) + x = xcrit - delta + if 0 ≤ x < xmax + ψ = x0 + x + fψ, = Spl.spline_eval(sq, ψ, 0) + push!(psiexl, ψ) + push!(qexl, fψ[4]) + end + end + end + end + end + + # Right endpoint + push!(psiexl, sq.xs[end]) + push!(qexl, sq.fs[end, 4]) + + equil.params.qextrema_psi = psiexl + equil.params.qextrema_q = qexl + equil.params.mextrema = length(psiexl) + # Compute derived q-values + q0 = sq.fs[1, 4] - sq.fs1[1, 4] * sq.xs[1] + qmax_edge = sq.fs[end, 4] + qmin = min(minimum(qexl), q0) + qmax = max(maximum(qexl), qmax_edge) + qa = sq.fs[end, 4] + sq.fs1[end, 4] * (1.0 - sq.xs[end]) + + f95 = Spl.spline_eval(sq, 0.95, 0) + q95 = f95[4] + + + # Print and store + println("q0: $q0, qmin: $qmin, qmax: $qmax, qa: $qa, q95: $q95, qmax_edge: $qmax_edge, psiexl: $(equil.params.qextrema_psi), qexl: $(equil.params.qextrema_q), mextrema: $(equil.params.mextrema)") + + equil.params.q0 = q0 + equil.params.qmin = qmin + equil.params.qmax = qmax + equil.params.qa = qa + equil.params.q95 = q95 + + return equil +end + + + + + +function equilibrium_gse!(equil::PlasmaEquilibrium) + println("Diagnosing Grad-Shafranov solution...") + + rzphi = equil.rzphi + sq = equil.sq + mpsi, mtheta = rzphi.mx, rzphi.my + ro, zo = equil.ro, equil.zo + psio = equil.psio + verbose = equil.params.verbose + diagnose_src = true #equil.params.diagnose_src + diagnose_maxima = equil.params.diagnose_maxima + + rfac = zeros(Float64, mtheta+1) + angle = zeros(Float64, mtheta+1) + r = zeros(Float64, mpsi+1, mtheta+1) + z = zeros(Float64, mpsi+1, mtheta+1) + + for ipsi in 0:mpsi + for itheta in 0:mtheta + rz_eval = Spl.bicube_eval(rzphi, rzphi.xs[ipsi+1], rzphi.ys[itheta+1], 0) + rfac[itheta+1] = sqrt(rz_eval[1]) + angle[itheta+1] = 2π * (rzphi.ys[itheta+1] + rz_eval[2]) + end + r[ipsi+1, :] .= ro .+ rfac .* cos.(angle) + z[ipsi+1, :] .= zo .+ rfac .* sin.(angle) + end + + flux_fs = zeros(Float64, mpsi+1, mtheta+1, 2) + for ipsi in 0:mpsi + for itheta in 0:mtheta + f, fx, fy = Spl.bicube_eval(rzphi, rzphi.xs[ipsi+1], rzphi.ys[itheta+1], 1) + f1, f2, f4 = f[1], f[2], f[4] + + fy1 = rzphi._fsy[ipsi+1, itheta+1, 1] + fy2 = rzphi._fsy[ipsi+1, itheta+1, 2] + fx1 = rzphi._fsx[ipsi+1, itheta+1, 1] + fx2 = rzphi._fsx[ipsi+1, itheta+1, 2] + + flux_fs[ipsi+1, itheta+1, 1] = fy1^2 / (4π^2 * f1) + (1 + fy2)^2 * 4 * f1 + flux_fs[ipsi+1, itheta+1, 2] = fx1 * fy1 / (4π^2 * f1) + fx2 * (1 + fy2) * 4 * f1 + + for iqty in 1:2 + flux_fs[ipsi+1, itheta+1, iqty] *= 2π * psio / f4 + end + end + end + + + + flux = Spl.BicubicSpline(collect(rzphi.xs), collect(rzphi.ys), flux_fs; bctypex=2, bctypey=2) + + source = zeros(Float64, mpsi+1, mtheta+1) + for ipsi in 0:mpsi + for itheta in 0:mtheta + rz_eval = Spl.bicube_eval(rzphi, rzphi.xs[ipsi+1], rzphi.ys[itheta+1], 0) + f4 = rz_eval[4] + s1 = sq.fs[ipsi+1, 1] + s1p = sq.fs1[ipsi+1, 1] + s2p = sq.fs1[ipsi+1, 2] + + denom = (2π * r[ipsi+1, itheta+1])^2 + source[ipsi+1, itheta+1] = f4 / (2π * psio * π^2) * (s1 * s1p / denom + s2p) + end + end + + total = flux.fsx[:, :, 1] .- flux.fsy[:, :, 2] .+ source + error = abs.(total) ./ maximum([maximum(abs.(flux.fsx[:, :, 1])), maximum(abs.(flux.fsy[:, :, 2])), maximum(abs.(source))]) + errlog = ifelse.(error .> 0, log10.(error), 0.0) + + if diagnose_maxima + fxmax = maximum(abs.(flux.fsx[:, :, 1])) + fymax = maximum(abs.(flux.fsy[:, :, 2])) + smax = maximum(abs.(source)) + emax = maximum(abs.(error)) + lmax = maximum(errlog) + jmax = ind2sub(size(errlog), argmax(errlog)) + println(" fxmax = $fxmax, fymax = $fymax, smax = $smax") + println(" emax = $emax, lmax = $lmax, maxloc = ", jmax .- 1) + end + + # Integrated error criterion + term = zeros(Float64, mpsi+1, 2) + for ipsi in 0:mpsi + fs_matrix = zeros(Float64, mtheta+1, 2) + fs_matrix[:, 1] = flux.fsx[ipsi+1, :, 1] + fs_matrix[:, 2] = source[ipsi+1, :] + + spline = Spl.CubicSpline(Vector(flux.ys), fs_matrix; bctype=2) + Spl.spline_integrate!(spline) + + term[ipsi+1, :] .= spline.fsi[end, :] + # spline will be automatically deallocated by finalizer + end + + totali = sum(term, dims=2) + errori = abs.(totali) + errlogi = @. ifelse(errori > 0, log10(errori), 0.0) + + if diagnose_src + println("Writing diagnostics to HDF5 files...") + + # Write contour data + h5open(joinpath(dirname(equil.config.control.eq_filename), "gsec.h5"), "w") do file + file["mpsi"] = mpsi + file["mtheta"] = mtheta + file["r"] = Float32.(r) + file["z"] = Float32.(z) + file["flux_fsx"] = Float32.(flux.fsx[:, :, 1]) + file["flux_fsy"] = Float32.(flux.fsy[:, :, 2]) + file["source"] = Float32.(source) + file["total"] = Float32.(total) + file["error"] = Float32.(error) + file["errlog"] = Float32.(errlog) + end + + # Write xy plot data + h5open(joinpath(dirname(equil.config.control.eq_filename), "gse.h5"), "w") do file + gse_data = Array{Float32, 3}(undef, mpsi+1, mtheta+1, 7) + for ipsi in 0:mpsi + for itheta in 0:mtheta + gse_data[ipsi+1, itheta+1, 1] = Float32(flux.ys[itheta+1]) + gse_data[ipsi+1, itheta+1, 2] = Float32(flux.xs[ipsi+1]) + gse_data[ipsi+1, itheta+1, 3] = Float32(flux.fs[ipsi+1, itheta+1, 1]) + gse_data[ipsi+1, itheta+1, 4] = Float32(flux.fs[ipsi+1, itheta+1, 2]) + gse_data[ipsi+1, itheta+1, 5] = Float32(source[ipsi+1, itheta+1]) + gse_data[ipsi+1, itheta+1, 6] = Float32(total[ipsi+1, itheta+1]) + gse_data[ipsi+1, itheta+1, 7] = Float32(error[ipsi+1, itheta+1]) + end + end + file["gse_data"] = gse_data + end + + # Write integrated error criterion + h5open(joinpath(dirname(equil.config.control.eq_filename), "gsei.h5"), "w") do file + file["xs"] = Float32.(flux.xs) + file["term"] = Float32.(term) + file["totali"] = Float32.(totali) + file["errori"] = Float32.(errori) + file["errlogi"] = Float32.(errlogi) + end + end + + + return equil + +end + + +end # module Equilibrium \ No newline at end of file diff --git a/src/Equilibrium/EquilibriumTypes.jl b/src/Equilibrium/EquilibriumTypes.jl new file mode 100644 index 000000000..4816a5cad --- /dev/null +++ b/src/Equilibrium/EquilibriumTypes.jl @@ -0,0 +1,394 @@ +#= +This file is the one stop shop for all the fundemental structures used in + creating equilibrium descriptions for the DCON ODE to use. +=# + +using Base: @kwdef + +# --- Helper function --- + + +function symbolize_keys(dict::Dict{String,Any}) + return Dict(Symbol(k) => v for (k, v) in dict) +end + + +# --- Main Structures for the Equilibrium Code --- + + +@kwdef mutable struct EquilibriumControl + eq_type::String = "efit" + eq_filename::String = "mypath" + + jac_type::String = "hamada" + power_bp::Int = 0 + power_b::Int = 0 + power_r::Int = 0 + + grid_type::String = "ldp" + psilow::Float64 = 1e-2 + psihigh::Float64 = 0.994 + mpsi::Int = 128 + mtheta::Int = 256 + + newq0::Int = 0 + etol::Float64 = 1e-7 + use_classic_splines::Bool = false + + input_only::Bool = false + use_galgrid::Bool = true + + """ + Modified internal constructor that enforces self consistency within the inputs + """ + function EquilibriumControl(eq_type, eq_filename, jac_type, power_bp, power_b, power_r, + grid_type, psilow, psihigh, mpsi, mtheta, newq0, etol, use_classic_splines, + input_only, use_galgrid) + if jac_type == "hamada" + @info "Forcing hamada coordinate jacobian exponents: power_*" + power_b = 0 + power_bp = 0 + power_r = 0 + elseif jac_type == "pest" + @info "Forcing pest coordinate jacobian exponents: power_*" + power_b = 0 + power_bp = 0 + power_r = 2 + elseif jac_type == "equal_arc" + @info "Forcing equal_arc coordinate jacobian exponents: power_*" + power_b = 0 + power_bp = 1 + power_r = 0 + elseif jac_type == "boozer" + @info "Forcing boozer coordinate jacobian exponents: power_*" + power_b = 2 + power_bp = 0 + power_r = 0 + elseif jac_type == "park" + @info "Forcing park coordinate jacobian exponents: power_*" + power_b = 1 + power_bp = 0 + power_r = 0 + elseif jac_type == "other" + @info "Using manual jacobian exponents: power b, bp, r = $(power_b), $(power_bp), $(power_r)" + elseif jac_type != "other" + error("Cannot recognize jac_type = $(jac_type)") + end + return new(eq_type, eq_filename, jac_type, power_bp, power_b, power_r, + grid_type, psilow, psihigh, mpsi, mtheta, newq0, etol, use_classic_splines, + input_only, use_galgrid) + end +end + +@kwdef mutable struct EquilibriumOutput + gse_flag::Bool = false + out_eq_1d::Bool = false + bin_eq_1d::Bool = false + out_eq_2d::Bool = false + bin_eq_2d::Bool = true + out_2d::Bool = false + bin_2d::Bool = false + dump_flag::Bool = false +end + + +""" + EquilibriumConfig(...) + +A container struct that bundles all necessary configuration settings originally specified in the equil + fortran namelsits. +""" +@kwdef mutable struct EquilibriumConfig + control::EquilibriumControl = EquilibriumControl() + output::EquilibriumOutput = EquilibriumOutput() +end +# + +""" +Constructor that allows users to form a EquilibriumConfig struct from dictionaries + for convinience when most of the defaults are fine. +""" +function EquilibriumConfig(control::Dict, output::Dict) + construct = EquilibriumControl(; control...) + outstruct = EquilibriumOutput(; output...) + return EquilibriumConfig(control=construct, output=outstruct) +end + +""" +Outer constructor for EquilibriumConfig that enables a toml file + interface for specifying the configuration settings +""" +# if this also have default, then conflicts with @kwdef mutable struct EquilibriumConfig. +function EquilibriumConfig(path::String) + raw = TOML.parsefile(path) + + # Extract EQUIL_CONTROL with default fallback + control_data = get(raw, "EQUIL_CONTROL", Dict()) + output_data = get(raw, "EQUIL_OUTPUT", Dict()) + + # Check for required fields in control_data + required_keys = ("eq_filename", "eq_type") + missingkeys = filter(k -> !haskey(control_data, k), required_keys) + + if !isempty(missingkeys) + error("Missing required key(s) in [EQUIL_CONTROL]: $(join(missing, ", "))") + end + + # Construct validated structs + control = EquilibriumControl(; symbolize_keys(control_data)...) + if !isabspath(control.eq_filename) + control.eq_filename = normpath(joinpath(dirname(path), control.eq_filename)) + end + output = EquilibriumOutput(; symbolize_keys(output_data)...) + + return EquilibriumConfig(control=control, output=output) +end + + + +""" + LargeAspectRatioConfig(...) + +A mutable struct holding parameters for the Large Aspect Ratio (LAR) plasma equilibrium model. + +## Fields: + +- `lar_r0`: The major radius of the plasma [m]. +- `lar_a`: The minor radius of the plasma [m]. +- `beta0`: The beta value on axis (normalized pressure). +- `q0`: The safety factor on axis. +- `p_pres`: The exponent for the pressure profile, defined as `p00 * (1 - (r / a)^2)^p_pres`. +- `p_sig`: The exponent that determines the shape of the current-related function profile. +- `sigma_type`: The type of sigma profile, can be "default" or "wesson". If "wesson", the sigma profile is defined as `sigma0 * (1 - (r / a)^2)^p_sig`. +- `mtau`: The number of grid points in the poloidal direction. +- `ma`: The number of grid points in the radial direction. +- `zeroth`: If set to true, it neglects the Shafranov shift +""" +@kwdef mutable struct LargeAspectRatioConfig + lar_r0::Float64 = 10.0 # Major radius of the plasma + lar_a::Float64 = 1.0 # Minor radius of the plasma + + beta0::Float64 = 1e-3 # beta on axis + q0::Float64 = 1.5 # q (safety factor) on axis + + p_pres::Float64 = 2.0 # p00 * (1-(r/a)**2)**p_pres + p_sig::Float64 = 1.0 # The exponent that determines the shape of the current-related function profile + + sigma_type::String = "default" # can be 'default' or 'wesson'. If 'wesson', switch sigma profile to sigma0*(1-(r/a)**2)**p_sig + + mtau::Int = 128 # the number of grid points in the poloidal direction + ma::Int = 128 # the number of grid points in the radial direction + + zeroth::Bool = false # If set to true, it neglects the Shafranov shift, creating an ideal concentric circular cross-section. +end + +""" +Outer constructor for LargeAspectRatioConfig that enables a toml file + interface for specifying the configuration settings +""" +function LargeAspectRatioConfig(path::String) + raw = TOML.parsefile(path) + input_data = get(raw, "LAR_INPUT", Dict()) + return LargeAspectRatioConfig(; symbolize_keys(input_data)...) +end + + + +""" + SolevevConfig(...) + +A mutable struct holding parameters for the Solev'ev (SOL) plasma equilibrium model. + +## Fields: + +- `mr`: number of radial grid zones +- `mz`: number of axial grid zones +- `ma`: number of flux grid zones +- `e`: elongation +- `a`: minor radius +- `r0`: major radius +- `q0`: safety factor at the o-point +- `p0fac`: scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) +- `b0fac`: scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) +- `f0fac`: scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +""" +@kwdef mutable struct SolevevConfig + mr::Int = 128 # number of radial grid zones + mz::Int = 128 # number of axial grid zones + ma::Int = 128 # number of flux grid zones + e::Float64 = 1.6 # elongation + a::Float64 = 0.33 # minor radius + r0::Float64 = 1.0 # major radius + q0::Float64 = 1.9 # safety factor at the o-point + p0fac::Float64 = 1 # scale on-axis pressure (P-> P+P0*p0fac. beta changes. Phi,q constant) + b0fac::Float64 = 1 # scale toroidal field at constant beta (s*Phi,s*f,s^2*P. bt changes. Shape,beta constant) + f0fac::Float64 = 1 # scale toroidal field at constant pressure (s*f. beta,q changes. Phi,p,bp constant) +end + +""" +Outer constructor for LarConfig that enables a toml file + interface for specifying the configuration settings +""" +function SolevevConfig(path::String) # if we use @kwdef, it generates SolevevConfig() so it conflicts with this line. + raw = TOML.parsefile(path) + input_data = get(raw, "SOL_INPUT", Dict()) + return SolevevConfig(; symbolize_keys(input_data)...) +end + + +""" + DirectRunInput(...) + +A container struct that bundles all necessary inputs for the `direct_run` function. +It is created by the `_read_efit` function after parsing the raw equilibrium file +and preparing the initial splines. + +## Fields: +- `equil_input`: The original `EquilInput` object. +- `sq_in` + # x value: psin + # Quantity 1: F = R*Bt [m T] + # Quantity 2: mu0 * Pressure (non-negative) [nt^2 / m^2 * mu0 = T^2] + # Quantity 3: q-profile + # Quantity 4: sqrt(psi_norm) +- `psi_in`: + # x, y value: R, Z [m] + # z value : poloidal flux adjusted to be zero at the boundary [Weber/radian] + # 1. ψ(R,Z) = ψ_boundary - ψ(R,Z) + # 2. if ψ = ψ * sign(ψ(centerR,centerZ)) +- `rmin`: Minimum R-coordinate of the computational grid [m]. +- `rmax`: Maximum R-coordinate of the computational grid [m]. +- `zmin`: Minimum Z-coordinate of the computational grid [m]. +- `zmax`: Maximum Z-coordinate of the computational grid [m]. +- `psio`: The total flux difference `abs(ψ_axis - ψ_boundary)` [Weber / radian]. +""" +mutable struct DirectRunInput + config::EquilibriumConfig + sq_in::Any # 1D profile spline (CubicSpline) + psi_in::Any # 2D flux spline (BicubicSpline) + rmin::Float64 # Minimum R-coordinate of the computational grid [m]. + rmax::Float64 # Maximum R-coordinate of the computational grid [m]. + zmin::Float64 # Minimum Z-coordinate of the computational grid [m]. + zmax::Float64 # Maximum Z-coordinate of the computational grid [m]. + psio::Float64 # The total flux difference |ψ_axis - ψ_boundary| [Weber / radian]. +end + +""" + InverseRunInput(...) + +A container struct for inputs to the `inverse_run` function. + +## Fields: +- `equil_input`: The original `EquilInput` object. +""" +mutable struct InverseRunInput + config::EquilibriumConfig + sq_in::Any # 1D spline input profile (e.g. F*Bt, Pressure, q) + rz_in::Any # 2D bicubic spline input for (R,Z) geometry + ro::Float64 # R axis location + zo::Float64 # Z axis location + psio::Float64 # Total flux difference |psi_axis - psi_boundary| +end + + + +@kwdef mutable struct EquilibriumParameters + ro::Union{Nothing,Float64} = nothing # R-coordinate of the magnetic axis [m] + zo::Union{Nothing,Float64} = nothing # Z-coordinate of the magnetic axis [m] + psio::Union{Nothing,Float64} = nothing # Total flux difference |Ψ_axis - Ψ_boundary| [Weber / radian] + rsep::Union{Nothing,Vector{Float64}} = nothing # R-coordinates of the plasma boundary [m] + zsep::Union{Nothing,Vector{Float64}} = nothing # Z-coordinates of the plasma boundary [m] + rext::Union{Nothing,Vector{Float64}} = nothing # R-coordinates of the plasma edge [m] + zext::Union{Nothing,Vector{Float64}} = nothing # Z-coordinates of the plasma edge [m] + psi0::Union{Nothing,Float64} = nothing # Normalized poloidal flux + b0::Union{Nothing,Float64} = nothing # Total magnetic field strength at the axis [T] + q0::Union{Nothing,Float64} = nothing # Safety factor at the axis + qmin::Union{Nothing,Float64} = nothing # Minimum safety factor in the plasma + qmax::Union{Nothing,Float64} = nothing # Maximum safety factor in the plasma + qa::Union{Nothing,Float64} = nothing # Safety factor at the plasma edge + q95::Union{Nothing,Float64} = nothing # Safety factor at 95% flux surface + qextrema_psi::Union{Nothing,Vector{Float64}} = nothing # Normalized poloidal flux values where q has extrema + qextrema_q::Union{Nothing,Vector{Float64}} = nothing # Safety factor values at the extrema points + mextrema::Union{Nothing,Int} = nothing # Number of extrema points in the q-profile + psi_norm::Union{Nothing,Float64} = nothing # Normalized poloidal flux at the axis + b_norm::Union{Nothing,Float64} = nothing # Normalized total magnetic field strength at the axis + psi_axis::Union{Nothing,Float64} = nothing # Normalized poloidal flux at the axis + psi_boundary::Union{Nothing,Float64} = nothing # Poloidal flux at the boundary + psi_boundary_norm::Union{Nothing,Float64} = nothing # Normalized poloidal flux at the boundary + psi_axis_norm::Union{Nothing,Float64} = nothing # Normalized poloidal flux at the axis + psi_boundary_offset::Union{Nothing,Float64} = nothing # Offset for the boundary poloidal flux + psi_axis_offset::Union{Nothing,Float64} = nothing # Offset for the axis poloidal flux + psi_boundary_sign::Union{Nothing,Int} = nothing # Sign of the boundary poloidal flux + psi_axis_sign::Union{Nothing,Int} = nothing # Sign of the axis poloidal flux + psi_boundary_zero::Union{Nothing,Bool} = nothing # Whether the boundary poloidal flux is zero + rmean::Union{Nothing,Float64} = nothing # Mean R-coordinate of the plasma [m] + amean::Union{Nothing,Float64} = nothing # Mean minor radius of the plasma [m] + aratio::Union{Nothing,Float64} = nothing # Aspect ratio of the plasma (R0/a) + kappa::Union{Nothing,Float64} = nothing # Elongation of the plasma cross-section + delta1::Union{Nothing,Float64} = nothing # Triangularity of the plasma cross-section (upper triangularity) + delta2::Union{Nothing,Float64} = nothing # Triangularity of the plasma cross-section (lower triangularity) + bt0::Union{Nothing,Float64} = nothing # Toroidal magnetic field at the axis [T] + crnt::Union{Nothing,Float64} = nothing # Plasma current at the axis [A] + bwall::Union{Nothing,Float64} = nothing # Toroidal magnetic field at the wall [T] + verbose::Bool = false # Whether to print verbose output + diagnose_src::Bool = false # Whether to diagnose source data + diagnose_maxima::Bool = false # Whether to diagnose maxima in the equilibrium + volume::Union{Nothing,Float64} = nothing # Plasma volume [m³] + betat::Union{Nothing,Float64} = nothing # Toroidal beta (normalized pressure) at the axis + betan::Union{Nothing,Float64} = nothing # Normalized beta at the axis + betaj::Union{Nothing,Float64} = nothing # Total beta at the axis + betap1::Union{Nothing,Float64} = nothing # Pressure beta at the axis + betap2::Union{Nothing,Float64} = nothing # Toroidal beta at the axis + betap3::Union{Nothing,Float64} = nothing # Poloidal beta at the axis + li1::Union{Nothing,Float64} = nothing # Internal inductance at the axis + li2::Union{Nothing,Float64} = nothing # External inductance at the axis + li3::Union{Nothing,Float64} = nothing # Total inductance at the axis +end + + + + + +""" + PlasmaEquilibrium(...) + +The final, self-contained result of the equilibrium reconstruction. This object +provides a complete representation of the processed plasma equilibrium in flux coordinates. + +## Fields: +- `equil_input`: The original `EquilInput` object used for the reconstruction. +- `sq`: The final 1D profile spline (`CubicSpline{Float64}`). + # x value: normalized psi + # Quantity 1: Toroidal Field Function * 2π, `F * 2π` (where `F = R * B_toroidal`) + # Quantity 2: Pressure * μ₀, `P * μ₀`. + # Quantity 3: dVdpsi + # Quantity 4: q +- `rzphi`: The final 2D flux-coordinate mapping spline (`BicubicSpline`). + # x value: normlized psi + # y value: SFL poloidal angle [0,1] + # Quantity 1: r_coord² = (R - ro)² + (Z - zo)² + # Quantity 2: Offset between the geometric poloidal angle (η) and the new angle (θ_new) + `η / (2π) - θ_new + # Quantity 3: ν in ϕ=2πζ+ν(ψ,θ) + # Quantity 4: Jacobian. +- `eqfun`: A 2D spline storing local physics and geometric quantities that vary across the flux surfaces. + # These are pre-calculated for efficient use in subsequent stability and transport codes. + # x value: Normalized poloidal flux, ψ_norm ∈ [0, 1]. + # y value: SFL poloidal angle, θ_new ∈ [0, 1]. + # Quantity 1: Total magnetic field strength, B [T] + # Quantity 2: (e₁⋅e₂ + q⋅e₃⋅e₁) / (J⋅B²). + # Quantity 3: (e₂⋅e₃ + q⋅e₃⋅e₃) / (J⋅B²). +- `ro`: R-coordinate of the magnetic axis [m]. +- `zo`: Z-coordinate of the magnetic axis [m]. +- `psio`: Total flux difference `|Ψ_axis - Ψ_boundary|` [Weber / radian]. +""" +mutable struct PlasmaEquilibrium + config::EquilibriumConfig + params::EquilibriumParameters # Parameters for the equilibrium + sq::Spl.CubicSpline # Final 1D profile spline + rzphi::Spl.BicubicSpline # Final 2D coordinate mapping spline + eqfun::Spl.BicubicSpline + ro::Float64 + zo::Float64 + psio::Float64 +end diff --git a/src/Equilibrium/InverseEquilibrium.jl b/src/Equilibrium/InverseEquilibrium.jl new file mode 100644 index 000000000..5d02f29d8 --- /dev/null +++ b/src/Equilibrium/InverseEquilibrium.jl @@ -0,0 +1,221 @@ +""" +Converts inverse equilibrium to straight-fieldline coordinates. Based on inverse.f +Of the entries we need to return: PlasmaEquilibrium(equil_params, sq_out, rzphi_out, eqfun_out, ro, zo, psio), +we only need to generate: sq_out, rzphi_out, eqfun_out. This is because we pass in InverseRunInput(equil_in, +sq_in, rz_in, ro, zo, psio). + +""" + +""" + inverse_extrap(xx::Matrix{Float64}, ff::Matrix{Float64}, x::Float64) -> Vector{Float64} + +Performs component-wise Lagrange extrapolation for a vector-valued function. + +## Arguments: +- `xx`: A (m × n) matrix where each row contains the x-values for each component. +- `ff`: A (m × n) matrix where each row contains function values at the corresponding `xx`. +- `x`: A scalar Float64 value at which to extrapolate. + +## Returns: +- A vector of length n representing the extrapolated function values at `x`. +""" +function inverse_extrap(xx::Matrix{Float64}, ff::Matrix{Float64}, x::Float64)::Vector{Float64} + m, n = size(ff) # m = number of data points, n = number of components + f = zeros(Float64, n) # Output vector + + for i in 1:m + term = copy(ff[i, :]) # Start with f_i (vector) + for j in 1:m + if j == i + continue + end + term .= term .* ((x .- xx[j, :]) ./ (xx[i, :] .- xx[j, :])) + end + f .+= term # Accumulate to output + end + + return f +end + + + +function equilibrium_solver(input::InverseRunInput) + println("--- Starting Inverse Equilibrium Processing ---") + # Extract input parameters + + config = input.config + rz_in = input.rz_in + sq_in = input.sq_in + ro = input.ro + zo = input.zo + psio = input.psio + + grid_type = config.control.grid_type + mpsi = config.control.mpsi + mtheta = config.control.mtheta + psilow = config.control.psilow + psihigh = config.control.psihigh + newq0 = config.control.newq0 + + me = 3 + interp = false + diagnose_rz_in = false + diagnose_rzphi = false + + # c----------------------------------------------------------------------- + # c allocate and define local arrays. + # c----------------------------------------------------------------------- + # sq_in._fs[:, 3] .= sqrt.(sq_in._xs) + rz_in._xs = sq_in._xs + rz_in._ys = collect(0:rz_in.my) ./ rz_in.my + + mx = rz_in.mx + my = rz_in.my + + x = rz_in.fs[:, :, 1] .- ro + y = rz_in.fs[:, :, 2] .- zo + r2 = x.^2 .+ y.^2 + + twopi = 2 * pi + + deta = zeros(Float64, mx+1, my+1) + for ipsi in 0:mx, itheta in 0:my + if r2[ipsi+1, itheta+1] == 0.0 + deta[ipsi+1, itheta+1] = 0.0 + else + deta[ipsi+1, itheta+1] = atan(y[ipsi+1, itheta+1], x[ipsi+1, itheta+1]) / twopi + end + end + + # c----------------------------------------------------------------------- + # c transform input coordinates from cartesian to polar. + # c----------------------------------------------------------------------- + for ipsi in 0:mx + for itheta in 1:my + Δ = deta[ipsi+1, itheta+1] - deta[ipsi+1, itheta] + if Δ > 0.5 + deta[ipsi+1, itheta+1] -= 1 + elseif Δ < -0.5 + deta[ipsi+1, itheta+1] += 1 + end + end + for itheta in 0:my + if r2[ipsi+1, itheta+1] > 0 + deta[ipsi+1, itheta+1] -= rz_in.ys[itheta+1] + end + end + end + + deta[1, :] = inverse_extrap(r2[2:me+1, :], deta[2:me+1, :], 0.0) + + rz_in_fs = zeros(Float64, mx+1, my+1, 3) + rz_in_fs[:, :, 1] = r2 + rz_in_fs[:, :, 2] = deta + + rz_spline = Spl.BicubicSpline(rz_, rz_in.xs, rz_in.ys; bctypex="extrap", bctypey="periodic") + + # c----------------------------------------------------------------------- + # c prepare new spline type for surface quantities. + # c----------------------------------------------------------------------- + + if grid_type in ["original", "orig"] + mpsi = size(sq_in._fs, 1) - 1 + end + + # c----------------------------------------------------------------------- + # c set up radial grid (only "ldp" implemented) + # c----------------------------------------------------------------------- + if grid_type == "ldp" + xs = psilow .+ (psihigh - psilow) .* (sin.(range(0.0, 1.0; length=mpsi+1) .* (π/2))).^2 + fs = zeros(Float64, mpsi+1, 4) + sq = Spl.spline_setup(xs, fs; bctype="extrap") + else + error("Only 'ldp' grid_type is implemented for now.") + end + + local rzphi::Spl.BicubicSplineType + local eqfun::Spl.BicubicSplineType + + # c----------------------------------------------------------------------- + # c prepare new bicube type for coordinates. + # c----------------------------------------------------------------------- + if mtheta == 0 + mtheta = rz_in.my + end + + # (/" r2 "," deta "," dphi "," jac "/) + rzphi_fs = zeros(Float64, mpsi+1, mtheta+1, 4) + rzphi_xs = copy(sq_xs) + rzphi_ys = collect(0:mtheta) ./ mtheta + + # (/" b0 "," "," " /) + eqfun_fs = zeros(Float64, mpsi+1, mtheta+1, 3) + eqfun_xs = copy(sq_xs) + eqfun_ys = collect(0:mtheta) ./ mtheta + + rzphi = Spl.bicube_setup(copy(sq.xs), collect(0:mtheta) ./ mtheta, rzphi_fs) + eqfun = Spl.bicube_setup(copy(sq.xs), collect(0:mtheta) ./ mtheta, eqfun_fs) + + + # spl_xs = zeros(Float64,mtheta+1) + # spl_fs = zeros(Float64,mtheta+1, 5) + # spl = Spl.spline_setup(spl_xs, spl_fs; bctype="extrap") + + for ipsi in 0:mpsi + psifac = rzphi_xs[ipsi+1] + f_sq_in = Spl.spline_eval(sq_in, psifac, 0) + spl_xs .= rzphi_ys + for itheta in 0:mtheta + theta = rzphi_ys[itheta+1] + f_rz_in, fx_rz_in, fy_rz_in = Spl.bicube_eval(new_rz_in, psifac, theta, 1) + f_sq_in = Spl.spline_eval(sq_in, psifac, 0) + + if f_rz_in[1] < 0 + error("Invalid extrapolation near axis, rerun with larger value of psilow") + end + + rfac = sqrt(f_rz_in[1]) + r = ro + rfac * cos(twopi * (theta + f_rz_in[2])) + jacfac = fx_rz_in[1] * (1 + fy_rz_in[2]) - fy_rz_in[1] * fx_rz_in[2] + w11 = (1 + fy_rz_in[2]) * twopi^ 2 * rfac / jacfac + w12 = -fy_rz_in[1] * pi / (rfac * jacfac) + bp = psio * sqrt(w11*w11 + w12*w12) / r + bt = f_sq_in[1] / r + b = sqrt(bp*bp + bt*bt) + + # spl.fs[itheta+1, 1] = f_rz_[1] + # spl.fs[itheta+1, 2] = f_rz_[2] + # spl.fs[itheta+1, 3] = r*jacfac + # spl.fs[itheta+1, 4] = spl.fs[itheta+1, 3]/(r*r) + # spl.fs[itheta+1, 5] = spl.fs[itheta+1, 3]*bp^(config.power_bp)*b^(config.power_b)/r^(config.power_r) + end + + # spl.xs = spl.integral!() + # spl.xs = spl.fsi[:, 5] ./ spl.fs[end, 5] + # spl.fs[:, 2] .= spl.fs[:, 2] .+ rzphi.ys .- spl.xs + # spl.fs[:, 4] .= (spl.fs[:, 3] ./ spl.fsi[end, 3]) ./ (spl.fs[:, 5] ./ spl.fsi[end, 5]) .* spl.fsi[end, 3] * twopi * pi + # spl.fs[:, 3] .= f_sq[1] * pi / psio .* (spl.fsi[:, 4] .- spl.fsi[end, 4] .* spl.xs) + # # spl.xs = Spl.spline_setup(spl.xs, spl.fs; bctype="periodic").integral!() + + for itheta in 0:mtheta + theta = rzphi_ys[itheta+1] + fs = Spl.spline_eval(spl, theta, 0) + rzphi_fs[ipsi+1, itheta+1, :] = fs[1:4] + end + + sq_fs[ipsi+1, 1] = f_sq_in[1] * twopi + sq_fs[ipsi+1, 2] = f_sq_in[2] + sq_fs[ipsi+1, 3] = spl.fsi[mtheta+1, 3] * twopi * pi # dV/d(psi) + sq_fs[ipsi+1, 4] = spl.fsi[mtheta+1, 4] * sq_fs[ipsi+1, 1] / (2 * twopi * psio) # q-profile + end + + # # sq = Spl.spline_setup(sq.xs, sq.fs; bctype="extrap") + # f = Spl.spline_eval(sq, sq.xs[1], 0) + # _, f1 = Spl.spline_eval(sq, sq.xs[1], 1) + # q0 = f[4] - f1[4] * sq.xs[1] + + # if newq0 == -1 + # newq0 = -q0 + # end + +end \ No newline at end of file diff --git a/src/Equilibrium/ReadEquilibrium.jl b/src/Equilibrium/ReadEquilibrium.jl new file mode 100644 index 000000000..9f645b0e7 --- /dev/null +++ b/src/Equilibrium/ReadEquilibrium.jl @@ -0,0 +1,409 @@ +#= +This file contains functions for reading equilibrium files from diferent codes + that use different formating and collecting the inputs required to form + a complete PlasmaEquilibrium using either direct or inverse construction +=# + + +""" +_read_1d_gfile_format(lines_block, num_values) + +Internal helper function to parse Fortran-style fixed-width numerical blocks +from a vector of strings. + +## Arguments: +- `lines_block`: A `Vector{String}` containing the lines to parse. +- `num_values`: The total number of `Float64` values to read from the block. +## Returns: +- A `Vector{Float64}` containing the parsed values. +""" +function _read_1d_gfile_format(lines_block::Vector{String}, num_values::Int) + data_str = join(lines_block) + field_width = 16 + parsed_values = Float64[] + num_read = 0 + + # Ensure the string length is a multiple of the field width for safe processing + safe_len = (length(data_str) ÷ field_width) * field_width + for i in 1:field_width:safe_len + num_read >= num_values && break + val_str = strip(data_str[i : i + field_width - 1]) + if !isempty(val_str) + try + push!(parsed_values, parse(Float64, val_str)) + num_read += 1 + catch e + @warn "Parsing error for substring: '$val_str'. Error: $e. Skipping." + end + end + end + + if num_read < num_values + @warn "Expected $num_values values, but only read $num_read." + end + return parsed_values +end + +""" + _read_efit(equil_in) + +Parses an EFIT g-file, creates initial 1D and 2D splines, and bundles +them into a `DirectRunInput` object. + +## Arguments: +- `equil_in`: The `EquilInput` object containing the filename and parameters. +## Returns: +- A `DirectRunInput` object ready for the direct solver. +""" +function read_efit(config::EquilibriumConfig) + println("--> Processing EFIT g-file: $(config.control.eq_filename)") + lines = readlines(config.control.eq_filename) + + # --- Parse Header --- + header1_parts = split(lines[1]) + nw = parse(Int, header1_parts[end-1]) + nh = parse(Int, header1_parts[end]) + println("--> Parsed from header: nw=$nw, nh=$nh") + + header_vals = _read_1d_gfile_format(lines[2:5], 20) + rdim, zdim, rcentr, rleft, zmid = header_vals[1:5] + rmaxis, zmaxis, simag, sibry = header_vals[6:9] + + # --- Parse Data Blocks --- + current_line_idx = 6 + function parse_block(num_pts) + num_lines = ceil(Int, num_pts / 5) + block = lines[current_line_idx : current_line_idx + num_lines - 1] + data = _read_1d_gfile_format(block, num_pts) + current_line_idx += num_lines + return data + end + + fpol_data = parse_block(nw) + pres_data = parse_block(nw) + ffprime_data = parse_block(nw) + pprime_data = parse_block(nw) + psi_flat_vec = parse_block(nw * nh) + qprof_data = parse_block(nw) + + psi_rz = reshape(psi_flat_vec, nw, nh) + println("--> All main data blocks parsed successfully.") + + # --- Create 1D Profile Spline (sq_in) --- + println("--> Creating 1D profile splines...") + psi_norm_grid = range(0.0, 1.0, length=nw) + sq_fs_nodes = hcat( + abs.(fpol_data), + max.(pres_data .* mu0, 0.0), + qprof_data, + sqrt.(psi_norm_grid) + ) + # According to Spline_document.txt, bctype=4 is Not-a-Knot + sq_in = Spl.CubicSpline(collect(psi_norm_grid), sq_fs_nodes, bctype=4) + println("--> 1D Spline fitting complete.") + + # --- Process and Normalize 2D Psi Data --- + psio_signed = sibry - simag + psi_proc = (sibry .- psi_rz) + psio = abs(psio_signed) + # Ensure psi at the magnetic axis is positive relative to the boundary + if psio_signed < 0.0 + psi_proc .*= -1.0 + end + + # --- Create 2D Psi Spline (psi_in) --- + println("--> Creating 2D psi spline...") + r_grid = range(rleft, rleft + rdim, length=nw) + z_grid = range(zmid - zdim / 2, zmid + zdim / 2, length=nh) + rmin, rmax = extrema(r_grid) + zmin, zmax = extrema(z_grid) + + psi_proc_3d = reshape(psi_proc, (nw, nh, 1)) + psi_in = Spl.BicubicSpline(collect(r_grid), collect(z_grid), psi_proc_3d, bctypex=4, bctypey=4) + println("--> 2D Spline fitting complete.") + + # --- Bundle everything for the solver --- + return DirectRunInput(config, sq_in, psi_in, rmin, rmax, zmin, zmax, psio) +end + +""" + _read_chease2(equil_in) + +Parses a chease2 file, creates initial 1D and 2D splines, finds magnetic axis, and bundles +them into a `InverseRunInput` object. + +## Arguments: +- `equil_in`: The `EquilInput` object containing the filename and parameters. +## Returns: +- A `InverseRunInput` object ready for the inverse solver. +""" +function read_chease2(config::EquilibriumConfig) + println("--> Reading CHEASE file: $(config.control.eq_filename)") + lines = readlines(config.control.eq_filename) + + # --- Parse Header (FORMAT 10: 3I5) --- + header_parts = split(lines[1]) + ntnova = parse(Int, header_parts[1]) + npsi1 = parse(Int, header_parts[2]) + nsym = parse(Int, header_parts[3]) + + # --- Parse axx (FORMAT 20: 1E22.15) --- + axx = parse(Float64, split(lines[2])[1]) + + # --- Pre-allocate Arrays --- + zcpr = zeros(npsi1 - 1) + zcppr = zeros(npsi1) + zq = zeros(npsi1) + zdq = zeros(npsi1) + ztmf = zeros(npsi1) + ztp = zeros(npsi1) + zfb = zeros(npsi1) + zfbp = zeros(npsi1) + zpsi = zeros(npsi1) + zpsim = zeros(npsi1 - 1) + + zrcp = zeros(ntnova + 3, npsi1) + zzcp = zeros(ntnova + 3, npsi1) + zjacm = zeros(ntnova + 3, npsi1) + zjac = zeros(ntnova + 3, npsi1) + + # --- Helper to parse 5E22.15 data per line --- + function parse_floats(lines_range) + data = Float64[] + for line in lines[lines_range] + for i in 0:4 + s = strip(line[22*i+1:min(end, 22*(i+1))]) + if !isempty(s) + push!(data, parse(Float64, s)) + end + end + end + return data + end + + # --- Compute line offsets --- + line_idx = 3 # Start after header (line 1) and axx (line 2) + + function load_vector!(vec) + count = length(vec) + lines_needed = cld(count, 5) + vec .= parse_floats(line_idx : line_idx + lines_needed - 1) + line_idx += lines_needed + end + + function load_matrix!(mat) + count = size(mat, 1) * size(mat, 2) + lines_needed = cld(count, 5) + data = parse_floats(line_idx : line_idx + lines_needed - 1) + line_idx += lines_needed + # Fill column-major (Fortran-style) + for j in 1:size(mat, 2) + for i in 1:size(mat, 1) + mat[i, j] = data[(j-1)*size(mat,1) + i] + end + end + end + + # --- Read Vectors --- + load_vector!(zcpr) + load_vector!(zcppr) + load_vector!(zq) + load_vector!(zdq) + load_vector!(ztmf) + load_vector!(ztp) + load_vector!(zfb) + load_vector!(zfbp) + load_vector!(zpsi) + load_vector!(zpsim) + + # --- Read Matrices --- + load_matrix!(zrcp) + load_matrix!(zzcp) + load_matrix!(zjacm) + load_matrix!(zjac) + + println("--> Parsed from header: ntnova = $ntnova, npsi1 = $npsi1, nsym = $nsym") + + # Number of spline intervals + ma = npsi1 - 1 + # Total ψ range for normalization + psio = zpsi[end] - zpsi[1] + # Normalize ψ to [0, 1] + xs = (zpsi .- zpsi[1]) ./ psio + # Construct fs matrix: (npsi1 rows, 4 columns) + fs = zeros(npsi1, 4) + fs[:, 1] .= zq .* zfb + fs[:, 2] .= zcppr + fs[:, 3] .= zq + # Fit spline with extrapolation boundary condition (bctype = 3) + sq_in = Spl.CubicSpline(xs, fs; bctype=3) + # --- Integrate pressure --- + Spl.spline_integrate!(sq_in) # Integrate in-place, sq_in.fsi filled + # Make a writable copy of the fs array + fs_copy = copy(sq_in.fs) + # Normalize pressure integral column (2nd column) + fs_copy[:, 2] .= (sq_in.fsi[:, 2] .- sq_in.fsi[ma, 2]) .* psio + # Refit spline using the modified fs_copy + sq_in = Spl.CubicSpline(sq_in._xs, fs_copy; bctype=3) + + # --- Copy 2D geometry arrays --- + mtau = ntnova+1 + ro = zrcp[1, 1] + zo = zzcp[1, 1] + ys = range(0, 2π, length=mtau) |> collect + # Allocate and fill fs array (radial × poloidal × 2 quantities) + fs = zeros(length(xs), length(ys), 2) + fs[:, :, 1] .= transpose(zrcp[1:ntnova+1, :]) + fs[:, :, 2] .= transpose(zzcp[1:ntnova+1, :]) + + + # Setup bicubic spline with periodic boundary conditions (bctype=2) + rz_in = Spl.BicubicSpline(xs, ys, fs; bctypex=2, bctypey=2) + println("--> Finished reading CHEASE equilibrium.") + println(" Magnetic axis at (ro=$ro, zo=$zo), psio=$psio") + return InverseRunInput(config,sq_in,rz_in,ro,zo,psio) +end + +""" + _read_chease(equil_config) + +Parses a binary CHEASE file, creates initial 1D and 2D splines, and bundles +them into a `InverseRunInput` object. + +## Arguments: +- `equil_config`: The `EquilConfig` object containing the filename and parameters. +## Returns: +- A `InverseRunInput` object ready for the inverse solver. +""" + +function read_chease(config::EquilibriumConfig) + println("--> Reading CHEASE file: $(config.control.eq_filename)") + diagnostics = false # Set to true to enable detailed print output + open(config.control.eq_filename, "r") do io + # Read first 3 integers + seekstart(io) + read(io, UInt32) # skip record length at start + ntnova = read(io, Int32) + npsi1 = read(io, Int32) + nsym = read(io, Int32) + read(io, UInt32) # skip record length at end + + if diagnostics + println("Header:") + println(" ntnova = $ntnova Type=$(typeof(ntnova)) Bytes=$(sizeof(ntnova))") + println(" npsi1 = $npsi1 Type=$(typeof(npsi1)) Bytes=$(sizeof(npsi1))") + println(" nsym = $nsym Type=$(typeof(nsym)) Bytes=$(sizeof(nsym))") + end + + # Read next 5 Float64 values (axx) + read(io, UInt32) # skip record length at start + axx = [read(io, Float64) for _ in 1:5] + if diagnostics + println("\naxx array (expected 5 Float64 values):") + for (i, val) in enumerate(axx) + println(" axx[$i] = $val Type=$(typeof(val)) Bytes=$(sizeof(val))") + end + end + read(io, UInt32) # skip record length at end + + # --- Helper function --- + function print_summary(name, arr) + n = length(arr) + first5 = arr[1:min(5, n)] + last5 = arr[max(1, n-4):end] + println("$name first 5: ", first5) + println("$name last 5: ", last5) + end + + # --- Pre-allocate Arrays --- + zcpr = zeros(npsi1 - 1) + zcppr = zeros(npsi1) + zq = zeros(npsi1) + zdq = zeros(npsi1) + ztmf = zeros(npsi1) + ztp = zeros(npsi1) + zfb = zeros(npsi1) + zfbp = zeros(npsi1) + zpsi = zeros(npsi1) + zpsim = zeros(npsi1 - 1) + + # --- Read 1D arrays from file --- + for (name, arr) in zip( + ("zcpr","zcppr","zq","zdq","ztmf","ztp","zfb","zfbp","zpsi","zpsim"), + (zcpr, zcppr, zq, zdq, ztmf, ztp, zfb, zfbp, zpsi, zpsim) + ) + read(io, UInt32) # skip record length at start + read!(io, arr) + read(io, UInt32) # skip record length at end + if diagnostics print_summary(name, arr); end + end + + # --- Prepare spline & geometry --- + ma = npsi1 - 1 + psio = zpsi[npsi1] - zpsi[1] + xs = (zpsi .- zpsi[1]) ./ psio + + fs = zeros(npsi1, 4) + fs[:, 1] .= ztmf + fs[:, 2] .= zcppr + fs[:, 3] .= zq + + sq_in = Spl.spline_setup(xs, fs; bctype=3) + Spl.spline_integrate!(sq_in) + fs_copy = copy(sq_in.fs) + fs_copy[:, 2] .= (sq_in.fsi[:, 2] .- sq_in.fsi[ma, 2]) .* psio + sq_in = Spl.spline_setup(sq_in._xs, fs_copy; bctype=3) + + # --- Setup parameters --- + mtau = ntnova + + # Allocate fs array (radial × poloidal × 2) + fs = zeros(npsi1, mtau, 2) + + # Allocate buffer (Fortran: ALLOCATE(buffer(ntnova+3, npsi1))) + buffer = zeros(Float64, ntnova+3, npsi1) + + # --- First read (R data) --- + read(io, UInt32) # skip record length at start + read!(io, buffer) # READ(in_unit) buffer + read(io, UInt32) # skip record length at end + ro = buffer[1, 1] # ro = buffer(1,1) + if diagnostics println("ro = $ro"); end + + # Fill with r-coordinates + fs[:, :, 1] .= transpose(buffer[1:ntnova, :]) + + # --- Second read (Z data) --- + read(io, UInt32) # skip record length at start + read!(io, buffer) # READ(in_unit) buffer + read(io, UInt32) # skip record length at end + zo = buffer[1, 1] # zo = buffer(1,1) + if diagnostics println("zo = $zo"); end + + # Fill with z-coordinates + fs[:, :, 2] .= transpose(buffer[1:ntnova, :]) + + # Construct ys grid (0..2π, length = mtau) + ys = range(0, 2π, length=mtau) |> collect + + # Setup bicubic spline with periodic boundary conditions + rz_in = Spl.bicube_setup(xs, ys, fs; bctypex=2, bctypey=2) + + if diagnostics + # --- Print first 5 and last 5 entries of each slice --- + for k in 1:2 + flat = vec(fs[:, :, k]) # flatten to 1D + n = length(flat) + println("Slice $k:") + println(" First 5 entries: ", flat[1:5]) + println(" Last 5 entries: ", flat[n-4:n]) + end + end + + + println("--> Finished reading CHEASE equilibrium.") + println(" Magnetic axis at (ro=$ro, zo=$zo), psio=$psio") + + return InverseRunInput(config, sq_in, rz_in, ro, zo, psio) + end +end \ No newline at end of file diff --git a/src/JPEC.jl b/src/JPEC.jl index 7b0217831..ed5cb889b 100644 --- a/src/JPEC.jl +++ b/src/JPEC.jl @@ -1,11 +1,23 @@ +# JPEC.jl module JPEC -include(joinpath(@__DIR__, "..", "deps", "build.jl")) - include("Splines/Splines.jl") +import .SplinesMod as Spl +export SplinesMod, Spl + +include("Equilibrium/Equilibrium.jl") +import .Equilibrium as Equilibrium +export Equilibrium + include("Vacuum/Vacuum.jl") -using .SplinesMod -using .VacuumMod +import .VacuumMod as VacuumMod +export VacuumMod + +include("DCON/DCON.jl") +import .DCON as DCON +export DCON +include(joinpath(@__DIR__, "..", "deps", "build_helpers.jl")) +export build_fortran, build_spline_fortran, build_vacuum_fortran -end \ No newline at end of file +end # module JPEC \ No newline at end of file diff --git a/src/Splines/BicubicSpline.jl b/src/Splines/BicubicSpline.jl index 3ce638b2b..53159fa56 100644 --- a/src/Splines/BicubicSpline.jl +++ b/src/Splines/BicubicSpline.jl @@ -1,251 +1,187 @@ -module BicubicSpline - -const libdir = joinpath(@__DIR__, "..", "..", "deps") -const libspline = joinpath(libdir, "libspline") - -export bicube_setup, bicube_eval - -mutable struct BicubicSplineType - handle::Ptr{Cvoid} - xs::Vector{Float64} - ys::Vector{Float64} - fs::Array{Float64,3} # 3D array for bicubic spline values - mx::Int64 - my::Int64 - nqty::Int64 - ix::Int32 # Index of x position in the spline - iy::Int32 # Index of y position in the spline - bctypex::Int32 # Boundary condition type for x - bctypey::Int32 # Boundary condition type for y +mutable struct BicubicSpline + handle::Ptr{Cvoid} + _xs::Vector{Float64} + _ys::Vector{Float64} + _fs::Array{Float64, 3} # 3D array for bicubic spline values + mx::Int + my::Int + nqty::Int + bctypex::Int32 # Boundary condition type for x + bctypey::Int32 # Boundary condition type for y + + _fsx::Array{Float64, 3} + _fsy::Array{Float64, 3} + _fsxy::Array{Float64, 3} end -function _MakeBicubicSpline(mx::Int64, my::Int64, nqty::Int64) - h = Ref{Ptr{Cvoid}}() - ccall((:bicube_c_create, libspline), Cvoid, - (Int64, Int64, Int64, Ref{Ptr{Cvoid}}), mx, my, nqty, h) - return BicubicSplineType(h[], Vector{Float64}(undef, mx), Vector{Float64}(undef, my), - Array{Float64,3}(undef, mx, my, nqty), mx, my, nqty, 0, 0, 0, 0) -end +@expose_fields BicubicSpline xs ys fs fsx fsy fsxy -function _bicube_setup(xs::Vector{Float64}, ys::Vector{Float64}, fs::Array{Float64,3}, bctypex::Int32, bctypey::Int32) - # xs -> Float64 (mx) - # ys -> Float64 (my) - # fs -> Float64 (mx, my, nqty) - if length(xs) != size(fs, 1) || length(ys) != size(fs, 2) - error("Length of xs must match number of rows in fs and length of ys must match number of columns in fs") +function _destroy_bicubic_spline(bicube::BicubicSpline) + if bicube.handle != C_NULL + ccall((:bicube_c_destroy, libspline), Cvoid, (Ptr{Cvoid},), bicube.handle) + Core.setfield!(bicube, :handle, C_NULL) end - mx = length(xs) - 1 - my = length(ys) - 1 - nqty = size(fs, 3) - bicube = _MakeBicubicSpline(mx, my, nqty) - bicube.xs = xs - bicube.ys = ys - bicube.fs = fs - bicube.bctypex = Int32(bctypex) - bicube.bctypey = Int32(bctypey) - - ccall((:bicube_c_setup, libspline), Cvoid, - (Ptr{Cvoid}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}), - bicube.handle, xs, ys, fs) - - ccall((:bicube_c_fit, libspline), Cvoid, - (Ptr{Cvoid}, Int32, Int32), bicube.handle, bctypex, bctypey) - return bicube end -""" - bicube_setup(xs, ys, fs, bctypex=1, bctypey=1) +function BicubicSpline(mx::Int, my::Int, nqty::Int, bctypex::Integer, bctypey::Integer; + xs::Vector{Float64} = Float64[], + ys::Vector{Float64} = Float64[], + fs::Array{Float64, 3} = Array{Float64}(undef, 0, 0, 0), + fsx = similar(fs), fsy = similar(fs), fsxy = similar(fs)) + h = Ref{Ptr{Cvoid}}() + ccall((:bicube_c_create, libspline), Cvoid, + (Int64, Int64, Int64, Ref{Ptr{Cvoid}}), mx, my, nqty, h) + return BicubicSpline(h[], xs, ys, fs, mx, my, nqty, Int32(bctypex), Int32(bctypey), fsx, fsy, fsxy) +end -Set up a bicubic spline interpolation for 2D data. +function _bicube_setup(xs::Vector{Float64}, ys::Vector{Float64}, fs::Array{Float64, 3}, bctypex::Integer, bctypey::Integer) + # xs -> Float64 (mx) + # ys -> Float64 (my) + # fs -> Float64 (mx, my, nqty) + @assert length(xs) == size(fs, 1) "Length of xs must match number of rows in fs" + @assert length(ys) == size(fs, 2) "Length of ys must match number of columns in fs" + mx = length(xs) - 1 + my = length(ys) - 1 + nqty = size(fs, 3) -# Arguments + bicube = BicubicSpline(mx, my, nqty, Int32(bctypex), Int32(bctypey); xs, ys, fs) - - `xs`: Vector of Float64 values representing the x-coordinates (must be monotonically increasing) - - `ys`: Vector of Float64 values representing the y-coordinates (must be monotonically increasing) - - `fs`: 3D array of Float64 values with dimensions (nx, ny, nqty) representing function values - - `bctypex`: Boundary condition type for x-direction (default is 1) - - `bctypey`: Boundary condition type for y-direction (default is 1) + ccall((:bicube_c_setup, libspline), Cvoid, + (Ptr{Cvoid}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}), + bicube.handle, xs, ys, fs) - + 1: Natural spline (zero second derivative at boundaries) - + 2: Periodic spline - + 3: Extrapolated spline - + 4: Not-a-knot spline + ccall((:bicube_c_fit, libspline), Cvoid, + (Ptr{Cvoid}, Int32, Int32, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}), + bicube.handle, bicube.bctypex, bicube.bctypey, bicube._fsx, bicube._fsy, bicube._fsxy) -# Returns + return bicube +end - - A `BicubicSplineType` object that can be used for 2D evaluation +""" +BicubicSpline(xs, ys, fs; + bctypex::Union{String, Int}="not-a-knot", bctypey::Union{String, Int}="not-a-knot") + + ## Arguments: + - `xs`: A vector of Float64 values representing the x-coordinates. + - `ys`: A vector of Float64 values representing the y-coordinates. + - `fs`: A 3D array of Float64 values representing the function values at the (x,y) coordinates. + ## Keyword Arguments: + - `bctypex`: An integer specifying the boundary condition type for x (Default is 4, not a knot) + - `bctypey`: An integer specifying the boundary condition type for y (Default is 4, not a knot) + ## Returns: + - A `BicubicSpline` object containing the spline handle, x-coordinates, y-coordinates, + function values, number of x-coordinates, number of y-coordinates, number of quantities, + and boundary condition types. +""" +function BicubicSpline(xs::Vector{Float64}, ys::Vector{Float64}, fs::Array{Float64, 3}; + bctypex::Union{String, Int}="not-a-knot", bctypey::Union{String, Int}="not-a-knot") -# Examples + bctype_code_x = parse_bctype(bctypex) + bctype_code_y = parse_bctype(bctypey) -```julia -# Create 2D grid -xs = collect(range(0.0; stop=2π, length=20)) -ys = collect(range(0.0; stop=2π, length=20)) + bicube = _bicube_setup(xs, ys, fs, Int32(bctype_code_x), Int32(bctype_code_y)) -# Create 3D function data array -fs = zeros(20, 20, 1) -for i in 1:20, j in 1:20 - fs[i, j, 1] = sin(xs[i]) * cos(ys[j]) -end + finalizer(_destroy_bicubic_spline, bicube) -# Set up bicubic spline -bcspline = bicube_setup(xs, ys, fs, 1, 1) -``` -""" -function bicube_setup(xs, ys, fs, bctypex::Int=1, bctypey::Int=1) - if !isa(xs, Vector{Float64}) || !isa(ys, Vector{Float64}) || !isa(fs, Array{Float64,3}) - error("xs must be a vector of Float64, ys must be a vector of Float64, and fs must be a 3D array of Float64") - end - bicube = _bicube_setup(xs, ys, fs, Int32(bctypex), Int32(bctypey)) - return bicube + return bicube end -function _bicube_eval(bicube::BicubicSplineType, x::Float64, y::Float64, derivs::Int=0) - # x -> Float64 - # y -> Float64 - # Returns a vector of Float64 (nqty) - f = Vector{Float64}(undef, bicube.nqty) - fx = Vector{Float64}(undef, bicube.nqty) - fy = Vector{Float64}(undef, bicube.nqty) - fxx = Vector{Float64}(undef, bicube.nqty) - fxy = Vector{Float64}(undef, bicube.nqty) - fyy = Vector{Float64}(undef, bicube.nqty) - if derivs == 0 - ccall((:bicube_c_eval, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Float64, Ptr{Float64}, Int32, Int32), - bicube.handle, x, y, f, bicube.ix, bicube.iy) - elseif derivs == 1 - ccall((:bicube_c_eval_deriv, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Float64, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Int32, Int32), - bicube.handle, x, y, f, fx, fy, bicube.ix, bicube.iy) - elseif derivs == 2 - ccall((:bicube_c_eval_deriv2, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Float64, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Int32, Int32), - bicube.handle, x, y, f, fx, fy, fxx, fxy, fyy, bicube.ix, bicube.iy) - else - error("Invalid number of derivatives requested: $derivs. Must be 0, 1, or 2.") - end - if derivs == 0 - return f - elseif derivs == 1 - return f, fx, fy - elseif derivs == 2 - return f, fx, fy, fxx, fxy, fyy - else - error("Invalid number of derivatives requested: $derivs. Must be 0, 1, or 2.") - end +function call_bicube_c_eval(bicube, x, y, f) + ccall((:bicube_c_eval, libspline), Cvoid, + (Ptr{Cvoid}, Float64, Float64, Ptr{Float64}), + bicube.handle, x, y, f) end - -function _bicube_eval(bicube::BicubicSplineType, xs::Vector{Float64}, ys::Vector{Float64}, derivs::Int=0) - # xs -> Float64 (any length) - # ys -> Float64 (any length) - # Returns a matrix of Float64 (length(xs), length(ys), nqty) - - n = length(xs) - m = length(ys) - # fs = Array{Float64}(undef, n, m, bicube.nqty) - # fsx = Array{Float64}(undef, n, m, bicube.nqty) - # fsy = Array{Float64}(undef, n, m, bicube.nqty) - # fsxx = Array{Float64}(undef, n, m, bicube.nqty) - # fsxy = Array{Float64}(undef, n, m, bicube.nqty) - # fsyy = Array{Float64}(undef, n, m, bicube.nqty) - # f = Vector{Float64}(undef, bicube.nqty) - # fx = Vector{Float64}(undef, bicube.nqty) - # fy = Vector{Float64}(undef, bicube.nqty) - # fxx = Vector{Float64}(undef, bicube.nqty) - # fxy = Vector{Float64}(undef, bicube.nqty) - # fyy = Vector{Float64}(undef, bicube.nqty) - fs = Array{Float64}(undef, n, m, bicube.nqty) - f = Vector{Float64}(undef, bicube.nqty) - if derivs > 0 - fsx = Array{Float64}(undef, n, m, bicube.nqty) - fsy = Array{Float64}(undef, n, m, bicube.nqty) - fx = Vector{Float64}(undef, bicube.nqty) - fy = Vector{Float64}(undef, bicube.nqty) - end - if derivs > 1 - fsxx = Array{Float64}(undef, n, m, bicube.nqty) - fsxy = Array{Float64}(undef, n, m, bicube.nqty) - fsyy = Array{Float64}(undef, n, m, bicube.nqty) - fxx = Vector{Float64}(undef, bicube.nqty) - fxy = Vector{Float64}(undef, bicube.nqty) - fyy = Vector{Float64}(undef, bicube.nqty) - end - for i in 1:n - for j in 1:m - if derivs == 0 - f = _bicube_eval(bicube, xs[i], ys[j], 0) - fs[i, j, :] = f - elseif derivs == 1 - f, fx, fy = _bicube_eval(bicube, xs[i], ys[j], 1) - fs[i, j, :] = f - fsx[i, j, :] = fx - fsy[i, j, :] = fy - elseif derivs == 2 - f, fx, fy, fxx, fxy, fyy = _bicube_eval(bicube, xs[i], ys[j], 2) - fs[i, j, :] = f - fsx[i, j, :] = fx - fsy[i, j, :] = fy - fsxx[i, j, :] = fxx - fsxy[i, j, :] = fxy - fsyy[i, j, :] = fyy - else - error("Invalid number of derivatives requested: $derivs. Must be 0, 1, or 2.") - end - end - end - if derivs == 0 - return fs - elseif derivs == 1 - return fs, fsx, fsy - elseif derivs == 2 - return fs, fsx, fsy, fsxx, fsxy, fsyy - else - error("Invalid number of derivatives requested: $derivs. Must be 0, 1, or 2.") - end +function call_bicube_c_eval(bicube, x, y, f, fx, fy) + ccall((:bicube_c_eval_deriv, libspline), Cvoid, + (Ptr{Cvoid}, Float64, Float64, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}), + bicube.handle, x, y, f, fx, fy) +end +function call_bicube_c_eval(bicube, x, y, f, fx, fy, fxx, fxy, fyy) + ccall((:bicube_c_eval_deriv2, libspline), Cvoid, + (Ptr{Cvoid}, Float64, Float64, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}), + bicube.handle, x, y, f, fx, fy, fxx, fxy, fyy) end """ - bicube_eval(bicube, x, y, derivs=0) - -Evaluate a bicubic spline at given 2D points. - -# Arguments - - - `bicube`: A `BicubicSplineType` object created by `bicube_setup` - - `x`: Float64 value or vector of x-coordinates to evaluate - - `y`: Float64 value or vector of y-coordinates to evaluate - - `derivs`: Integer specifying derivative level (default is 0): - - + 0: Function values only - + 1: Function values and first derivatives (∂f/∂x, ∂f/∂y) - + 2: Function values, first and second derivatives (∂f/∂x, ∂f/∂y, ∂²f/∂x², ∂²f/∂x∂y, ∂²f/∂y²) - -# Returns - - - If `derivs=0`: 3D array of function values (length(x) × length(y) × nqty) - - If `derivs=1`: Tuple of (values, x_derivatives, y_derivatives) - - If `derivs=2`: Tuple of (values, x_derivatives, y_derivatives, xx_derivatives, xy_derivatives, yy_derivatives) - -# Examples - -```julia -# Evaluate at single point -bcspline = bicube_setup(xs, ys, fs, 1, 1) -f_vals = bicube_eval(bcspline, π / 2, π / 4) - -# Evaluate on grid -x_eval = collect(range(0, 2π; length=50)) -y_eval = collect(range(0, 2π; length=50)) -f_vals = bicube_eval(bcspline, x_eval, y_eval) - -# Get derivatives -f_vals, fx, fy = bicube_eval(bcspline, x_eval, y_eval, 1) -``` +bicube_eval(bicube::BicubicSpline, x, y, derivs::Int=0) + ## Arguments: + - `bicube`: A `BicubicSpline` object. + - `x`: A Float64 value or a vector of Float64 values representing the x-coordinates to evaluate the bicubic spline at. + - `y`: A Float64 value or a vector of Float64 values representing the y-coordinates to evaluate the bicubic spline at. + ## Returns: + - If `x` and `y` are single Float64 values, returns a vector of Float64 values representing the function values at that (x,y) coordinate. + - If `x` and `y` are vectors of Float64 values, returns a 3D array of Float64 values where each slice corresponds to the function values at + the respective (x,y) coordinates in `x` and `y`. """ -function bicube_eval(bicube::BicubicSplineType, x, y, derivs::Int=0) - return _bicube_eval(bicube, x, y, derivs) +function bicube_eval(bicube::BicubicSpline, x::Float64, y::Float64, derivs::Int=0) + # x -> Float64 + # y -> Float64 + # Returns a vector of Float64 (nqty) + @assert derivs in 0:2 "Invalid number of derivatives requested: $derivs. Must be 0, 1, or 2." + + f = Vector{Float64}(undef, bicube.nqty) + + if derivs == 0 + call_bicube_c_eval(bicube, x, y, f) + return f + elseif derivs == 1 + fx, fy = similar(f), similar(f) + call_bicube_c_eval(bicube, x, y, f, fx, fy) + return f, fx, fy + elseif derivs == 2 + fx, fy = similar(f), similar(f) + fxx, fxy, fyy = similar(f), similar(f), similar(f) + call_bicube_c_eval(bicube, x, y, f, fx, fy, fxx, fxy, fyy) + return f, fx, fy, fxx, fxy, fyy + end end -end # module BicubicSpline \ No newline at end of file +function bicube_eval(bicube::BicubicSpline, xs::Vector{Float64}, ys::Vector{Float64}, derivs::Int=0) + # xs -> Float64 (any length) + # ys -> Float64 (any length) + # Returns a matrix of Float64 (length(xs), length(ys), nqty) + @assert derivs in 0:2 "Invalid number of derivatives requested: $derivs. Must be 0, 1, or 2." + + n = length(xs) + m = length(ys) + + fs = Array{Float64}(undef, n, m, bicube.nqty) + f = Vector{Float64}(undef, bicube.nqty) + if derivs > 0 + fsx, fsy = similar(fs), similar(fs) + fx, fy = similar(f), similar(f) + end + if derivs > 1 + fsxx, fsxy, fsyy = similar(fs), similar(fs), similar(fs) + fxx, fxy, fyy = similar(f), similar(f), similar(f) + end + for (i, x) in enumerate(xs) + for (j, y) in enumerate(ys) + if derivs == 0 + call_bicube_c_eval(bicube, x, y, f) + fs[i, j, :] .= f + elseif derivs == 1 + call_bicube_c_eval(bicube, x, y, f, fx, fy) + fs[i, j, :] .= f + fsx[i, j, :] .= fx + fsy[i, j, :] .= fy + elseif derivs == 2 + call_bicube_c_eval(bicube, x, y, f, fx, fy, fxx, fxy, fyy) + fs[i, j, :] .= f + fsx[i, j, :] .= fx + fsy[i, j, :] .= fy + fsxx[i, j, :] .= fxx + fsxy[i, j, :] .= fxy + fsyy[i, j, :] .= fyy + end + end + end + if derivs == 0 + return fs + elseif derivs == 1 + return fs, fsx, fsy + elseif derivs == 2 + return fs, fsx, fsy, fsxx, fsxy, fsyy + end +end diff --git a/src/Splines/CubicSpline.jl b/src/Splines/CubicSpline.jl index a3b6200c6..fb7954349 100644 --- a/src/Splines/CubicSpline.jl +++ b/src/Splines/CubicSpline.jl @@ -1,411 +1,234 @@ -module CubicSpline - -const libdir = joinpath(@__DIR__, "..", "..", "deps") -const libspline = joinpath(libdir, "libspline") - -export spline_setup, spline_eval - -abstract type CubicSplineType end - -mutable struct RealSplineType <: CubicSplineType - handle::Ptr{Cvoid} - xs::Vector{Float64} - fs::Matrix{Float64} - mx::Int64 - nqty::Int64 - ix::Int32 # Index of x position in the spline +# fortran function names +call_spline_c_create(::Type{Float64}, mx, nqty, h) = ccall((:spline_c_create, libspline), Cvoid, (Int64, Int64, Ref{Ptr{Cvoid}}), mx, nqty, h) +call_spline_c_create(::Type{ComplexF64}, mx, nqty, h) = ccall((:cspline_c_create, libspline), Cvoid, (Int64, Int64, Ref{Ptr{Cvoid}}), mx, nqty, h) +call_spline_c_setup(::Type{Float64}, spline, xs, fs) = ccall((:spline_c_setup, libspline), Cvoid, (Ptr{Cvoid}, Ptr{Float64}, Ptr{Float64}), spline.handle, xs, fs) +call_spline_c_setup(::Type{ComplexF64}, spline, xs, fs) = ccall((:cspline_c_setup, libspline), Cvoid, (Ptr{Cvoid}, Ptr{Float64}, Ptr{ComplexF64}), spline.handle, xs, fs) +call_spline_c_fit(::Type{Float64}, spline) = ccall((:spline_c_fit, libspline), Cvoid, (Ptr{Cvoid}, Int32, Ptr{Float64}), spline.handle, spline.bctype, spline._fs1) +call_spline_c_fit(::Type{ComplexF64}, spline) = ccall((:cspline_c_fit, libspline), Cvoid, (Ptr{Cvoid}, Int32, Ptr{ComplexF64}), spline.handle, spline.bctype, spline._fs1) +call_spline_c_eval(::Type{Float64}, spline, x, f) = ccall((:spline_c_eval, libspline), Cvoid, (Ptr{Cvoid}, Float64, Ptr{Float64}), spline.handle, x, f) +call_spline_c_eval(::Type{ComplexF64}, spline, x, f) = ccall((:cspline_c_eval, libspline), Cvoid, (Ptr{Cvoid}, Float64, Ptr{ComplexF64}), spline.handle, x, f) +call_spline_c_eval(::Type{Float64}, spline, x, f, f1) = ccall((:spline_c_eval_deriv, libspline), Cvoid, (Ptr{Cvoid}, Float64, Ptr{Float64}, Ptr{Float64}), spline.handle, x, f, f1) +call_spline_c_eval(::Type{ComplexF64}, spline, x, f, f1) = ccall((:cspline_c_eval_deriv, libspline), Cvoid, (Ptr{Cvoid}, Float64, Ptr{ComplexF64}, Ptr{ComplexF64}), spline.handle, x, f, f1) +call_spline_c_eval(::Type{Float64}, spline, x, f, f1, f2) = ccall((:spline_c_eval_deriv2, libspline), Cvoid, (Ptr{Cvoid}, Float64, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}), spline.handle, x, f, f1, f2) +call_spline_c_eval(::Type{ComplexF64}, spline, x, f, f1, f2) = ccall((:cspline_c_eval_deriv2, libspline), Cvoid, (Ptr{Cvoid}, Float64, Ptr{ComplexF64}, Ptr{ComplexF64}, Ptr{ComplexF64}), spline.handle, x, f, f1, f2) +call_spline_c_eval(::Type{Float64}, spline, x, f, f1, f2, f3) = ccall((:spline_c_eval_deriv3, libspline), Cvoid, (Ptr{Cvoid}, Float64, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}), spline.handle, x, f, f1, f2, f3) +call_spline_c_eval(::Type{ComplexF64}, spline, x, f, f1, f2, f3) = ccall((:cspline_c_eval_deriv3, libspline), Cvoid, (Ptr{Cvoid}, Float64, Ptr{ComplexF64}, Ptr{ComplexF64}, Ptr{ComplexF64}, Ptr{ComplexF64}), spline.handle, x, f, f1, f2, f3) +call_spline_c_int(::Type{Float64}, spline) = ccall((:spline_c_int, libspline), Cvoid, (Ptr{Cvoid}, Ptr{Float64}), spline.handle, spline._fsi) +call_spline_c_int(::Type{ComplexF64}, spline) = ccall((:cspline_c_int, libspline), Cvoid, (Ptr{Cvoid}, Ptr{ComplexF64}), spline.handle, spline._fsi) +call_spline_c_destroy(::Type{Float64}, spline) = ccall((:spline_c_destroy, libspline), Cvoid, (Ptr{Cvoid},), spline.handle) +call_spline_c_destroy(::Type{ComplexF64}, spline) = ccall((:cspline_c_destroy, libspline), Cvoid, (Ptr{Cvoid},), spline.handle) + +mutable struct CubicSpline{T<:Union{Float64, ComplexF64}} + handle::Ptr{Cvoid} + _xs::Vector{Float64} + _fs::Matrix{T} + mx::Int + nqty::Int bctype::Int32 # Boundary condition type + _fsi::Matrix{T} # To store integrals at gridpoint + _fs1::Matrix{T} # To store 1-deriv at gridpoint end -mutable struct ComplexSplineType <: CubicSplineType - handle::Ptr{Cvoid} - xs::Vector{Float64} - fs::Matrix{ComplexF64} - mx::Int64 - nqty::Int64 - ix::Int32 # Index of x position in the spline - bctype::Int32 # Boundary condition type +function CubicSpline(unmanaged_handle::Ptr{Cvoid}, xs::Vector{Float64}, fs::Matrix{T}, mx::Int, nqty::Int) where {T<:Union{Float64, ComplexF64}} + fsi = Matrix{T}(undef, 0, 0) + fs1 = Matrix{T}(undef, 0, 0) + return CubicSpline(unmanaged_handle, xs, fs, mx, nqty, zero(Int32), fsi, fs1) end -function _MakeSpline(mx::Int64, nqty::Int64) - h = Ref{Ptr{Cvoid}}() - ccall((:spline_c_create, libspline), Cvoid, - (Int64, Int64, Ref{Ptr{Cvoid}}), mx, nqty, h) - return RealSplineType(h[], Vector{Float64}(undef, mx), Matrix{Float64}(undef, mx, nqty), mx, nqty, 0, 0) -end - -function _MakeCSpline(mx::Int64, nqty::Int64) - h = Ref{Ptr{Cvoid}}() - ccall((:cspline_c_create, libspline), Cvoid, - (Int64, Int64, Ref{Ptr{Cvoid}}), mx, nqty, h) - return ComplexSplineType(h[], Vector{Float64}(undef, mx), Matrix{ComplexF64}(undef, mx, nqty), mx, nqty, 0, 0) -end +@expose_fields CubicSpline xs fs fsi fs1 -function _spline_setup(xs::Vector{Float64}, fs::Vector{Float64}, bctype::Int32) - # xs -> Float64 (mx) - # fs -> Float64 (mx, nqty) - if length(xs) != length(fs) - error("Length of xs must match length of fs") +function _destroy_spline(spline::CubicSpline{T}) where {T<:Union{Float64, ComplexF64}} + if spline.handle != C_NULL + call_spline_c_destroy(T, spline) + setfield!(spline, :handle, C_NULL) end - mx = length(xs) - 1 - nqty = 1 # Default to 1 quantity if not specified - spline = _MakeSpline(mx, nqty) - spline.xs = xs - # Convert fs to a matrix with one column - fs_matrix = reshape(fs, mx, nqty) - spline.fs = fs_matrix - spline.bctype = Int32(bctype) - - ccall((:spline_c_setup, libspline), Cvoid, - (Ptr{Cvoid}, Ptr{Float64}, Ptr{Float64}), - spline.handle, xs, fs_matrix) - - ccall((:spline_c_fit, libspline), Cvoid, - (Ptr{Cvoid}, Int32), spline.handle, bctype) - return spline end -function _spline_setup(xs::Vector{Float64}, fs::Matrix{Float64}, bctype::Int32) - # xs -> Float64 (mx) - # fs -> Float64 (mx, nqty) - if length(xs) != size(fs, 1) - error("Length of xs must match number of rows in fs") - end - mx = length(xs) - 1 - nqty = size(fs, 2) - spline = _MakeSpline(mx, nqty) - spline.xs = xs - spline.fs = fs - spline.bctype = Int32(bctype) - - ccall((:spline_c_setup, libspline), Cvoid, - (Ptr{Cvoid}, Ptr{Float64}, Ptr{Float64}), - spline.handle, xs, fs) - - ccall((:spline_c_fit, libspline), Cvoid, - (Ptr{Cvoid}, Int32), spline.handle, bctype) - return spline +function CubicSpline(xs::Vector{Float64}, fs::Vector{<:Union{Float64, ComplexF64}}, bctype::Int32) + @assert length(xs) == length(fs) "Length of xs must match length of fs" + fs_matrix = reshape(fs, length(xs), 1) # Convert to a column vector + return CubicSpline(xs, fs_matrix, bctype) end -function _spline_setup(xs::Vector{Float64}, fs::Vector{ComplexF64}, bctype::Int32) - # xs -> Float64 (mx) - # fs -> ComplexF64 (mx, nqty) - print("hi") - if length(xs) != length(fs) - error("Length of xs must match length of fs") - end - mx = length(xs) - 1 - nqty = 1 # Default to 1 quantity if not specified - spline = _MakeCSpline(mx, nqty) - spline.xs = xs - # Convert fs to a matrix with one column - fs_matrix = reshape(fs, mx, nqty) - spline.fs = fs_matrix - spline.bctype = Int32(bctype) +function CubicSpline(xs::Vector{Float64}, fs::Matrix{T}, bctype::Int32) where {T <: Union{Float64, ComplexF64}} + # xs -> Float64 (mx) + # fs -> ComplexF64 (mx, nqty) + @assert length(xs) == size(fs, 1) "Length of xs must match number of rows in fs" - ccall((:cspline_c_setup, libspline), Cvoid, - (Ptr{Cvoid}, Ptr{Float64}, Ptr{ComplexF64}), - spline.handle, xs, fs_matrix) + mx = length(xs)-1 + nqty = size(fs, 2) + h = Ref{Ptr{Cvoid}}() + call_spline_c_create(T, mx, nqty, h) - ccall((:cspline_c_fit, libspline), Cvoid, - (Ptr{Cvoid}, Int32), spline.handle, bctype) - return spline -end - -function _spline_setup(xs::Vector{Float64}, fs::Matrix{ComplexF64}, bctype::Int32) - # xs -> Float64 (mx) - # fs -> ComplexF64 (mx, nqty) - if length(xs) != size(fs, 1) - error("Length of xs must match number of rows in fs") - end - mx = length(xs) - 1 - nqty = size(fs, 2) - spline = _MakeCSpline(mx, nqty) - spline.xs = xs - spline.fs = fs - spline.bctype = Int32(bctype) + fsi = Matrix{T}(undef, mx+1, nqty) + fs1 = Matrix{T}(undef, mx+1, nqty) - ccall((:cspline_c_setup, libspline), Cvoid, - (Ptr{Cvoid}, Ptr{Float64}, Ptr{ComplexF64}), - spline.handle, xs, fs) + spline = CubicSpline(h[], xs, fs, mx, nqty, bctype, fsi, fs1) - ccall((:cspline_c_fit, libspline), Cvoid, - (Ptr{Cvoid}, Int32), spline.handle, bctype) - return spline + call_spline_c_setup(T, spline, xs, fs) + call_spline_c_fit(T, spline) + return spline end """ - spline_setup(xs, fs, bctype=1) - -Set up a cubic spline interpolation. - -# Arguments - - - `xs`: A vector of Float64 values representing the x-coordinates (must be monotonically increasing) - - `fs`: A vector or matrix of Float64/ComplexF64 values representing the function values at the x-coordinates - - `bctype`: An integer specifying the boundary condition type (default is 1): - - + 1: Natural spline (zero second derivative at endpoints) - + 2: Periodic spline - + 3: Extrapolated spline - + 4: Not-a-knot spline + CubicSpline(xs, fs; bctype="not-a-knot") + + Arguments: + - `xs`: A vector of Float64 values representing the x-coordinates. + - `fs`: A vector or matrix of Float64/ComplexF64 values representing the function values at the x-coordinates. + Keyword Arguments: + - `bctype`: Boundary condition type for the cubic spline in `x`. + - 1: Natural spline (default) + - 2: Periodic spline + - 3: Extrapolated spline + - 4: "Not-a-knot" spline + + Returns: + - A `CubicSpline` object containing the spline handle, x-coordinates, function values, + number of x-coordinates, number of quantities, and index of x position in the spline. +""" +function CubicSpline(xs::Vector{Float64}, fs::Union{Vector{T}, Matrix{T}}; + bctype::Union{String, Int}="not-a-knot") where {T <: Union{Float64, ComplexF64}} -# Returns + bctype_code = parse_bctype(bctype) - - A `CubicSplineType` object that can be used for evaluation + if T === ComplexF64 && bctype_code == 1 + error("Complex spline doesn't have natural spline. (bctype = 1/natural)") + end -# Examples + spline = CubicSpline(xs, fs, Int32(bctype_code)) -```julia -# 1D spline -xs = collect(range(0.0; stop=2π, length=21)) -fs = sin.(xs) -spline = spline_setup(xs, fs, 1) + finalizer(_destroy_spline, spline) -# Multi-quantity spline -fs_matrix = hcat(sin.(xs), cos.(xs)) -spline = spline_setup(xs, fs_matrix, 1) -``` -""" -function spline_setup(xs, fs, bctype::Int=1) - if !isa(xs, Vector{Float64}) - error("xs must be a vector of Float64") - end - if !isa(fs, Vector{Float64}) && !isa(fs, Matrix{Float64}) && !isa(fs, Vector{ComplexF64}) && !isa(fs, Matrix{ComplexF64}) - error("fs must be a vector or matrix of Float64 or ComplexF64") - end - spline = _spline_setup(xs, fs, Int32(bctype)) - return spline + return spline end - -function _spline_eval(spline::RealSplineType, x::Float64, derivs::Int=0) - # x -> Float64 - # Returns a vector of Float64 (nqty) - if derivs == 0 - f = Vector{Float64}(undef, spline.nqty) - - ccall((:spline_c_eval, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Ptr{Float64}, Int32), - spline.handle, x, f, spline.ix) - return f - elseif derivs == 1 - f = Vector{Float64}(undef, spline.nqty) - f1 = Vector{Float64}(undef, spline.nqty) - ccall((:spline_c_eval_deriv, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Ptr{Float64}, Ptr{Float64}, Int32), - spline.handle, x, f, f1, spline.ix) - return f, f1 - elseif derivs == 2 - f = Vector{Float64}(undef, spline.nqty) - f1 = Vector{Float64}(undef, spline.nqty) - f2 = Vector{Float64}(undef, spline.nqty) - ccall((:spline_c_eval_deriv2, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Int32), - spline.handle, x, f, f1, f2, spline.ix) - return f, f1, f2 - elseif derivs == 3 - f = Vector{Float64}(undef, spline.nqty) - f1 = Vector{Float64}(undef, spline.nqty) - f2 = Vector{Float64}(undef, spline.nqty) - f3 = Vector{Float64}(undef, spline.nqty) - ccall((:spline_c_eval_deriv3, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Int32), - spline.handle, x, f, f1, f2, f3, spline.ix) - return f, f1, f2, f3 - else - error("Invalid number of derivatives requested: $derivs. Must be 0, 1, 2, or 3.") - end +""" +spline_eval(spline::CubicSpline{T}, x, derivs::Int=0) where {T<:Union{Float64, ComplexF64}} + ## Arguments: + - `spline`: A `Spline` object created by `CubicSpline`. + - `x`: A Float64 value or a vector of Float64 values representing the x-coordinates to evaluate the spline at. + ## Returns: + - If `x` is a single Float64 value, returns a vector of Float64 values representing the function values at that x-coordinate. + - If `x` is a vector of Float64 values, returns a matrix of Float64 values where each row corresponds to the function values at + the respective x-coordinate in `x`. + - Depending on the derivatives requested, it may return additional vectors for the first, second, or third derivatives. +""" +function spline_eval(spline::CubicSpline{T}, x::Float64, derivs::Int=0) where {T<:Union{Float64, ComplexF64}} + # x -> Float64 + # Returns a vector of T (nqty) + @assert (derivs in 0:3) "Invalid number of derivatives requested: $derivs. Must be 0, 1, 2, or 3." + + f = Vector{T}(undef, spline.nqty) + if derivs == 0 + call_spline_c_eval(T, spline, x, f) + return f + elseif derivs == 1 + f1 = similar(f) + call_spline_c_eval(T, spline, x, f, f1) + return f, f1 + elseif derivs == 2 + f1, f2 = similar(f), similar(f) + call_spline_c_eval(T, spline, x, f, f1, f2) + return f, f1, f2 + elseif derivs == 3 + f1, f2, f3 = similar(f), similar(f), similar(f) + call_spline_c_eval(T, spline, x, f, f1, f2, f3) + return f, f1, f2, f3 + end end -function _spline_eval(spline::RealSplineType, xs::Vector{Float64}, derivs::Int=0) +function spline_eval(spline::CubicSpline{T}, xs::Vector{Float64}, derivs::Int=0) where {T<:Union{Float64, ComplexF64}} # xs -> Float64 (any length) - # Returns a matrix of Float64 (length(xs), nqty) + # Returns a matrix of T (length(xs), nqty) + @assert (derivs in 0:3) "Invalid number of derivatives requested: $derivs. Must be 0, 1, 2, or 3." n = length(xs) - fs = Matrix{Float64}(undef, n, spline.nqty) - f = Vector{Float64}(undef, spline.nqty) - if derivs > 0 - fs1 = Matrix{Float64}(undef, n, spline.nqty) - f1 = Vector{Float64}(undef, spline.nqty) - end - if derivs > 1 - fs2 = Matrix{Float64}(undef, n, spline.nqty) - f2 = Vector{Float64}(undef, spline.nqty) - end - if derivs > 2 - fs3 = Matrix{Float64}(undef, n, spline.nqty) - f3 = Vector{Float64}(undef, spline.nqty) - end - for i in 1:n - if derivs == 0 - f = _spline_eval(spline, xs[i], 0) - fs[i, :] = f - elseif derivs == 1 - f, f1 = _spline_eval(spline, xs[i], 1) - fs[i, :] = f - fs1[i, :] = f1 - elseif derivs == 2 - f, f1, f2 = _spline_eval(spline, xs[i], 2) - fs[i, :] = f - fs1[i, :] = f1 - fs2[i, :] = f2 - elseif derivs == 3 - f, f1, f2, f3 = _spline_eval(spline, xs[i], 3) - fs[i, :] = f - fs1[i, :] = f1 - fs2[i, :] = f2 - fs3[i, :] = f3 - else - error("Invalid number of derivatives requested: $derivs. Must be 0, 1, 2, or 3.") - end - end - if derivs == 0 - return fs - elseif derivs == 1 - return fs, fs1 - elseif derivs == 2 - return fs, fs1, fs2 - elseif derivs == 3 - return fs, fs1, fs2, fs3 - else - error("Invalid number of derivatives requested: $derivs. Must be 0, 1, 2, or 3.") - end + fs = Matrix{T}(undef, n, spline.nqty) + f = Vector{T}(undef, spline.nqty) + if derivs > 0 + fs1, f1 = similar(fs), similar(f) + end + if derivs > 1 + fs2, f2 = similar(fs), similar(f) + end + if derivs > 2 + fs3, f3 = similar(fs), similar(f) + end + for (i, x) in enumerate(xs) + if derivs == 0 + call_spline_c_eval(T, spline, x, f) + fs[i, :] .= f + elseif derivs == 1 + call_spline_c_eval(T, spline, x, f, f1) + fs[i, :] .= f + fs1[i, :] .= f1 + elseif derivs == 2 + call_spline_c_eval(T, spline, x, f, f1, f2) + fs[i, :] .= f + fs1[i, :] .= f1 + fs2[i, :] .= f2 + elseif derivs == 3 + call_spline_c_eval(T, spline, x, f, f1, f2, f3) + fs[i, :] .= f + fs1[i, :] .= f1 + fs2[i, :] .= f2 + fs3[i, :] .= f3 + end + end + + if derivs == 0 + return fs + elseif derivs == 1 + return fs, fs1 + elseif derivs == 2 + return fs, fs1, fs2 + elseif derivs == 3 + return fs, fs1, fs2, fs3 + end end -function _spline_eval(spline::ComplexSplineType, x::Float64, derivs::Int=0) - # x -> Float64 - # Returns a vector of ComplexF64 (nqty) - f1 = Vector{ComplexF64}(undef, spline.nqty) - f2 = Vector{ComplexF64}(undef, spline.nqty) - f3 = Vector{ComplexF64}(undef, spline.nqty) - if derivs == 0 - f = Vector{ComplexF64}(undef, spline.nqty) - ccall((:cspline_c_eval, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Ptr{ComplexF64}, Int32), - spline.handle, x, f, spline.ix) - return f - elseif derivs == 1 - f = Vector{ComplexF64}(undef, spline.nqty) - f1 = Vector{ComplexF64}(undef, spline.nqty) - ccall((:cspline_c_eval_deriv, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Ptr{ComplexF64}, Ptr{ComplexF64}, Int32), - spline.handle, x, f, f1, spline.ix) - return f, f1 - elseif derivs == 2 - f = Vector{ComplexF64}(undef, spline.nqty) - f1 = Vector{ComplexF64}(undef, spline.nqty) - f2 = Vector{ComplexF64}(undef, spline.nqty) - ccall((:cspline_c_eval_deriv2, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Ptr{ComplexF64}, Ptr{ComplexF64}, Ptr{ComplexF64}, Int32), - spline.handle, x, f, f1, f2, spline.ix) - return f, f1, f2 - elseif derivs == 3 - f = Vector{ComplexF64}(undef, spline.nqty) - f1 = Vector{ComplexF64}(undef, spline.nqty) - f2 = Vector{ComplexF64}(undef, spline.nqty) - f3 = Vector{ComplexF64}(undef, spline.nqty) - ccall((:cspline_c_eval_deriv3, libspline), Cvoid, - (Ptr{Cvoid}, Float64, Ptr{ComplexF64}, Ptr{ComplexF64}, Ptr{ComplexF64}, Ptr{ComplexF64}, Int32), - spline.handle, x, f, f1, f2, f3, spline.ix) - return f, f1, f2, f3 - else - error("Invalid number of derivatives requested: $derivs. Must be 0, 1, 2, or 3.") - end -end +""" + spline_eval!(f, spline, x; derivs=0, f1=nothing, f2=nothing, f3=nothing) + +In-place evaluation of `CubicSpline` at a single point `x`. + +Arguments: +- `f`: preallocated vector for the function values (length = spline.nqty). +- `spline`: the cubic spline object. +- `x`: Float64 input point. +- `derivs`: number of derivatives to evaluate (0–3). +- `f1`, `f2`, `f3`: optional preallocated vectors for first, second, third derivatives. + +Results are written into `f` (and optionally `f1`, `f2`, `f3`). +""" +function spline_eval!(f::Vector{T}, spline::CubicSpline{T}, x::Float64; + derivs::Int=0, f1=nothing, f2=nothing, f3=nothing) where {T<:Union{Float64, ComplexF64}} + @assert (derivs in 0:3) "Invalid number of derivatives requested: $derivs" -function _spline_eval(spline::ComplexSplineType, xs::Vector{Float64}, derivs::Int=0) - # xs -> Float64 (any length) - # Returns a matrix of ComplexF64 (length(xs), nqty) - n = length(xs) - fs = Matrix{ComplexF64}(undef, n, spline.nqty) - f = Vector{ComplexF64}(undef, spline.nqty) - if derivs > 0 - fs1 = Matrix{ComplexF64}(undef, n, spline.nqty) - f1 = Vector{ComplexF64}(undef, spline.nqty) - end - if derivs > 1 - fs2 = Matrix{ComplexF64}(undef, n, spline.nqty) - f2 = Vector{ComplexF64}(undef, spline.nqty) - end - if derivs > 2 - fs3 = Matrix{ComplexF64}(undef, n, spline.nqty) - f3 = Vector{ComplexF64}(undef, spline.nqty) - end - for i in 1:n - if derivs == 0 - f = _spline_eval(spline, xs[i], 0) - fs[i, :] = f - elseif derivs == 1 - f, f1 = _spline_eval(spline, xs[i], 1) - fs[i, :] = f - fs1[i, :] = f1 - elseif derivs == 2 - f, f1, f2 = _spline_eval(spline, xs[i], 2) - fs[i, :] = f - fs1[i, :] = f1 - fs2[i, :] = f2 - elseif derivs == 3 - f, f1, f2, f3 = _spline_eval(spline, xs[i], 3) - fs[i, :] = f - fs1[i, :] = f1 - fs2[i, :] = f2 - fs3[i, :] = f3 - else - error("Invalid number of derivatives requested: $derivs. Must be 0, 1, 2, or 3.") - end - end if derivs == 0 - return fs + call_spline_c_eval(T, spline, x, f) elseif derivs == 1 - return fs, fs1 + @assert f1 !== nothing "Need preallocated f1" + call_spline_c_eval(T, spline, x, f, f1) elseif derivs == 2 - return fs, fs1, fs2 + @assert f1 !== nothing && f2 !== nothing "Need preallocated f1, f2" + call_spline_c_eval(T, spline, x, f, f1, f2) elseif derivs == 3 - return fs, fs1, fs2, fs3 - else - error("Invalid number of derivatives requested: $derivs. Must be 0, 1, 2, or 3.") + @assert f1 !== nothing && f2 !== nothing && f3 !== nothing "Need preallocated f1, f2, f3" + call_spline_c_eval(T, spline, x, f, f1, f2, f3) end + return nothing end """ - spline_eval(spline, x, derivs=0) - -Evaluate a cubic spline at given points. - -# Arguments - - - `spline`: A `CubicSplineType` object created by `spline_setup` - - `x`: A Float64 value or vector of Float64 values representing the x-coordinates to evaluate - - `derivs`: Integer specifying derivative level (default is 0): + spline_integrate!(spline::CubicSpline{T}) where {T<:Union{Float64, ComplexF64}} - + 0: Function values only - + 1: Function values and first derivatives - + 2: Function values, first and second derivatives + ## Arguments: + - `spline`: A mutable `Spline` object". -# Returns - - - If `derivs=0`: Matrix of function values (length(x) × nqty) - - If `derivs=1`: Tuple of (values, first_derivatives) - - If `derivs=2`: Tuple of (values, first_derivatives, second_derivatives) - -# Examples - -```julia -# Evaluate at single point -spline = spline_setup(xs, fs, 1) -f_vals = spline_eval(spline, π / 2) - -# Evaluate at multiple points -x_eval = [π / 4, π / 2, 3π / 4] -f_vals = spline_eval(spline, x_eval) - -# Get derivatives -f_vals, f_derivs = spline_eval(spline, x_eval, 1) -``` + ## Returns: + - Nothing. Updates `spline._fsi` in place so that + `spline._fsi[i, :]` equals `∫_{xs[1]}^{xs[i]} f(x) dx` for each component. """ -function spline_eval(spline::CubicSplineType, x, derivs::Int=0) - return _spline_eval(spline, x, derivs) -end - -end +spline_integrate!(spline::CubicSpline{T}) where {T<:Union{Float64, ComplexF64}} = call_spline_c_int(T, spline) diff --git a/src/Splines/FourierSpline.jl b/src/Splines/FourierSpline.jl new file mode 100644 index 000000000..3845ef334 --- /dev/null +++ b/src/Splines/FourierSpline.jl @@ -0,0 +1,271 @@ +mutable struct FourierSpline + handle::Ptr{Cvoid} + _xs::Vector{Float64} + _ys::Vector{Float64} + _fs::Array{Float64, 3} + mx::Int + my::Int + mband::Int + nqty::Int + bctype::Int32 + fit_method::Int32 + cs::CubicSpline{ComplexF64} +end + +@expose_fields FourierSpline xs ys fs + + +function _destroy_fspline(fspline::FourierSpline) + if fspline.handle != C_NULL + ccall((:fspline_c_destroy, libspline), Cvoid, (Ptr{Cvoid},), fspline.handle) + Core.setfield!(fspline, :handle, C_NULL) + end +end + +function FourierSpline(mx::Int, my::Int, mband::Int, nqty::Int, bctype::Int32, fit_method::Int32) + h = Ref{Ptr{Cvoid}}() + ccall((:fspline_c_create, libspline), Cvoid, + (Int64, Int64, Int64, Int64, Ref{Ptr{Cvoid}}), + mx, my, mband, nqty, h) + + handle = h[] + if handle == C_NULL + error("Failed to create fspline handle in Fortran library.") + end + + # Return a partially initialized struct with empty data arrays + return FourierSpline(handle, Float64[], Float64[], + Array{Float64, 3}(undef, 0, 0, 0), + mx, my, mband, nqty, bctype, fit_method,nothing) +end + +function _fspline_setup(xs::Vector{Float64}, ys::Vector{Float64}, fs::Array{Float64, 3}, + mband::Int, bctype::Int32, fit_method::Int32, fit_flag::Bool) + + mx = length(xs) - 1 + my = length(ys) - 1 + nqty = size(fs, 3) + + h = Ref{Ptr{Cvoid}}() + ccall((:fspline_c_create, libspline), Cvoid, + (Int64, Int64, Int64, Int64, Ref{Ptr{Cvoid}}), + mx, my, mband, nqty, h) + + handle = h[] + ccall((:fspline_c_setup, libspline), Cvoid, + (Ptr{Cvoid}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}), + handle, xs, ys, fs) + if fit_method == 1 + ccall((:fspline_c_fit_1, libspline), Cvoid, + (Ptr{Cvoid}, Int32, Bool), + handle, bctype, fit_flag) + elseif fit_method == 2 + ccall((:fspline_c_fit_2, libspline), Cvoid, + (Ptr{Cvoid}, Int32, Bool), + handle, bctype, fit_flag) + else + error("Internal error: Invalid fit_method passed to _fspline_setup.") + end + + # 1. Get the handle to the embedded cspline object + + cs_handle_ref = Ref{Ptr{Cvoid}}() + ccall((:fspline_c_get_cspline_handle, libspline), Cvoid, + (Ptr{Cvoid}, Ref{Ptr{Cvoid}}), + handle, cs_handle_ref) + cs_handle = cs_handle_ref[] + + # 2. Get the dimensions and data for the cspline + cs_mx = mx + cs_nqty = (mband + 1) * nqty + cs_fs = Matrix{ComplexF64}(undef, cs_mx + 1, cs_nqty) + ccall((:fspline_c_get_cspline_fs, libspline), Cvoid, + (Ptr{Cvoid}, Ptr{ComplexF64}), + handle, cs_fs) + unmanaged_cspline = CubicSpline(cs_handle, xs, cs_fs, cs_mx, cs_nqty) + + # 4. Assign it to the parent object + return FourierSpline(handle, xs, ys, fs, mx, my, mband, nqty, bctype, fit_method, unmanaged_cspline) +end + +""" +FourierSpline(xs::Vector{Float64}, ys::Vector{Float64}, fs::Array{Float64, 3}, + mband::Int; bctype::Union{String, Int}="not-a-knot", fit_method::Int=1, fit_flag::Bool=true) + + Creates and fits a function of two variables, f(x, y), to a cubic spline + in the x-direction and a Fourier series in the y-direction. The y-direction + is assumed to be periodic. + + ## Arguments: + - `xs`: Vector of x-coordinates (length `mx`+1). + - `ys`: Vector of y-coordinates (length `my`+1, periodic direction). + - `fs`: 3D array of function values with dimensions (`mx`+1, `my`+1, `nqty`). + - `mband`: Number of Fourier modes (harmonics) to keep, from 0 to `mband`. + + ## Keyword Arguments: + - `bctype`: Boundary condition type for the cubic spline in `x`. + - 1: Natural spline (default) + - 2: Periodic spline + - 3: Extrapolated spline + - 4: "Not-a-knot" spline + - `fit_method`: Algorithm for computing Fourier coefficients. + - 1: Integration method (for non-uniform `y` grids). + - 2: Fast Fourier Transform (FFT) method (requires `length(ys)-1` to be a power of 2). + + ## Returns: + - A `FourierSpline` object ready for evaluation. +""" +function FourierSpline(xs::Vector{Float64}, ys::Vector{Float64}, fs::Array{Float64, 3}, + mband::Int; bctype::Union{String, Int}="not-a-knot", fit_method::Int=1, fit_flag::Bool=true) + + @assert length(xs) == size(fs, 1) "Length of xs must match number of rows in fs" + @assert length(ys) == size(fs, 2) "Length of ys must match number of columns in fs" + + @assert fit_method in (1, 2) "Invalid `fit_method`. Choose 1 or 2." + if fit_method == 2 + my = length(ys) - 1 + @assert ispow2(my) "For `fit_method=2` (FFT), `length(ys)-1` (is $my) must be a power of 2." + @assert 2 * mband <= my - 1 "For `fit_method=2` (FFT), `2*mband` must not be greater than `(length(ys)-1) - 1`. Got 2*$(mband) > $(my-1)." + end + + bctype_code = parse_bctype(bctype) + + @assert bctype_code != 1 "Fourier spline doesn't have natural spline. (bctype = 1/natural)" + # Call the internal setup function that creates and fits the spline + fspline = _fspline_setup(xs, ys, fs, mband, Int32(bctype_code), Int32(fit_method), fit_flag) + + # Add a finalizer to ensure the Fortran object is deallocated when the Julia object is garbage collected. + finalizer(_destroy_fspline, fspline) + + return fspline +end + +function call_fspline_c_eval(spl, x, y, f) + ccall((:fspline_c_eval, libspline), Cvoid, + # (handle, x, y, f_out) + (Ptr{Cvoid}, Float64, Float64, Ptr{Float64}), + spl.handle, x, y, f) +end + +function call_fspline_c_eval_deriv(spl, x, y, f, fx, fy) + ccall((:fspline_c_eval_deriv, libspline), Cvoid, + # (handle, x, y, f_out, fx_out, fy_out) + (Ptr{Cvoid}, Float64, Float64, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}), + spl.handle, x, y, f, fx, fy) +end + +function call_fspline_c_eval_deriv2(spl, x, y, f, fx, fy, fxx, fxy, fyy) + ccall((:fspline_c_eval_deriv2, libspline), Cvoid, + # (handle, x, y, f_out, fx_out, fy_out, fxx_out, fxy_out, fyy_out) + (Ptr{Cvoid}, Float64, Float64, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64}), + spl.handle, x, y, f, fx, fy, fxx, fxy, fyy) +end + +""" +fspline_eval(fspline::FourierSpline, x::Float64, y::Float64, derivs::Int=0) + + Evaluates a fitted Fourier-Spline at given coordinates. + + ## Arguments: + - `fspline`: A `FourierSpline` object. + - `x`: A `Float64` x-coordinate. + - `y`: A `Float64` y-coordinate. + + ## Returns: + - If `x`, `y` are scalars: A tuple containing the function value(s) and any requested derivatives. If nqty=1, the results are scalars, otherwise they are vectors. +""" +function fspline_eval(fspline::FourierSpline, x::Float64, y::Float64, derivs::Int=0) + + @assert (derivs in 0:2) "Invalid number of derivatives requested: $derivs. Must be 0, 1, or 2." + + f = Vector{Float64}(undef, fspline.nqty) + if derivs == 0 + call_fspline_c_eval(fspline, x, y, f) + results = f + + elseif derivs == 1 + fx, fy = similar(f), similar(f) + call_fspline_c_eval_deriv(fspline, x, y, f, fx, fy) + results = (f, fx, fy) + + elseif derivs == 2 + fx, fy = similar(f), similar(f) + fxx, fxy, fyy = similar(f), similar(f), similar(f) + call_fspline_c_eval_deriv2(fspline, x, y, f, fx, fy, fxx, fxy, fyy) + results = (f, fx, fy, fxx, fxy, fyy) + + end + + if fspline.nqty == 1 + if isa(results, Tuple) + return map(vec -> vec[1], results) + else + return results[1] + end + end + + return results +end + + +""" +fspline_eval(fspline::FourierSpline, xs::Vector{Float64}, ys::Vector{Float64}, derivs::Int=0) + + Evaluates a fitted Fourier-Spline at given coordinates. + + ## Arguments: + - `fspline`: A `FourierSpline` object. + - `x`: A `Vector{Float64}` of x-coordinates. + - `y`: A `Vector{Float64}` of y-coordinates. + + ## Returns: + - If `x`, `y` are vectors: A tuple of 3D arrays for the function values and derivatives on the grid defined by `x` and `y`. +""" +function fspline_eval(fspline::FourierSpline, xs::Vector{Float64}, ys::Vector{Float64}, derivs::Int=0) + # xs -> Float64 (any length) + # ys -> Float64 (any length) + # Returns a matrix of Float64 (length(xs), length(ys), nqty) + + @assert (derivs in 0:2) "Invalid number of derivatives requested: $derivs. Must be 0, 1, or 2." + + n = length(xs) + m = length(ys) + fs = Array{Float64}(undef, n, m, fspline.nqty) + f = Vector{Float64}(undef, fspline.nqty) + if derivs > 0 + fsx, fsy = similar(fs), similar(fs) + fx, fy = similar(f), similar(f) + end + if derivs > 1 + fsxx, fsxy, fsyy = similar(fs), similar(fs), similar(fs) + fxx, fxy, fyy = similar(f), similar(f), similar(f) + end + for (i, x) in enumerate(xs) + for (j, y) in enumerate(ys) + if derivs == 0 + call_fspline_c_eval(fspline, x, y, f) + fs[i, j, :] .= f + elseif derivs == 1 + call_fspline_c_eval_deriv(fspline, x, y, f, fx, fy) + fs[i, j, :] .= f + fsx[i, j, :] .= fx + fsy[i, j, :] .= fy + elseif derivs == 2 + call_fspline_c_eval_deriv2(fspline, x, y, f, fx, fy, fxx, fxy, fyy) + fs[i, j, :] .= f + fsx[i, j, :] .= fx + fsy[i, j, :] .= fy + fsxx[i, j, :] .= fxx + fsxy[i, j, :] .= fxy + fsyy[i, j, :] .= fyy + end + end + end + if derivs == 0 + return fs + elseif derivs == 1 + return fs, fsx, fsy + elseif derivs == 2 + return fs, fsx, fsy, fsxx, fsxy, fsyy + end +end \ No newline at end of file diff --git a/src/Splines/Helper.jl b/src/Splines/Helper.jl new file mode 100644 index 000000000..19c1163b8 --- /dev/null +++ b/src/Splines/Helper.jl @@ -0,0 +1,110 @@ +const BCTYPE_MAP = Dict( + "natural" => 1, # unstable + "periodic" => 2, + "extrap" => 3, + "not-a-knot" => 4, + "notaknot" => 4 +) + +""" + parse_bctype(bctype) + +Internal helper to parse a boundary condition into a validated integer code. + +## Arguments: +- `bctype`: The boundary condition as a `String` or `Int`. Valid options are: + - `"natural"` or `1` + - `"periodic"` or `2` + - `"extrap"` or `3` + - `"not-a-knot"` or `4` + +## Returns: +- A validated `Int` code (1-4). +""" +function parse_bctype(bctype::String) + normalized_bctype = replace(lowercase(bctype), r"[-_\s]" => "") + if haskey(BCTYPE_MAP, normalized_bctype) + return BCTYPE_MAP[normalized_bctype] + else + error("Invalid string for `bctype`: '$bctype'. Valid options are: $(keys(BCTYPE_MAP))") + end +end + +function parse_bctype(bctype::Int) + # If it's already an integer, validate it. + if bctype in values(BCTYPE_MAP) + return bctype + else + error("Invalid integer for `bctype`: $bctype. Valid options are: $(collect(values(BCTYPE_MAP)))") + end +end + +#==============================================================================# +# Read-Only Interface Utilities +#==============================================================================# + +""" + ReadOnlyArray{T,N,A} + +A thin wrapper that provides a read-only view. +""" +struct ReadOnlyArray{T,N,A<:AbstractArray{T,N}} <: AbstractArray{T,N} + data::A +end + +Base.size(A::ReadOnlyArray) = size(A.data) +Base.getindex(A::ReadOnlyArray, I...) = @inbounds A.data[I...] +Base.setindex!(::ReadOnlyArray, args...) = + throw(ArgumentError("Cannot modify a read-only array.")) + + + """ + @expose_fields TypeName field1 field2 ... + + Create a *read-only public interface* for a struct while still allowing + internal code to mutate the underlying buffers. + + For every symbol `field` you list (e.g. `fs`, `fs1`), + + * an **internal** field named `:_field` (e.g. `:_fs`, `:_fs1`) is assumed to + exist in `TypeName`; + * the macro generates the following methods: + """ + +macro expose_fields(typ, fields...) + # 1) Create a list of internal field names (Symbol) + internal_syms = map(f -> Symbol("_" * string(f)), fields) + # 2) Convert to a tuple literal AST (planted here as a QuoteNode) + internal_tuple = Expr(:tuple, map(x->QuoteNode(x), internal_syms)...) + + quote + ######## getproperty ######## + function Base.getproperty(s::$(esc(typ)), fld::Symbol) + $( + foldr( + (f, rest) -> :( + if fld === $(QuoteNode(f)) + return ReadOnlyArray(getfield(s, $(QuoteNode(Symbol("_", f))))) + else + $rest + end + ), + fields, + init = :(return getfield(s, fld)) + ) + ) + end + + ######## setproperty! ######## + function Base.setproperty!(s::$(esc(typ)), fld::Symbol, val) + # (where internal_tuple is of the form (: _fs1, :_fs2, ...)) + if fld in $(internal_tuple) + return setfield!(s, fld, val) + end + throw(ArgumentError( + "Cannot modify property ':$fld'. " * + "$(string($(esc(typ)))) fields are read-only." + )) + end + end +end \ No newline at end of file diff --git a/src/Splines/Splines.jl b/src/Splines/Splines.jl index 6827b2580..b55db563d 100644 --- a/src/Splines/Splines.jl +++ b/src/Splines/Splines.jl @@ -1,12 +1,16 @@ module SplinesMod +const libdir = joinpath(@__DIR__, "..", "..", "deps") +const libspline = joinpath(libdir, "libspline") + +include("Helper.jl") + include("CubicSpline.jl") include("BicubicSpline.jl") +include("FourierSpline.jl") -using .CubicSpline: spline_setup, spline_eval, CubicSplineType, RealSplineType, ComplexSplineType -using .BicubicSpline: bicube_setup, bicube_eval, BicubicSplineType - -export spline_setup, spline_eval, CubicSplineType, RealSplineType, ComplexSplineType -export bicube_setup, bicube_eval, BicubicSplineType +export spline_eval, spline_integrate!, CubicSpline +export bicube_eval, BicubicSpline +export fspline_eval, FourierSpline -end \ No newline at end of file +end diff --git a/src/Splines/fortran/bicube.f b/src/Splines/fortran/bicube.f index 91b7e38b7..ddd783d63 100644 --- a/src/Splines/fortran/bicube.f +++ b/src/Splines/fortran/bicube.f @@ -31,28 +31,28 @@ c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - MODULE bicube_mod - USE spline_mod - IMPLICIT NONE + module bicube_mod + use spline_mod + implicit none - TYPE :: bicube_type - INTEGER :: mx,my,nqty,ix,iy - REAL(r8), DIMENSION(:,:), ALLOCATABLE :: xext,yext,fext - REAL(r8), DIMENSION(2) :: x0,y0 - REAL(r8), DIMENSION(:), ALLOCATABLE :: xs,ys - REAL(r8), DIMENSION(:,:), ALLOCATABLE :: xpower,ypower - REAL(r8), DIMENSION(:,:,:), ALLOCATABLE :: fs,fsx,fsy,fsxy - REAL(r8), DIMENSION(:), ALLOCATABLE :: f,fx,fy,fxx,fxy,fyy - REAL(r8), DIMENSION(:,:,:,:,:), ALLOCATABLE :: cmats - REAL(r8), DIMENSION(:,:,:,:,:), ALLOCATABLE :: gs,gsx,gsy,gsxy, + type :: bicube_type + integer :: mx,my,nqty,ix,iy + real(r8), dimension(:,:), allocatable :: xext,yext,fext + real(r8), dimension(2) :: x0,y0 + real(r8), dimension(:), allocatable :: xs,ys + real(r8), dimension(:,:), allocatable :: xpower,ypower + real(r8), dimension(:,:,:), allocatable :: fs,fsx,fsy,fsxy + real(r8), dimension(:), allocatable :: f,fx,fy,fxx,fxy,fyy + real(r8), dimension(:,:,:,:,:), allocatable :: cmats + real(r8), dimension(:,:,:,:,:), allocatable :: gs,gsx,gsy,gsxy, $ gsxx,gsyy - CHARACTER(6) :: xtitle,ytitle - CHARACTER(6), DIMENSION(:), ALLOCATABLE :: title - CHARACTER(6) :: name - LOGICAL, DIMENSION(2) :: periodic - END TYPE bicube_type + character(6) :: xtitle,ytitle + character(6), dimension(:), allocatable :: title + character(6) :: name + logical, dimension(2) :: periodic + end type bicube_type - CONTAINS + contains c----------------------------------------------------------------------- c subprogram 1. bicube_alloc. c allocates space for bicube_type. @@ -60,10 +60,10 @@ MODULE bicube_mod c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_alloc(bcs,mx,my,nqty) + subroutine bicube_alloc(bcs,mx,my,nqty) - INTEGER, INTENT(IN) :: mx,my,nqty - TYPE(bicube_type), INTENT(OUT) :: bcs + integer, intent(in) :: mx,my,nqty + type(bicube_type), intent(out) :: bcs c----------------------------------------------------------------------- c set scalars. c----------------------------------------------------------------------- @@ -72,25 +72,25 @@ SUBROUTINE bicube_alloc(bcs,mx,my,nqty) bcs%ix=0 bcs%iy=0 bcs%nqty=nqty - bcs%periodic=.FALSE. + bcs%periodic=.false. c----------------------------------------------------------------------- c allocate space. c----------------------------------------------------------------------- - ALLOCATE(bcs%xs(0:mx)) - ALLOCATE(bcs%ys(0:my)) - ALLOCATE(bcs%fs(0:mx,0:my,nqty)) - ALLOCATE(bcs%fsx(0:mx,0:my,nqty)) - ALLOCATE(bcs%fsy(0:mx,0:my,nqty)) - ALLOCATE(bcs%fsxy(0:mx,0:my,nqty)) - ALLOCATE(bcs%title(nqty)) - ALLOCATE(bcs%f(nqty)) - ALLOCATE(bcs%fx(nqty)) - ALLOCATE(bcs%fy(nqty)) - ALLOCATE(bcs%fxx(nqty)) - ALLOCATE(bcs%fxy(nqty)) - ALLOCATE(bcs%fyy(nqty)) - ALLOCATE(bcs%xpower(2,nqty),bcs%ypower(2,nqty)) - ALLOCATE(bcs%xext(2,nqty),bcs%yext(2,nqty),bcs%fext(2,nqty)) + allocate(bcs%xs(0:mx)) + allocate(bcs%ys(0:my)) + allocate(bcs%fs(0:mx,0:my,nqty)) + allocate(bcs%fsx(0:mx,0:my,nqty)) + allocate(bcs%fsy(0:mx,0:my,nqty)) + allocate(bcs%fsxy(0:mx,0:my,nqty)) + allocate(bcs%title(nqty)) + allocate(bcs%f(nqty)) + allocate(bcs%fx(nqty)) + allocate(bcs%fy(nqty)) + allocate(bcs%fxx(nqty)) + allocate(bcs%fxy(nqty)) + allocate(bcs%fyy(nqty)) + allocate(bcs%xpower(2,nqty),bcs%ypower(2,nqty)) + allocate(bcs%xext(2,nqty),bcs%yext(2,nqty),bcs%fext(2,nqty)) bcs%xpower=0 bcs%ypower=0 bcs%x0=0 @@ -98,8 +98,8 @@ SUBROUTINE bicube_alloc(bcs,mx,my,nqty) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_alloc + return + end subroutine bicube_alloc c----------------------------------------------------------------------- c subprogram 2. bicube_dealloc. c deallocates space for bicube_type. @@ -107,39 +107,39 @@ END SUBROUTINE bicube_alloc c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_dealloc(bcs) + subroutine bicube_dealloc(bcs) - TYPE(bicube_type), INTENT(INOUT) :: bcs + type(bicube_type), intent(inout) :: bcs c----------------------------------------------------------------------- c allocate space. c----------------------------------------------------------------------- - DEALLOCATE(bcs%xs) - DEALLOCATE(bcs%ys) - DEALLOCATE(bcs%fs) - DEALLOCATE(bcs%fsx) - DEALLOCATE(bcs%fsy) - DEALLOCATE(bcs%fsxy) - DEALLOCATE(bcs%title) - DEALLOCATE(bcs%f) - DEALLOCATE(bcs%fx) - DEALLOCATE(bcs%fy) - DEALLOCATE(bcs%fxx) - DEALLOCATE(bcs%fxy) - DEALLOCATE(bcs%fyy) - DEALLOCATE(bcs%xpower,bcs%ypower) - DEALLOCATE(bcs%xext,bcs%yext,bcs%fext) - IF(ALLOCATED(bcs%cmats))DEALLOCATE(bcs%cmats) - IF(ALLOCATED(bcs%gs))DEALLOCATE(bcs%gs) - IF(ALLOCATED(bcs%gsx))DEALLOCATE(bcs%gsx) - IF(ALLOCATED(bcs%gsy))DEALLOCATE(bcs%gsy) - IF(ALLOCATED(bcs%gsxx))DEALLOCATE(bcs%gsxx) - IF(ALLOCATED(bcs%gsxy))DEALLOCATE(bcs%gsxy) - IF(ALLOCATED(bcs%gsyy))DEALLOCATE(bcs%gsyy) + deallocate(bcs%xs) + deallocate(bcs%ys) + deallocate(bcs%fs) + deallocate(bcs%fsx) + deallocate(bcs%fsy) + deallocate(bcs%fsxy) + deallocate(bcs%title) + deallocate(bcs%f) + deallocate(bcs%fx) + deallocate(bcs%fy) + deallocate(bcs%fxx) + deallocate(bcs%fxy) + deallocate(bcs%fyy) + deallocate(bcs%xpower,bcs%ypower) + deallocate(bcs%xext,bcs%yext,bcs%fext) + if(allocated(bcs%cmats))deallocate(bcs%cmats) + if(allocated(bcs%gs))deallocate(bcs%gs) + if(allocated(bcs%gsx))deallocate(bcs%gsx) + if(allocated(bcs%gsy))deallocate(bcs%gsy) + if(allocated(bcs%gsxx))deallocate(bcs%gsxx) + if(allocated(bcs%gsxy))deallocate(bcs%gsxy) + if(allocated(bcs%gsyy))deallocate(bcs%gsyy) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_dealloc + return + end subroutine bicube_dealloc c----------------------------------------------------------------------- c subprogram 3. bicube_fit. c fits functions to bicubic splines. @@ -147,17 +147,17 @@ END SUBROUTINE bicube_dealloc c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_fit(bcs,endmode1,endmode2) + subroutine bicube_fit(bcs,endmode1,endmode2) - TYPE(bicube_type), INTENT(INOUT), TARGET :: bcs - CHARACTER(*), INTENT(IN) :: endmode1,endmode2 + type(bicube_type), intent(inout), TARGET :: bcs + integer, intent(in) :: endmode1,endmode2 - INTEGER :: iqty,iside,ix,iy - REAL(r8), DIMENSION(0:bcs%mx) :: xfac - REAL(r8), DIMENSION(0:bcs%my) :: yfac - TYPE(spline_type) :: spl + integer :: iqty,iside,ix,iy + real(r8), dimension(0:bcs%mx) :: xfac + real(r8), dimension(0:bcs%my) :: yfac + type(spline_type) :: spl - REAL(r8), DIMENSION(:,:,:), POINTER :: fs,fsx,fsy,fsxy + real(r8), dimension(:,:,:), POinTER :: fs,fsx,fsy,fsxy c----------------------------------------------------------------------- c set pointers. c----------------------------------------------------------------------- @@ -168,72 +168,72 @@ SUBROUTINE bicube_fit(bcs,endmode1,endmode2) c----------------------------------------------------------------------- c extract x powers. c----------------------------------------------------------------------- - DO iside=1,2 - DO iqty=1,bcs%nqty - IF(bcs%xpower(iside,iqty) /= 0)THEN + do iside=1,2 + do iqty=1,bcs%nqty + if(bcs%xpower(iside,iqty) /= 0)then xfac=1/ABS(bcs%xs-bcs%x0(iside))**bcs%xpower(iside,iqty) - DO iy=0,bcs%my + do iy=0,bcs%my bcs%fs(:,iy,iqty)=bcs%fs(:,iy,iqty)*xfac - ENDDO - ENDIF - ENDDO - ENDDO + enddo + endif + enddo + enddo c----------------------------------------------------------------------- c extract y powers. c----------------------------------------------------------------------- - DO iside=1,2 - DO iqty=1,bcs%nqty - IF(bcs%ypower(iside,iqty) /= 0)THEN + do iside=1,2 + do iqty=1,bcs%nqty + if(bcs%ypower(iside,iqty) /= 0)then yfac=1/ABS(bcs%ys-bcs%y0(iside))**bcs%ypower(iside,iqty) - DO ix=0,bcs%mx + do ix=0,bcs%mx bcs%fs(ix,:,iqty)=bcs%fs(ix,:,iqty)*yfac - ENDDO - ENDIF - ENDDO - ENDDO + enddo + endif + enddo + enddo c----------------------------------------------------------------------- c set periodicity. c----------------------------------------------------------------------- - bcs%periodic=(/endmode1 == "periodic",endmode2 == "periodic"/) - IF(bcs%periodic(1))bcs%fs(bcs%mx,:,:)=bcs%fs(0,:,:) - IF(bcs%periodic(2))bcs%fs(:,bcs%my,:)=bcs%fs(:,0,:) + bcs%periodic=(/endmode1 == 2,endmode2 == 2/) !2=periodic + if(bcs%periodic(1))bcs%fs(bcs%mx,:,:)=bcs%fs(0,:,:) + if(bcs%periodic(2))bcs%fs(:,bcs%my,:)=bcs%fs(:,0,:) c----------------------------------------------------------------------- c evaluate y derivatives. c----------------------------------------------------------------------- - CALL spline_alloc(spl,bcs%my,bcs%mx+1) + call spline_alloc(spl,bcs%my,bcs%mx+1) spl%xs=bcs%ys - DO iqty=1,bcs%nqty + do iqty=1,bcs%nqty spl%fs=TRANSPOSE(bcs%fs(:,:,iqty)) - CALL spline_fit(spl,endmode2) + call spline_fit(spl,endmode2) bcs%fsy(:,:,iqty)=TRANSPOSE(spl%fs1) - ENDDO - CALL spline_dealloc(spl) + enddo + call spline_dealloc(spl) c----------------------------------------------------------------------- c evaluate x derivatives. c----------------------------------------------------------------------- spl%mx=bcs%mx spl%nqty=bcs%my+1 - CALL spline_alloc(spl,bcs%mx,bcs%my+1) + call spline_alloc(spl,bcs%mx,bcs%my+1) spl%xs=bcs%xs - DO iqty=1,bcs%nqty + do iqty=1,bcs%nqty spl%fs=bcs%fs(:,:,iqty) - CALL spline_fit(spl,endmode1) + call spline_fit(spl,endmode1) bcs%fsx(:,:,iqty)=spl%fs1 - ENDDO + enddo c----------------------------------------------------------------------- c evaluate mixed derivatives. c----------------------------------------------------------------------- - DO iqty=1,bcs%nqty + do iqty=1,bcs%nqty spl%fs=bcs%fsy(:,:,iqty) - CALL spline_fit(spl,endmode1) + call spline_fit(spl,endmode1) bcs%fsxy(:,:,iqty)=spl%fs1 - ENDDO - CALL spline_dealloc(spl) + enddo + call spline_dealloc(spl) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_fit + return + end subroutine bicube_fit c----------------------------------------------------------------------- c subprogram 4. bicube_lsfit. c least-square fit to cubic splines of piecewise-constant functions. @@ -241,21 +241,21 @@ END SUBROUTINE bicube_fit c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_lsfit(bcs) + subroutine bicube_lsfit(bcs) - TYPE(bicube_type), INTENT(INOUT) :: bcs + type(bicube_type), intent(inout) :: bcs - LOGICAL, PARAMETER :: diagnose=.FALSE. - INTEGER :: ix,iy,nx,ny,mx,my,nrhs,n,info,i,j,k,l,kd,ldab - INTEGER, DIMENSION(4*(bcs%mx+1)*(bcs%my+1)) :: ipiv - REAL(r8), PARAMETER :: + logical, PARAMETER :: diagnose=.false. + integer :: ix,iy,nx,ny,mx,my,nrhs,n,info,i,j,k,l,kd,ldab + integer, dimension(4*(bcs%mx+1)*(bcs%my+1)) :: ipiv + real(r8), PARAMETER :: $ a0=13/35._r8,a1=9/70._r8,b0=11/210._r8,b1=13/420._r8 - REAL(r8), DIMENSION(0:bcs%mx+1) :: dx - REAL(r8), DIMENSION(0:bcs%my+1) :: dy - REAL(r8), DIMENSION(4,0:bcs%mx,0:bcs%my,bcs%nqty) :: rhs - REAL(r8), DIMENSION(0:bcs%mx+1,0:bcs%my+1,bcs%nqty) :: g - REAL(r8), DIMENSION(4,4,-1:1,-1:1,0:bcs%mx,0:bcs%my) :: amat - REAL(r8), DIMENSION(:,:), ALLOCATABLE :: ab + real(r8), dimension(0:bcs%mx+1) :: dx + real(r8), dimension(0:bcs%my+1) :: dy + real(r8), dimension(4,0:bcs%mx,0:bcs%my,bcs%nqty) :: rhs + real(r8), dimension(0:bcs%mx+1,0:bcs%my+1,bcs%nqty) :: g + real(r8), dimension(4,4,-1:1,-1:1,0:bcs%mx,0:bcs%my) :: amat + real(r8), dimension(:,:), allocatable :: ab c----------------------------------------------------------------------- c define sizes. c----------------------------------------------------------------------- @@ -279,7 +279,7 @@ SUBROUTINE bicube_lsfit(bcs) c----------------------------------------------------------------------- c least squares fit, function values. c----------------------------------------------------------------------- - DO iy=0,ny + do iy=0,ny amat(1,1,0,0,0:nx,iy)=a0**2 $ *(dx(0:nx)+dx(1:nx+1))*(dy(iy)+dy(iy+1)) amat(1,1,-1,0,0:nx,iy)=a0*a1*dx(0:nx)*(dy(iy)+dy(iy+1)) @@ -290,11 +290,11 @@ SUBROUTINE bicube_lsfit(bcs) amat(1,1,-1,+1,0:nx,iy)=a1**2*dx(0:nx)*dy(iy+1) amat(1,1,+1,-1,0:nx,iy)=a1**2*dx(1:nx+1)*dy(iy) amat(1,1,+1,+1,0:nx,iy)=a1**2*dx(1:nx+1)*dy(iy+1) - ENDDO + enddo c----------------------------------------------------------------------- c least squares fit, x derivatiives. c----------------------------------------------------------------------- - DO iy=0,ny + do iy=0,ny amat(1,2,0,0,0:nx,iy)=a0*b0 $ *(dx(1:nx+1)**2-dx(0:nx)**2)*(dy(iy)+dy(iy+1)) amat(1,2,-1,0,0:nx,iy)=+a0*b1*(dy(iy)+dy(iy+1))*dx(0:nx)**2 @@ -303,11 +303,11 @@ SUBROUTINE bicube_lsfit(bcs) amat(1,2,+1,-1,0:nx,iy)=-a1*b1*dx(1:nx+1)**2*dy(iy) amat(1,2,-1,+1,0:nx,iy)=+a1*b1*dx(0:nx)**2*dy(iy+1) amat(1,2,+1,+1,0:nx,iy)=-a1*b1*dx(1:nx+1)**2*dy(iy+1) - ENDDO + enddo c----------------------------------------------------------------------- c least squares fit, y derivatiives. c----------------------------------------------------------------------- - DO ix=0,nx + do ix=0,nx amat(1,3,0,0,ix,0:ny)=a0*b0 $ *(dy(1:ny+1)**2-dy(0:ny)**2)*(dx(ix)+dx(ix+1)) amat(1,3,-1,0,ix,0:ny)=+a0*b1*(dx(ix)+dx(ix+1))*dy(0:ny)**2 @@ -316,11 +316,11 @@ SUBROUTINE bicube_lsfit(bcs) amat(1,3,+1,-1,ix,0:ny)=-a1*b1*dy(1:ny+1)**2*dx(ix) amat(1,3,-1,+1,ix,0:ny)=+a1*b1*dy(0:ny)**2*dx(ix+1) amat(1,3,+1,+1,ix,0:ny)=-a1*b1*dy(1:ny+1)**2*dx(ix+1) - ENDDO + enddo c----------------------------------------------------------------------- c least squares fit, mixed derivatives. c----------------------------------------------------------------------- - DO iy=0,ny + do iy=0,ny amat(1,4,0,0,0:nx,iy)=b0**2 $ *(dx(0:nx)**2-dx(1:nx+1)**2)*(dy(iy)**2-dy(iy+1)**2) amat(1,4,-1,0,0:nx,iy)=+b0*b1*dx(0:nx)**2 @@ -335,80 +335,80 @@ SUBROUTINE bicube_lsfit(bcs) amat(1,4,-1,+1,0:nx,iy)=-b1**2*dx(0:nx)**2*dy(iy+1)**2 amat(1,4,+1,-1,0:nx,iy)=-b1**2*dx(1:nx+1)**2*dy(iy)**2 amat(1,4,+1,+1,0:nx,iy)=b1**2*dx(1:nx+1)**2*dy(iy+1)**2 - ENDDO + enddo c----------------------------------------------------------------------- c least squares fit, rhs. c----------------------------------------------------------------------- - DO iy=0,ny - DO ix=0,nx + do iy=0,ny + do ix=0,nx rhs(1,ix,iy,:) $ =(dx(ix)*g(ix,iy,:)+dx(ix+1)*g(ix+1,iy,:))*dy(iy) $ +(dx(ix)*g(ix,iy+1,:)+dx(ix+1)*g(ix+1,iy+1,:))*dy(iy+1) - ENDDO - ENDDO + enddo + enddo rhs=rhs/4 c----------------------------------------------------------------------- c continuity of second x-derivatives. c----------------------------------------------------------------------- - DO ix=1,nx-1 + do ix=1,nx-1 amat(2,1,-1,0,ix,0:ny)=3/dx(ix)**2 amat(2,1,0,0,ix,0:ny)=3/dx(ix+1)**2-3/dx(ix)**2 amat(2,1,1,0,ix,0:ny)=-3/dx(ix+1)**2 amat(2,2,-1,0,ix,0:ny)=1/dx(ix) amat(2,2,0,0,ix,0:ny)=2/dx(ix)+2/dx(ix+1) amat(2,2,1,0,ix,0:ny)=1/dx(ix+1) - ENDDO + enddo amat(2,2,0,0,0:nx:nx,0:ny)=1 c----------------------------------------------------------------------- c continuity of second y-derivatives. c----------------------------------------------------------------------- - DO iy=1,ny-1 + do iy=1,ny-1 amat(3,1,0,-1,0:nx,iy)=3/dy(iy)**2 amat(3,1,0,0,0:nx,iy)=3/dy(iy+1)**2-3/dy(iy)**2 amat(3,1,0,1,0:nx,iy)=-3/dy(iy+1)**2 amat(3,3,0,-1,0:nx,iy)=1/dy(iy) amat(3,3,0,0,0:nx,iy)=2/dy(iy)+2/dy(iy+1) amat(3,3,0,1,0:nx,iy)=1/dy(iy+1) - ENDDO + enddo amat(3,3,0,0,0:nx,0:ny:ny)=1 c----------------------------------------------------------------------- c continuity of mixed second derivatives. c----------------------------------------------------------------------- - DO ix=1,nx-1 + do ix=1,nx-1 amat(4,3,-1,0,ix,0:ny)=3/dx(ix)**2 amat(4,3,0,0,ix,0:ny)=3/dx(ix+1)**2-3/dx(ix)**2 amat(4,3,1,0,ix,0:ny)=-3/dx(ix+1)**2 amat(4,4,-1,0,ix,0:ny)=1/dx(ix) amat(4,4,0,0,ix,0:ny)=2/dx(ix)+2/dx(ix+1) amat(4,4,1,0,ix,0:ny)=1/dx(ix+1) - ENDDO + enddo amat(4,4,0,0,0:nx:nx,0:ny)=1 c----------------------------------------------------------------------- c transfer matrix to lapack band storage. c----------------------------------------------------------------------- - ALLOCATE(ab(ldab,n)) + allocate(ab(ldab,n)) ab=0 - DO ix=0,nx - DO mx=MAX(-ix,-1),MIN(nx-ix,1) - DO iy=0,ny - DO my=MAX(-iy,-1),MIN(ny-iy,1) - DO k=1,4 - DO l=1,4 + do ix=0,nx + do mx=MAX(-ix,-1),Min(nx-ix,1) + do iy=0,ny + do my=MAX(-iy,-1),Min(ny-iy,1) + do k=1,4 + do l=1,4 i=4*(iy*(nx+1)+ix)+k j=4*((iy+my)*(nx+1)+ix+mx)+l ab(2*kd+1+i-j,j)=amat(k,l,mx,my,ix,iy) - ENDDO - ENDDO - ENDDO - ENDDO - ENDDO - ENDDO + enddo + enddo + enddo + enddo + enddo + enddo c----------------------------------------------------------------------- c factor and solve. c----------------------------------------------------------------------- - CALL dgbtrf(n,n,kd,kd,ab,ldab,ipiv,info) - CALL dgbtrs('N',n,kd,kd,nrhs,ab,ldab,ipiv,rhs,n,info) - DEALLOCATE(ab) + call dgbtrf(n,n,kd,kd,ab,ldab,ipiv,info) + call dgbtrs('N',n,kd,kd,nrhs,ab,ldab,ipiv,rhs,n,info) + deallocate(ab) c----------------------------------------------------------------------- c compute output. c----------------------------------------------------------------------- @@ -419,8 +419,8 @@ SUBROUTINE bicube_lsfit(bcs) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_lsfit + return + end subroutine bicube_lsfit c----------------------------------------------------------------------- c subprogram 5. bicube_eval. c evaluates bicubic spline function. @@ -428,29 +428,29 @@ END SUBROUTINE bicube_lsfit c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_eval(bcs,x,y,mode) + subroutine bicube_eval(bcs,x,y,mode) - TYPE(bicube_type), INTENT(INOUT) :: bcs - REAL(r8), INTENT(IN) :: x,y - INTEGER, INTENT(IN) :: mode + type(bicube_type), intent(inout) :: bcs + real(r8), intent(in) :: x,y + integer, intent(in) :: mode - INTEGER :: i,iqty,iside - REAL(r8) :: dx,dy,xx,yy,g,gx,gy,gxx,gyy,gxy,xfac,yfac - REAL(r8), DIMENSION (4,4,bcs%nqty) :: c + integer :: i,iqty,iside + real(r8) :: dx,dy,xx,yy,g,gx,gy,gxx,gyy,gxy,xfac,yfac + real(r8), dimension (4,4,bcs%nqty) :: c c----------------------------------------------------------------------- c preliminary computations. c----------------------------------------------------------------------- - IF(bcs%mx==0 .OR. bcs%my==0)THEN - WRITE(*, *) 'ERROR: Bicubic spline entitled "',bcs%title,'"' - IF(bcs%mx==0)THEN - WRITE(*, *) 'has 0 elements specified for x axis ' + if(bcs%mx==0 .OR. bcs%my==0)then + write(*, *) 'ERROR: Bicubic spline entitled "',bcs%title,'"' + if(bcs%mx==0)then + write(*, *) 'has 0 elements specified for x axis ' $ //TRIM(bcs%xtitle) - ELSE - WRITE(*, *) 'has 0 elements specified for y axis ' + else + write(*, *) 'has 0 elements specified for y axis ' $ //TRIM(bcs%ytitle) - ENDIF - STOP - ENDIF + endif + stop + endif bcs%ix=max(bcs%ix,0) bcs%ix=min(bcs%ix,bcs%mx-1) bcs%iy=max(bcs%iy,0) @@ -460,83 +460,83 @@ SUBROUTINE bicube_eval(bcs,x,y,mode) c----------------------------------------------------------------------- c normalize x interval for periodic splines. c----------------------------------------------------------------------- - IF(bcs%periodic(1))THEN - DO - IF(xx < bcs%xs(bcs%mx))EXIT + if(bcs%periodic(1))then + do + if(xx < bcs%xs(bcs%mx))EXIT xx=xx-bcs%xs(bcs%mx) - ENDDO - DO - IF(xx >= bcs%xs(0))EXIT + enddo + do + if(xx >= bcs%xs(0))EXIT xx=xx+bcs%xs(bcs%mx) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c find x interval. c----------------------------------------------------------------------- - DO - IF(bcs%ix <= 0)EXIT - IF(xx >= bcs%xs(bcs%ix))EXIT + do + if(bcs%ix <= 0)EXIT + if(xx >= bcs%xs(bcs%ix))EXIT bcs%ix=bcs%ix-1 - ENDDO - DO - IF(bcs%ix >= bcs%mx-1)EXIT - IF(xx < bcs%xs(bcs%ix+1))EXIT + enddo + do + if(bcs%ix >= bcs%mx-1)EXIT + if(xx < bcs%xs(bcs%ix+1))EXIT bcs%ix=bcs%ix+1 - ENDDO + enddo c----------------------------------------------------------------------- c normalize y interval for periodic splines. c----------------------------------------------------------------------- - IF(bcs%periodic(2))THEN - DO - IF(yy < bcs%ys(bcs%my))EXIT + if(bcs%periodic(2))then + do + if(yy < bcs%ys(bcs%my))EXIT yy=yy-bcs%ys(bcs%my) - ENDDO - DO - IF(yy >= bcs%ys(0))EXIT + enddo + do + if(yy >= bcs%ys(0))EXIT yy=yy+bcs%ys(bcs%my) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c find y interval. c----------------------------------------------------------------------- - DO - IF(bcs%iy <= 0)EXIT - IF(yy >= bcs%ys(bcs%iy))EXIT + do + if(bcs%iy <= 0)EXIT + if(yy >= bcs%ys(bcs%iy))EXIT bcs%iy=bcs%iy-1 - ENDDO - DO - IF(bcs%iy >= bcs%my-1)EXIT - IF(yy < bcs%ys(bcs%iy+1))EXIT + enddo + do + if(bcs%iy >= bcs%my-1)EXIT + if(yy < bcs%ys(bcs%iy+1))EXIT bcs%iy=bcs%iy+1 - ENDDO + enddo c----------------------------------------------------------------------- c find offsets and compute local coefficients. c----------------------------------------------------------------------- dx=xx-bcs%xs(bcs%ix) dy=yy-bcs%ys(bcs%iy) - IF(ALLOCATED(bcs%cmats))THEN + if(allocated(bcs%cmats))then c=bcs%cmats(:,:,bcs%ix+1,bcs%iy+1,:) - ELSE + else c=bicube_getco(bcs) - ENDIF + endif c----------------------------------------------------------------------- c evaluate f. c----------------------------------------------------------------------- bcs%f=0 - DO i=4,1,-1 + do i=4,1,-1 bcs%f=bcs%f*dx $ +((c(i,4,:)*dy $ +c(i,3,:))*dy $ +c(i,2,:))*dy $ +c(i,1,:) - ENDDO + enddo c----------------------------------------------------------------------- c evaluate first derivatives of f c----------------------------------------------------------------------- - IF(mode > 0)THEN + if(mode > 0)then bcs%fx=0 bcs%fy=0 - DO i=4,1,-1 + do i=4,1,-1 bcs%fy=bcs%fy*dx $ +(c(i,4,:)*3*dy $ +c(i,3,:)*2)*dy @@ -545,103 +545,103 @@ SUBROUTINE bicube_eval(bcs,x,y,mode) $ +(c(4,i,:)*3*dx $ +c(3,i,:)*2)*dx $ +c(2,i,:) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c evaluate second derivatives of f c----------------------------------------------------------------------- - IF(mode > 1)THEN + if(mode > 1)then bcs%fxx=0 bcs%fyy=0 bcs%fxy=0 - DO i=4,1,-1 + do i=4,1,-1 bcs%fyy=bcs%fyy*dx $ +(c(i,4,:)*3*dy $ +c(i,3,:))*2 bcs%fxx=bcs%fxx*dy $ +(c(4,i,:)*3*dx $ +c(3,i,:))*2 - ENDDO - DO i=4,2,-1 + enddo + do i=4,2,-1 bcs%fxy=bcs%fxy*dx $ +((c(i,4,:)*3*dy $ +c(i,3,:)*2)*dy $ +c(i,2,:))*(i-1) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c restore x powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dx=x-bcs%x0(iside) - DO iqty=1,bcs%nqty - IF(bcs%xpower(iside,iqty) == 0)CYCLE + do iqty=1,bcs%nqty + if(bcs%xpower(iside,iqty) == 0)cycle xfac=ABS(dx)**bcs%xpower(iside,iqty) g=bcs%f(iqty)*xfac - IF(mode > 0)THEN + if(mode > 0)then gx=(bcs%fx(iqty)+bcs%f(iqty) $ *bcs%xpower(iside,iqty)/dx)*xfac gy=bcs%fy(iqty)*xfac - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then gxx=(bcs%fxx(iqty)+bcs%xpower(iside,iqty)/dx $ *(2*bcs%fx(iqty)+(bcs%xpower(iside,iqty)-1) $ *bcs%f(iqty)/dx))*xfac gxy=(bcs%fxy(iqty)+bcs%fy(iqty) $ *bcs%xpower(iside,iqty)/dx)*xfac gyy=bcs%fyy(iqty)*xfac - ENDIF + endif bcs%f(iqty)=g - IF(mode > 0)THEN + if(mode > 0)then bcs%fx(iqty)=gx bcs%fy(iqty)=gy - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then bcs%fxx(iqty)=gxx bcs%fxy(iqty)=gxy bcs%fyy(iqty)=gyy - ENDIF - ENDDO - ENDDO + endif + enddo + enddo c----------------------------------------------------------------------- c restore y powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dy=y-bcs%y0(iside) - DO iqty=1,bcs%nqty - IF(bcs%ypower(iside,iqty) == 0)CYCLE + do iqty=1,bcs%nqty + if(bcs%ypower(iside,iqty) == 0)cycle yfac=ABS(dy)**bcs%ypower(iside,iqty) g=bcs%f(iqty)*yfac - IF(mode > 0)THEN + if(mode > 0)then gx=bcs%fx(iqty)*yfac gy=(bcs%fy(iqty)+bcs%f(iqty) $ *bcs%ypower(iside,iqty)/dy)*yfac - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then gxx=bcs%fxx(iqty)*yfac gxy=(bcs%fxy(iqty)+bcs%fy(iqty) $ *bcs%ypower(iside,iqty)/dy)*yfac gyy=(bcs%fyy(iqty)+bcs%ypower(iside,iqty)/dy $ *(2*bcs%fy(iqty)+(bcs%ypower(iside,iqty)-1) $ *bcs%f(iqty)/dy))*yfac - ENDIF + endif bcs%f(iqty)=g - IF(mode > 0)THEN + if(mode > 0)then bcs%fx(iqty)=gx bcs%fy(iqty)=gy - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then bcs%fxx(iqty)=gxx bcs%fxy(iqty)=gxy bcs%fyy(iqty)=gyy - ENDIF - ENDDO - ENDDO + endif + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_eval + return + end subroutine bicube_eval c----------------------------------------------------------------------- c subprogram 5a. bicube_eval_external. c evaluates bicubic spline function with external arrays (parallel). @@ -649,111 +649,111 @@ END SUBROUTINE bicube_eval c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_eval_external(bcs, x, y, mode, - $ b_ix, b_iy, b_f, b_fx, b_fy, b_fxx, b_fxy, b_fyy) + subroutine bicube_eval_external(bcs, x, y, mode, + $ b_f, b_fx, b_fy, b_fxx, b_fxy, b_fyy) - TYPE(bicube_type), INTENT(IN) :: bcs - REAL(r8), INTENT(IN) :: x,y - INTEGER, INTENT(IN) :: mode + type(bicube_type), intent(in) :: bcs + real(r8), intent(in) :: x,y + integer, intent(in) :: mode - INTEGER :: i,iqty,iside - REAL(r8) :: dx,dy,xx,yy,g,gx,gy,gxx,gxy,gyy,xfac,yfac - REAL(r8), DIMENSION (4,4,bcs%nqty) :: c + integer :: i,iqty,iside + integer :: ix, iy, i_low, i_high, i_mid + real(r8) :: dx,dy,xx,yy,g,gx,gy,gxx,gxy,gyy,xfac,yfac + real(r8), dimension (4,4,bcs%nqty) :: c - INTEGER, INTENT(INOUT) :: b_ix,b_iy - REAL(r8), DIMENSION(:), INTENT(INOUT) :: b_f,b_fx,b_fy - REAL(r8), DIMENSION(:), INTENT(INOUT) :: b_fxx,b_fxy,b_fyy -c----------------------------------------------------------------------- -c error-check for mode number--external array is limited. -c----------------------------------------------------------------------- - IF (mode > 1) THEN - CALL program_stop("Set bicube_eval_external mode <=1 !") - ENDIF + real(r8), dimension(:), intent(inout) :: b_f + real(r8), dimension(:), intent(inout), optional :: b_fx,b_fy + real(r8), dimension(:), intent(inout), optional :: b_fxx, + $ b_fxy,b_fyy c----------------------------------------------------------------------- c preliminary computations. c----------------------------------------------------------------------- - b_ix=max(b_ix,0) - b_ix=min(b_ix,bcs%mx-1) - b_iy=max(b_iy,0) - b_iy=min(b_iy,bcs%my-1) xx=x yy=y c----------------------------------------------------------------------- c normalize x interval for periodic splines. c----------------------------------------------------------------------- - IF(bcs%periodic(1))THEN - DO - IF(xx < bcs%xs(bcs%mx))EXIT + if(bcs%periodic(1))then + do + if(xx < bcs%xs(bcs%mx))EXIT xx=xx-bcs%xs(bcs%mx) - ENDDO - DO - IF(xx >= bcs%xs(0))EXIT + enddo + do + if(xx >= bcs%xs(0))EXIT xx=xx+bcs%xs(bcs%mx) - ENDDO - ENDIF -c----------------------------------------------------------------------- -c find x interval. -c----------------------------------------------------------------------- - DO - IF(b_ix <= 0)EXIT - IF(xx >= bcs%xs(b_ix))EXIT - b_ix=b_ix-1 - ENDDO - DO - IF(b_ix >= bcs%mx-1)EXIT - IF(xx < bcs%xs(b_ix+1))EXIT - b_ix=b_ix+1 - ENDDO + enddo + endif +c----------------------------------------------------------------------- +c find x interval using Binary search +c----------------------------------------------------------------------- + i_low = 0 + i_high = bcs%mx - 1 + do while (i_low <= i_high) + i_mid = i_low + (i_high - i_low) / 2 + if (xx < bcs%xs(i_mid)) then + i_high = i_mid - 1 + else if (xx >= bcs%xs(i_mid + 1)) then + i_low = i_mid + 1 + else + ix = i_mid + exit + endif + end do + if (i_low > i_high) ix = min(max(i_low - 1, 0), bcs%mx - 1) c----------------------------------------------------------------------- c normalize y interval for periodic splines. c----------------------------------------------------------------------- - IF(bcs%periodic(2))THEN - DO - IF(yy < bcs%ys(bcs%my))EXIT + if(bcs%periodic(2))then + do + if(yy < bcs%ys(bcs%my))EXIT yy=yy-bcs%ys(bcs%my) - ENDDO - DO - IF(yy >= bcs%ys(0))EXIT + enddo + do + if(yy >= bcs%ys(0))EXIT yy=yy+bcs%ys(bcs%my) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c find y interval. c----------------------------------------------------------------------- - DO - IF(b_iy <= 0)EXIT - IF(yy >= bcs%ys(b_iy))EXIT - b_iy=b_iy-1 - ENDDO - DO - IF(b_iy >= bcs%my-1)EXIT - IF(yy < bcs%ys(b_iy+1))EXIT - b_iy=b_iy+1 - ENDDO + i_low = 0 + i_high = bcs%my - 1 + do while (i_low <= i_high) + i_mid = i_low + (i_high - i_low) / 2 + if (yy < bcs%ys(i_mid)) then + i_high = i_mid - 1 + else if (yy >= bcs%ys(i_mid + 1)) then + i_low = i_mid + 1 + else + iy = i_mid + exit + endif + end do + if (i_low > i_high) iy = min(max(i_low - 1, 0), bcs%my - 1) c----------------------------------------------------------------------- c find offsets and compute local coefficients. c----------------------------------------------------------------------- - dx=xx-bcs%xs(b_ix) - dy=yy-bcs%ys(b_iy) - call bicube_getco_external_sub(bcs,b_ix,b_iy,c) + dx=xx-bcs%xs(ix) + dy=yy-bcs%ys(iy) + call bicube_getco_external_sub(bcs,ix,iy,c) c----------------------------------------------------------------------- c evaluate f. c----------------------------------------------------------------------- b_f=0 - DO i=4,1,-1 + do i=4,1,-1 b_f=b_f*dx $ +((c(i,4,:)*dy $ +c(i,3,:))*dy $ +c(i,2,:))*dy $ +c(i,1,:) - ENDDO + enddo c----------------------------------------------------------------------- c evaluate first derivatives of f c----------------------------------------------------------------------- - IF(mode > 0)THEN + if(mode > 0)then b_fx=0 b_fy=0 - DO i=4,1,-1 + do i=4,1,-1 b_fy=b_fy*dx $ +(c(i,4,:)*3*dy $ +c(i,3,:)*2)*dy @@ -762,103 +762,103 @@ SUBROUTINE bicube_eval_external(bcs, x, y, mode, $ +(c(4,i,:)*3*dx $ +c(3,i,:)*2)*dx $ +c(2,i,:) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c evaluate second derivatives of f c----------------------------------------------------------------------- - IF(mode > 1)THEN + if(mode > 1)then b_fxx=0 b_fyy=0 b_fxy=0 - DO i=4,1,-1 + do i=4,1,-1 b_fyy=b_fyy*dx $ +(c(i,4,:)*3*dy $ +c(i,3,:))*2 b_fxx=b_fxx*dy $ +(c(4,i,:)*3*dx $ +c(3,i,:))*2 - ENDDO - DO i=4,2,-1 + enddo + do i=4,2,-1 b_fxy=b_fxy*dx $ +((c(i,4,:)*3*dy $ +c(i,3,:)*2)*dy $ +c(i,2,:))*(i-1) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c restore x powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dx=x-bcs%x0(iside) - DO iqty=1,bcs%nqty - IF(bcs%xpower(iside,iqty) == 0)CYCLE + do iqty=1,bcs%nqty + if(bcs%xpower(iside,iqty) == 0)cycle xfac=ABS(dx)**bcs%xpower(iside,iqty) g=b_f(iqty)*xfac - IF(mode > 0)THEN + if(mode > 0)then gx=(b_fx(iqty)+b_f(iqty) $ *bcs%xpower(iside,iqty)/dx)*xfac gy=b_fy(iqty)*xfac - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then gxx=(b_fxx(iqty)+bcs%xpower(iside,iqty)/dx $ *(2*bcs%fx(iqty)+(bcs%xpower(iside,iqty)-1) $ *b_f(iqty)/dx))*xfac gxy=(b_fxy(iqty)+bcs%fy(iqty) $ *bcs%xpower(iside,iqty)/dx)*xfac gyy=b_fyy(iqty)*xfac - ENDIF + endif b_f(iqty)=g - IF(mode > 0)THEN + if(mode > 0)then b_fx(iqty)=gx b_fy(iqty)=gy - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then b_fxx(iqty)=gxx b_fxy(iqty)=gxy b_fyy(iqty)=gyy - ENDIF - ENDDO - ENDDO + endif + enddo + enddo c----------------------------------------------------------------------- c restore y powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dy=y-bcs%y0(iside) - DO iqty=1,bcs%nqty - IF(bcs%ypower(iside,iqty) == 0)CYCLE + do iqty=1,bcs%nqty + if(bcs%ypower(iside,iqty) == 0)cycle yfac=ABS(dy)**bcs%ypower(iside,iqty) g=b_f(iqty)*yfac - IF(mode > 0)THEN + if(mode > 0)then gx=b_fx(iqty)*yfac gy=(b_fy(iqty)+b_f(iqty) $ *bcs%ypower(iside,iqty)/dy)*yfac - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then gxx=b_fxx(iqty)*yfac gxy=(b_fxy(iqty)+b_fy(iqty) $ *bcs%ypower(iside,iqty)/dy)*yfac gyy=(b_fyy(iqty)+bcs%ypower(iside,iqty)/dy $ *(2*bcs%fy(iqty)+(bcs%ypower(iside,iqty)-1) $ *b_f(iqty)/dy))*yfac - ENDIF + endif b_f(iqty)=g - IF(mode > 0)THEN + if(mode > 0)then b_fx(iqty)=gx b_fy(iqty)=gy - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then b_fxx(iqty)=gxx b_fxy(iqty)=gxy b_fyy(iqty)=gyy - ENDIF - ENDDO - ENDDO + endif + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_eval_external + return + end subroutine bicube_eval_external c----------------------------------------------------------------------- c subprogram 6. bicube_getco. c computes coefficient matrices. @@ -868,13 +868,13 @@ END SUBROUTINE bicube_eval_external c----------------------------------------------------------------------- FUNCTION bicube_getco(bcs) RESULT(cmat) - TYPE(bicube_type), INTENT(IN) :: bcs - REAL(r8), DIMENSION(4,4,bcs%nqty) :: cmat + type(bicube_type), intent(in) :: bcs + real(r8), dimension(4,4,bcs%nqty) :: cmat - REAL(r8) :: hxfac,hxfac2,hxfac3 - REAL(r8) :: hyfac,hyfac2,hyfac3 - REAL(r8), DIMENSION(3:4,4) :: gxmat,gymat - REAL(r8), DIMENSION(4,4,bcs%nqty) :: temp + real(r8) :: hxfac,hxfac2,hxfac3 + real(r8) :: hyfac,hyfac2,hyfac3 + real(r8), dimension(3:4,4) :: gxmat,gymat + real(r8), dimension(4,4,bcs%nqty) :: temp c----------------------------------------------------------------------- c compute gxmat. c----------------------------------------------------------------------- @@ -953,8 +953,8 @@ FUNCTION bicube_getco(bcs) RESULT(cmat) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END FUNCTION bicube_getco + return + end FUNCTION bicube_getco c----------------------------------------------------------------------- c subprogram 6a. bicube_getco_external. c computes coefficient matrices for external arrays. @@ -964,14 +964,14 @@ END FUNCTION bicube_getco c----------------------------------------------------------------------- FUNCTION bicube_getco_external(bcs,b_ix,b_iy) RESULT(cmat) - TYPE(bicube_type), INTENT(IN) :: bcs - INTEGER, INTENT(IN) :: b_ix, b_iy - REAL(r8), DIMENSION(4,4,bcs%nqty) :: cmat + type(bicube_type), intent(in) :: bcs + integer, intent(in) :: b_ix, b_iy + real(r8), dimension(4,4,bcs%nqty) :: cmat - REAL(r8) :: hxfac,hxfac2,hxfac3 - REAL(r8) :: hyfac,hyfac2,hyfac3 - REAL(r8), DIMENSION(3:4,4) :: gxmat,gymat - REAL(r8), DIMENSION(4,4,bcs%nqty) :: temp + real(r8) :: hxfac,hxfac2,hxfac3 + real(r8) :: hyfac,hyfac2,hyfac3 + real(r8), dimension(3:4,4) :: gxmat,gymat + real(r8), dimension(4,4,bcs%nqty) :: temp c----------------------------------------------------------------------- c compute gxmat. c----------------------------------------------------------------------- @@ -1050,8 +1050,8 @@ FUNCTION bicube_getco_external(bcs,b_ix,b_iy) RESULT(cmat) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END FUNCTION bicube_getco_external + return + end FUNCTION bicube_getco_external c----------------------------------------------------------------------- c subprogram 6b. bicube_getco_external_sub. c computes coefficient matrices for external arrays. @@ -1060,16 +1060,16 @@ END FUNCTION bicube_getco_external c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_getco_external_sub(bcs,b_ix,b_iy, cmat) + subroutine bicube_getco_external_sub(bcs,b_ix,b_iy, cmat) - TYPE(bicube_type), INTENT(IN) :: bcs - INTEGER, INTENT(IN) :: b_ix, b_iy - REAL(r8), DIMENSION(4,4,bcs%nqty), INTENT(OUT) :: cmat + type(bicube_type), intent(in) :: bcs + integer, intent(in) :: b_ix, b_iy + real(r8), dimension(4,4,bcs%nqty), intent(out) :: cmat - REAL(r8) :: hxfac,hxfac2,hxfac3 - REAL(r8) :: hyfac,hyfac2,hyfac3 - REAL(r8), DIMENSION(3:4,4) :: gxmat,gymat - REAL(r8), DIMENSION(4,4,bcs%nqty) :: temp + real(r8) :: hxfac,hxfac2,hxfac3 + real(r8) :: hyfac,hyfac2,hyfac3 + real(r8), dimension(3:4,4) :: gxmat,gymat + real(r8), dimension(4,4,bcs%nqty) :: temp c----------------------------------------------------------------------- c compute gxmat. c----------------------------------------------------------------------- @@ -1148,8 +1148,8 @@ SUBROUTINE bicube_getco_external_sub(bcs,b_ix,b_iy, cmat) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_getco_external_sub + return + end subroutine bicube_getco_external_sub c----------------------------------------------------------------------- c subprogram 7. bicube_all_eval. c evaluates bicubic splines in all intervals. @@ -1157,110 +1157,110 @@ END SUBROUTINE bicube_getco_external_sub c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_all_eval(bcs,dx,dy,f,fx,fy,fxx,fyy,fxy,mode) + subroutine bicube_all_eval(bcs,dx,dy,f,fx,fy,fxx,fyy,fxy,mode) - TYPE(bicube_type), INTENT(INOUT) :: bcs - REAL(r8), INTENT(IN) :: dx,dy - REAL(r8), INTENT(OUT), DIMENSION(bcs%mx,bcs%my,bcs%nqty) :: + type(bicube_type), intent(inout) :: bcs + real(r8), intent(in) :: dx,dy + real(r8), intent(out), dimension(bcs%mx,bcs%my,bcs%nqty) :: $ f,fx,fy,fxx,fyy,fxy - INTEGER, INTENT(IN) :: mode + integer, intent(in) :: mode - INTEGER :: i,ix,iy,iqty,iside - REAL(r8), DIMENSION(bcs%mx) :: dxv - REAL(r8), DIMENSION(bcs%my) :: dyv + integer :: i,ix,iy,iqty,iside + real(r8), dimension(bcs%mx) :: dxv + real(r8), dimension(bcs%my) :: dyv - REAL(R8), DIMENSION(bcs%mx) :: dxx,xfac - REAL(R8), DIMENSION(bcs%my) :: dyy,yfac - REAL(R8), DIMENSION(bcs%mx,bcs%my) :: g,gx,gy,gxx,gxy,gyy + real(R8), dimension(bcs%mx) :: dxx,xfac + real(R8), dimension(bcs%my) :: dyy,yfac + real(R8), dimension(bcs%mx,bcs%my) :: g,gx,gy,gxx,gxy,gyy c----------------------------------------------------------------------- c compute local displacements and coefficients. c----------------------------------------------------------------------- dxv=(bcs%xs(1:bcs%mx)-bcs%xs(0:bcs%mx-1))*dx dyv=(bcs%ys(1:bcs%my)-bcs%ys(0:bcs%my-1))*dy - CALL bicube_all_getco(bcs) + call bicube_all_getco(bcs) c----------------------------------------------------------------------- c evaluate f. c----------------------------------------------------------------------- f=0 - DO i=4,1,-1 - IF(i /= 4)THEN - DO ix=1,bcs%mx + do i=4,1,-1 + if(i /= 4)then + do ix=1,bcs%mx f(ix,:,:)=f(ix,:,:)*dxv(ix) - ENDDO - ENDIF - DO iy=1,bcs%my + enddo + endif + do iy=1,bcs%my f(:,iy,:)=f(:,iy,:) $ +((bcs%cmats(i,4,:,iy,:)*dyv(iy) $ +bcs%cmats(i,3,:,iy,:))*dyv(iy) $ +bcs%cmats(i,2,:,iy,:))*dy $ +bcs%cmats(i,1,:,iy,:) - ENDDO - ENDDO + enddo + enddo c----------------------------------------------------------------------- c evaluate fx. c----------------------------------------------------------------------- - IF(mode > 0)THEN + if(mode > 0)then fx=0 - DO i=4,1,-1 - IF(i /= 4)THEN - DO iy=1,bcs%my + do i=4,1,-1 + if(i /= 4)then + do iy=1,bcs%my fx(:,iy,:)=fx(:,iy,:)*dyv(iy) - ENDDO - ENDIF - DO ix=1,bcs%mx + enddo + endif + do ix=1,bcs%mx fx(ix,:,:)=fx(ix,:,:) $ +(bcs%cmats(4,i,ix,:,:)*3*dxv(ix) $ +bcs%cmats(3,i,ix,:,:)*2)*dxv(ix) $ +bcs%cmats(2,i,ix,:,:) - ENDDO - ENDDO + enddo + enddo c----------------------------------------------------------------------- c evaluate fy. c----------------------------------------------------------------------- fy=0 - DO i=4,1,-1 - IF(i /= 4)THEN - DO ix=1,bcs%mx + do i=4,1,-1 + if(i /= 4)then + do ix=1,bcs%mx fy(ix,:,:)=fy(ix,:,:)*dxv(ix) - ENDDO - ENDIF - DO iy=1,bcs%my + enddo + endif + do iy=1,bcs%my fy(:,iy,:)=fy(:,iy,:) $ +(bcs%cmats(i,4,:,iy,:)*3*dyv(iy) $ +bcs%cmats(i,3,:,iy,:)*2)*dyv(iy) $ +bcs%cmats(i,2,:,iy,:) - ENDDO - ENDDO - ENDIF + enddo + enddo + endif c----------------------------------------------------------------------- c evaluate fxx. c----------------------------------------------------------------------- - IF(mode > 1)THEN + if(mode > 1)then fxx=0 - DO i=4,1,-1 - IF(i /= 4)THEN - DO iy=1,bcs%my + do i=4,1,-1 + if(i /= 4)then + do iy=1,bcs%my fxx(:,iy,:)=fxx(:,iy,:)*dyv(iy) - ENDDO - ENDIF - DO ix=1,bcs%mx + enddo + endif + do ix=1,bcs%mx fxx(ix,:,:)=fxx(ix,:,:) $ +(bcs%cmats(4,i,ix,:,:)*3*dxv(ix) $ +bcs%cmats(3,i,ix,:,:))*2 - ENDDO - ENDDO + enddo + enddo c----------------------------------------------------------------------- c evaluate fyy and fxy c----------------------------------------------------------------------- fyy=0 - DO i=4,1,-1 - IF(i /= 4)THEN - DO ix=1,bcs%mx + do i=4,1,-1 + if(i /= 4)then + do ix=1,bcs%mx fyy(ix,:,:)=fyy(ix,:,:)*dxv(ix) fxy(ix,:,:)=fxy(ix,:,:)*dxv(ix) - ENDDO - ENDIF - DO iy=1,bcs%my + enddo + endif + do iy=1,bcs%my fyy(:,iy,:)=fyy(:,iy,:) $ +(bcs%cmats(i,4,:,iy,:)*3*dyv(iy) $ +bcs%cmats(i,3,:,iy,:))*2 @@ -1268,86 +1268,86 @@ SUBROUTINE bicube_all_eval(bcs,dx,dy,f,fx,fy,fxx,fyy,fxy,mode) $ +((bcs%cmats(i,4,:,iy,:)*3*dyv(iy) $ +bcs%cmats(i,3,:,iy,:)*2)*dyv(iy) $ +bcs%cmats(i,2,:,iy,:))*(i-1) - ENDDO - ENDDO - ENDIF + enddo + enddo + endif c----------------------------------------------------------------------- c restore x powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dxx=(bcs%xs(0:bcs%mx-1)+dxv(1:bcs%mx))-bcs%x0(iside) - DO iqty=1,bcs%nqty - IF(bcs%xpower(iside,iqty) == 0)CYCLE + do iqty=1,bcs%nqty + if(bcs%xpower(iside,iqty) == 0)cycle xfac=dxx**bcs%xpower(iside,iqty) - DO iy=1,bcs%my + do iy=1,bcs%my g(:,iy)=f(:,iy,iqty)*xfac - IF(mode > 0)THEN + if(mode > 0)then gx(:,iy)=(fx(:,iy,iqty)+f(:,iy,iqty) $ *bcs%xpower(iside,iqty)/dxx)*xfac gy(:,iy)=fy(:,iy,iqty)*xfac - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then gxy(:,iy)=(fxy(:,iy,iqty)+fy(:,iy,iqty) $ *bcs%xpower(iside,iqty)/dxx)*xfac gxx(:,iy)=(fxx(:,iy,iqty)+bcs%xpower(iside,iqty)/dxx $ *(2*fx(:,iy,iqty)+(bcs%xpower(iside,iqty)-1) $ *f(:,iy,iqty)/dxx))*xfac gyy(:,iy)=fyy(:,iy,iqty)*xfac - ENDIF + endif f(:,iy,iqty)=g(:,iy) - IF(mode > 0)THEN + if(mode > 0)then fx(:,iy,iqty)=gx(:,iy) fy(:,iy,iqty)=gy(:,iy) - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then fxx(:,iy,iqty)=gxx(:,iy) fxy(:,iy,iqty)=gxy(:,iy) fyy(:,iy,iqty)=gyy(:,iy) - ENDIF - ENDDO - ENDDO - ENDDO + endif + enddo + enddo + enddo c----------------------------------------------------------------------- c restore y powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dyy=(bcs%ys(0:bcs%my-1)+dyv(1:bcs%my))-bcs%y0(iside) - DO iqty=1,bcs%nqty - IF(bcs%ypower(iside,iqty) == 0)CYCLE + do iqty=1,bcs%nqty + if(bcs%ypower(iside,iqty) == 0)cycle yfac=dyy**bcs%ypower(iside,iqty) - DO ix=1,bcs%mx + do ix=1,bcs%mx g(ix,:)=f(ix,:,iqty)*yfac - IF(mode > 0)THEN + if(mode > 0)then gy(ix,:)=(fy(ix,:,iqty)+f(ix,:,iqty) $ *bcs%ypower(iside,iqty)/dyy)*yfac gx(ix,:)=fx(ix,:,iqty)*yfac - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then gxx(ix,:)=fxx(ix,:,iqty)*yfac gxy(ix,:)=(fxy(ix,:,iqty)+fx(ix,:,iqty) $ *bcs%ypower(iside,iqty)/dyy)*yfac gyy(ix,:)=(fyy(ix,:,iqty)+bcs%ypower(iside,iqty)/dyy $ *(2*fy(ix,:,iqty)+(bcs%ypower(iside,iqty)-1) $ *f(ix,:,iqty)/dyy))*yfac - ENDIF + endif f(ix,:,iqty)=g(ix,:) - IF(mode > 0)THEN + if(mode > 0)then fx(ix,:,iqty)=gx(ix,:) fy(ix,:,iqty)=gy(ix,:) - ENDIF - IF(mode > 1)THEN + endif + if(mode > 1)then fxx(ix,:,iqty)=gxx(ix,:) fxy(ix,:,iqty)=gxy(ix,:) fyy(ix,:,iqty)=gyy(ix,:) - ENDIF - ENDDO - ENDDO - ENDDO + endif + enddo + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_all_eval + return + end subroutine bicube_all_eval c----------------------------------------------------------------------- c subprogram 8. bicube_all_getco. c computes coefficient matrices in all intervals. @@ -1355,24 +1355,24 @@ END SUBROUTINE bicube_all_eval c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_all_getco(bcs) + subroutine bicube_all_getco(bcs) - TYPE(bicube_type), INTENT(INOUT) :: bcs + type(bicube_type), intent(inout) :: bcs - INTEGER :: ix,iy - REAL(r8), DIMENSION(bcs%mx) :: hxfac,hxfac2,hxfac3 - REAL(r8), DIMENSION(bcs%my) :: hyfac,hyfac2,hyfac3 - REAL(r8), DIMENSION(3:4,4,bcs%mx) :: gxmat - REAL(r8), DIMENSION(3:4,4,bcs%my) :: gymat - REAL(r8), DIMENSION(4,4,bcs%mx,bcs%my,bcs%nqty) :: temp + integer :: ix,iy + real(r8), dimension(bcs%mx) :: hxfac,hxfac2,hxfac3 + real(r8), dimension(bcs%my) :: hyfac,hyfac2,hyfac3 + real(r8), dimension(3:4,4,bcs%mx) :: gxmat + real(r8), dimension(3:4,4,bcs%my) :: gymat + real(r8), dimension(4,4,bcs%mx,bcs%my,bcs%nqty) :: temp c----------------------------------------------------------------------- c allocate space. c----------------------------------------------------------------------- - IF(ALLOCATED(bcs%cmats))THEN - RETURN - ELSE - ALLOCATE(bcs%cmats(4,4,bcs%mx,bcs%my,bcs%nqty)) - ENDIF + if(allocated(bcs%cmats))then + return + else + allocate(bcs%cmats(4,4,bcs%mx,bcs%my,bcs%nqty)) + endif c----------------------------------------------------------------------- c compute gxmat. c----------------------------------------------------------------------- @@ -1424,7 +1424,7 @@ SUBROUTINE bicube_all_getco(bcs) c multiply by gymat^T. c----------------------------------------------------------------------- temp(:,1:2,:,:,:)=bcs%cmats(:,1:2,:,:,:) - DO iy=1,bcs%my + do iy=1,bcs%my temp(:,3,:,iy,:) $ =bcs%cmats(:,1,:,iy,:)*gymat(3,1,iy) $ +bcs%cmats(:,2,:,iy,:)*gymat(3,2,iy) @@ -1435,12 +1435,12 @@ SUBROUTINE bicube_all_getco(bcs) $ +bcs%cmats(:,2,:,iy,:)*gymat(4,2,iy) $ +bcs%cmats(:,3,:,iy,:)*gymat(4,3,iy) $ +bcs%cmats(:,4,:,iy,:)*gymat(4,4,iy) - ENDDO + enddo c----------------------------------------------------------------------- c multiply by gxmat. c----------------------------------------------------------------------- bcs%cmats(1:2,:,:,:,:)=temp(1:2,:,:,:,:) - DO ix=1,bcs%mx + do ix=1,bcs%mx bcs%cmats(3,:,ix,:,:) $ =gxmat(3,1,ix)*temp(1,:,ix,:,:) $ +gxmat(3,2,ix)*temp(2,:,ix,:,:) @@ -1451,12 +1451,12 @@ SUBROUTINE bicube_all_getco(bcs) $ +gxmat(4,2,ix)*temp(2,:,ix,:,:) $ +gxmat(4,3,ix)*temp(3,:,ix,:,:) $ +gxmat(4,4,ix)*temp(4,:,ix,:,:) - ENDDO + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_all_getco + return + end subroutine bicube_all_getco c----------------------------------------------------------------------- c subprogram 9. bicube_write_xy. c produces ascii and binary output for bicubic spline fits. @@ -1464,97 +1464,97 @@ END SUBROUTINE bicube_all_getco c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_write_xy(bcs,out,bin,iua,iub,interp) + subroutine bicube_write_xy(bcs,out,bin,iua,iub,interp) - TYPE(bicube_type), INTENT(INOUT) :: bcs - LOGICAL, INTENT(IN) :: out,bin - INTEGER, INTENT(IN) :: iua,iub - LOGICAL, INTENT(IN) :: interp + type(bicube_type), intent(inout) :: bcs + logical, intent(in) :: out,bin + integer, intent(in) :: iua,iub + logical, intent(in) :: interp - INTEGER :: ix,iy,jx,jy,iqty - REAL(r8) :: x,y,dx,dy + integer :: ix,iy,jx,jy,iqty + real(r8) :: x,y,dx,dy - CHARACTER(80) :: format1,format2 + character(80) :: format1,format2 c----------------------------------------------------------------------- c write formats. c----------------------------------------------------------------------- - 10 FORMAT(1x,"iy = ",i3,", ",a6," = ",1p,e11.3) - 20 FORMAT(1x,"iy = ",i3,", jy = ",i1,", ",a6," = ",1p,e11.3) - 30 FORMAT('(/3x,"ix",4x,a,1x,',i3.3,'(4x,a6,1x)/)') - 40 FORMAT('(i5,1p,e11.3,',i3.3,'e11.3)') + 10 format(1x,"iy = ",i3,", ",a6," = ",1p,e11.3) + 20 format(1x,"iy = ",i3,", jy = ",i1,", ",a6," = ",1p,e11.3) + 30 format('(/3x,"ix",4x,a,1x,',i3.3,'(4x,a6,1x)/)') + 40 format('(i5,1p,e11.3,',i3.3,'e11.3)') c----------------------------------------------------------------------- c abort. c----------------------------------------------------------------------- - IF(.NOT. (out. OR. bin))RETURN + if(.not. (out. OR. bin))return c----------------------------------------------------------------------- c create format statements. c----------------------------------------------------------------------- - IF(out)THEN - WRITE(format1,30)bcs%nqty - WRITE(format2,40)bcs%nqty - ENDIF + if(out)then + write(format1,30)bcs%nqty + write(format2,40)bcs%nqty + endif c----------------------------------------------------------------------- c write input data. c----------------------------------------------------------------------- - IF(out)WRITE(iua,'(1x,a/)')"input data" - DO iy=0,bcs%my + if(out)write(iua,'(1x,a/)')"input data" + do iy=0,bcs%my y=bcs%ys(iy) - IF(out)then - WRITE(iua,10)iy,bcs%ytitle,bcs%ys(iy) - WRITE(iua,format1)bcs%xtitle, + if(out)then + write(iua,10)iy,bcs%ytitle,bcs%ys(iy) + write(iua,format1)bcs%xtitle, $ (bcs%title(iqty),iqty=1,bcs%nqty) - ENDIF - DO ix=0,bcs%mx + endif + do ix=0,bcs%mx x=bcs%xs(ix) - CALL bicube_eval(bcs,x,y,0) - IF(out)WRITE(iua,format2)ix,x,bcs%f - IF(bin)WRITE(iub)REAL(x,4),REAL(bcs%f,4) - ENDDO - IF(out)WRITE(iua,format1)bcs%xtitle, + call bicube_eval(bcs,x,y,0) + if(out)write(iua,format2)ix,x,bcs%f + if(bin)write(iub)real(x,4),real(bcs%f,4) + enddo + if(out)write(iua,format1)bcs%xtitle, $ (bcs%title(iqty),iqty=1,bcs%nqty) - IF(bin)WRITE(iub) - ENDDO + if(bin)write(iub) + enddo c----------------------------------------------------------------------- c begin loops over y for interpolated data. c----------------------------------------------------------------------- - IF(interp)THEN - IF(out)WRITE(iua,'(1x,a/)')"interpolated data" - DO iy=0,bcs%my-1 + if(interp)then + if(out)write(iua,'(1x,a/)')"interpolated data" + do iy=0,bcs%my-1 dy=(bcs%ys(iy+1)-bcs%ys(iy))/4 - DO jy=0,4 + do jy=0,4 y=bcs%ys(iy)+dy*jy - IF(out)then - WRITE(iua,20)iy,jy,bcs%ytitle,y - WRITE(iua,format1)bcs%xtitle, + if(out)then + write(iua,20)iy,jy,bcs%ytitle,y + write(iua,format1)bcs%xtitle, $ (bcs%title(iqty),iqty=1,bcs%nqty) - ENDIF + endif c----------------------------------------------------------------------- c begin loops over x for interpolated data. c----------------------------------------------------------------------- - DO ix=0,bcs%mx-1 + do ix=0,bcs%mx-1 dx=(bcs%xs(ix+1)-bcs%xs(ix))/4 - DO jx=0,4 + do jx=0,4 x=bcs%xs(ix)+dx*jx - CALL bicube_eval(bcs,x,y,0) - IF(out)WRITE(iua,format2)ix,x,bcs%f - IF(bin)WRITE(iub)REAL(x,4),REAL(bcs%f,4) - ENDDO - IF(out)WRITE(iua,'()') - ENDDO + call bicube_eval(bcs,x,y,0) + if(out)write(iua,format2)ix,x,bcs%f + if(bin)write(iub)real(x,4),real(bcs%f,4) + enddo + if(out)write(iua,'()') + enddo c----------------------------------------------------------------------- c complete loops over y. c----------------------------------------------------------------------- - IF(out)WRITE(iua,format1)bcs%xtitle, + if(out)write(iua,format1)bcs%xtitle, $ (bcs%title(iqty),iqty=1,bcs%nqty) - IF(bin)WRITE(iub) - ENDDO - ENDDO - ENDIF + if(bin)write(iub) + enddo + enddo + endif c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_write_xy + return + end subroutine bicube_write_xy c----------------------------------------------------------------------- c subprogram 10. bicube_write_yx. c produces ascii and binary output for bicubic spline fits. @@ -1562,97 +1562,97 @@ END SUBROUTINE bicube_write_xy c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_write_yx(bcs,out,bin,iua,iub,interp) + subroutine bicube_write_yx(bcs,out,bin,iua,iub,interp) - TYPE(bicube_type), INTENT(INOUT) :: bcs - LOGICAL, INTENT(IN) :: out,bin - INTEGER, INTENT(IN) :: iua,iub - LOGICAL, INTENT(IN) :: interp + type(bicube_type), intent(inout) :: bcs + logical, intent(in) :: out,bin + integer, intent(in) :: iua,iub + logical, intent(in) :: interp - INTEGER :: ix,iy,jx,jy,iqty - REAL(r8) :: x,y,dx,dy + integer :: ix,iy,jx,jy,iqty + real(r8) :: x,y,dx,dy - CHARACTER(80) :: format1,format2 + character(80) :: format1,format2 c----------------------------------------------------------------------- c write formats. c----------------------------------------------------------------------- - 10 FORMAT(1x,"ix = ",i3,", ",a6," = ",1p,e11.3) - 20 FORMAT(1x,"ix = ",i3,", jx = ",i1,", ",a6," = ",1p,e11.3) - 30 FORMAT('(/4x,"iy",4x,a6,1x,',i3.3,'(4x,a6,1x)/)') - 40 FORMAT('(i6,1p,e11.3,',i3.3,'e11.3)') + 10 format(1x,"ix = ",i3,", ",a6," = ",1p,e11.3) + 20 format(1x,"ix = ",i3,", jx = ",i1,", ",a6," = ",1p,e11.3) + 30 format('(/4x,"iy",4x,a6,1x,',i3.3,'(4x,a6,1x)/)') + 40 format('(i6,1p,e11.3,',i3.3,'e11.3)') c----------------------------------------------------------------------- c abort. c----------------------------------------------------------------------- - IF(.NOT. (out. OR. bin))RETURN + if(.not. (out. OR. bin))return c----------------------------------------------------------------------- c create format statements. c----------------------------------------------------------------------- - IF(out)THEN - WRITE(format1,30)bcs%nqty - WRITE(format2,40)bcs%nqty - WRITE(iua,'(1x,a/)')"input data" - ENDIF + if(out)then + write(format1,30)bcs%nqty + write(format2,40)bcs%nqty + write(iua,'(1x,a/)')"input data" + endif c----------------------------------------------------------------------- c write input data. c----------------------------------------------------------------------- - DO ix=0,bcs%mx + do ix=0,bcs%mx x=bcs%xs(ix) - IF(out)then - WRITE(iua,10)ix,bcs%xtitle,bcs%xs(ix) - WRITE(iua,format1)bcs%ytitle, + if(out)then + write(iua,10)ix,bcs%xtitle,bcs%xs(ix) + write(iua,format1)bcs%ytitle, $ (bcs%title(iqty),iqty=1,bcs%nqty) - ENDIF - DO iy=0,bcs%my + endif + do iy=0,bcs%my y=bcs%ys(iy) - CALL bicube_eval(bcs,x,y,0) - IF(out)WRITE(iua,format2)iy,y,bcs%f - IF(bin)WRITE(iub)REAL(y,4),REAL(bcs%f,4) - ENDDO - IF(out)WRITE(iua,format1)bcs%ytitle, + call bicube_eval(bcs,x,y,0) + if(out)write(iua,format2)iy,y,bcs%f + if(bin)write(iub)real(y,4),real(bcs%f,4) + enddo + if(out)write(iua,format1)bcs%ytitle, $ (bcs%title(iqty),iqty=1,bcs%nqty) - IF(bin)WRITE(iub) - ENDDO + if(bin)write(iub) + enddo c----------------------------------------------------------------------- c begin loops over x for interpolated data. c----------------------------------------------------------------------- - IF(interp)THEN - IF(out)WRITE(iua,'(1x,a/)')"interpolated data" - DO ix=0,bcs%mx-1 + if(interp)then + if(out)write(iua,'(1x,a/)')"interpolated data" + do ix=0,bcs%mx-1 dx=(bcs%xs(ix+1)-bcs%xs(ix))/4 - DO jx=0,4 + do jx=0,4 x=bcs%xs(ix)+dx*jx - IF(out)then - WRITE(iua,20)ix,jx,bcs%xtitle,x - WRITE(iua,format1)bcs%ytitle, + if(out)then + write(iua,20)ix,jx,bcs%xtitle,x + write(iua,format1)bcs%ytitle, $ (bcs%title(iqty),iqty=1,bcs%nqty) - ENDIF + endif c----------------------------------------------------------------------- c begin loops over y for interpolated data. c----------------------------------------------------------------------- - DO iy=0,bcs%my-1 + do iy=0,bcs%my-1 dy=(bcs%ys(iy+1)-bcs%ys(iy))/4 - DO jy=0,4 + do jy=0,4 y=bcs%ys(iy)+dy*jy - CALL bicube_eval(bcs,x,y,0) - IF(out)WRITE(iua,format2)iy,y,bcs%f - IF(bin)WRITE(iub)REAL(y,4),REAL(bcs%f,4) - ENDDO - IF(out)WRITE(iua,'()') - ENDDO + call bicube_eval(bcs,x,y,0) + if(out)write(iua,format2)iy,y,bcs%f + if(bin)write(iub)real(y,4),real(bcs%f,4) + enddo + if(out)write(iua,'()') + enddo c----------------------------------------------------------------------- c complete loops over x. c----------------------------------------------------------------------- - IF(out)WRITE(iua,format1)bcs%ytitle, + if(out)write(iua,format1)bcs%ytitle, $ (bcs%title(iqty),iqty=1,bcs%nqty) - IF(bin)WRITE(iub) - ENDDO - ENDDO - ENDIF + if(bin)write(iub) + enddo + enddo + endif c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_write_yx + return + end subroutine bicube_write_yx c----------------------------------------------------------------------- c subprogram 11. bicube_write_arrays. c produces ascii and binary output for bicubic spline fits. @@ -1660,64 +1660,64 @@ END SUBROUTINE bicube_write_yx c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_write_arrays(bcs,out,iua,iqty) + subroutine bicube_write_arrays(bcs,out,iua,iqty) - TYPE(bicube_type), INTENT(INOUT) :: bcs - LOGICAL, INTENT(IN) :: out - INTEGER, INTENT(IN) :: iua,iqty + type(bicube_type), intent(inout) :: bcs + logical, intent(in) :: out + integer, intent(in) :: iua,iqty - CHARACTER(80) :: format1,format2 - INTEGER :: ix,iy,my + character(80) :: format1,format2 + integer :: ix,iy,my c----------------------------------------------------------------------- c formats. c----------------------------------------------------------------------- - 10 FORMAT('(/2x,"ix/iy",',i3.3,'(3x,i3.3,5x)/)') - 20 FORMAT('(i5,1p,',i3.3,'e11.3)') + 10 format('(/2x,"ix/iy",',i3.3,'(3x,i3.3,5x)/)') + 20 format('(i5,1p,',i3.3,'e11.3)') c----------------------------------------------------------------------- c abort. c----------------------------------------------------------------------- - IF(.NOT. out)RETURN - my=MIN(bcs%my,32) - WRITE(iua,'(a,i2/)')"iqty = ",iqty + if(.not. out)return + my=Min(bcs%my,32) + write(iua,'(a,i2/)')"iqty = ",iqty c----------------------------------------------------------------------- c write fs. c----------------------------------------------------------------------- - WRITE(format1,10)my+1 - WRITE(format2,20)my+1 - WRITE(iua,"(a)")"fs:" - WRITE(iua,format1)(iy,iy=0,my) - WRITE(iua,format2)(ix,(bcs%fs(ix,iy,iqty),iy=0,my), + write(format1,10)my+1 + write(format2,20)my+1 + write(iua,"(a)")"fs:" + write(iua,format1)(iy,iy=0,my) + write(iua,format2)(ix,(bcs%fs(ix,iy,iqty),iy=0,my), $ ix=0,bcs%mx) - WRITE(iua,format1)(iy,iy=0,my) + write(iua,format1)(iy,iy=0,my) c----------------------------------------------------------------------- c write fsx. c----------------------------------------------------------------------- - WRITE(iua,"(a)")"fsx:" - WRITE(iua,format1)(iy,iy=0,my) - WRITE(iua,format2)(ix,(bcs%fsx(ix,iy,iqty),iy=0,my), + write(iua,"(a)")"fsx:" + write(iua,format1)(iy,iy=0,my) + write(iua,format2)(ix,(bcs%fsx(ix,iy,iqty),iy=0,my), $ ix=0,bcs%mx) - WRITE(iua,format1)(iy,iy=0,my) + write(iua,format1)(iy,iy=0,my) c----------------------------------------------------------------------- c write fsy. c----------------------------------------------------------------------- - WRITE(iua,"(a)")"fsy:" - WRITE(iua,format1)(iy,iy=0,my) - WRITE(iua,format2)(ix,(bcs%fsy(ix,iy,iqty),iy=0,my), + write(iua,"(a)")"fsy:" + write(iua,format1)(iy,iy=0,my) + write(iua,format2)(ix,(bcs%fsy(ix,iy,iqty),iy=0,my), $ ix=0,bcs%mx) - WRITE(iua,format1)(iy,iy=0,my) + write(iua,format1)(iy,iy=0,my) c----------------------------------------------------------------------- c write fsxy. c----------------------------------------------------------------------- - WRITE(iua,"(a)")"fsxy:" - WRITE(iua,format1)(iy,iy=0,my) - WRITE(iua,format2)(ix,(bcs%fsxy(ix,iy,iqty),iy=0,my), + write(iua,"(a)")"fsxy:" + write(iua,format1)(iy,iy=0,my) + write(iua,format2)(ix,(bcs%fsxy(ix,iy,iqty),iy=0,my), $ ix=0,bcs%mx) - WRITE(iua,format1)(iy,iy=0,my) + write(iua,format1)(iy,iy=0,my) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_write_arrays + return + end subroutine bicube_write_arrays c----------------------------------------------------------------------- c subprogram 12. bicube_copy. c copies one bicube type to another. @@ -1725,15 +1725,15 @@ END SUBROUTINE bicube_write_arrays c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_copy(bcs1,bcs2) + subroutine bicube_copy(bcs1,bcs2) - TYPE(bicube_type), INTENT(IN) :: bcs1 - TYPE(bicube_type), INTENT(INOUT) :: bcs2 + type(bicube_type), intent(in) :: bcs1 + type(bicube_type), intent(inout) :: bcs2 c----------------------------------------------------------------------- c computations. c----------------------------------------------------------------------- - IF(ALLOCATED(bcs2%xs))CALL bicube_dealloc(bcs2) - CALL bicube_alloc(bcs2,bcs1%mx,bcs1%my,bcs1%nqty) + if(allocated(bcs2%xs))call bicube_dealloc(bcs2) + call bicube_alloc(bcs2,bcs1%mx,bcs1%my,bcs1%nqty) bcs2%xs=bcs1%xs bcs2%ys=bcs1%ys bcs2%fs=bcs1%fs @@ -1755,8 +1755,8 @@ SUBROUTINE bicube_copy(bcs1,bcs2) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_copy + return + end subroutine bicube_copy c----------------------------------------------------------------------- c subprogram 13. bicube_extrema. c finds extrema. @@ -1764,17 +1764,17 @@ END SUBROUTINE bicube_copy c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bicube_extrema(bcs) + subroutine bicube_extrema(bcs) - TYPE(bicube_type), INTENT(INOUT) :: bcs + type(bicube_type), intent(inout) :: bcs - CHARACTER(80) :: message - INTEGER :: iext,iqty,it - INTEGER, PARAMETER :: itmax=20 - INTEGER, DIMENSION(2,2) :: jext - REAL(r8), PARAMETER :: eps=1e-10 - REAL(r8) :: x,y,dx,dy,lx,ly,lf,f,df,adet - REAL(r8), DIMENSION(2,2) :: amat,ainv + character(80) :: message + integer :: iext,iqty,it + integer, PARAMETER :: itmax=20 + integer, dimension(2,2) :: jext + real(r8), PARAMETER :: eps=1e-10 + real(r8) :: x,y,dx,dy,lx,ly,lf,f,df,adet + real(r8), dimension(2,2) :: amat,ainv c----------------------------------------------------------------------- c compute lengths. c----------------------------------------------------------------------- @@ -1783,8 +1783,8 @@ SUBROUTINE bicube_extrema(bcs) c----------------------------------------------------------------------- c start loops over iqty. c----------------------------------------------------------------------- - DO iqty=1,bcs%nqty - jext(:,1)=MINLOC(bcs%fs(:,:,iqty))-1 + do iqty=1,bcs%nqty + jext(:,1)=MinLOC(bcs%fs(:,:,iqty))-1 jext(:,2)=MAXLOC(bcs%fs(:,:,iqty))-1 bcs%fext(1,iqty)=bcs%fs(jext(1,1),jext(2,1),iqty) bcs%fext(2,iqty)=bcs%fs(jext(1,2),jext(2,2),iqty) @@ -1792,7 +1792,7 @@ SUBROUTINE bicube_extrema(bcs) c----------------------------------------------------------------------- c start loops over extrema. c----------------------------------------------------------------------- - DO iext=1,2 + do iext=1,2 x=bcs%xs(jext(1,iext)) y=bcs%ys(jext(2,iext)) f=HUGE(f) @@ -1802,10 +1802,10 @@ SUBROUTINE bicube_extrema(bcs) c----------------------------------------------------------------------- c locate extema by newton iteration. c----------------------------------------------------------------------- - DO - CALL bicube_eval(bcs,x,y,2) + do + call bicube_eval(bcs,x,y,2) df=bcs%f(iqty)-f - IF(ABS(dx) < eps*lx .OR. ABS(dy) < eps*ly + if(ABS(dx) < eps*lx .OR. ABS(dy) < eps*ly $ .OR. ABS(df) < eps*lf .OR. it >= itmax)EXIT it=it+1 f=bcs%f(iqty) @@ -1823,27 +1823,27 @@ SUBROUTINE bicube_extrema(bcs) dy=-ainv(2,1)*bcs%fx(iqty)-ainv(2,2)*bcs%fy(iqty) x=x+dx y=y+dy - ENDDO + enddo c----------------------------------------------------------------------- c abort on failure. c----------------------------------------------------------------------- - IF(it >= itmax)THEN - WRITE(message,'(a,i3,a)') + if(it >= itmax)then + write(message,'(a,i3,a)') $ "bicube_extrema: convergence failure for iqty = ", $ iqty,"." - CALL program_stop(message) - ENDIF + call program_stop(message) + endif c----------------------------------------------------------------------- c finish loops over iext and iqty. c----------------------------------------------------------------------- bcs%xext(iext,iqty)=x bcs%yext(iext,iqty)=y bcs%fext(iext,iqty)=bcs%f(iqty) - ENDDO - ENDDO + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bicube_extrema - END MODULE bicube_mod + return + end subroutine bicube_extrema + end module bicube_mod diff --git a/src/Splines/fortran/cspline.f b/src/Splines/fortran/cspline.f index df1f1767b..1476f2bdc 100644 --- a/src/Splines/fortran/cspline.f +++ b/src/Splines/fortran/cspline.f @@ -35,24 +35,24 @@ c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - MODULE cspline_mod - USE spline_mod - IMPLICIT NONE - - TYPE :: cspline_type - INTEGER :: mx,nqty,ix - REAL(r8), DIMENSION(:), POINTER :: xs - REAL(r8), DIMENSION(2) :: x0 - REAL(r8), DIMENSION(:,:), POINTER :: xpower - COMPLEX(r8), DIMENSION(:), POINTER :: f,f1,f2,f3 - COMPLEX(r8), DIMENSION(:,:), POINTER :: fs,fs1,fsi - CHARACTER(6), DIMENSION(:), POINTER :: title - CHARACTER(6) :: name - LOGICAL :: periodic - LOGICAL :: allocated=.FALSE. - END TYPE cspline_type - - CONTAINS + module cspline_mod + use spline_mod + implicit none + + type :: cspline_type + integer :: mx,nqty,ix + real(r8), dimension(:), POinTER :: xs + real(r8), dimension(2) :: x0 + real(r8), dimension(:,:), POinTER :: xpower + complex(r8), dimension(:), POinTER :: f,f1,f2,f3 + complex(r8), dimension(:,:), POinTER :: fs,fs1,fsi + character(6), dimension(:), POinTER :: title + character(6) :: name + logical :: periodic + logical :: allocated=.false. + end type cspline_type + + contains c----------------------------------------------------------------------- c subprogram 1. cspline_alloc. c allocates space for cspline_type. @@ -60,17 +60,17 @@ MODULE cspline_mod c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_alloc(spl,mx,nqty) - - INTEGER, INTENT(IN) :: mx,nqty - TYPE(cspline_type), INTENT(INOUT) :: spl + subroutine cspline_alloc(spl,mx,nqty) + + integer, intent(in) :: mx,nqty + type(cspline_type), intent(inout) :: spl c----------------------------------------------------------------------- c safety check. c----------------------------------------------------------------------- - IF(spl%allocated)THEN - CALL program_stop("cspline_alloc: already allocated") - ENDIF + if(spl%allocated)then + call program_stop("cspline_alloc: already allocated") + endif c----------------------------------------------------------------------- c set scalars. @@ -78,28 +78,28 @@ SUBROUTINE cspline_alloc(spl,mx,nqty) spl%mx=mx spl%nqty=nqty spl%ix=0 - spl%periodic=.FALSE. + spl%periodic=.false. c----------------------------------------------------------------------- c allocate space. c----------------------------------------------------------------------- - ALLOCATE(spl%xs(0:mx)) - ALLOCATE(spl%f(nqty)) - ALLOCATE(spl%f1(nqty)) - ALLOCATE(spl%f2(nqty)) - ALLOCATE(spl%f3(nqty)) - ALLOCATE(spl%title(0:nqty)) - ALLOCATE(spl%fs(0:mx,nqty)) - ALLOCATE(spl%fs1(0:mx,nqty)) - ALLOCATE(spl%xpower(2,nqty)) + allocate(spl%xs(0:mx)) + allocate(spl%f(nqty)) + allocate(spl%f1(nqty)) + allocate(spl%f2(nqty)) + allocate(spl%f3(nqty)) + allocate(spl%title(0:nqty)) + allocate(spl%fs(0:mx,nqty)) + allocate(spl%fs1(0:mx,nqty)) + allocate(spl%xpower(2,nqty)) spl%xpower=0 spl%x0=0 - NULLIFY(spl%fsi) - spl%allocated=.TRUE. + NULLifY(spl%fsi) + spl%allocated=.true. c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_alloc + return + end subroutine cspline_alloc c----------------------------------------------------------------------- c subprogram 2. cspline_dealloc. c deallocates space for cspline_type. @@ -107,37 +107,37 @@ END SUBROUTINE cspline_alloc c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_dealloc(spl) - - TYPE(cspline_type), INTENT(INOUT) :: spl + subroutine cspline_dealloc(spl) + + type(cspline_type), intent(inout) :: spl c----------------------------------------------------------------------- c safety check. c----------------------------------------------------------------------- - IF(.NOT.spl%allocated)THEN - CALL program_stop("cspline_dealloc: not allocated") - ENDIF + if(.not.spl%allocated)then + call program_stop("cspline_dealloc: not allocated") + endif c----------------------------------------------------------------------- c deallocate space. c----------------------------------------------------------------------- - DEALLOCATE(spl%xs) - DEALLOCATE(spl%f) - DEALLOCATE(spl%f1) - DEALLOCATE(spl%f2) - DEALLOCATE(spl%f3) - DEALLOCATE(spl%title) - DEALLOCATE(spl%fs) - DEALLOCATE(spl%fs1) - DEALLOCATE(spl%xpower) - IF(ASSOCIATED(spl%fsi))DEALLOCATE(spl%fsi) - spl%allocated=.FALSE. + deallocate(spl%xs) + deallocate(spl%f) + deallocate(spl%f1) + deallocate(spl%f2) + deallocate(spl%f3) + deallocate(spl%title) + deallocate(spl%fs) + deallocate(spl%fs1) + deallocate(spl%xpower) + if(ASSOCIATED(spl%fsi))deallocate(spl%fsi) + spl%allocated=.false. c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_dealloc + return + end subroutine cspline_dealloc c----------------------------------------------------------------------- c subprogram 3. cspline_fit. c router between Glasser and classic spline fits. @@ -145,25 +145,26 @@ END SUBROUTINE cspline_dealloc c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_fit(spl,endmode) + subroutine cspline_fit(spl,endmode) - TYPE(cspline_type), INTENT(INOUT) :: spl - CHARACTER(*), INTENT(IN) :: endmode + type(cspline_type), intent(inout) :: spl + integer, intent(in) :: endmode c----------------------------------------------------------------------- c switch between csplines. c----------------------------------------------------------------------- - IF (use_classic_splines .AND. - $ (endmode.EQ."extrap".OR.endmode.EQ."natural"))THEN - CALL cspline_fit_classic(spl,endmode) - ELSE - CALL cspline_fit_ahg(spl,endmode) - ENDIF +c - use_classic_splines is always False +c if (use_classic_splines .and. +c $ (endmode == 3 .OR. endmode == 1))then ! 3 = Extrapolate, 1= natural +c call cspline_fit_classic(spl,endmode) +c else + call cspline_fit_ahg(spl,endmode) +c endif c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_fit + return + end subroutine cspline_fit c----------------------------------------------------------------------- c subprogram 4. cspline_fit_classic. c classical spline solution as in spline.f, but now with complex r @@ -173,62 +174,62 @@ END SUBROUTINE cspline_fit c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_fit_classic(spl,endmode) - TYPE(cspline_type), INTENT(INOUT) :: spl - CHARACTER(*), INTENT(IN) :: endmode - REAL(r8), DIMENSION(:),ALLOCATABLE :: d,l,u,h - COMPLEX(r8), DIMENSION(:,:),ALLOCATABLE :: r - REAL(r8), DIMENSION(0:spl%mx) :: xfac + subroutine cspline_fit_classic(spl,endmode) + type(cspline_type), intent(inout) :: spl + integer, intent(in) :: endmode + real(r8), dimension(:),allocatable :: d,l,u,h + complex(r8), dimension(:,:),allocatable :: r + real(r8), dimension(0:spl%mx) :: xfac - INTEGER :: iside,iqty,i - COMPLEX(r8),DIMENSION(spl%nqty) :: bs,cs,ds + integer :: iside,iqty,i + complex(r8),dimension(spl%nqty) :: bs,cs,ds c----------------------------------------------------------------------- c extract powers. c----------------------------------------------------------------------- - DO iside=1,2 - DO iqty=1,spl%nqty - IF(spl%xpower(iside,iqty) /= 0)THEN + do iside=1,2 + do iqty=1,spl%nqty + if(spl%xpower(iside,iqty) /= 0)then xfac=1/ABS(spl%xs-spl%x0(iside))**spl%xpower(iside,iqty) spl%fs(:,iqty)=spl%fs(:,iqty)*xfac - ENDIF - ENDDO - ENDDO - ALLOCATE (d(0:spl%mx),l(spl%mx),u(spl%mx),r(0:spl%mx,spl%nqty)) - ALLOCATE (h(0:spl%mx-1)) + endif + enddo + enddo + allocate (d(0:spl%mx),l(spl%mx),u(spl%mx),r(0:spl%mx,spl%nqty)) + allocate (h(0:spl%mx-1)) c----------------------------------------------------------------------- c compute tridiagnol matrix for natural B.C. c----------------------------------------------------------------------- - DO i=0,spl%mx-1 + do i=0,spl%mx-1 h(i)=spl%xs(i+1)-spl%xs(i) - ENDDO + enddo d(0)=1 - DO i=1,spl%mx-1 + do i=1,spl%mx-1 d(i)=2*(h(i-1)+h(i)) - ENDDO + enddo d(spl%mx)=1 - DO i=1,spl%mx-1 + do i=1,spl%mx-1 l(i)=h(i-1) - ENDDO + enddo l(spl%mx)=0 u(1)=0 - DO i=2,spl%mx + do i=2,spl%mx u(i)=h(i-1) - ENDDO + enddo r(0,:)=0 - DO i=1,spl%mx-1 + do i=1,spl%mx-1 r(i,:)=( (spl%fs(i+1,:)-spl%fs(i,:))/h(i) $ -(spl%fs(i,:)-spl%fs(i-1,:))/h(i-1) )*six - ENDDO + enddo r(spl%mx,:)=0 - IF (endmode=="extrap") THEN - CALL cspline_get_yp(spl%xs(0:3),spl%fs(0:3,:), + if (endmode==3) then ! 3 = Extrapolated + call cspline_get_yp(spl%xs(0:3),spl%fs(0:3,:), $ spl%xs(0),r(0,:),spl%nqty) - CALL cspline_get_yp(spl%xs(spl%mx-3:spl%mx), + call cspline_get_yp(spl%xs(spl%mx-3:spl%mx), $ spl%fs(spl%mx-3:spl%mx,:),spl%xs(spl%mx), $ r(spl%mx,:),spl%nqty) d(0)=2*h(0) @@ -239,19 +240,19 @@ SUBROUTINE cspline_fit_classic(spl,endmode) r(spl%mx,:)=( r(spl%mx,:) $ -(spl%fs(spl%mx,:)-spl%fs(spl%mx-1,:))/h(spl%mx-1) )*six - ENDIF + endif c----------------------------------------------------------------------- c solve and contrruct spline. c----------------------------------------------------------------------- - CALL cspline_thomas(l,d,u,r,spl%mx+1,spl%nqty) + call cspline_thomas(l,d,u,r,spl%mx+1,spl%nqty) - DO i=0, spl%mx-1 + do i=0, spl%mx-1 bs=(spl%fs(i+1,:)-spl%fs(i,:))/h(i) $ - half*h(i)*r(i,:) $ - h(i)*(r(i+1,:)-r(i,:))/six spl%fs1(i,:)=bs - ENDDO + enddo ds=(r(spl%mx,:)-r(spl%mx-1,:))/(h(spl%mx-1)*six) cs=r(spl%mx-1,:)*half i=spl%mx-1 @@ -260,12 +261,12 @@ SUBROUTINE cspline_fit_classic(spl,endmode) $ - h(i)*(r(i+1,:)-r(i,:))/six i=spl%mx spl%fs1(i,:)=bs+h(i-1)*(cs*2+h(i-1)*ds*3) - DEALLOCATE (d,l,u,r,h) + deallocate (d,l,u,r,h) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_fit_classic + return + end subroutine cspline_fit_classic c----------------------------------------------------------------------- c subprogram 5. cspline_fit_ahg. c fits complex functions to cubic splines. @@ -273,47 +274,47 @@ END SUBROUTINE cspline_fit_classic c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_fit_ahg(spl,endmode) - - TYPE(cspline_type), INTENT(INOUT) :: spl - CHARACTER(*), INTENT(IN) :: endmode - - INTEGER :: iqty,iside - REAL(r8), DIMENSION(-1:1,0:spl%mx) :: a - REAL(r8), DIMENSION(spl%mx) :: b - REAL(r8), DIMENSION(4) :: cl,cr - REAL(r8), DIMENSION(0:spl%mx) :: xfac + subroutine cspline_fit_ahg(spl,endmode) + + type(cspline_type), intent(inout) :: spl + integer, intent(in) :: endmode + + integer :: iqty,iside + real(r8), dimension(-1:1,0:spl%mx) :: a + real(r8), dimension(spl%mx) :: b + real(r8), dimension(4) :: cl,cr + real(r8), dimension(0:spl%mx) :: xfac c----------------------------------------------------------------------- c extract powers. c----------------------------------------------------------------------- - DO iside=1,2 - DO iqty=1,spl%nqty - IF(spl%xpower(iside,iqty) /= 0)THEN + do iside=1,2 + do iqty=1,spl%nqty + if(spl%xpower(iside,iqty) /= 0)then xfac=1/ABS(spl%xs-spl%x0(iside))**spl%xpower(iside,iqty) spl%fs(:,iqty)=spl%fs(:,iqty)*xfac - ENDIF - ENDDO - ENDDO + endif + enddo + enddo c----------------------------------------------------------------------- c set up grid matrix. c----------------------------------------------------------------------- - CALL cspline_fac(spl,a,b,cl,cr,endmode) + call cspline_fac(spl,a,b,cl,cr,endmode) c----------------------------------------------------------------------- c compute first derivatives, interior. c----------------------------------------------------------------------- - DO iqty=1,spl%nqty + do iqty=1,spl%nqty spl%fs1(1:spl%mx-1,iqty)= $ 3*((spl%fs(2:spl%mx,iqty)-spl%fs(1:spl%mx-1,iqty)) $ *b(2:spl%mx) $ +(spl%fs(1:spl%mx-1,iqty)-spl%fs(0:spl%mx-2,iqty)) $ *b(1:spl%mx-1)) - ENDDO + enddo c----------------------------------------------------------------------- c extrapolation boundary conditions. c----------------------------------------------------------------------- - SELECT CASE(endmode) - CASE("extrap") - DO iqty=1,spl%nqty + select case(endmode) + case(3) ! 3 = Extrapolate + do iqty=1,spl%nqty spl%fs1(0,iqty)=SUM(cl(1:4)*spl%fs(0:3,iqty)) spl%fs1(spl%mx,iqty)=SUM(cr(1:4) $ *spl%fs(spl%mx:spl%mx-3:-1,iqty)) @@ -322,18 +323,18 @@ SUBROUTINE cspline_fit_ahg(spl,endmode) spl%fs1(spl%mx-1,iqty)= $ spl%fs1(spl%mx-1,iqty)-spl%fs1(spl%mx,iqty) $ /(spl%xs(spl%mx)-spl%xs(spl%mx-1)) - ENDDO - CALL cspline_trilus(a(:,1:spl%mx-1),spl%fs1(1:spl%mx-1,:)) + enddo + call cspline_trilus(a(:,1:spl%mx-1),spl%fs1(1:spl%mx-1,:)) c----------------------------------------------------------------------- c not-a-knot boundary conditions. c----------------------------------------------------------------------- - CASE("not-a-knot") + case(4) ! 4 = not-a-knot spl%fs1(1,:)=spl%fs1(1,:)-(2*spl%fs(1,:) $ -spl%fs(0,:)-spl%fs(2,:))*2*b(1) spl%fs1(spl%mx-1,:)=spl%fs1(spl%mx-1,:) $ +(2*spl%fs(spl%mx-1,:)-spl%fs(spl%mx,:) $ -spl%fs(spl%mx-2,:))*2*b(spl%mx) - CALL cspline_trilus(a(:,1:spl%mx-1),spl%fs1(1:spl%mx-1,:)) + call cspline_trilus(a(:,1:spl%mx-1),spl%fs1(1:spl%mx-1,:)) spl%fs1(0,:)=(2*(2*spl%fs(1,:)-spl%fs(0,:)-spl%fs(2,:)) $ +(spl%fs1(1,:)+spl%fs1(2,:))*(spl%xs(2)-spl%xs(1)) $ -spl%fs1(1,:)*(spl%xs(1)-spl%xs(0)))/(spl%xs(1)-spl%xs(0)) @@ -348,23 +349,23 @@ SUBROUTINE cspline_fit_ahg(spl,endmode) c----------------------------------------------------------------------- c periodic boundary conditions. c----------------------------------------------------------------------- - CASE("periodic") - spl%periodic=.TRUE. + case(2) ! 2 = Periodic + spl%periodic=.true. spl%fs1(0,:)=3*((spl%fs(1,:)-spl%fs(0,:))*b(1) $ +(spl%fs(0,:)-spl%fs(spl%mx-1,:))*b(spl%mx)) - CALL cspline_morrison(a(:,0:spl%mx-1),spl%fs1(0:spl%mx-1,:)) + call cspline_morrison(a(:,0:spl%mx-1),spl%fs1(0:spl%mx-1,:)) spl%fs1(spl%mx,:)=spl%fs1(0,:) c----------------------------------------------------------------------- c unrecognized boundary condition. c----------------------------------------------------------------------- - CASE DEFAULT - CALL program_stop("Cannot recognize endmode = "//TRIM(endmode)) - END SELECT + case default + call program_stop("Cannot recognize endmode") + end select c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_fit_ahg + return + end subroutine cspline_fit_ahg c----------------------------------------------------------------------- c subprogram 6. cspline_fac. c sets up matrix for cubic spline fitting. @@ -372,29 +373,29 @@ END SUBROUTINE cspline_fit_ahg c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_fac(spl,a,b,cl,cr,endmode) - - TYPE(cspline_type), INTENT(IN) :: spl - REAL(r8), DIMENSION(-1:1,0:spl%mx), INTENT(OUT) :: a - REAL(r8), DIMENSION(spl%mx), INTENT(OUT) :: b - REAL(r8), DIMENSION(4), INTENT(OUT) :: cl,cr - CHARACTER(*), INTENT(IN) :: endmode - - INTEGER :: j + subroutine cspline_fac(spl,a,b,cl,cr,endmode) + + type(cspline_type), intent(in) :: spl + real(r8), dimension(-1:1,0:spl%mx), intent(out) :: a + real(r8), dimension(spl%mx), intent(out) :: b + real(r8), dimension(4), intent(out) :: cl,cr + integer, intent(in) :: endmode + + integer :: j c----------------------------------------------------------------------- c compute interior matrix. c----------------------------------------------------------------------- b=1/(spl%xs(1:spl%mx)-spl%xs(0:spl%mx-1)) - DO j=1,spl%mx-1 + do j=1,spl%mx-1 a(-1,j)=b(j) a(0,j)=2*(b(j)+b(j+1)) a(1,j)=b(j+1) - ENDDO + enddo c----------------------------------------------------------------------- c extrapolation boundary conditions. c----------------------------------------------------------------------- - SELECT CASE(endmode) - CASE("extrap") + select case(endmode) + case(3) ! 3 = Extrapolate b=b*b cl(1)=(spl%xs(0)*(3*spl%xs(0) $ -2*(spl%xs(1)+spl%xs(2)+spl%xs(3))) @@ -434,11 +435,11 @@ SUBROUTINE cspline_fac(spl,a,b,cl,cr,endmode) $ /((spl%xs(spl%mx-3)-spl%xs(spl%mx)) $ *(spl%xs(spl%mx-3)-spl%xs(spl%mx-1)) $ *(spl%xs(spl%mx-3)-spl%xs(spl%mx-2))) - CALL cspline_triluf(a(:,1:spl%mx-1)) + call cspline_triluf(a(:,1:spl%mx-1)) c----------------------------------------------------------------------- c not-a-knot boundary conditions. c----------------------------------------------------------------------- - CASE("not-a-knot") + case(4) ! 4 = not-a-knot b=b*b a(0,1)=a(0,1)+(spl%xs(2)+spl%xs(0)-2*spl%xs(1))*b(1) a(1,1)=a(1,1)+(spl%xs(2)-spl%xs(1))*b(1) @@ -447,27 +448,27 @@ SUBROUTINE cspline_fac(spl,a,b,cl,cr,endmode) $ -spl%xs(spl%mx))*b(spl%mx) a(-1,spl%mx-1)=a(-1,spl%mx-1) $ +(spl%xs(spl%mx-1)-spl%xs(spl%mx-2))*b(spl%mx) - CALL cspline_triluf(a(:,1:spl%mx-1)) + call cspline_triluf(a(:,1:spl%mx-1)) c----------------------------------------------------------------------- c periodic boundary conditions. c----------------------------------------------------------------------- - CASE("periodic") + case(2) ! 2 = Periodic a(0,0:spl%mx:spl%mx)=2*(b(spl%mx)+b(1)) a(1,0)=b(1) a(-1,0)=b(spl%mx) b=b*b - CALL cspline_sherman(a(:,0:spl%mx-1)) + call cspline_sherman(a(:,0:spl%mx-1)) c----------------------------------------------------------------------- c unrecognized boundary condition. c----------------------------------------------------------------------- - CASE DEFAULT - CALL program_stop("Cannot recognize endmode = "//TRIM(endmode)) - END SELECT + case default + call program_stop("Cannot recognize endmode") + end select c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_fac + return + end subroutine cspline_fac c----------------------------------------------------------------------- c subprogram 7. cspline_eval. c evaluates complex cubic spline function. @@ -475,47 +476,47 @@ END SUBROUTINE cspline_fac c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_eval(spl,x,mode) - - TYPE(cspline_type), INTENT(INOUT) :: spl - REAL(r8), INTENT(IN) :: x - INTEGER, INTENT(IN) :: mode - - INTEGER :: iqty,iside - REAL(r8) :: xx,d,z,z1,xfac,dx - COMPLEX(r8) :: g,g1,g2,g3 + subroutine cspline_eval(spl,x,mode) + + type(cspline_type), intent(inout) :: spl + real(r8), intent(in) :: x + integer, intent(in) :: mode + + integer :: iqty,iside + real(r8) :: xx,d,z,z1,xfac,dx + complex(r8) :: g,g1,g2,g3 c----------------------------------------------------------------------- c preliminary computations. c----------------------------------------------------------------------- xx=x spl%ix=MAX(spl%ix,0) - spl%ix=MIN(spl%ix,spl%mx-1) + spl%ix=Min(spl%ix,spl%mx-1) c----------------------------------------------------------------------- c normalize interval for periodic splines. c----------------------------------------------------------------------- - IF(spl%periodic)THEN - DO - IF(xx < spl%xs(spl%mx))EXIT + if(spl%periodic)then + do + if(xx < spl%xs(spl%mx))EXIT xx=xx-spl%xs(spl%mx) - ENDDO - DO - IF(xx >= spl%xs(0))EXIT + enddo + do + if(xx >= spl%xs(0))EXIT xx=xx+spl%xs(spl%mx) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c find cubic spline interval. c----------------------------------------------------------------------- - DO - IF(spl%ix <= 0)EXIT - IF(xx >= spl%xs(spl%ix))EXIT + do + if(spl%ix <= 0)EXIT + if(xx >= spl%xs(spl%ix))EXIT spl%ix=spl%ix-1 - ENDDO - DO - IF(spl%ix >= spl%mx-1)EXIT - IF(xx < spl%xs(spl%ix+1))EXIT + enddo + do + if(spl%ix >= spl%mx-1)EXIT + if(xx < spl%xs(spl%ix+1))EXIT spl%ix=spl%ix+1 - ENDDO + enddo c----------------------------------------------------------------------- c evaluate offset and related quantities. c----------------------------------------------------------------------- @@ -532,59 +533,59 @@ SUBROUTINE cspline_eval(spl,x,mode) c----------------------------------------------------------------------- c evaluate first derivatives. c----------------------------------------------------------------------- - IF(mode > 0)THEN + if(mode > 0)then spl%f1=6*(spl%fs(spl%ix+1,:) $ -spl%fs(spl%ix,:))*z*z1/d $ +spl%fs1(spl%ix,:)*z1*(3*z1-2) $ +spl%fs1(spl%ix+1,:)*z*(3*z-2) - ENDIF + endif c----------------------------------------------------------------------- c evaluate second derivatives. c----------------------------------------------------------------------- - IF(mode > 1)THEN + if(mode > 1)then spl%f2=(6*(spl%fs(spl%ix+1,:) $ -spl%fs(spl%ix,:))*(z1-z)/d $ -spl%fs1(spl%ix,:)*(6*z1-2) $ +spl%fs1(spl%ix+1,:)*(6*z-2))/d - ENDIF + endif c----------------------------------------------------------------------- c evaluate third derivatives. c----------------------------------------------------------------------- - IF(mode > 2)THEN + if(mode > 2)then spl%f3=(12*(spl%fs(spl%ix,:) $ -spl%fs(spl%ix+1,:))/d $ +6*(spl%fs1(spl%ix,:) $ +spl%fs1(spl%ix+1,:)))/(d*d) - ENDIF + endif c----------------------------------------------------------------------- c restore powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dx=x-spl%x0(iside) - DO iqty=1,spl%nqty - IF(spl%xpower(iside,iqty) == 0)CYCLE + do iqty=1,spl%nqty + if(spl%xpower(iside,iqty) == 0)cycle xfac=ABS(dx)**spl%xpower(iside,iqty) g=spl%f(iqty)*xfac - IF(mode > 0)g1=(spl%f1(iqty)+spl%f(iqty) + if(mode > 0)g1=(spl%f1(iqty)+spl%f(iqty) $ *spl%xpower(iside,iqty)/dx)*xfac - IF(mode > 1)g2=(spl%f2(iqty)+spl%xpower(iside,iqty)/dx + if(mode > 1)g2=(spl%f2(iqty)+spl%xpower(iside,iqty)/dx $ *(2*spl%f1(iqty)+(spl%xpower(iside,iqty)-1) $ *spl%f(iqty)/dx))*xfac - IF(mode > 2)g3=(spl%f3(iqty)+spl%xpower(iside,iqty)/dx + if(mode > 2)g3=(spl%f3(iqty)+spl%xpower(iside,iqty)/dx $ *(3*spl%f2(iqty)+(spl%xpower(iside,iqty)-1)/dx $ *(3*spl%f1(iqty)+(spl%xpower(iside,iqty)-2)/dx $ *spl%f(iqty))))*xfac spl%f(iqty)=g - IF(mode > 0)spl%f1(iqty)=g1 - IF(mode > 1)spl%f2(iqty)=g2 - IF(mode > 2)spl%f3(iqty)=g3 - ENDDO - ENDDO + if(mode > 0)spl%f1(iqty)=g1 + if(mode > 1)spl%f2(iqty)=g2 + if(mode > 2)spl%f3(iqty)=g3 + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_eval + return + end subroutine cspline_eval c----------------------------------------------------------------------- c subprogram 8. cspline_eval_external. c evaluates complex cubic splines with external arrays (parallel). @@ -592,20 +593,20 @@ END SUBROUTINE cspline_eval c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_eval_external(spl,x,s_ix,s_f,s_f1,s_f2,s_f3) + subroutine cspline_eval_external(spl,x,s_f,s_f1,s_f2,s_f3) - TYPE(cspline_type), INTENT(IN) :: spl - REAL(r8), INTENT(IN) :: x + type(cspline_type), intent(in) :: spl + real(r8), intent(in) :: x - INTEGER :: iqty,iside - REAL(r8) :: xx,d,z,z1,dx - COMPLEX(r8) :: g,g1,g2,g3 + integer :: iqty,iside + integer :: ix, i_low, i_high, i_mid + real(r8) :: xx,d,z,z1,dx + complex(r8) :: g,g1,g2,g3 - INTEGER, INTENT(INOUT) :: s_ix - COMPLEX(r8), DIMENSION(:), INTENT(INOUT) :: s_f - COMPLEX(r8), DIMENSION(:),OPTIONAL,INTENT(OUT) :: s_f1,s_f2,s_f3 + complex(r8), dimension(:), intent(inout) :: s_f + complex(r8), dimension(:),optional,intent(out) :: s_f1,s_f2,s_f3 - REAL(r8) :: xpow,xfac + real(r8) :: xpow,xfac c----------------------------------------------------------------------- c zero out external array. c----------------------------------------------------------------------- @@ -614,104 +615,112 @@ SUBROUTINE cspline_eval_external(spl,x,s_ix,s_f,s_f1,s_f2,s_f3) c preliminary computations. c----------------------------------------------------------------------- xx=x - s_ix=MAX(s_ix,0) - s_ix=MIN(s_ix,spl%mx-1) c----------------------------------------------------------------------- c normalize interval for periodic splines. c----------------------------------------------------------------------- - IF(spl%periodic)THEN - DO - IF(xx < spl%xs(spl%mx))EXIT + if(spl%periodic)then + do + if(xx < spl%xs(spl%mx))EXIT xx=xx-spl%xs(spl%mx) - ENDDO - DO - IF(xx >= spl%xs(0))EXIT + enddo + do + if(xx >= spl%xs(0))EXIT xx=xx+spl%xs(spl%mx) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- -c find cubic spline interval. +c find cubic spline interval using Binary Search c----------------------------------------------------------------------- - DO - IF(s_ix <= 0)EXIT - IF(xx >= spl%xs(s_ix))EXIT - s_ix=s_ix-1 - ENDDO - DO - IF(s_ix >= spl%mx-1)EXIT - IF(xx < spl%xs(s_ix+1))EXIT - s_ix=s_ix+1 - ENDDO + i_low = 0 + i_high = spl%mx - 1 + + do while (i_low <= i_high) + i_mid = i_low + (i_high - i_low) / 2 + if (xx < spl%xs(i_mid)) then + i_high = i_mid - 1 + else if (xx >= spl%xs(i_mid + 1)) then + i_low = i_mid + 1 + else + ! We found the interval: xs(i_mid) <= xx < xs(i_mid+1) + ix = i_mid + exit + endif + enddo + + ! If the search fails, treat it as a boundary value. + if (i_low > i_high) then + ix = min(max(i_low - 1, 0), spl%mx - 1) + endif c----------------------------------------------------------------------- c evaluate offset and related quantities. c----------------------------------------------------------------------- - d=spl%xs(s_ix+1)-spl%xs(s_ix) - z=(xx-spl%xs(s_ix))/d + d=spl%xs(ix+1)-spl%xs(ix) + z=(xx-spl%xs(ix))/d z1=1-z c----------------------------------------------------------------------- c evaluate functions. c----------------------------------------------------------------------- - s_f=spl%fs(s_ix,:)*z1*z1*(3-2*z1) - $ +spl%fs(s_ix+1,:)*z*z*(3-2*z) - $ +d*z*z1*(spl%fs1(s_ix,:)*z1 - $ -spl%fs1(s_ix+1,:)*z) + s_f=spl%fs(ix,:)*z1*z1*(3-2*z1) + $ +spl%fs(ix+1,:)*z*z*(3-2*z) + $ +d*z*z1*(spl%fs1(ix,:)*z1 + $ -spl%fs1(ix+1,:)*z) c----------------------------------------------------------------------- c evaluate first derivatives. c----------------------------------------------------------------------- - IF(PRESENT(s_f1))THEN - s_f1=6*(spl%fs(s_ix+1,:) - $ -spl%fs(s_ix,:))*z*z1/d - $ +spl%fs1(s_ix,:)*z1*(3*z1-2) - $ +spl%fs1(s_ix+1,:)*z*(3*z-2) - ENDIF + if(present(s_f1))then + s_f1=6*(spl%fs(ix+1,:) + $ -spl%fs(ix,:))*z*z1/d + $ +spl%fs1(ix,:)*z1*(3*z1-2) + $ +spl%fs1(ix+1,:)*z*(3*z-2) + endif c----------------------------------------------------------------------- c evaluate second derivatives. c----------------------------------------------------------------------- - IF(PRESENT(s_f2))THEN - s_f2=(6*(spl%fs(s_ix+1,:) - $ -spl%fs(s_ix,:))*(z1-z)/d - $ -spl%fs1(s_ix,:)*(6*z1-2) - $ +spl%fs1(s_ix+1,:)*(6*z-2))/d - ENDIF + if(present(s_f2))then + s_f2=(6*(spl%fs(ix+1,:) + $ -spl%fs(ix,:))*(z1-z)/d + $ -spl%fs1(ix,:)*(6*z1-2) + $ +spl%fs1(ix+1,:)*(6*z-2))/d + endif c----------------------------------------------------------------------- c evaluate third derivatives. c----------------------------------------------------------------------- - IF(PRESENT(s_f3))THEN - s_f3=(12*(spl%fs(s_ix,:) - $ -spl%fs(s_ix+1,:))/d - $ +6*(spl%fs1(s_ix,:) - $ +spl%fs1(s_ix+1,:)))/(d*d) - ENDIF + if(present(s_f3))then + s_f3=(12*(spl%fs(ix,:) + $ -spl%fs(ix+1,:))/d + $ +6*(spl%fs1(ix,:) + $ +spl%fs1(ix+1,:)))/(d*d) + endif c----------------------------------------------------------------------- c restore powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dx=ABS(x-spl%x0(iside)) - DO iqty=1,spl%nqty + do iqty=1,spl%nqty xpow = spl%xpower(iside,iqty) - IF(xpow == 0)CYCLE + if(xpow == 0)cycle xfac=dx**xpow g=s_f(iqty)*xfac - IF(PRESENT(s_f1))g1=(s_f1(iqty)+s_f(iqty) + if(present(s_f1))g1=(s_f1(iqty)+s_f(iqty) $ *spl%xpower(iside,iqty)/dx)*xfac - IF(PRESENT(s_f2))g2=(s_f2(iqty)+spl%xpower(iside,iqty)/dx + if(present(s_f2))g2=(s_f2(iqty)+spl%xpower(iside,iqty)/dx $ *(2*s_f1(iqty)+(spl%xpower(iside,iqty)-1) $ *s_f(iqty)/dx))*xfac - IF(PRESENT(s_f3))g3=(s_f3(iqty)+spl%xpower(iside,iqty)/dx + if(present(s_f3))g3=(s_f3(iqty)+spl%xpower(iside,iqty)/dx $ *(3*s_f2(iqty)+(spl%xpower(iside,iqty)-1)/dx $ *(3*s_f1(iqty)+(spl%xpower(iside,iqty)-2)/dx $ *s_f(iqty))))*xfac s_f(iqty)=g - IF(PRESENT(s_f1))s_f1(iqty)=g1 - IF(PRESENT(s_f2))s_f2(iqty)=g2 - IF(PRESENT(s_f3))s_f3(iqty)=g3 - ENDDO - ENDDO + if(present(s_f1))s_f1(iqty)=g1 + if(present(s_f2))s_f2(iqty)=g2 + if(present(s_f3))s_f3(iqty)=g3 + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_eval_external + return + end subroutine cspline_eval_external c----------------------------------------------------------------------- c subprogram 9. cspline_all_eval. c evaluates cubic spline function. @@ -719,18 +728,18 @@ END SUBROUTINE cspline_eval_external c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_all_eval(spl,z,f,f1,f2,f3,mode) + subroutine cspline_all_eval(spl,z,f,f1,f2,f3,mode) - TYPE(cspline_type), INTENT(INOUT) :: spl - REAL(r8), INTENT(IN) :: z - COMPLEX(r8), DIMENSION(spl%mx,spl%nqty), INTENT(OUT) :: + type(cspline_type), intent(inout) :: spl + real(r8), intent(in) :: z + complex(r8), dimension(spl%mx,spl%nqty), intent(out) :: $ f,f1,f2,f3 - INTEGER, INTENT(IN) :: mode + integer, intent(in) :: mode - INTEGER :: iqty,nqty,n,iside - REAL(r8) :: z1 - REAL(r8), DIMENSION(spl%mx) :: d,xfac,dx - COMPLEX(r8), DIMENSION(spl%mx) :: g,g1,g2,g3 + integer :: iqty,nqty,n,iside + real(r8) :: z1 + real(r8), dimension(spl%mx) :: d,xfac,dx + complex(r8), dimension(spl%mx) :: g,g1,g2,g3 c----------------------------------------------------------------------- c evaluate offset and related quantities. c----------------------------------------------------------------------- @@ -741,70 +750,70 @@ SUBROUTINE cspline_all_eval(spl,z,f,f1,f2,f3,mode) c----------------------------------------------------------------------- c evaluate functions. c----------------------------------------------------------------------- - DO iqty=1,nqty + do iqty=1,nqty f(:,iqty)=spl%fs(0:n-1,iqty)*z1*z1*(3-2*z1) $ +spl%fs(1:n,iqty)*z*z*(3-2*z) $ +d*z*z1*(spl%fs1(0:n-1,iqty)*z1-spl%fs1(1:n,iqty)*z) - ENDDO + enddo c----------------------------------------------------------------------- c evaluate first derivatives. c----------------------------------------------------------------------- - IF(mode > 0)THEN - DO iqty=1,nqty + if(mode > 0)then + do iqty=1,nqty f1(:,iqty)=6*(spl%fs(1:n,iqty)-spl%fs(0:n-1,iqty))*z*z1/d $ +spl%fs1(0:n-1,iqty)*z1*(3*z1-2) $ +spl%fs1(1:n,iqty)*z*(3*z-2) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c evaluate second derivatives. c----------------------------------------------------------------------- - IF(mode > 1)THEN - DO iqty=1,nqty + if(mode > 1)then + do iqty=1,nqty f2(:,iqty)=(6*(spl%fs(1:n,iqty)-spl%fs(0:n-1,iqty))*(z1-z)/d $ -spl%fs1(0:n-1,iqty)*(6*z1-2) $ +spl%fs1(1:n,iqty)*(6*z-2))/d - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c evaluate third derivatives. c----------------------------------------------------------------------- - IF(mode > 2)THEN - DO iqty=1,nqty + if(mode > 2)then + do iqty=1,nqty f3(:,iqty)=(12*(spl%fs(0:n-1,iqty)-spl%fs(1:n,iqty))/d $ +6*(spl%fs1(0:n-1,iqty)+spl%fs1(1:n,iqty)))/(d*d) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c restore powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dx=(spl%xs(0:spl%mx-1)+z*d(1:spl%mx))-spl%x0(iside) - DO iqty=1,spl%nqty - IF(spl%xpower(iside,iqty) == 0)CYCLE + do iqty=1,spl%nqty + if(spl%xpower(iside,iqty) == 0)cycle xfac=ABS(dx)**spl%xpower(iside,iqty) g=f(:,iqty)*xfac - IF(mode > 0)g1=(f1(:,iqty) + if(mode > 0)g1=(f1(:,iqty) $ +f(:,iqty)*spl%xpower(iside,iqty)/dx)*xfac - IF(mode > 1)g2=(f2(:,iqty)+spl%xpower(iside,iqty)/dx + if(mode > 1)g2=(f2(:,iqty)+spl%xpower(iside,iqty)/dx $ *(2*f1(:,iqty)+(spl%xpower(iside,iqty)-1) $ *f(:,iqty)/dx))*xfac - $ - IF(mode > 2)g3=(f3(:,iqty)+spl%xpower(iside,iqty)/dx + $ + if(mode > 2)g3=(f3(:,iqty)+spl%xpower(iside,iqty)/dx $ *(3*f2(:,iqty)+(spl%xpower(iside,iqty)-1)/dx $ *(3*f1(:,iqty)+(spl%xpower(iside,iqty)-2)/dx $ *f(:,iqty))))*xfac f(:,iqty)=g - IF(mode > 0)f1(:,iqty)=g1 - IF(mode > 1)f2(:,iqty)=g2 - IF(mode > 2)f3(:,iqty)=g3 - ENDDO - ENDDO + if(mode > 0)f1(:,iqty)=g1 + if(mode > 1)f2(:,iqty)=g2 + if(mode > 2)f3(:,iqty)=g3 + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_all_eval + return + end subroutine cspline_all_eval c----------------------------------------------------------------------- c subprogram 10. cspline_write. c produces ascii and binary output. @@ -812,88 +821,88 @@ END SUBROUTINE cspline_all_eval c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_write(spl,out,bin,iua,iub,interp) + subroutine cspline_write(spl,out,bin,iua,iub,interp) - TYPE(cspline_type), INTENT(INOUT) :: spl - LOGICAL, INTENT(IN) :: out,bin - INTEGER, INTENT(IN) :: iua,iub - LOGICAL, INTENT(IN) :: interp + type(cspline_type), intent(inout) :: spl + logical, intent(in) :: out,bin + integer, intent(in) :: iua,iub + logical, intent(in) :: interp - CHARACTER(80) :: format1,format2 - INTEGER :: i,j - REAL(r8) :: x,dx + character(80) :: format1,format2 + integer :: i,j + real(r8) :: x,dx c----------------------------------------------------------------------- c formats. c----------------------------------------------------------------------- - 10 FORMAT('(/4x,"i",4x,a6,1x,',i2.2,'(2x,"re ",a6,2x,"im ",a6)/)') - 20 FORMAT('(i5,1p,',i2.2,'e11.3)') -! 30 FORMAT('(/4x,"i",2x,"j",',i2.2,'(4x,a6,1x)/)') + 10 format('(/4x,"i",4x,a6,1x,',i2.2,'(2x,"re ",a6,2x,"im ",a6)/)') + 20 format('(i5,1p,',i2.2,'e11.3)') +! 30 format('(/4x,"i",2x,"j",',i2.2,'(4x,a6,1x)/)') c----------------------------------------------------------------------- c abort. c----------------------------------------------------------------------- - IF(.NOT.out.AND..NOT.bin)RETURN + if(.not.out.and..not.bin)return c----------------------------------------------------------------------- c print ascii tables of node values and derivatives. c----------------------------------------------------------------------- - IF(out)THEN - WRITE(format1,10)spl%nqty - WRITE(format2,20)2*spl%nqty+1 - WRITE(iua,'(/1x,a)')'node values:' - WRITE(iua,format1)spl%title(0), + if(out)then + write(format1,10)spl%nqty + write(format2,20)2*spl%nqty+1 + write(iua,'(/1x,a)')'node values:' + write(iua,format1)spl%title(0), $ (spl%title(i),spl%title(i),i=1,spl%nqty) - ENDIF - DO i=0,spl%mx - CALL cspline_eval(spl,spl%xs(i),0) - IF(out)WRITE(iua,format2)spl%xs(i),spl%f - IF(bin)WRITE(iub)REAL(spl%xs(i),4), - $ REAL(spl%f,4),REAL(AIMAG(spl%f),4) - ENDDO - IF(out)WRITE(iua,format1)spl%title(0), + endif + do i=0,spl%mx + call cspline_eval(spl,spl%xs(i),0) + if(out)write(iua,format2)spl%xs(i),spl%f + if(bin)write(iub)real(spl%xs(i),4), + $ real(spl%f,4),real(AIMAG(spl%f),4) + enddo + if(out)write(iua,format1)spl%title(0), $ (spl%title(i),spl%title(i),i=1,spl%nqty) - IF(bin)WRITE(iub) - IF(.NOT. interp)RETURN + if(bin)write(iub) + if(.not. interp)return c----------------------------------------------------------------------- c print header for interpolated values. c----------------------------------------------------------------------- - IF(out)THEN - WRITE(iua,'(/1x,a)')'interpolated values:' - WRITE(iua,format1)spl%title(0), + if(out)then + write(iua,'(/1x,a)')'interpolated values:' + write(iua,format1)spl%title(0), $ (spl%title(i),spl%title(i),i=1,spl%nqty) - ENDIF + endif c----------------------------------------------------------------------- c print interpolated values. c----------------------------------------------------------------------- - DO i=0,spl%mx-1 + do i=0,spl%mx-1 dx=(spl%xs(i+1)-spl%xs(i))/4 - DO j=0,4 + do j=0,4 x=spl%xs(i)+j*dx - CALL cspline_eval(spl,x,0) - IF(out)WRITE(iua,format2)i,x,spl%f - IF(bin)WRITE(iub)REAL(x,4), - $ REAL(spl%f,4),REAL(AIMAG(spl%f),4) - ENDDO - ENDDO + call cspline_eval(spl,x,0) + if(out)write(iua,format2)i,x,spl%f + if(bin)write(iub)real(x,4), + $ real(spl%f,4),real(AIMAG(spl%f),4) + enddo + enddo c----------------------------------------------------------------------- c print final interpolated values. c----------------------------------------------------------------------- x=spl%xs(spl%mx) - CALL cspline_eval(spl,x,0) - IF(out)THEN - WRITE(iua,format2)i,x,spl%f - WRITE(iua,format1)spl%title(0), + call cspline_eval(spl,x,0) + if(out)then + write(iua,format2)i,x,spl%f + write(iua,format1)spl%title(0), $ (spl%title(i),spl%title(i),i=1,spl%nqty) - ENDIF - IF(bin)THEN - WRITE(iub)REAL(x,4), - $ REAL(spl%f,4),REAL(AIMAG(spl%f),4) - WRITE(iub) - CALL bin_close(bin_unit) - ENDIF + endif + if(bin)then + write(iub)real(x,4), + $ real(spl%f,4),real(AIMAG(spl%f),4) + write(iub) + call bin_close(bin_unit) + endif c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_write + return + end subroutine cspline_write c----------------------------------------------------------------------- c subprogram 11. cspline_write_log c produces ascii and binary output of logs. @@ -901,149 +910,149 @@ END SUBROUTINE cspline_write c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_write_log(spl,out,bin,iua,iub,interp,stride, + subroutine cspline_write_log(spl,out,bin,iua,iub,interp,stride, $ xend) - TYPE(cspline_type), INTENT(INOUT) :: spl - LOGICAL, INTENT(IN) :: out,bin - INTEGER, INTENT(IN) :: iua,iub - INTEGER, INTENT(IN) :: stride - LOGICAL, INTENT(IN) :: interp - REAL(r8), DIMENSION(2) :: xend + type(cspline_type), intent(inout) :: spl + logical, intent(in) :: out,bin + integer, intent(in) :: iua,iub + integer, intent(in) :: stride + logical, intent(in) :: interp + real(r8), dimension(2) :: xend - CHARACTER(50) :: format1,format2 - INTEGER :: iqty,ix,j,offset - REAL(r8), PARAMETER :: epsilon=-20*alog10 - REAL(r8) :: x,dx - REAL(r8), DIMENSION(2) :: xlog - COMPLEX(r8), DIMENSION(spl%nqty/stride) :: flog + character(50) :: format1,format2 + integer :: iqty,ix,j,offset + real(r8), PARAMETER :: epsilon=-20*alog10 + real(r8) :: x,dx + real(r8), dimension(2) :: xlog + complex(r8), dimension(spl%nqty/stride) :: flog c----------------------------------------------------------------------- c formats. c----------------------------------------------------------------------- - 10 FORMAT('(/4x,"i",4x,a6,1x,',i2.2,'(2x,"re ",a6,2x,"im ",a6)/)') - 20 FORMAT('(i5,1p,',i2.2,'e11.3)') + 10 format('(/4x,"i",4x,a6,1x,',i2.2,'(2x,"re ",a6,2x,"im ",a6)/)') + 20 format('(i5,1p,',i2.2,'e11.3)') c----------------------------------------------------------------------- c abort. c----------------------------------------------------------------------- - IF(.NOT. out .AND. .NOT. bin)RETURN - IF(MOD(spl%nqty,stride) /= 0)THEN - WRITE(*,'(2(a,i3))')"Cspline_write_log: nqty = ",spl%nqty, + if(.not. out .and. .not. bin)return + if(MOD(spl%nqty,stride) /= 0)then + write(*,'(2(a,i3))')"Cspline_write_log: nqty = ",spl%nqty, $ " is not an integral multiple of stride = ",stride - STOP - ENDIF + stop + endif c----------------------------------------------------------------------- c write title and start loop over offsets. c----------------------------------------------------------------------- - IF(OUT)WRITE(iua,'(1x,a)') + if(out)write(iua,'(1x,a)') $ "Output from cspline_write_log for "//TRIM(spl%name)//":" - DO offset=1,stride + do offset=1,stride c----------------------------------------------------------------------- c print ascii table of node values. c----------------------------------------------------------------------- - IF(out)THEN - WRITE(format1,10)spl%nqty/stride - WRITE(format2,20)2*spl%nqty/stride+1 - WRITE(iua,'(/1x,a,i3,a)') + if(out)then + write(format1,10)spl%nqty/stride + write(format2,20)2*spl%nqty/stride+1 + write(iua,'(/1x,a,i3,a)') $ "input values for offset = ",offset-1,":" - WRITE(iua,format1)spl%title(0),(spl%title(iqty), + write(iua,format1)spl%title(0),(spl%title(iqty), $ spl%title(iqty),iqty=offset,spl%nqty,stride) - DO ix=0,spl%mx - CALL cspline_eval(spl,spl%xs(ix),0) - WRITE(iua,format2)ix,spl%xs(ix), + do ix=0,spl%mx + call cspline_eval(spl,spl%xs(ix),0) + write(iua,format2)ix,spl%xs(ix), $ spl%f(offset:spl%nqty:stride) - ENDDO - WRITE(iua,format1)spl%title(0),(spl%title(iqty), + enddo + write(iua,format1)spl%title(0),(spl%title(iqty), $ spl%title(iqty),iqty=offset,spl%nqty,stride) - ENDIF + endif c----------------------------------------------------------------------- c compute logs. c----------------------------------------------------------------------- - IF(bin)THEN - DO ix=0,spl%mx + if(bin)then + do ix=0,spl%mx xlog=LOG10(ABS(spl%xs(ix)-xend)) - CALL cspline_eval(spl,spl%xs(ix),0) + call cspline_eval(spl,spl%xs(ix),0) WHERE(spl%f(offset:spl%nqty:stride) /= 0) flog=LOG(spl%f(offset:spl%nqty:stride)) - ELSEWHERE + elseWHERE flog=epsilon - ENDWHERE + endWHERE c----------------------------------------------------------------------- c print binary table of node values. c----------------------------------------------------------------------- - WRITE(iub)REAL(spl%xs(ix),4),REAL(xlog,4), - $ (REAL(REAL(flog(iqty))/alog10,4), - $ REAL(AIMAG(flog(iqty))*rtod,4), + write(iub)real(spl%xs(ix),4),real(xlog,4), + $ (real(real(flog(iqty))/alog10,4), + $ real(AIMAG(flog(iqty))*rtod,4), $ iqty=1,SIZE(flog)) - ENDDO - WRITE(iub) - ENDIF + enddo + write(iub) + endif c----------------------------------------------------------------------- c print header for interpolated values. c----------------------------------------------------------------------- - IF(interp)THEN - IF(out)THEN - WRITE(iua,'(/1x,a,i3)') + if(interp)then + if(out)then + write(iua,'(/1x,a,i3)') $ "interpolated values for offset = ",offset,":" - WRITE(iua,format1)spl%title(0), + write(iua,format1)spl%title(0), $ (spl%title(iqty),spl%title(iqty), $ iqty=offset,spl%nqty,stride) - ENDIF + endif c----------------------------------------------------------------------- c print interpolated values. c----------------------------------------------------------------------- - DO ix=0,spl%mx-1 + do ix=0,spl%mx-1 dx=(spl%xs(ix+1)-spl%xs(ix))/4 - DO j=0,3 + do j=0,3 x=spl%xs(ix)+j*dx xlog=LOG10(ABS(x-xend)) - CALL cspline_eval(spl,x,0) - IF(out)WRITE(iua,format2)ix,x,(spl%f(iqty), + call cspline_eval(spl,x,0) + if(out)write(iua,format2)ix,x,(spl%f(iqty), $ iqty=offset,spl%nqty,stride) - IF(bin)THEN + if(bin)then WHERE(spl%f(offset:spl%nqty:stride) /= 0) flog=LOG(spl%f(offset:spl%nqty:stride)) - ELSEWHERE + elseWHERE flog=epsilon - ENDWHERE - WRITE(iub)REAL(x,4),REAL(xlog,4), - $ (REAL(DREAL(flog(iqty))/alog10,4), - $ REAL(AIMAG(flog(iqty))*rtod,4), + endWHERE + write(iub)real(x,4),real(xlog,4), + $ (real(Dreal(flog(iqty))/alog10,4), + $ real(AIMAG(flog(iqty))*rtod,4), $ iqty=1,SIZE(flog)) - ENDIF - ENDDO - IF(out)WRITE(iua,'(1x)') - ENDDO + endif + enddo + if(out)write(iua,'(1x)') + enddo c----------------------------------------------------------------------- c print final interpolated values. c----------------------------------------------------------------------- x=spl%xs(spl%mx) xlog=LOG10(ABS(x-xend)) - CALL cspline_eval(spl,x,0) - IF(out)THEN - WRITE(iua,format2)ix,x,(spl%f(iqty), + call cspline_eval(spl,x,0) + if(out)then + write(iua,format2)ix,x,(spl%f(iqty), $ iqty=offset,spl%nqty,stride) - WRITE(iua,format1)spl%title(0),(spl%title(iqty), + write(iua,format1)spl%title(0),(spl%title(iqty), $ spl%title(iqty),iqty=offset,spl%nqty,stride) - ENDIF - IF(bin)THEN + endif + if(bin)then WHERE(spl%f(offset:spl%nqty:stride) /= 0) flog=LOG(spl%f(offset:spl%nqty:stride)) - ELSEWHERE + elseWHERE flog=epsilon - ENDWHERE - WRITE(iub)REAL(x,4),REAL(xlog,4), - $ (REAL(DREAL(flog(iqty))/alog10,4), - $ REAL(AIMAG(flog(iqty))*rtod,4), + endWHERE + write(iub)real(x,4),real(xlog,4), + $ (real(Dreal(flog(iqty))/alog10,4), + $ real(AIMAG(flog(iqty))*rtod,4), $ iqty=1,SIZE(flog)) - WRITE(iub) - ENDIF - ENDIF - ENDDO + write(iub) + endif + endif + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_write_log + return + end subroutine cspline_write_log c----------------------------------------------------------------------- c subprogram 12. cspline_int. c integrates complex cubic splines. @@ -1051,54 +1060,54 @@ END SUBROUTINE cspline_write_log c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_int(spl) + subroutine cspline_int(spl) - TYPE(cspline_type), INTENT(INOUT) :: spl + type(cspline_type), intent(inout) :: spl - INTEGER :: ix,iqty,ig - REAL(r8), DIMENSION(spl%mx) :: dx - COMPLEX(r8), DIMENSION(spl%mx,spl%nqty) :: term,f,f1,f2,f3 + integer :: ix,iqty,ig + real(r8), dimension(spl%mx) :: dx + complex(r8), dimension(spl%mx,spl%nqty) :: term,f,f1,f2,f3 - INTEGER, PARAMETER :: mg=4 - REAL(r8), DIMENSION(mg) :: xg=(1+(/-0.861136311594053_r8, + integer, PARAMETER :: mg=4 + real(r8), dimension(mg) :: xg=(1+(/-0.861136311594053_r8, $ -0.339981043584856_r8,0.339981043584856_r8, $ 0.861136311594053_r8/))/2 - REAL(r8), DIMENSION(mg) :: wg=(/0.347854845137454_r8, + real(r8), dimension(mg) :: wg=(/0.347854845137454_r8, $ 0.652145154862546_r8,0.652145154862546_r8, $ 0.347854845137454_r8/)/2 c----------------------------------------------------------------------- c preliminary computations. c----------------------------------------------------------------------- - IF(.NOT.ASSOCIATED(spl%fsi))ALLOCATE(spl%fsi(0:spl%mx,spl%nqty)) + if(.not.ASSOCIATED(spl%fsi))allocate(spl%fsi(0:spl%mx,spl%nqty)) dx=spl%xs(1:spl%mx)-spl%xs(0:spl%mx-1) term=0 c----------------------------------------------------------------------- c compute integrals over intervals. c----------------------------------------------------------------------- - DO iqty=1,spl%nqty - IF(spl%xpower(1,iqty) == 0 .AND. spl%xpower(2,iqty) == 0)THEN + do iqty=1,spl%nqty + if(spl%xpower(1,iqty) == 0 .and. spl%xpower(2,iqty) == 0)then term(:,iqty)=dx/12 $ *(6*(spl%fs(0:spl%mx-1,iqty)+spl%fs(1:spl%mx,iqty)) $ +dx*(spl%fs1(0:spl%mx-1,iqty)-spl%fs1(1:spl%mx,iqty))) - ELSE - DO ig=1,mg - CALL cspline_all_eval(spl,xg(ig),f,f1,f2,f3,0) + else + do ig=1,mg + call cspline_all_eval(spl,xg(ig),f,f1,f2,f3,0) term(:,iqty)=term(:,iqty)+dx*wg(ig)*f(:,iqty) - ENDDO - ENDIF - ENDDO + enddo + endif + enddo c----------------------------------------------------------------------- c accumulate over intervals. c----------------------------------------------------------------------- spl%fsi(0,:)=0 - DO ix=1,spl%mx + do ix=1,spl%mx spl%fsi(ix,:)=spl%fsi(ix-1,:)+term(ix,:) - ENDDO + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_int + return + end subroutine cspline_int c----------------------------------------------------------------------- c subprogram 13. cspline_triluf. c performs tridiagonal LU factorization. @@ -1106,40 +1115,40 @@ END SUBROUTINE cspline_int c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_triluf(a) + subroutine cspline_triluf(a) - REAL(r8), DIMENSION(-1:,:), INTENT(INOUT) :: a + real(r8), dimension(-1:,:), intent(inout) :: a - INTEGER :: i,j,k,jmin,jmax,n + integer :: i,j,k,jmin,jmax,n c----------------------------------------------------------------------- c begin loop over rows and define limits. c----------------------------------------------------------------------- n=SIZE(a,2) - DO i=1,n + do i=1,n jmin=MAX(1-i,-1) - jmax=MIN(n-i,1) + jmax=Min(n-i,1) c----------------------------------------------------------------------- c compute lower elements. c----------------------------------------------------------------------- - DO j=jmin,-1 - DO k=MAX(jmin,j-1),j-1 + do j=jmin,-1 + do k=MAX(jmin,j-1),j-1 a(j,i)=a(j,i)-a(k,i)*a(j-k,i+k) - ENDDO + enddo a(j,i)=a(j,i)*a(0,i+j) - ENDDO + enddo c----------------------------------------------------------------------- c compute diagonal element c----------------------------------------------------------------------- - DO k=MAX(jmin,-1),-1 + do k=MAX(jmin,-1),-1 a(0,i)=a(0,i)-a(k,i)*a(-k,i+k) - ENDDO + enddo a(0,i)=1/a(0,i) - ENDDO + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_triluf + return + end subroutine cspline_triluf c----------------------------------------------------------------------- c subprogram 14. cspline_trilus. c performs tridiagonal LU solution. @@ -1147,35 +1156,35 @@ END SUBROUTINE cspline_triluf c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_trilus(a,x) + subroutine cspline_trilus(a,x) - REAL(r8), DIMENSION(-1:,:), INTENT(IN) :: a - COMPLEX(r8), DIMENSION(:,:), INTENT(INOUT) :: x + real(r8), dimension(-1:,:), intent(in) :: a + complex(r8), dimension(:,:), intent(inout) :: x - INTEGER :: i,j,n + integer :: i,j,n c----------------------------------------------------------------------- c down sweep. c----------------------------------------------------------------------- n=SIZE(a,2) - DO i=1,n - DO j=MAX(1-i,-1),-1 + do i=1,n + do j=MAX(1-i,-1),-1 x(i,:)=x(i,:)-a(j,i)*x(i+j,:) - ENDDO - ENDDO + enddo + enddo c----------------------------------------------------------------------- c up sweep. c----------------------------------------------------------------------- - DO i=n,1,-1 - DO j=1,MIN(n-i,1) + do i=n,1,-1 + do j=1,Min(n-i,1) x(i,:)=x(i,:)-a(j,i)*x(i+j,:) - ENDDO + enddo x(i,:)=x(i,:)*a(0,i) - ENDDO + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_trilus + return + end subroutine cspline_trilus c----------------------------------------------------------------------- c subprogram 15. cspline_sherman. c uses Sherman-Morrison formula to factor periodic matrix. @@ -1183,27 +1192,28 @@ END SUBROUTINE cspline_trilus c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_sherman(a) + subroutine cspline_sherman(a) - REAL(r8), DIMENSION(-1:,:), INTENT(INOUT) :: a + real(r8), dimension(-1:,:), intent(inout) :: a - INTEGER :: j,n - COMPLEX(r8), DIMENSION(SIZE(a,2),1) :: u + integer :: j,n + complex(r8), dimension(SIZE(a,2),1) :: u c----------------------------------------------------------------------- c prepare matrices. c----------------------------------------------------------------------- n=SIZE(a,2) a(0,1)=a(0,1)-a(-1,1) a(0,n)=a(0,n)-a(-1,1) - u=RESHAPE((/one,(zero,j=2,n-1),one/),SHAPE(u)) - CALL cspline_triluf(a) - CALL cspline_trilus(a,u) - a(-1,1)=REAL(a(-1,1)/(1+a(-1,1)*(u(1,1)+u(n,1))),r8) + u=RESHAPE((/(1.0_r8, 0.0_r8),((0.0_r8, 0.0_r8),j=2,n-1) + $ ,(1.0_r8, 0.0_r8)/),SHAPE(u)) + call cspline_triluf(a) + call cspline_trilus(a,u) + a(-1,1)=real(a(-1,1)/(1+a(-1,1)*(u(1,1)+u(n,1))),r8) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_sherman + return + end subroutine cspline_sherman c----------------------------------------------------------------------- c subprogram 16. cspline_morrison. c uses Sherman-Morrison formula to solve periodic matrix. @@ -1211,27 +1221,27 @@ END SUBROUTINE cspline_sherman c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_morrison(a,x) + subroutine cspline_morrison(a,x) - REAL(r8), DIMENSION(-1:,:), INTENT(IN) :: a - COMPLEX(r8), DIMENSION(:,:), INTENT(INOUT) :: x + real(r8), dimension(-1:,:), intent(in) :: a + complex(r8), dimension(:,:), intent(inout) :: x - INTEGER :: n - COMPLEX(r8), DIMENSION(SIZE(x,1),SIZE(x,2)) :: y + integer :: n + complex(r8), dimension(SIZE(x,1),SIZE(x,2)) :: y c----------------------------------------------------------------------- c solve for x. c----------------------------------------------------------------------- n=SIZE(a,2) y=x - CALL cspline_trilus(a,y) + call cspline_trilus(a,y) x(1,:)=x(1,:)-a(-1,1)*(y(1,:)+y(n,:)) x(n,:)=x(n,:)-a(-1,1)*(y(1,:)+y(n,:)) - CALL cspline_trilus(a,x) + call cspline_trilus(a,x) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_morrison + return + end subroutine cspline_morrison c----------------------------------------------------------------------- c subprogram 17. cspline_thomas. c thomas method to solve tri-diagnol (complex) matrix @@ -1239,13 +1249,13 @@ END SUBROUTINE cspline_morrison c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_thomas(l,d,u,b,n,m) + subroutine cspline_thomas(l,d,u,b,n,m) - INTEGER, INTENT(IN):: n,m - REAL(r8), DIMENSION(n), INTENT(INOUT):: d - REAL(r8), DIMENSION(n-1), INTENT(INOUT):: l,u - COMPLEX(r8), DIMENSION(n,m), INTENT(INOUT):: b - INTEGER:: i + integer, intent(in):: n,m + real(r8), dimension(n), intent(inout):: d + real(r8), dimension(n-1), intent(inout):: l,u + complex(r8), dimension(n,m), intent(inout):: b + integer:: i c----------------------------------------------------------------------- c calculate tri-diagno matrix c l=[A(1,2),A(2,3),...,A(n-1,n)]; @@ -1253,21 +1263,21 @@ SUBROUTINE cspline_thomas(l,d,u,b,n,m) c u=[A(2,1),A(3,2),...,A(n,n-1)]; c b is n row m column matrix c----------------------------------------------------------------------- - DO i = 2, n + do i = 2, n l(i-1) = l(i-1)/d(i-1) d(i) = d(i) - u(i-1) * l(i-1) b(i,:) = b(i,:) - b(i-1,:) * l(i-1) - ENDDO + enddo b(n,:) = b(n,:) / d(n); - DO i = n-1, 1, -1 + do i = n-1, 1, -1 b(i,:) = (b(i,:) - u(i) * b(i+1,:)) / d(i); - ENDDO + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_thomas + return + end subroutine cspline_thomas c----------------------------------------------------------------------- c subprogram 18. cspline_get_yp. c get yi' with four points for spline boundary condtion. @@ -1275,17 +1285,17 @@ END SUBROUTINE cspline_thomas c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_get_yp(x,y,xi,yip,nqty) - INTEGER, INTENT(IN) :: nqty - INTEGER :: n,nrhs,lda,info,ldb,i - INTEGER, DIMENSION(4) :: ipiv - REAL(r8) :: dx - REAL(r8), INTENT(IN) :: xi - COMPLEX(r8), DIMENSION(nqty),INTENT(OUT) :: yip - REAL(r8), DIMENSION(4), INTENT(IN) :: x - COMPLEX(r8), DIMENSION(4,nqty), INTENT(IN) :: y - COMPLEX(r8), DIMENSION(4,nqty) :: b - COMPLEX(r8), DIMENSION(4,4) :: a + subroutine cspline_get_yp(x,y,xi,yip,nqty) + integer, intent(in) :: nqty + integer :: n,nrhs,lda,info,ldb,i + integer, dimension(4) :: ipiv + real(r8) :: dx + real(r8), intent(in) :: xi + complex(r8), dimension(nqty),intent(out) :: yip + real(r8), dimension(4), intent(in) :: x + complex(r8), dimension(4,nqty), intent(in) :: y + complex(r8), dimension(4,nqty) :: b + complex(r8), dimension(4,4) :: a n=4 nrhs=nqty lda=N @@ -1295,22 +1305,22 @@ SUBROUTINE cspline_get_yp(x,y,xi,yip,nqty) a(1,4)=1 b(1,:)=y(1,:) - DO i=2,n + do i=2,n dx=x(i)-x(1) a(i,1)=dx*dx*dx a(i,2)=dx*dx a(i,3)=dx a(i,4)=1 b(i,:)=y(i,:) - ENDDO - CALL zgesv(n,nrhs,a,lda,ipiv,b,ldb,info) + enddo + call zgesv(n,nrhs,a,lda,ipiv,b,ldb,info) dx=xi-x(1) yip=(3*b(1,:)*dx+2*b(2,:))*dx+b(3,:) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_get_yp + return + end subroutine cspline_get_yp c----------------------------------------------------------------------- c subprogram 14. cspline_copy. c copies one cspline_type to another. @@ -1318,15 +1328,15 @@ END SUBROUTINE cspline_get_yp c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE cspline_copy(spl1,spl2) + subroutine cspline_copy(spl1,spl2) - TYPE(cspline_type), INTENT(IN) :: spl1 - TYPE(cspline_type), INTENT(INOUT) :: spl2 + type(cspline_type), intent(in) :: spl1 + type(cspline_type), intent(inout) :: spl2 c----------------------------------------------------------------------- c computations. c----------------------------------------------------------------------- - IF(ASSOCIATED(spl2%xs))CALL cspline_dealloc(spl2) - CALL cspline_alloc(spl2,spl1%mx,spl1%nqty) + if(ASSOCIATED(spl2%xs))call cspline_dealloc(spl2) + call cspline_alloc(spl2,spl1%mx,spl1%nqty) spl2%xs=spl1%xs spl2%fs=spl1%fs spl2%fs1=spl1%fs1 @@ -1338,6 +1348,6 @@ SUBROUTINE cspline_copy(spl1,spl2) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE cspline_copy - END MODULE cspline_mod + return + end subroutine cspline_copy + end module cspline_mod diff --git a/src/Splines/fortran/defs.f b/src/Splines/fortran/defs.f index 968acc5f2..c93df8a1a 100644 --- a/src/Splines/fortran/defs.f +++ b/src/Splines/fortran/defs.f @@ -9,7 +9,7 @@ c----------------------------------------------------------------------- module defs_mod implicit none - + integer, parameter :: $ r4=selected_real_kind(6,37), $ r8=selected_real_kind(15,307), @@ -29,6 +29,8 @@ module defs_mod integer, parameter :: bin_unit = 10 integer, parameter :: out_unit = 11 + complex(r8), PARAMETER :: ifac=(0,1) + contains c----------------------------------------------------------------------- c subprogram 1. timer. @@ -37,78 +39,78 @@ module defs_mod c----------------------------------------------------------------------- c delcarations. c----------------------------------------------------------------------- - SUBROUTINE timer(mode,unit,op_cpuseconds,op_wallseconds) - - INTEGER, INTENT(IN) :: mode,unit - REAL(r4), INTENT(OUT), OPTIONAL :: op_cpuseconds,op_wallseconds + subroutine timer(mode,unit,op_cpuseconds,op_wallseconds) + + integer, intent(in) :: mode,unit + real(r4), intent(out), optional :: op_cpuseconds,op_wallseconds - INTEGER(i8), SAVE :: count_rate, wall_start - REAL(r4), SAVE :: start - REAL(r4) :: seconds - INTEGER(i8) :: hrs,mins,secs, wall_seconds, count_max + integer(i8), save :: count_rate, wall_start + real(r4), save :: start + real(r4) :: seconds + integer(i8) :: hrs,mins,secs, wall_seconds, count_max c----------------------------------------------------------------------- c format statements. c----------------------------------------------------------------------- - 10 FORMAT(1x,a,1p,e10.3,a) + 10 format(1x,a,1p,e10.3,a) c----------------------------------------------------------------------- c computations. c----------------------------------------------------------------------- - IF(mode == 0)THEN - CALL CPU_TIME(start) - CALL SYSTEM_CLOCK(wall_start) - ELSE + if(mode == 0)then + call CPU_TIME(start) + call SYSTEM_CLOCK(wall_start) + else ! report cpu time - CALL CPU_time(seconds) + call CPU_time(seconds) seconds=seconds-start secs = int(seconds) hrs = secs/(60*60) mins = (secs-hrs*60*60)/60 secs = secs-hrs*60*60-mins*60 - IF(PRESENT(op_cpuseconds))THEN + if(present(op_cpuseconds))then ! simply provide the time to the caller op_cpuseconds = seconds - ELSE + else ! write the time to terminal and file - IF(hrs>0)THEN - WRITE(*,'(1x,a,i3,a,i2,a,i2,a)') "Total cpu time = ", + if(hrs>0)then + write(*,'(1x,a,i3,a,i2,a,i2,a)') "Total cpu time = ", $ hrs," hours, ",mins," minutes, ",secs," seconds" - ELSEIF(mins>0)THEN - WRITE(*,'(1x,a,i2,a,i2,a)') "Total cpu time = ", + elseif(mins>0)then + write(*,'(1x,a,i2,a,i2,a)') "Total cpu time = ", $ mins," minutes, ",secs," seconds" - ELSEIF(secs>0)THEN - WRITE(*,'(1x,a,i2,a)') "Total cpu time = ",secs, + elseif(secs>0)then + write(*,'(1x,a,i2,a)') "Total cpu time = ",secs, $ " seconds" - ENDIF - WRITE(unit,10) "Total cpu time = ",seconds," seconds" - ENDIF + endif + write(unit,10) "Total cpu time = ",seconds," seconds" + endif ! report wall time - CALL SYSTEM_CLOCK(wall_seconds, count_rate, count_max) - seconds=REAL(wall_seconds-wall_start, r4)/REAL(count_rate, r4) + call SYSTEM_CLOCK(wall_seconds, count_rate, count_max) + seconds=real(wall_seconds-wall_start, r4)/real(count_rate, r4) secs = int(seconds) hrs = secs/(60*60) mins = (secs-hrs*60*60)/60 secs = secs-hrs*60*60-mins*60 - IF(PRESENT(op_wallseconds))THEN + if(present(op_wallseconds))then op_wallseconds = seconds - ELSE - IF(hrs>0)THEN - WRITE(*,'(1x,a,i3,a,i2,a,i2,a)') "Total wall time = ", + else + if(hrs>0)then + write(*,'(1x,a,i3,a,i2,a,i2,a)') "Total wall time = ", $ hrs," hours, ",mins," minutes, ",secs," seconds" - ELSEIF(mins>0)THEN - WRITE(*,'(1x,a,i2,a,i2,a)') "Total wall time = ", + elseif(mins>0)then + write(*,'(1x,a,i2,a,i2,a)') "Total wall time = ", $ mins," minutes, ",secs," seconds" - ELSEIF(secs>0)THEN - WRITE(*,'(1x,a,i2,a)') "Total wall time = ",secs, + elseif(secs>0)then + write(*,'(1x,a,i2,a)') "Total wall time = ",secs, $ " seconds" - ENDIF - WRITE(unit,10) "Total wall time = ",seconds," seconds" - ENDIF - ENDIF + endif + write(unit,10) "Total wall time = ",seconds," seconds" + endif + endif c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE timer + return + end subroutine timer c----------------------------------------------------------------------- c subprogram 2. bin_open. c opens a binary input or output file. @@ -116,32 +118,32 @@ END SUBROUTINE timer c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bin_open(unit,name,stat,pos,convert_type) + subroutine bin_open(unit,name,stat,pos,convert_type) - CHARACTER(*), INTENT(IN) :: name,stat,pos,convert_type - INTEGER, INTENT(IN) :: unit + character(*), intent(in) :: name,stat,pos,convert_type + integer, intent(in) :: unit c----------------------------------------------------------------------- c open file. c----------------------------------------------------------------------- - SELECT CASE(convert_type) - CASE("none") - OPEN(UNIT=unit,FILE=name,STATUS=stat,POSITION=pos, - $ FORM="UNFORMATTED") - CASE("big") - OPEN(UNIT=unit,FILE=name,STATUS=stat,POSITION=pos, - $ FORM="UNFORMATTED",CONVERT="BIG_ENDIAN") - CASE("little") - OPEN(UNIT=unit,FILE=name,STATUS=stat,POSITION=pos, - $ FORM="UNFORMATTED",CONVERT="LITTLE_ENDIAN") - CASE DEFAULT - CALL program_stop + select case(convert_type) + case("none") + open(UNIT=unit,FILE=name,STATUS=stat,POSITION=pos, + $ FORM="UNformatTED") + case("big") + open(UNIT=unit,FILE=name,STATUS=stat,POSITION=pos, + $ FORM="UNformatTED",CONVERT="BIG_endIAN") + case("little") + open(UNIT=unit,FILE=name,STATUS=stat,POSITION=pos, + $ FORM="UNformatTED",CONVERT="LITTLE_endIAN") + case default + call program_stop $ ("Cannot recognize convert_type = "//TRIM(convert_type)) - END SELECT + end select c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bin_open + return + end subroutine bin_open c----------------------------------------------------------------------- c subprogram 3. bin_close. c close a binary input or output file. @@ -149,18 +151,18 @@ END SUBROUTINE bin_open c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bin_close(unit) + subroutine bin_close(unit) - INTEGER, INTENT(IN) :: unit + integer, intent(in) :: unit c----------------------------------------------------------------------- c work. c----------------------------------------------------------------------- - CLOSE(UNIT=unit) + close(UNIT=unit) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bin_close + return + end subroutine bin_close c----------------------------------------------------------------------- c subprogram 4. ascii_open. c opens a ascii input or output file. @@ -168,19 +170,19 @@ END SUBROUTINE bin_close c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE ascii_open(unit,name,stat) + subroutine ascii_open(unit,name,stat) - CHARACTER(*), INTENT(IN) :: name,stat - INTEGER, INTENT(IN) :: unit + character(*), intent(in) :: name,stat + integer, intent(in) :: unit c----------------------------------------------------------------------- c open file. c----------------------------------------------------------------------- - OPEN(UNIT=unit,FILE=name,STATUS=stat) + open(UNIT=unit,FILE=name,STATUS=stat) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE ascii_open + return + end subroutine ascii_open c----------------------------------------------------------------------- c subprogram 5. ascii_close. c close a ascii input or output file. @@ -188,18 +190,18 @@ END SUBROUTINE ascii_open c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE ascii_close(unit) + subroutine ascii_close(unit) - INTEGER, INTENT(IN) :: unit + integer, intent(in) :: unit c----------------------------------------------------------------------- c work. c----------------------------------------------------------------------- - CLOSE(UNIT=unit) + close(UNIT=unit) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE ascii_close + return + end subroutine ascii_close c----------------------------------------------------------------------- c subprogram 6. program_stop. c terminates program with message, calls timer, closes output file. @@ -207,19 +209,19 @@ END SUBROUTINE ascii_close c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE program_stop(message) + subroutine program_stop(message) - CHARACTER(*), INTENT(IN) :: message + character(*), intent(in) :: message c----------------------------------------------------------------------- c write completion message. c----------------------------------------------------------------------- - CALL timer(1,out_unit) - CALL ascii_close(out_unit) - WRITE(*,'(1x,2a)') 'PROGRAM STOP => ', TRIM(message) + call timer(1,out_unit) + call ascii_close(out_unit) + write(*,'(1x,2a)') 'PROGRAM stop => ', TRIM(message) c----------------------------------------------------------------------- c write completion message. c----------------------------------------------------------------------- - STOP - END SUBROUTINE program_stop + stop + end subroutine program_stop end module defs_mod \ No newline at end of file diff --git a/src/Splines/fortran/fft.f b/src/Splines/fortran/fft.f new file mode 100644 index 000000000..f22464059 --- /dev/null +++ b/src/Splines/fortran/fft.f @@ -0,0 +1,165 @@ +c----------------------------------------------------------------------- +c file fft.f. +c fast fourier transform routines. +c Numerical Recipes in Fortran, Second Edition, p. 501, four1. +c Fortran 90 complex arithmetic version by Alan H. Glasser. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. fft_mod. +c 1. fft_run. +c 2. fft_write. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c subprogram 0. fft_mod. +c module declarations. +c----------------------------------------------------------------------- + module fft_mod + use defs_mod + implicit none + + contains +c----------------------------------------------------------------------- +c subprogram 1. fft_run. +c performs fast fourier transform. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + FUNCTION fft_run(f,sign) RESULT(g) + + complex(r8), dimension(:,:), intent(in) :: f + complex(r8), dimension(SIZE(f,1),SIZE(f,2)) :: g + integer, intent(in) :: sign + + integer :: i,istep,j,m,mmax,n + complex(r8) :: w,wp + complex(r8), dimension(SIZE(f,2)) :: temp +c----------------------------------------------------------------------- +c preliminary computations. +c----------------------------------------------------------------------- + n=SIZE(f,1) + select case(sign) + case(-1) + g=f/n + case(1) + g=f + case default + write(*,'(a,i2,a)')"sign = ",sign," is illegal, must be +/- 1" + stop + end select +c----------------------------------------------------------------------- +c bit reversal. +c----------------------------------------------------------------------- + j=1 + do i=1,n + if(j > i)then + temp(:)=g(j,:) + g(j,:)=g(i,:) + g(i,:)=temp + endif + m=n/2 + do + if(m < 1 .OR. j <= m)EXIT + j=j-m + m=m/2 + enddo + j=j+m + enddo +c----------------------------------------------------------------------- +c Danielson-Lanczos loop. +c----------------------------------------------------------------------- + mmax=1 + do + if(n <= mmax)EXIT + istep=2*mmax + wp=EXP(pi*ifac/(sign*mmax)) + w=1 + do m=1,mmax + do i=m,n,istep + j=i+mmax + temp=w*g(j,:) + g(j,:)=g(i,:)-temp + g(i,:)=g(i,:)+temp + enddo + w=w*wp + enddo + mmax=istep + enddo +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end FUNCTION fft_run +c----------------------------------------------------------------------- +c subprogram 2. fft_write. +c ascii and binary output of fast fourier transform. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + subroutine fft_write(t,f,g,h,out,bin,out_unit,bin_unit) + + real(r8), dimension(:), intent(in) :: t + complex(r8), dimension(:,:), intent(in) :: f,g,h + logical :: out,bin + integer :: out_unit,bin_unit + + integer :: i,k,n + real(r8) :: dt,tperiod,dfreq,freqmax + + integer, dimension(SIZE(t)) :: m + real(r8), dimension(SIZE(t)) :: freq + complex(r8), dimension(SIZE(g,1),SIZE(g,2)) :: gg +c----------------------------------------------------------------------- +c format statements. +c----------------------------------------------------------------------- + 10 format(/6x,"n",7x,"dt",6x,"tperiod",5x,"dfreq",5x,"freqmax" + $ //i8,1p,4e11.3/) + 20 format(/7x,"i",6x,"m",7x,"t",9x,"freq",7x,"re f",7x,"im f",7x, + $ "re g",7x,"im g",7x,"re h",7x,"im h"/) + 30 format(2i8,1p,8e11.3) +c----------------------------------------------------------------------- +c compute scalars. +c----------------------------------------------------------------------- + n=SIZE(t) + dt=t(2)-t(1) + tperiod=n*dt + dfreq=1/(n*dt) + freqmax=dfreq*n/2 +c----------------------------------------------------------------------- +c compute auxiliary arrays. +c----------------------------------------------------------------------- + m(1:n/2-1)=(/(i,i=1-n/2,-1)/) + m(n/2:n)=(/(i,i=0,n/2)/) + freq=m*dfreq + gg(1:n/2-1,:)=g(n/2+2:n,:) + gg(n/2:n,:)=g(1:n/2+1,:) +c----------------------------------------------------------------------- +c diagnose fft. +c----------------------------------------------------------------------- + write(out_unit,10)n,dt,tperiod,dfreq,freqmax + do k=1,SIZE(f,2) + if(out)then + write(out_unit,'(/a,i3)')"k = ",k + write(out_unit,20) + endif + do i=1,n + if(out)write(out_unit,30)i-1,m(i),t(i),freq(i), + $ f(i,k),gg(i,k),h(i,k) + if(bin)write(bin_unit) + $ real(i-1,4),real(m(i),4),real(t(i),4),real(freq(i),4), + $ real(real(f(i,k)),4),real(AIMAG(f(i,k)),4), + $ real(real(gg(i,k)),4),real(AIMAG(gg(i,k)),4), + $ real(real(h(i,k)),4),real(AIMAG(h(i,k)),4) + enddo + if(out)write(out_unit,20) + if(bin)write(bin_unit) + enddo +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fft_write + end module fft_mod \ No newline at end of file diff --git a/src/Splines/fortran/fspline.f b/src/Splines/fortran/fspline.f new file mode 100644 index 000000000..edfda20c9 --- /dev/null +++ b/src/Splines/fortran/fspline.f @@ -0,0 +1,876 @@ +c----------------------------------------------------------------------- +c file fspline.f. +c fits functions to cubic spline in x and Fourier series in y. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c code organization. +c----------------------------------------------------------------------- +c 0. fspline_mod. +c 1. fspline_alloc. +c 2. fspline_dealloc. +c 3. fspline_fit_1. +c 4. fspline_fit_2. +c 5. fspline_eval. +c 6. fspline_eval_external +c 7. fspline_all_eval. +c 8. fspline_write_xy. +c 9. fspline_write_yx. +c 10. fspline_copy. +c----------------------------------------------------------------------- +c subprogram 0. fspline_type definition. +c defines fspline_type. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + module fspline_mod + use defs_mod + use spline_mod + use cspline_mod + use fft_mod + implicit none + + type :: fspline_type + integer :: mx,my,mband,nqty + real(r8), dimension(:), POinTER :: xs,ys + real(r8), dimension(:,:,:), POinTER :: fs + type(cspline_type) :: cs + real(r8), dimension(:), POinTER :: f,fx,fy,fxx,fxy,fyy + character(6) :: xtitle,ytitle + character(6), dimension(:), POinTER :: title + character(6) :: name + end type fspline_type + + contains +c----------------------------------------------------------------------- +c subprogram 1. fspline_alloc. +c allocates space for fspline_type. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + subroutine fspline_alloc(fst,mx,my,mband,nqty) + + integer, intent(in) :: mx,my,mband,nqty + type(fspline_type), intent(out) :: fst +c----------------------------------------------------------------------- +c allocate space. +c----------------------------------------------------------------------- + fst%mx=mx + fst%my=my + fst%mband=mband + fst%nqty=nqty + allocate(fst%xs(0:mx)) + allocate(fst%ys(0:my)) + allocate(fst%fs(0:mx,0:my,nqty)) + allocate(fst%title(nqty)) + allocate(fst%f(nqty)) + allocate(fst%fx(nqty)) + allocate(fst%fy(nqty)) + allocate(fst%fxx(nqty)) + allocate(fst%fxy(nqty)) + allocate(fst%fyy(nqty)) + call cspline_alloc(fst%cs,mx,(mband+1)*nqty) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_alloc +c----------------------------------------------------------------------- +c subprogram 2. fspline_dealloc. +c deallocates space for fspline_type. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + subroutine fspline_dealloc(fst) + + type(fspline_type), intent(inout) :: fst +c----------------------------------------------------------------------- +c allocate space. +c----------------------------------------------------------------------- + deallocate(fst%xs) + deallocate(fst%ys) + deallocate(fst%fs) + deallocate(fst%title) + deallocate(fst%f) + deallocate(fst%fx) + deallocate(fst%fy) + deallocate(fst%fxx) + deallocate(fst%fxy) + deallocate(fst%fyy) + call cspline_dealloc(fst%cs) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_dealloc +c----------------------------------------------------------------------- +c subprogram 3. fspline_fit_1. +c fits functions to fsplines by integrating periodic splines. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + subroutine fspline_fit_1(fst,endmode,fit_flag) + + type(fspline_type), intent(inout) :: fst + integer, intent(in) :: endmode + logical, intent(in) :: fit_flag + + integer :: m,ix,iq,mx,my,mband,nqty,j + real(r8), PARAMETER :: eps=1e-3 + real(r8), allocatable, dimension(:) :: delta,d4fac,delta4 + real(r8), allocatable, dimension(:,:,:) :: fs,fsy + complex(r8), allocatable, dimension(:) :: expfac0,expfac + complex(r8), allocatable, dimension(:) :: dexpfac0,dexpfac + complex(r8), allocatable, dimension(:) :: alpha1,alpha2, + $ beta1,beta2 + complex(r8), allocatable, dimension(:,:,:) :: coef + type(spline_type) :: spl +c----------------------------------------------------------------------- +c allocate. +c----------------------------------------------------------------------- + allocate (delta(fst%my),d4fac(fst%my),delta4(fst%my)) + allocate (fs(0:fst%mx,0:fst%my,fst%nqty), + $ fsy(0:fst%mx,0:fst%my,fst%nqty)) + allocate (expfac0(0:fst%my),expfac(0:fst%my)) + allocate (dexpfac0(fst%my),dexpfac(fst%my)) + allocate (alpha1(fst%my),alpha2(fst%my), + $ beta1(fst%my),beta2(fst%my)) + allocate (coef(0:fst%mx,0:fst%mband,fst%nqty)) +c----------------------------------------------------------------------- +c copy sizes and zero Fourier coefficients. +c----------------------------------------------------------------------- + mx=fst%mx + my=fst%my + mband=fst%mband + nqty=fst%nqty + coef=0 +c----------------------------------------------------------------------- +c prepare principal periodic functions. +c----------------------------------------------------------------------- + delta=fst%ys(1:my)-fst%ys(0:my-1) + delta4=delta**4 + d4fac=1/delta4 + do ix=0,my + expfac0(ix)=EXP(-ifac*fst%ys(ix)) + enddo + dexpfac0=expfac0(0:my-1)/expfac0(1:my) + expfac=1 + dexpfac=1 +c----------------------------------------------------------------------- +c compute y derivatives. +c----------------------------------------------------------------------- + call spline_alloc(spl,my,mx+1) + spl%xs=fst%ys + do iq=1,nqty + spl%fs=TRANSPOSE(fst%fs(:,:,iq)) + call spline_fit(spl,2) + fsy(:,:,iq)=TRANSPOSE(spl%fs1) + enddo + fs=fst%fs + call spline_dealloc(spl) +c----------------------------------------------------------------------- +c compute alpha's and beta's. +c----------------------------------------------------------------------- + do m=0,mband + WHERE(ABS(m*delta) > eps) + alpha1=(dexpfac*(12._r8-ifac*m*delta*(6._r8+(m*delta)**2)) + $ -6._r8*(2._r8+ifac*m*delta))*d4fac/m**4 + beta1=(dexpfac*(6._r8-m*delta*(4*ifac+m*delta)) + $ -2._r8*(3._r8+ifac*m*delta))*d4fac/m**4 + elseWHERE + alpha1=.5_r8+7._r8*ifac*m*delta/20._r8-2._r8* + $ (m*delta)**2/15._r8 + beta1=1._r8/12._r8+ifac*m*delta/20._r8-(m*delta)**2/60._r8 + endWHERE + alpha1=alpha1*delta/twopi + beta1=beta1*delta**2/twopi + alpha2=CONJG(alpha1)*expfac(0:my-1) + beta2=CONJG(beta1)*expfac(0:my-1) + alpha1=alpha1*expfac(1:my) + beta1=beta1*expfac(1:my) +c----------------------------------------------------------------------- +c compute Fourier coefficients. +c----------------------------------------------------------------------- + do iq=1,nqty + do ix=0,mx + coef(ix,m,iq)=coef(ix,m,iq)+SUM( + $ alpha1*fs(ix,0:my-1,iq)+alpha2*fs(ix,1:my,iq) + $ +beta1*fsy(ix,0:my-1,iq)-beta2*fsy(ix,1:my,iq)) + enddo + enddo + +c----------------------------------------------------------------------- +c advance to next Fourier component. +c----------------------------------------------------------------------- + expfac=expfac*expfac0 + dexpfac=dexpfac*dexpfac0 + enddo +c----------------------------------------------------------------------- +c fit Fourier coefficients to cubic splines as functions of x. +c----------------------------------------------------------------------- + fst%cs%xs=fst%xs +c fst%cs%fs=RESHAPE(coef,(/mx+1,(mband+1)*nqty/)) +c following line is replace of RESHAPE. + j = 0 + do iq = 1, nqty + do m = 0, mband + j = j + 1 + fst%cs%fs(:, j) = coef(:, m, iq) + enddo + enddo + if(fit_flag)call cspline_fit(fst%cs,endmode) + fst%cs%name=fst%name + fst%cs%title(0)=" x " + j=0 + do iq=1,nqty + do m=0,mband + j=j+1 + write(fst%cs%title(j),'("cs",i1,"_",i2.2)')iq,m + enddo + enddo +c----------------------------------------------------------------------- +c deallocate. +c----------------------------------------------------------------------- + deallocate (delta,d4fac,delta4) + deallocate (fs,fsy) + deallocate (expfac0,expfac) + deallocate (dexpfac0,dexpfac) + deallocate (alpha1,alpha2,beta1,beta2) + deallocate (coef) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_fit_1 +c----------------------------------------------------------------------- +c subprogram 4. fspline_fit_2. +c fits functions to fsplines using Fast Fourier Transform. +c----------------------------------------------------------------------- + subroutine fspline_fit_2(fst,endmode,fit_flag) + + type(fspline_type), intent(inout) :: fst + integer, intent(in) :: endmode + logical, intent(in) :: fit_flag + + character(64) :: message + integer :: iqty,j,m,mband,mx,my,nqty,p2 + complex(r8), allocatable, dimension(:,:,:) :: f,g + + complex(r8), allocatable, dimension(:,:) :: temp_in, temp_out + integer :: ix, k +c----------------------------------------------------------------------- +c allocate. +c----------------------------------------------------------------------- + allocate (f(0:fst%my-1,0:fst%mx,fst%nqty), + $ g(0:fst%my-1,0:fst%mx,fst%nqty)) +c----------------------------------------------------------------------- +c abort if my is not a power of 2. +c----------------------------------------------------------------------- + p2=1 + my=fst%my + do + my=my/2 + if(my == 0)EXIT + p2=p2*2 + enddo + if(fst%my /= p2)then + write(message,'(a,i3,a)') + $ "fft_fit_2: my = ",fst%my," is not a power of 2" + call program_stop(message) + endif +c----------------------------------------------------------------------- +c abort if 2*mband > my-1. +c----------------------------------------------------------------------- + if(2*fst%mband > fst%my-1)then + write(message,'(a,i3,a,i3)') + $ "fft_fit_2: 2*mband = ",2*fst%mband," > my-1 = ",fst%my-1 + call program_stop(message) + endif +c----------------------------------------------------------------------- +c copy sizes and zero Fourier coefficients. +c----------------------------------------------------------------------- + mx=fst%mx + my=fst%my + mband=fst%mband + nqty=fst%nqty +c----------------------------------------------------------------------- +c set up for Fast Fourier Transform. +c----------------------------------------------------------------------- + + + do iqty=1,nqty + f(:,:,iqty)=TRANSPOSE(fst%fs(:,0:my-1,iqty)) + enddo + +c RESHAPE made unknown ERROR so replaced. +c 323 ~ 345 line ( from allocate (temp_in ...) to deallocate(temp_in, )) +c is replace of +c g=RESHAPE(fft_run(RESHAPE(f,(/my,(mx+1)*nqty/)),-1), +c $ (/my,mx+1,nqty/)) + + allocate (temp_in(my, (mx+1)*nqty)) + k = 0 + do iqty = 1, nqty + do ix = 0, mx + k = k + 1 + temp_in(:, k) = f(:, ix, iqty) + end do + end do + + allocate (temp_out(my, (mx+1)*nqty)) + + temp_out = fft_run(temp_in, -1) + + + k = 0 + do iqty = 1, nqty + do ix = 0, mx + k = k + 1 + g(:, ix, iqty) = temp_out(:, k) + end do + end do + + deallocate(temp_in, temp_out) +c----------------------------------------------------------------------- +c copy Fourier coefficients from g to the cspline structure +c----------------------------------------------------------------------- + j=1 + do iqty=1,nqty + do m=0,mband + fst%cs%fs(:,j)=g(m,:,iqty) + j=j+1 + enddo + enddo +c----------------------------------------------------------------------- +c fit Fourier coefficients to cubic splines as functions of x. +c----------------------------------------------------------------------- + fst%cs%xs=fst%xs + if(fit_flag)call cspline_fit(fst%cs,endmode) + fst%cs%name=fst%name + fst%cs%title(0)=" x " + j=0 + do iqty=1,nqty + do m=0,mband + j=j+1 + write(fst%cs%title(j),'("cs",i1,"_",i2.2)')iqty,m + enddo + enddo +c----------------------------------------------------------------------- +c dellocate. +c----------------------------------------------------------------------- + deallocate (f,g) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_fit_2 +c----------------------------------------------------------------------- +c subprogram 5. fspline_eval. +c evaluates fspline function. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + subroutine fspline_eval(fst,x,y,mode) + + type(fspline_type), intent(inout) :: fst + real(r8), intent(in) :: x,y + integer, intent(in) :: mode + + integer :: m + complex(r8) :: expfac,expfac0 + complex(r8), dimension(fst%nqty) :: term,termx,termxx + complex(r8), dimension(0:fst%mband,fst%nqty) :: c,cx,cxx +c----------------------------------------------------------------------- +c evaluate cubic splines and m = 0 terms for functions. +c----------------------------------------------------------------------- + call cspline_eval(fst%cs,x,mode) + c=RESHAPE(fst%cs%f,(/fst%mband+1,fst%nqty/)) + fst%f=c(0,:) +c----------------------------------------------------------------------- +c evaluate m = 0 terms for first derivatives. +c----------------------------------------------------------------------- + if(mode > 0)then + cx=RESHAPE(fst%cs%f1,(/fst%mband+1,fst%nqty/)) + fst%fx=cx(0,:) + fst%fy=0 + endif +c----------------------------------------------------------------------- +c evaluate m = 0 terms for second derivatives. +c----------------------------------------------------------------------- + if(mode > 1)then + cxx=RESHAPE(fst%cs%f2,(/fst%mband+1,fst%nqty/)) + fst%fxx=cxx(0,:) + fst%fyy=0 + fst%fxy=0 + endif +c----------------------------------------------------------------------- +c evaluate m > 1 for functions. +c----------------------------------------------------------------------- + expfac0=EXP(ifac*y) + expfac=2 + do m=1,fst%mband + expfac=expfac*expfac0 + term=c(m,:)*expfac + fst%f=fst%f+term + if(mode < 1)cycle +c----------------------------------------------------------------------- +c evaluate m > 1 for first derivatives. +c----------------------------------------------------------------------- + termx=cx(m,:)*expfac + fst%fx=fst%fx+termx + fst%fy=fst%fy+term*ifac*m + if(mode < 2)cycle +c----------------------------------------------------------------------- +c evaluate m > 1 for second derivatives. +c----------------------------------------------------------------------- + termxx=cxx(m,:)*expfac + fst%fxx=fst%fxx+termxx + fst%fxy=fst%fxy+termx*ifac*m + fst%fyy=fst%fyy-term*m*m + enddo +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_eval +c----------------------------------------------------------------------- +c subprogram 7. fspline_eval_external. +c evaluates fspline function (parallel), preserving original logic. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + subroutine fspline_eval_external(fst, x, y, mode, f_f, + $ f_fx, f_fy, f_fxx, f_fxy, f_fyy) + + type(fspline_type), intent(in) :: fst + real(r8), intent(in) :: x, y + integer, intent(in) :: mode + + integer :: m + complex(r8) :: expfac, expfac0 + complex(r8), dimension(fst%nqty) :: term, termx, termxx + complex(r8), dimension(0:fst%mband, fst%nqty) :: c, cx, cxx + + ! Local arrays + complex(r8), dimension(fst%cs%nqty) :: cs_f, cs_f1, cs_f2 + + ! Output arrays + real(r8), dimension(fst%nqty), intent(out) :: f_f + real(r8), dimension(fst%nqty), intent(out), optional :: f_fx, + $ f_fy + real(r8), dimension(fst%nqty), intent(out), optional :: f_fxx, + $ f_fxy, f_fyy + +c----------------------------------------------------------------------- +c zero out output arrays +c----------------------------------------------------------------------- + f_f = 0.0_r8 + if (present(f_fx)) f_fx = 0.0_r8 + if (present(f_fy)) f_fy = 0.0_r8 + if (present(f_fxx)) f_fxx = 0.0_r8 + if (present(f_fxy)) f_fxy = 0.0_r8 + if (present(f_fyy)) f_fyy = 0.0_r8 + +c----------------------------------------------------------------------- +c evaluate cubic splines +c----------------------------------------------------------------------- + select case(mode) + case (0) + call cspline_eval_external(fst%cs, x, + $ cs_f) + case (1) + call cspline_eval_external(fst%cs, x, + $ cs_f, cs_f1) + case (2) + call cspline_eval_external(fst%cs, x, cs_f, + $ cs_f1, cs_f2) + end select + +c----------------------------------------------------------------------- +c evaluate m = 0 terms for functions. +c----------------------------------------------------------------------- + c = RESHAPE(cs_f, (/fst%mband + 1, fst%nqty/)) + f_f = real(c(0, :)) + +c----------------------------------------------------------------------- +c evaluate m = 0 terms for first derivatives. +c----------------------------------------------------------------------- + if (mode > 0) then + cx = RESHAPE(cs_f1, (/fst%mband + 1, fst%nqty/)) + f_fx = real(cx(0, :)) + f_fy = 0.0_r8 + endif + +c----------------------------------------------------------------------- +c evaluate m = 0 terms for second derivatives. +c----------------------------------------------------------------------- + if (mode > 1) then + cxx = RESHAPE(cs_f2, (/fst%mband + 1, fst%nqty/)) + f_fxx = real(cxx(0, :)) + f_fyy = 0.0_r8 + f_fxy = 0.0_r8 + endif +c----------------------------------------------------------------------- +c evaluate m > 1 for functions +c----------------------------------------------------------------------- + expfac0 = EXP(ifac * y) + expfac = 2.0_r8 + do m = 1, fst%mband + expfac = expfac * expfac0 + term = c(m, :) * expfac + + f_f = f_f + real(term) + if (mode < 1) cycle +c----------------------------------------------------------------------- +c evaluate m > 1 for first derivatives. +c----------------------------------------------------------------------- + termx = cx(m, :) * expfac + f_fx = f_fx + real(termx) + f_fy = f_fy + real(term * ifac * m) + if (mode < 2) cycle +c----------------------------------------------------------------------- +c evaluate m > 1 for second derivatives. +c----------------------------------------------------------------------- + termxx = cxx(m, :) * expfac + f_fxx = f_fxx + real(termxx) + f_fxy = f_fxy + real(termx * ifac * m) + f_fyy = f_fyy - real(term) * m * m + enddo +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_eval_external +c----------------------------------------------------------------------- +c subprogram 6. fspline_all_eval. +c evaluates fsplines in all intervals. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + subroutine fspline_all_eval(fst,dx,dy,f,fx,fy,fxx,fyy,fxy,mode) + + type(fspline_type), intent(inout) :: fst + real(r8), intent(in) :: dx,dy + real(r8), intent(out), dimension(fst%mx,fst%my,fst%nqty) :: + $ f,fx,fy,fxx,fyy,fxy + integer, intent(in) :: mode + + integer :: m,iy + real(r8), dimension(fst%my) :: y + complex(r8), dimension(fst%my) :: expfac,expfac0 + complex(r8), allocatable, dimension(:,:) :: f0,f1,f2,f3 + complex(r8), allocatable, dimension(:,:,:) :: + $ term,termx,termxx + complex(r8), allocatable, dimension(:,:,:) :: c,cx,cxx +c----------------------------------------------------------------------- +c allocate. +c----------------------------------------------------------------------- + allocate (f0(fst%my,fst%nqty*(fst%mx+1)), + $ f1(fst%my,fst%nqty*(fst%mx+1)), + $ f2(fst%my,fst%nqty*(fst%mx+1)), + $ f3(fst%my,fst%nqty*(fst%mx+1))) + allocate (term(fst%mx,fst%my,fst%nqty), + $ termx(fst%mx,fst%my,fst%nqty), + $ termxx(fst%mx,fst%my,fst%nqty)) + allocate (c(fst%mx,0:fst%mband,fst%nqty), + $ cx(fst%mx,0:fst%mband,fst%nqty), + $ cxx(fst%mx,0:fst%mband,fst%nqty)) +c----------------------------------------------------------------------- +c evaluate cubic splines and m = 0 terms for functions. +c----------------------------------------------------------------------- + call cspline_all_eval(fst%cs,dx,f0,f1,f2,f3,mode) + c=RESHAPE(f0,(/fst%mx,fst%mband+1,fst%nqty/)) + do iy=1,fst%my + f(:,iy,:)=c(:,0,:) + enddo +c----------------------------------------------------------------------- +c evaluate m = 0 terms for first derivatives. +c----------------------------------------------------------------------- + if(mode > 0)then + cx=RESHAPE(f1,(/fst%mx,fst%mband+1,fst%nqty/)) + do iy=1,fst%my + fx(:,iy,:)=cx(:,0,:) + enddo + fy=0 + endif +c----------------------------------------------------------------------- +c evaluate m = 0 terms for second derivatives. +c----------------------------------------------------------------------- + if(mode > 1)then + cxx=RESHAPE(f2,(/fst%mx,fst%mband+1,fst%nqty/)) + do iy=1,fst%my + fxx(:,iy,:)=cxx(:,0,:) + enddo + fxy=0 + fyy=0 + endif +c----------------------------------------------------------------------- +c evaluate m > 0 terms for functions. +c----------------------------------------------------------------------- + y=fst%ys(0:fst%my-1)+dy*(fst%ys(1:fst%my)-fst%ys(0:fst%my-1)) + expfac0=EXP(ifac*y) + expfac=2 + do m=1,fst%mband + expfac=expfac*expfac0 + do iy=1,fst%my + term(:,iy,:)=c(:,m,:)*expfac(iy) + enddo + f=f+term + if(mode < 1)cycle +c----------------------------------------------------------------------- +c evaluate m > 0 terms for first derivatives. +c----------------------------------------------------------------------- + do iy=1,fst%my + termx(:,iy,:)=cx(:,m,:)*expfac(iy) + enddo + fx=fx+termx + fy=fy+term*ifac*m + if(mode < 2)cycle +c----------------------------------------------------------------------- +c evaluate m > 0 terms for second derivatives. +c----------------------------------------------------------------------- + do iy=1,fst%my + termxx(:,iy,:)=cxx(:,m,:)*expfac(iy) + enddo + fxx=fxx+termxx + fxy=fxy+termx*ifac*m + fyy=fyy-term*m*m + enddo +c----------------------------------------------------------------------- +c deallcoate. +c----------------------------------------------------------------------- + deallocate (f0,f1,f2,f3) + deallocate (term,termx,termxx) + deallocate (c,cx,cxx) + +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_all_eval +c----------------------------------------------------------------------- +c subprogram 8. fspline_write_xy. +c produces ascii and binary output for fspline fits. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + subroutine fspline_write_xy(fst,out,bin,interpolate,filename) + + type(fspline_type), intent(inout) :: fst + logical, intent(in) :: out,bin,interpolate + character(*) :: filename + + integer :: ix,iy,jx,jy,iqty + real(r8) :: x,y,dx,dy + + character(80) :: format2,format1 +c----------------------------------------------------------------------- +c write formats. +c----------------------------------------------------------------------- + 10 format(/1x,'ix = ',i3,', x = ',1p,e11.3) + 20 format(/1x,'ix = ',i3,', jx = ',i1,', x = ',1p,e11.3) + 30 format('(/4x,"iy",6x,"y",4x,',i1,'(6x,"f",i1,3x)/)') + 40 format('(i6,1p,e11.3,',i3.3,'e11.3)') +c----------------------------------------------------------------------- +c open binary output file. +c----------------------------------------------------------------------- + if(.not. (out. OR. bin))return + if(bin)call bin_open(bin_unit,TRIM(filename), + $ "UNKNOWN","REWinD","none") +c----------------------------------------------------------------------- +c write input data. +c----------------------------------------------------------------------- + if(out)then + write(out_unit,'(1x,a)')"input data" + write(format1,30)fst%nqty + write(format2,40)fst%nqty + endif + do iy=0,fst%my + y=fst%ys(iy) + if(out)then + write(out_unit,10)iy,fst%ys(iy) + write(out_unit,format1)(iqty,iqty=1,fst%nqty) + endif + do ix=0,fst%mx + x=fst%xs(ix) + fst%f=fst%fs(ix,iy,:) + if(out)write(out_unit,format2)ix,x,fst%f + if(bin)write(bin_unit)real(x,4),real(fst%f,4) + enddo + if(out)write(out_unit,format1)(iqty,iqty=1,fst%nqty) + if(bin)write(bin_unit) + enddo +c----------------------------------------------------------------------- +c begin loops over y for interpolated data. +c----------------------------------------------------------------------- + if(interpolate)then + if(out)write(out_unit,'(1x,a)')"interpolated data" + do iy=0,fst%my-1 + dy=(fst%ys(iy+1)-fst%ys(iy))/4 + do jy=0,4 + y=fst%ys(iy)+dy*jy + if(out)then + write(out_unit,20)iy,jy,y + write(out_unit,format1)(iqty,iqty=1,fst%nqty) + endif +c----------------------------------------------------------------------- +c begin loops over x for interpolated data. +c----------------------------------------------------------------------- + do ix=0,fst%mx-1 + dx=(fst%xs(ix+1)-fst%xs(ix))/4 + do jx=0,4 + x=fst%xs(ix)+dx*jx + call fspline_eval(fst,x,y,0) + if(out)write(out_unit,format2)ix,x,fst%f + if(bin)write(bin_unit)real(x,4),real(fst%f,4) + enddo + if(out)write(out_unit,'()') + enddo +c----------------------------------------------------------------------- +c complete loops over y. +c----------------------------------------------------------------------- + if(out)write(out_unit,format1)(iqty,iqty=1,fst%nqty) + if(bin)write(bin_unit) + enddo + enddo + endif +c----------------------------------------------------------------------- +c close binary output file. +c----------------------------------------------------------------------- + if(bin)call bin_close(bin_unit) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_write_xy +c----------------------------------------------------------------------- +c subprogram 9. fspline_write_yx. +c produces ascii and binary output for fspline fits. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + subroutine fspline_write_yx(fst,out,bin,interpolate,filename) + + type(fspline_type), intent(inout) :: fst + logical, intent(in) :: out,bin,interpolate + character(*) :: filename + + integer :: ix,iy,jx,jy,iqty + real(r8) :: x,y,dx,dy + + character(80) :: format2,format1 +c----------------------------------------------------------------------- +c write formats. +c----------------------------------------------------------------------- + 10 format(/1x,'ix = ',i3,', x = ',1p,e11.3) + 20 format(/1x,'ix = ',i3,', jx = ',i1,', x = ',1p,e11.3) + 30 format('(/4x,"iy",6x,"y",4x,',i1,'(6x,"f",i1,3x)/)') + 40 format('(i6,1p,e11.3,',i3.3,'e11.3)') +c----------------------------------------------------------------------- +c open binary output file. +c----------------------------------------------------------------------- + if(.not. (out. OR. bin))return + if(bin)call bin_open(bin_unit,TRIM(filename), + $ "UNKNOWN","REWinD","none") +c----------------------------------------------------------------------- +c write input data. +c----------------------------------------------------------------------- + if(out)then + write(out_unit,'(1x,a)')"input data" + write(format1,30)fst%nqty + write(format2,40)fst%nqty + endif + do ix=0,fst%mx + x=fst%xs(ix) + if(out)then + write(out_unit,10)ix,fst%xs(ix) + write(out_unit,format1)(iqty,iqty=1,fst%nqty) + endif + do iy=0,fst%my + y=fst%ys(iy) + fst%f=fst%fs(ix,iy,:) + if(out)write(out_unit,format2)iy,y,fst%f + if(bin)write(bin_unit)real(y,4),real(fst%f,4) + enddo + if(out)write(out_unit,format1)(iqty,iqty=1,fst%nqty) + if(bin)write(bin_unit) + enddo +c----------------------------------------------------------------------- +c begin loops over x for interpolated data. +c----------------------------------------------------------------------- + if(interpolate)then + if(out)write(out_unit,'(1x,a)')"interpolated data" + do ix=0,fst%mx-1 + dx=(fst%xs(ix+1)-fst%xs(ix))/4 + do jx=0,4 + x=fst%xs(ix)+dx*jx + if(out)then + write(out_unit,20)ix,jx,x + write(out_unit,format1)(iqty,iqty=1,fst%nqty) + endif +c----------------------------------------------------------------------- +c begin loops over y for interpolated data. +c----------------------------------------------------------------------- + do iy=0,fst%my-1 + dy=(fst%ys(iy+1)-fst%ys(iy))/4 + do jy=0,4 + y=fst%ys(iy)+dy*jy + call fspline_eval(fst,x,y,0) + if(out)write(out_unit,format2)iy,y,fst%f + if(bin)write(bin_unit)real(y,4),real(fst%f,4) + enddo + if(out)write(out_unit,'()') + enddo +c----------------------------------------------------------------------- +c complete loops over x. +c----------------------------------------------------------------------- + if(out)write(out_unit,format1)(iqty,iqty=1,fst%nqty) + if(bin)write(bin_unit) + enddo + enddo + endif +c----------------------------------------------------------------------- +c close binary output file. +c----------------------------------------------------------------------- + if(bin)call bin_close(bin_unit) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_write_yx +c----------------------------------------------------------------------- +c subprogram 10. fspline_copy. +c copies one fspline type to another. +c----------------------------------------------------------------------- +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + subroutine fspline_copy(fst1,fst2) + + type(fspline_type), intent(in) :: fst1 + type(fspline_type), intent(inout) :: fst2 +c----------------------------------------------------------------------- +c computations. +c----------------------------------------------------------------------- + if(ASSOCIATED(fst2%xs))call fspline_dealloc(fst2) + call fspline_alloc(fst2,fst1%mx,fst1%my,fst1%mband,fst1%nqty) + call cspline_copy(fst1%cs,fst2%cs) + fst2%xs=fst1%xs + fst2%ys=fst1%ys + fst2%fs=fst1%fs + fst2%name=fst1%name + fst2%title=fst1%title +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_copy + end module fspline_mod \ No newline at end of file diff --git a/src/Splines/fortran/makefile b/src/Splines/fortran/makefile index 6d899c202..28fea1457 100644 --- a/src/Splines/fortran/makefile +++ b/src/Splines/fortran/makefile @@ -16,14 +16,16 @@ F90 = $(FC) $(FFLAGS) $(RECURSFLAG) OBJS = \ defs.o \ + fft.o \ spline.o \ cspline.o \ + fspline.o \ bicube.o \ spline_c_api.o # targets -all : $(OUTLIB) +all : $(OUTLIB) $(OUTLIB): $(OBJS) $(FC) $(LDFLAGS) -o $@ $^ $(LIBS) @@ -36,5 +38,7 @@ clean: spline.o: defs.o cspline.o: defs.o spline.o +fft.o: defs.o +fspline.o: defs.o spline.o cspline.o fft.o bicube.o: defs.o spline.o -spline_c_api.o: defs.o spline.o cspline.o bicube.o +spline_c_api.o: defs.o spline.o cspline.o bicube.o fft.o fspline.o \ No newline at end of file diff --git a/src/Splines/fortran/spline.f b/src/Splines/fortran/spline.f index ea42470e3..96f61dfec 100644 --- a/src/Splines/fortran/spline.f +++ b/src/Splines/fortran/spline.f @@ -40,22 +40,22 @@ c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - MODULE spline_mod - USE defs_mod - IMPLICIT NONE - - LOGICAL :: use_classic_splines = .FALSE. - TYPE :: spline_type - INTEGER :: mx,nqty,ix - REAL(r8), DIMENSION(:), ALLOCATABLE :: xs,f,f1,f2,f3 - REAL(r8), DIMENSION(:,:), ALLOCATABLE :: fs,fs1,fsi,xpower - REAL(r8), DIMENSION(2) :: x0 - CHARACTER(6), DIMENSION(:), ALLOCATABLE :: title - CHARACTER(6) :: name - LOGICAL :: periodic=.FALSE., allocated=.FALSE. - END TYPE spline_type - - CONTAINS + module spline_mod + use defs_mod + implicit none + + logical :: use_classic_splines = .false. + type :: spline_type + integer :: mx,nqty,ix + real(r8), dimension(:), allocatable :: xs,f,f1,f2,f3 + real(r8), dimension(:,:), allocatable :: fs,fs1,fsi,xpower + real(r8), dimension(2) :: x0 + character(6), dimension(:), allocatable :: title + character(6) :: name + logical :: periodic=.false., allocated=.false. + end type spline_type + + contains c----------------------------------------------------------------------- c subprogram 1. spline_alloc. c allocates space for spline_type. @@ -63,44 +63,44 @@ MODULE spline_mod c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_alloc(spl,mx,nqty) + subroutine spline_alloc(spl,mx,nqty) - INTEGER, INTENT(IN) :: mx,nqty - TYPE(spline_type), INTENT(INOUT) :: spl - ! IF(spl%allocated) CALL spline_dealloc(spl) + integer, intent(in) :: mx,nqty + type(spline_type), intent(inout) :: spl + ! if(spl%allocated) call spline_dealloc(spl) c----------------------------------------------------------------------- c safety check. c----------------------------------------------------------------------- - IF(spl%allocated) - $ CALL program_stop("spline_alloc: spline already allocated") - + if(spl%allocated) + $ call program_stop("spline_alloc: spline already allocated") + c----------------------------------------------------------------------- c set scalars. c----------------------------------------------------------------------- spl%mx=mx spl%nqty=nqty spl%ix=0 - spl%periodic=.FALSE. + spl%periodic=.false. c----------------------------------------------------------------------- c allocate space. c----------------------------------------------------------------------- - ALLOCATE(spl%xs(0:mx)) - ALLOCATE(spl%f(nqty)) - ALLOCATE(spl%f1(nqty)) - ALLOCATE(spl%f2(nqty)) - ALLOCATE(spl%f3(nqty)) - ALLOCATE(spl%title(0:nqty)) - ALLOCATE(spl%fs(0:mx,nqty)) - ALLOCATE(spl%fs1(0:mx,nqty)) - ALLOCATE(spl%xpower(2,nqty)) + allocate(spl%xs(0:mx)) + allocate(spl%f(nqty)) + allocate(spl%f1(nqty)) + allocate(spl%f2(nqty)) + allocate(spl%f3(nqty)) + allocate(spl%title(0:nqty)) + allocate(spl%fs(0:mx,nqty)) + allocate(spl%fs1(0:mx,nqty)) + allocate(spl%xpower(2,nqty)) spl%xpower=0 spl%x0=0 - spl%allocated=.TRUE. + spl%allocated=.true. c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_alloc + return + end subroutine spline_alloc c----------------------------------------------------------------------- c subprogram 2. spline_dealloc. c deallocates space for spline_type. @@ -108,33 +108,33 @@ END SUBROUTINE spline_alloc c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_dealloc(spl) + subroutine spline_dealloc(spl) - TYPE(spline_type), INTENT(INOUT) :: spl + type(spline_type), intent(inout) :: spl c----------------------------------------------------------------------- c safety check. c----------------------------------------------------------------------- - IF(.NOT.spl%allocated) - $ CALL program_stop("spline_dealloc: spline not allocated") + if(.not.spl%allocated) + $ call program_stop("spline_dealloc: spline not allocated") c----------------------------------------------------------------------- c deallocate space. c----------------------------------------------------------------------- - DEALLOCATE(spl%xs) - DEALLOCATE(spl%f) - DEALLOCATE(spl%f1) - DEALLOCATE(spl%f2) - DEALLOCATE(spl%f3) - DEALLOCATE(spl%title) - DEALLOCATE(spl%fs) - DEALLOCATE(spl%fs1) - DEALLOCATE(spl%xpower) - IF(ALLOCATED(spl%fsi))DEALLOCATE(spl%fsi) - spl%allocated=.FALSE. + deallocate(spl%xs) + deallocate(spl%f) + deallocate(spl%f1) + deallocate(spl%f2) + deallocate(spl%f3) + deallocate(spl%title) + deallocate(spl%fs) + deallocate(spl%fs1) + deallocate(spl%xpower) + if(allocated(spl%fsi))deallocate(spl%fsi) + spl%allocated=.false. c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_dealloc + return + end subroutine spline_dealloc c----------------------------------------------------------------------- c subprogram 3. spline_fit. c switch between cubic splines. @@ -142,24 +142,24 @@ END SUBROUTINE spline_dealloc c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_fit(spl,endmode) + subroutine spline_fit(spl,endmode) - TYPE(spline_type), INTENT(INOUT) :: spl - CHARACTER(*), INTENT(IN) :: endmode + type(spline_type), intent(inout) :: spl + integer, intent(in) :: endmode c----------------------------------------------------------------------- c switch between two spline_fit. c----------------------------------------------------------------------- - IF (use_classic_splines .AND. - $ (endmode.EQ."extrap".OR.endmode.EQ."natural"))THEN - CALL spline_fit_classic(spl,endmode) - ELSE - CALL spline_fit_ahg(spl,endmode) - ENDIF + if (use_classic_splines .and. + $ (endmode == 3 .OR. endmode == 1))then ! 3 = Extrapolate, 1 = Natural + call spline_fit_classic(spl,endmode) + else + call spline_fit_ahg(spl,endmode) + endif c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_fit + return + end subroutine spline_fit c----------------------------------------------------------------------- c subprogram 4. spline_fit_ahg. c fits real functions to cubic splines. @@ -167,47 +167,47 @@ END SUBROUTINE spline_fit c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_fit_ahg(spl,endmode) + subroutine spline_fit_ahg(spl,endmode) - TYPE(spline_type), INTENT(INOUT) :: spl - CHARACTER(*), INTENT(IN) :: endmode + type(spline_type), intent(inout) :: spl + integer, intent(in) :: endmode - INTEGER :: iqty,iside - REAL(r8), DIMENSION(-1:1,0:spl%mx) :: a - REAL(r8), DIMENSION(spl%mx) :: b - REAL(r8), DIMENSION(4) :: cl,cr - REAL(r8), DIMENSION(0:spl%mx) :: xfac + integer :: iqty,iside + real(r8), dimension(-1:1,0:spl%mx) :: a + real(r8), dimension(spl%mx) :: b + real(r8), dimension(4) :: cl,cr + real(r8), dimension(0:spl%mx) :: xfac c----------------------------------------------------------------------- c extract powers. c----------------------------------------------------------------------- - DO iside=1,2 - DO iqty=1,spl%nqty - IF(spl%xpower(iside,iqty) /= 0)THEN + do iside=1,2 + do iqty=1,spl%nqty + if(spl%xpower(iside,iqty) /= 0)then xfac=1/ABS(spl%xs-spl%x0(iside))**spl%xpower(iside,iqty) spl%fs(:,iqty)=spl%fs(:,iqty)*xfac - ENDIF - ENDDO - ENDDO + endif + enddo + enddo c----------------------------------------------------------------------- c set up grid matrix. c----------------------------------------------------------------------- - CALL spline_fac(spl,a,b,cl,cr,endmode) + call spline_fac(spl,a,b,cl,cr,endmode) c----------------------------------------------------------------------- c compute first derivatives, interior. c----------------------------------------------------------------------- - DO iqty=1,spl%nqty + do iqty=1,spl%nqty spl%fs1(1:spl%mx-1,iqty)= $ 3*((spl%fs(2:spl%mx,iqty)-spl%fs(1:spl%mx-1,iqty)) $ *b(2:spl%mx) $ +(spl%fs(1:spl%mx-1,iqty)-spl%fs(0:spl%mx-2,iqty)) $ *b(1:spl%mx-1)) - ENDDO + enddo c----------------------------------------------------------------------- c extrapolation boundary conditions. c----------------------------------------------------------------------- - SELECT CASE(endmode) - CASE("extrap") - DO iqty=1,spl%nqty + select case(endmode) + case(3) ! 3 = Extrapolate + do iqty=1,spl%nqty spl%fs1(0,iqty)=SUM(cl(1:4)*spl%fs(0:3,iqty)) spl%fs1(spl%mx,iqty)=SUM(cr(1:4) $ *spl%fs(spl%mx:spl%mx-3:-1,iqty)) @@ -216,18 +216,18 @@ SUBROUTINE spline_fit_ahg(spl,endmode) spl%fs1(spl%mx-1,iqty)= $ spl%fs1(spl%mx-1,iqty)-spl%fs1(spl%mx,iqty) $ /(spl%xs(spl%mx)-spl%xs(spl%mx-1)) - ENDDO - CALL spline_trilus(a(:,1:spl%mx-1),spl%fs1(1:spl%mx-1,:)) + enddo + call spline_trilus(a(:,1:spl%mx-1),spl%fs1(1:spl%mx-1,:)) c----------------------------------------------------------------------- c not-a-knot boundary conditions. c----------------------------------------------------------------------- - CASE("not-a-knot") + case(4) ! 4 = not-a-knot spl%fs1(1,:)=spl%fs1(1,:)-(2*spl%fs(1,:) $ -spl%fs(0,:)-spl%fs(2,:))*2*b(1) spl%fs1(spl%mx-1,:)=spl%fs1(spl%mx-1,:) $ +(2*spl%fs(spl%mx-1,:)-spl%fs(spl%mx,:) $ -spl%fs(spl%mx-2,:))*2*b(spl%mx) - CALL spline_trilus(a(:,1:spl%mx-1),spl%fs1(1:spl%mx-1,:)) + call spline_trilus(a(:,1:spl%mx-1),spl%fs1(1:spl%mx-1,:)) spl%fs1(0,:)=(2*(2*spl%fs(1,:)-spl%fs(0,:)-spl%fs(2,:)) $ +(spl%fs1(1,:)+spl%fs1(2,:))*(spl%xs(2)-spl%xs(1)) $ -spl%fs1(1,:)*(spl%xs(1)-spl%xs(0)))/(spl%xs(1)-spl%xs(0)) @@ -242,23 +242,23 @@ SUBROUTINE spline_fit_ahg(spl,endmode) c----------------------------------------------------------------------- c periodic boudary conditions. c----------------------------------------------------------------------- - CASE("periodic") - spl%periodic=.TRUE. + case(2) ! 2 = Periodic + spl%periodic=.true. spl%fs1(0,:)=3*((spl%fs(1,:)-spl%fs(0,:))*b(1) $ +(spl%fs(0,:)-spl%fs(spl%mx-1,:))*b(spl%mx)) - CALL spline_morrison(a(:,0:spl%mx-1),spl%fs1(0:spl%mx-1,:)) + call spline_morrison(a(:,0:spl%mx-1),spl%fs1(0:spl%mx-1,:)) spl%fs1(spl%mx,:)=spl%fs1(0,:) c----------------------------------------------------------------------- c unrecognized boundary condition. c----------------------------------------------------------------------- - CASE DEFAULT - CALL program_stop("Cannot recognize endmode = "//TRIM(endmode)) - END SELECT + case default + call program_stop("Cannot recognize endmode") + end select c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_fit_ahg + return + end subroutine spline_fit_ahg c----------------------------------------------------------------------- c subprogram 5. spline_fit_classic. c classical way to solve spline coefficients @@ -268,62 +268,62 @@ END SUBROUTINE spline_fit_ahg c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_fit_classic(spl,endmode) - TYPE(spline_type), INTENT(INOUT) :: spl - CHARACTER(*), INTENT(IN) :: endmode - REAL(r8), DIMENSION(:),ALLOCATABLE :: d,l,u,h - REAL(r8), DIMENSION(:,:),ALLOCATABLE :: r - REAL(r8), DIMENSION(0:spl%mx) :: xfac + subroutine spline_fit_classic(spl,endmode) + type(spline_type), intent(inout) :: spl + integer, intent(in) :: endmode + real(r8), dimension(:),allocatable :: d,l,u,h + real(r8), dimension(:,:),allocatable :: r + real(r8), dimension(0:spl%mx) :: xfac - INTEGER :: iside,iqty,i - REAL(r8),DIMENSION(spl%nqty) :: bs,cs,ds + integer :: iside,iqty,i + real(r8),dimension(spl%nqty) :: bs,cs,ds c----------------------------------------------------------------------- c extract powers. c----------------------------------------------------------------------- - DO iside=1,2 - DO iqty=1,spl%nqty - IF(spl%xpower(iside,iqty) /= 0)THEN + do iside=1,2 + do iqty=1,spl%nqty + if(spl%xpower(iside,iqty) /= 0)then xfac=1/ABS(spl%xs-spl%x0(iside))**spl%xpower(iside,iqty) spl%fs(:,iqty)=spl%fs(:,iqty)*xfac - ENDIF - ENDDO - ENDDO - ALLOCATE (d(0:spl%mx),l(spl%mx),u(spl%mx),r(0:spl%mx,spl%nqty)) - ALLOCATE (h(0:spl%mx-1)) + endif + enddo + enddo + allocate (d(0:spl%mx),l(spl%mx),u(spl%mx),r(0:spl%mx,spl%nqty)) + allocate (h(0:spl%mx-1)) c----------------------------------------------------------------------- c compute tridiagnol matrix for natural B.C. c----------------------------------------------------------------------- - DO i=0,spl%mx-1 + do i=0,spl%mx-1 h(i)=spl%xs(i+1)-spl%xs(i) - ENDDO + enddo d(0)=1 - DO i=1,spl%mx-1 + do i=1,spl%mx-1 d(i)=2*(h(i-1)+h(i)) - ENDDO + enddo d(spl%mx)=1 - DO i=1,spl%mx-1 + do i=1,spl%mx-1 l(i)=h(i-1) - ENDDO + enddo l(spl%mx)=0 u(1)=0 - DO i=2,spl%mx + do i=2,spl%mx u(i)=h(i-1) - ENDDO + enddo r(0,:)=0 - DO i=1,spl%mx-1 + do i=1,spl%mx-1 r(i,:)=( (spl%fs(i+1,:)-spl%fs(i,:))/h(i) $ -(spl%fs(i,:)-spl%fs(i-1,:))/h(i-1) )*6 - ENDDO + enddo r(spl%mx,:)=0 - IF (endmode=="extrap") THEN - CALL spline_get_yp(spl%xs(0:3),spl%fs(0:3,:), + if (endmode==3) then ! 3 = Extrapolate + call spline_get_yp(spl%xs(0:3),spl%fs(0:3,:), $ spl%xs(0),r(0,:),spl%nqty) - CALL spline_get_yp(spl%xs(spl%mx-3:spl%mx), + call spline_get_yp(spl%xs(spl%mx-3:spl%mx), $ spl%fs(spl%mx-3:spl%mx,:),spl%xs(spl%mx), $ r(spl%mx,:),spl%nqty) d(0)=2*h(0) @@ -334,19 +334,19 @@ SUBROUTINE spline_fit_classic(spl,endmode) r(spl%mx,:)=( r(spl%mx,:) $ -(spl%fs(spl%mx,:)-spl%fs(spl%mx-1,:))/h(spl%mx-1) )*6 - ENDIF + endif c----------------------------------------------------------------------- c solve and contrruct spline. c----------------------------------------------------------------------- - CALL spline_thomas(l,d,u,r,spl%mx+1,spl%nqty) + call spline_thomas(l,d,u,r,spl%mx+1,spl%nqty) - DO i=0, spl%mx-1 + do i=0, spl%mx-1 bs=(spl%fs(i+1,:)-spl%fs(i,:))/h(i) $ - 0.5*h(i)*r(i,:) $ - h(i)*(r(i+1,:)-r(i,:))/6 spl%fs1(i,:)=bs - ENDDO + enddo ds=(r(spl%mx,:)-r(spl%mx-1,:))/(h(spl%mx-1)*6) cs=r(spl%mx-1,:)*0.5 i=spl%mx-1 @@ -355,12 +355,12 @@ SUBROUTINE spline_fit_classic(spl,endmode) $ - h(i)*(r(i+1,:)-r(i,:))/6 i=spl%mx spl%fs1(i,:)=bs+h(i-1)*(cs*2+h(i-1)*ds*3) - DEALLOCATE (d,l,u,r,h) + deallocate (d,l,u,r,h) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_fit_classic + return + end subroutine spline_fit_classic c----------------------------------------------------------------------- c subprogram 6. spline_fit_ha. c fits real functions to highly accurate cubic splines @@ -370,31 +370,31 @@ END SUBROUTINE spline_fit_classic c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_fit_ha(spl,endmode) - TYPE(spline_type), INTENT(INOUT) :: spl - CHARACTER(*), INTENT(IN) :: endmode - - INTEGER ::icount,icoef,imx,iqty,istart,jstart,info,iside - INTEGER :: ndim,nqty,kl,ku,ldab,nvar - INTEGER, DIMENSION(:), ALLOCATABLE :: ipiv - INTEGER, DIMENSION(:,:), ALLOCATABLE :: imap - REAL(r8) :: x0,x1,x2,dx - REAL(r8), DIMENSION(0:spl%mx) :: xfac - REAL(r8), DIMENSION(:,:), ALLOCATABLE :: rhs,locrhs,fs,locrhs0, + subroutine spline_fit_ha(spl,endmode) + type(spline_type), intent(inout) :: spl + integer, intent(in) :: endmode + + integer ::icount,icoef,imx,iqty,istart,jstart,info,iside + integer :: ndim,nqty,kl,ku,ldab,nvar + integer, dimension(:), allocatable :: ipiv + integer, dimension(:,:), allocatable :: imap + real(r8) :: x0,x1,x2,dx + real(r8), dimension(0:spl%mx) :: xfac + real(r8), dimension(:,:), allocatable :: rhs,locrhs,fs,locrhs0, $ locrhs1,tmpmat - REAL(r8), DIMENSION(:,:),ALLOCATABLE :: mat,locmat,locmat0,locmat1 - REAL(r8), DIMENSION(:,:,:),ALLOCATABLE :: coef + real(r8), dimension(:,:),allocatable :: mat,locmat,locmat0,locmat1 + real(r8), dimension(:,:,:),allocatable :: coef c----------------------------------------------------------------------- c extract powers. c----------------------------------------------------------------------- - DO iside=1,2 - DO iqty=1,spl%nqty - IF(spl%xpower(iside,iqty) /= 0)THEN + do iside=1,2 + do iqty=1,spl%nqty + if(spl%xpower(iside,iqty) /= 0)then xfac=1/ABS(spl%xs-spl%x0(iside))**spl%xpower(iside,iqty) spl%fs(:,iqty)=spl%fs(:,iqty)*xfac - ENDIF - ENDDO - ENDDO + endif + enddo + enddo c----------------------------------------------------------------------- c contruct grid and related matrix block. c five unknow variables at each interval a,b,c,e,f @@ -403,30 +403,30 @@ SUBROUTINE spline_fit_ha(spl,endmode) c----------------------------------------------------------------------- nqty=spl%nqty nvar=5 - ALLOCATE (coef(nvar,0:spl%mx-1,nqty),imap(nvar,0:spl%mx-1)) - ALLOCATE (fs(0:spl%mx,nqty)) + allocate (coef(nvar,0:spl%mx-1,nqty),imap(nvar,0:spl%mx-1)) + allocate (fs(0:spl%mx,nqty)) icount=1 - DO imx=0, spl%mx-1 - DO icoef=1,nvar + do imx=0, spl%mx-1 + do icoef=1,nvar imap(icoef,imx)=icount icount=icount+1 - ENDDO - ENDDO + enddo + enddo ndim=icount-1 kl=nvar*3 ku=kl ldab=2*kl+ku+1 - ALLOCATE(mat(ldab,ndim),rhs(ndim,nqty),ipiv(ndim)) + allocate(mat(ldab,ndim),rhs(ndim,nqty),ipiv(ndim)) mat=0 rhs=0 fs=spl%fs(:,:) c----------------------------------------------------------------------- c contruct local matrix in each interval. c----------------------------------------------------------------------- - ALLOCATE(locmat(nvar,nvar*3),locmat0(nvar,nvar*3), + allocate(locmat(nvar,nvar*3),locmat0(nvar,nvar*3), & locmat1(nvar,nvar*2),tmpmat(nvar,nvar*2)) - ALLOCATE(locrhs(nvar,nqty),locrhs0(nvar,nqty),locrhs1(nvar,nqty)) - DO imx=1,spl%mx-2 + allocate(locrhs(nvar,nqty),locrhs0(nvar,nqty),locrhs1(nvar,nqty)) + do imx=1,spl%mx-2 x0=spl%xs(imx-1) x1=spl%xs(imx) x2=spl%xs(imx+1) @@ -469,9 +469,9 @@ SUBROUTINE spline_fit_ha(spl,endmode) c----------------------------------------------------------------------- istart=imap(1,imx) jstart=imap(1,imx-1) - CALL spline_fill_matrix(mat,locmat,istart,jstart,kl,ku) + call spline_fill_matrix(mat,locmat,istart,jstart,kl,ku) rhs(istart:istart+nvar-1,:)=locrhs - ENDDO + enddo c----------------------------------------------------------------------- c boundary condition c----------------------------------------------------------------------- @@ -509,11 +509,11 @@ SUBROUTINE spline_fit_ha(spl,endmode) locmat1(5,5)=1 locmat1(5,nvar+5)=-1 - SELECT CASE(endmode) + select case(endmode) c----------------------------------------------------------------------- c not-a-knot boundary conditions. c----------------------------------------------------------------------- - CASE("not-a-knot") + case(4) ! 4 = not-a-knot locmat0(1,nvar+1)=6 locmat0(1,2*nvar+1)=-6 locmat0(5,nvar+5)=1 @@ -528,9 +528,9 @@ SUBROUTINE spline_fit_ha(spl,endmode) c extrap boudary conditions, use first and last four points to c calculate y'(0) and y'(1). c----------------------------------------------------------------------- - CASE("extrap") + case(3) ! 3 = Extrapolate locmat0(1,nvar+3)=1 - CALL spline_get_yp(spl%xs(0:3),spl%fs(0:3,:), + call spline_get_yp(spl%xs(0:3),spl%fs(0:3,:), $ spl%xs(0),locrhs0(1,:),nqty) locmat0(5,nvar+5)=1 @@ -540,7 +540,7 @@ SUBROUTINE spline_fit_ha(spl,endmode) locmat1(3,nvar+1)=3*dx*dx locmat1(3,nvar+2)=2*dx locmat1(3,nvar+3)=1 - CALL spline_get_yp(spl%xs(spl%mx-3:spl%mx), + call spline_get_yp(spl%xs(spl%mx-3:spl%mx), $ spl%fs(spl%mx-3:spl%mx,:),spl%xs(spl%mx),locrhs1(3,:),nqty) locmat1(4,nvar+4)=1 @@ -548,7 +548,7 @@ SUBROUTINE spline_fit_ha(spl,endmode) c----------------------------------------------------------------------- c natural boudary conditions. c----------------------------------------------------------------------- - CASE("natural") + case(1) ! 1 = Natural locmat0(1,nvar+2)=2 locmat0(5,nvar+5)=1 @@ -563,20 +563,20 @@ SUBROUTINE spline_fit_ha(spl,endmode) c----------------------------------------------------------------------- c periodic boudary conditions. c----------------------------------------------------------------------- - CASE("periodic") + case(2) ! 2 = Periodic c----------------------------------------------------------------------- c s'0(x0)=s'm-1(xm). c----------------------------------------------------------------------- - DO iqty=1,nqty - IF (ABS(spl%fs(0,iqty)-spl%fs(spl%mx,iqty)) > 1E-15) THEN - WRITE(*,*) + do iqty=1,nqty + if (ABS(spl%fs(0,iqty)-spl%fs(spl%mx,iqty)) > 1E-15) then + write(*,*) $ "Warning: first and last points are different. - $ IQTY= ",IQTY,", averaged value is used."// - $ TRIM(endmode) + $ IQTY= ",IQTY,", averaged value is used." +c ,endmode spl%fs(0,iqty)=(spl%fs(0,iqty)+spl%fs(spl%mx,iqty))*0.5 spl%fs(spl%mx,iqty)=spl%fs(0,iqty) - ENDIF - ENDDO + endif + enddo locmat0(1,nvar+3)=1 locmat0(1,nvar+4)=-1 @@ -594,21 +594,21 @@ SUBROUTINE spline_fit_ha(spl,endmode) locmat0(5,nvar+2)=2 locmat0(5,nvar+5)=-1 - spl%periodic=.TRUE. + spl%periodic=.true. c----------------------------------------------------------------------- c unrecognized boundary condition. c----------------------------------------------------------------------- - CASE DEFAULT - CALL program_stop - $ ("Cannot recognize endmode = "//TRIM(endmode)) - END SELECT + case default + call program_stop + $ ("Cannot recognize endmode") + end select c----------------------------------------------------------------------- c fill global matrix at x0 c----------------------------------------------------------------------- istart=imap(1,0) jstart=imap(1,0) tmpmat=locmat0(:,nvar+1:3*nvar) - CALL spline_fill_matrix(mat,tmpmat,istart,jstart,kl,ku) + call spline_fill_matrix(mat,tmpmat,istart,jstart,kl,ku) rhs(istart:istart+nvar-1,:)=locrhs0 c----------------------------------------------------------------------- c fill global matrix at xm @@ -616,44 +616,44 @@ SUBROUTINE spline_fit_ha(spl,endmode) istart=imap(1,spl%mx-1) jstart=imap(1,spl%mx-2) tmpmat=locmat1(:,1:2*nvar) - CALL spline_fill_matrix(mat,tmpmat,istart,jstart,kl,ku) + call spline_fill_matrix(mat,tmpmat,istart,jstart,kl,ku) rhs(istart:istart+nvar-1,:)=locrhs1 c----------------------------------------------------------------------- c solve global matrix c----------------------------------------------------------------------- - CALL dgbtrf(ndim,ndim,kl,ku,mat,ldab,ipiv,info) - IF (info .NE. 0) THEN - CALL program_stop + call dgbtrf(ndim,ndim,kl,ku,mat,ldab,ipiv,info) + if (info .NE. 0) then + call program_stop $ ("Error: LU factorization of spline matrix info ne 0") - ENDIF - CALL dgbtrs("N",ndim,kl,ku,nqty,mat,ldab,ipiv,rhs,ndim,info ) - IF (info .NE. 0) THEN - CALL program_stop + endif + call dgbtrs("N",ndim,kl,ku,nqty,mat,ldab,ipiv,rhs,ndim,info ) + if (info .NE. 0) then + call program_stop $ ("Error: solve spline matrix info ne 0") - ENDIF + endif c----------------------------------------------------------------------- c get spl%fs1. c----------------------------------------------------------------------- - DO imx=0, spl%mx-1 - DO icoef=1,nvar + do imx=0, spl%mx-1 + do icoef=1,nvar coef(icoef,imx,:)=rhs(imap(icoef,imx),:) - ENDDO + enddo spl%fs1(imx,:)=coef(3,imx,:) - ENDDO + enddo dx=spl%xs(imx)-spl%xs(imx-1) spl%fs1(imx,:)=coef(3,imx-1,:) $ +dx*(coef(2,imx-1,:)*2+dx*coef(1,imx-1,:)*3) - DEALLOCATE (coef,imap) - DEALLOCATE (fs) - DEALLOCATE(mat,rhs,ipiv) - DEALLOCATE(locmat,locmat0,locmat1,tmpmat) - DEALLOCATE(locrhs,locrhs0,locrhs1) + deallocate (coef,imap) + deallocate (fs) + deallocate(mat,rhs,ipiv) + deallocate(locmat,locmat0,locmat1,tmpmat) + deallocate(locrhs,locrhs0,locrhs1) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_fit_ha + return + end subroutine spline_fit_ha c----------------------------------------------------------------------- c subprogram 7. spline_fac. c sets up matrix for cubic spline fitting. @@ -661,29 +661,29 @@ END SUBROUTINE spline_fit_ha c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_fac(spl,a,b,cl,cr,endmode) + subroutine spline_fac(spl,a,b,cl,cr,endmode) - TYPE(spline_type), INTENT(IN) :: spl - REAL(r8), DIMENSION(-1:1,0:spl%mx), INTENT(OUT) :: a - REAL(r8), DIMENSION(spl%mx), INTENT(OUT) :: b - REAL(r8), DIMENSION(4), INTENT(OUT) :: cl,cr - CHARACTER(*), INTENT(IN) :: endmode + type(spline_type), intent(in) :: spl + real(r8), dimension(-1:1,0:spl%mx), intent(out) :: a + real(r8), dimension(spl%mx), intent(out) :: b + real(r8), dimension(4), intent(out) :: cl,cr + integer, intent(in) :: endmode - INTEGER :: j + integer :: j c----------------------------------------------------------------------- c compute interior matrix. c----------------------------------------------------------------------- b=1/(spl%xs(1:spl%mx)-spl%xs(0:spl%mx-1)) - DO j=1,spl%mx-1 + do j=1,spl%mx-1 a(-1,j)=b(j) a(0,j)=2*(b(j)+b(j+1)) a(1,j)=b(j+1) - ENDDO + enddo c----------------------------------------------------------------------- c extrapolation boundary conditions. c----------------------------------------------------------------------- - SELECT CASE(endmode) - CASE("extrap") + select case(endmode) + case(3) ! 3 = Extrapolate b=b*b cl(1)=(spl%xs(0)*(3*spl%xs(0) $ -2*(spl%xs(1)+spl%xs(2)+spl%xs(3))) @@ -723,11 +723,11 @@ SUBROUTINE spline_fac(spl,a,b,cl,cr,endmode) $ /((spl%xs(spl%mx-3)-spl%xs(spl%mx)) $ *(spl%xs(spl%mx-3)-spl%xs(spl%mx-1)) $ *(spl%xs(spl%mx-3)-spl%xs(spl%mx-2))) - CALL spline_triluf(a(:,1:spl%mx-1)) + call spline_triluf(a(:,1:spl%mx-1)) c----------------------------------------------------------------------- c not-a-knot boundary conditions. c----------------------------------------------------------------------- - CASE("not-a-knot") + case(4) ! 4 = not-a-knot b=b*b a(0,1)=a(0,1)+(spl%xs(2)+spl%xs(0)-2*spl%xs(1))*b(1) a(1,1)=a(1,1)+(spl%xs(2)-spl%xs(1))*b(1) @@ -736,27 +736,27 @@ SUBROUTINE spline_fac(spl,a,b,cl,cr,endmode) $ -spl%xs(spl%mx))*b(spl%mx) a(-1,spl%mx-1)=a(-1,spl%mx-1) $ +(spl%xs(spl%mx-1)-spl%xs(spl%mx-2))*b(spl%mx) - CALL spline_triluf(a(:,1:spl%mx-1)) + call spline_triluf(a(:,1:spl%mx-1)) c----------------------------------------------------------------------- c periodic boundary conditions. c----------------------------------------------------------------------- - CASE("periodic") + case(2) ! 2 = Periodic a(0,0:spl%mx:spl%mx)=2*(b(spl%mx)+b(1)) a(1,0)=b(1) a(-1,0)=b(spl%mx) b=b*b - CALL spline_sherman(a(:,0:spl%mx-1)) + call spline_sherman(a(:,0:spl%mx-1)) c----------------------------------------------------------------------- c unrecognized boundary condition. c----------------------------------------------------------------------- - CASE DEFAULT - CALL program_stop("Cannot recognize endmode = "//TRIM(endmode)) - END SELECT + case default + call program_stop("Cannot recognize endmode") + end select c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_fac + return + end subroutine spline_fac c----------------------------------------------------------------------- c subprogram 8. spline_eval. c evaluates real cubic spline function. @@ -764,45 +764,45 @@ END SUBROUTINE spline_fac c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_eval(spl,x,mode) + subroutine spline_eval(spl,x,mode) - TYPE(spline_type), INTENT(INOUT) :: spl - REAL(r8), INTENT(IN) :: x - INTEGER, INTENT(IN) :: mode + type(spline_type), intent(inout) :: spl + real(r8), intent(in) :: x + integer, intent(in) :: mode - INTEGER :: iqty,iside - REAL(r8) :: xx,d,z,z1,xfac,dx - REAL(r8) :: g,g1,g2,g3 + integer :: iqty,iside + real(r8) :: xx,d,z,z1,xfac,dx + real(r8) :: g,g1,g2,g3 c----------------------------------------------------------------------- c preliminary computations. c----------------------------------------------------------------------- xx=x spl%ix=MAX(spl%ix,0) - spl%ix=MIN(spl%ix,spl%mx-1) + spl%ix=Min(spl%ix,spl%mx-1) c----------------------------------------------------------------------- c normalize interval for periodic splines. c----------------------------------------------------------------------- - IF(spl%periodic)THEN - DO - IF(xx < spl%xs(spl%mx))EXIT + if(spl%periodic)then + do + if(xx < spl%xs(spl%mx))EXIT xx=xx-spl%xs(spl%mx) - ENDDO - DO - IF(xx >= spl%xs(0))EXIT + enddo + do + if(xx >= spl%xs(0))EXIT xx=xx+spl%xs(spl%mx) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c find cubic spline interval. c----------------------------------------------------------------------- - DO - IF(xx >= spl%xs(spl%ix).OR.spl%ix <= 0)EXIT + do + if(xx >= spl%xs(spl%ix).OR.spl%ix <= 0)EXIT spl%ix=spl%ix-1 - ENDDO - DO - IF(xx < spl%xs(spl%ix+1).OR.spl%ix >= spl%mx-1)EXIT + enddo + do + if(xx < spl%xs(spl%ix+1).OR.spl%ix >= spl%mx-1)EXIT spl%ix=spl%ix+1 - ENDDO + enddo c----------------------------------------------------------------------- c evaluate offset and related quantities. c----------------------------------------------------------------------- @@ -819,59 +819,59 @@ SUBROUTINE spline_eval(spl,x,mode) c----------------------------------------------------------------------- c evaluate first derivatives. c----------------------------------------------------------------------- - IF(mode > 0)THEN + if(mode > 0)then spl%f1=6*(spl%fs(spl%ix+1,1:spl%nqty) $ -spl%fs(spl%ix,1:spl%nqty))*z*z1/d $ +spl%fs1(spl%ix,1:spl%nqty)*z1*(3*z1-2) $ +spl%fs1(spl%ix+1,1:spl%nqty)*z*(3*z-2) - ENDIF + endif c----------------------------------------------------------------------- c evaluate second derivatives. c----------------------------------------------------------------------- - IF(mode > 1)THEN + if(mode > 1)then spl%f2=(6*(spl%fs(spl%ix+1,1:spl%nqty) $ -spl%fs(spl%ix,1:spl%nqty))*(z1-z)/d $ -spl%fs1(spl%ix,1:spl%nqty)*(6*z1-2) $ +spl%fs1(spl%ix+1,1:spl%nqty)*(6*z-2))/d - ENDIF + endif c----------------------------------------------------------------------- c evaluate third derivatives. c----------------------------------------------------------------------- - IF(mode > 2)THEN + if(mode > 2)then spl%f3=(12*(spl%fs(spl%ix,1:spl%nqty) $ -spl%fs(spl%ix+1,1:spl%nqty))/d $ +6*(spl%fs1(spl%ix,1:spl%nqty) $ +spl%fs1(spl%ix+1,1:spl%nqty)))/(d*d) - ENDIF + endif c----------------------------------------------------------------------- c restore powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dx=x-spl%x0(iside) - DO iqty=1,spl%nqty - IF(spl%xpower(iside,iqty) == 0)CYCLE + do iqty=1,spl%nqty + if(spl%xpower(iside,iqty) == 0)cycle xfac=ABS(dx)**spl%xpower(iside,iqty) g=spl%f(iqty)*xfac - IF(mode > 0)g1=(spl%f1(iqty)+spl%f(iqty) + if(mode > 0)g1=(spl%f1(iqty)+spl%f(iqty) $ *spl%xpower(iside,iqty)/dx)*xfac - IF(mode > 1)g2=(spl%f2(iqty)+spl%xpower(iside,iqty)/dx + if(mode > 1)g2=(spl%f2(iqty)+spl%xpower(iside,iqty)/dx $ *(2*spl%f1(iqty)+(spl%xpower(iside,iqty)-1) $ *spl%f(iqty)/dx))*xfac - IF(mode > 2)g3=(spl%f3(iqty)+spl%xpower(iside,iqty)/dx + if(mode > 2)g3=(spl%f3(iqty)+spl%xpower(iside,iqty)/dx $ *(3*spl%f2(iqty)+(spl%xpower(iside,iqty)-1)/dx $ *(3*spl%f1(iqty)+(spl%xpower(iside,iqty)-2)/dx $ *spl%f(iqty))))*xfac spl%f(iqty)=g - IF(mode > 0)spl%f1(iqty)=g1 - IF(mode > 1)spl%f2(iqty)=g2 - IF(mode > 2)spl%f3(iqty)=g3 - ENDDO - ENDDO + if(mode > 0)spl%f1(iqty)=g1 + if(mode > 1)spl%f2(iqty)=g2 + if(mode > 2)spl%f3(iqty)=g3 + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_eval + return + end subroutine spline_eval c----------------------------------------------------------------------- c subprogram 9. spline_eval_external c evaluates real cubic spline with external arrays (parallel). @@ -879,117 +879,130 @@ END SUBROUTINE spline_eval c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_eval_external(spl,x,s_ix,s_f,s_f1,s_f2,s_f3) + subroutine spline_eval_external(spl,x,s_f,s_f1,s_f2,s_f3) + + type(spline_type), intent(in) :: spl + real(r8), intent(in) :: x - TYPE(spline_type), INTENT(IN) :: spl - REAL(r8), INTENT(IN) :: x + integer :: iqty,iside + integer :: ix, i_low, i_high, i_mid + real(r8) :: xx,d,z,z1,xfac,dx + real(r8) :: g,g1,g2,g3 - INTEGER :: iqty,iside - REAL(r8) :: xx,d,z,z1,xfac,dx - REAL(r8) :: g,g1,g2,g3 - INTEGER, INTENT(INOUT) :: s_ix - REAL(r8), DIMENSION(:), INTENT(OUT) :: s_f - REAL(r8), DIMENSION(:), OPTIONAL, INTENT(OUT) :: s_f1,s_f2,s_f3 + real(r8), dimension(:), intent(out) :: s_f + real(r8), dimension(:), optional, intent(out) :: s_f1,s_f2,s_f3 + c----------------------------------------------------------------------- c preliminary computations. c----------------------------------------------------------------------- xx=x - s_ix=MAX(s_ix,0) - s_ix=MIN(s_ix,spl%mx-1) c----------------------------------------------------------------------- c normalize interval for periodic splines. c----------------------------------------------------------------------- - IF(spl%periodic)THEN - DO - IF(xx < spl%xs(spl%mx))EXIT + if(spl%periodic)then + do + if(xx < spl%xs(spl%mx))EXIT xx=xx-spl%xs(spl%mx) - ENDDO - DO - IF(xx >= spl%xs(0))EXIT + enddo + do + if(xx >= spl%xs(0))EXIT xx=xx+spl%xs(spl%mx) - ENDDO - ENDIF + enddo + endif + c----------------------------------------------------------------------- -c find cubic spline interval. +c find cubic spline interval using Binary Search c----------------------------------------------------------------------- - DO - IF(xx >= spl%xs(s_ix).OR.s_ix <= 0)EXIT - s_ix=s_ix-1 - ENDDO - DO - IF(xx < spl%xs(s_ix+1).OR.s_ix >= spl%mx-1)EXIT - s_ix=s_ix+1 - ENDDO + i_low = 0 + i_high = spl%mx - 1 + + do while (i_low <= i_high) + i_mid = i_low + (i_high - i_low) / 2 + if (xx < spl%xs(i_mid)) then + i_high = i_mid - 1 + else if (xx >= spl%xs(i_mid + 1)) then + i_low = i_mid + 1 + else + ! We found the interval: xs(i_mid) <= xx < xs(i_mid+1) + ix = i_mid + exit + endif + enddo + + ! If the search fails, treat it as a boundary value. + if (i_low > i_high) then + ix = min(max(i_low - 1, 0), spl%mx - 1) + endif c----------------------------------------------------------------------- c evaluate offset and related quantities. c----------------------------------------------------------------------- - d=spl%xs(s_ix+1)-spl%xs(s_ix) - z=(xx-spl%xs(s_ix))/d + d=spl%xs(ix+1)-spl%xs(ix) + z=(xx-spl%xs(ix))/d z1=1-z c----------------------------------------------------------------------- c evaluate functions. c----------------------------------------------------------------------- - s_f=spl%fs(s_ix,1:spl%nqty)*z1*z1*(3-2*z1) - $ +spl%fs(s_ix+1,1:spl%nqty)*z*z*(3-2*z) - $ +d*z*z1*(spl%fs1(s_ix,1:spl%nqty)*z1 - $ -spl%fs1(s_ix+1,1:spl%nqty)*z) + s_f=spl%fs(ix,1:spl%nqty)*z1*z1*(3-2*z1) + $ +spl%fs(ix+1,1:spl%nqty)*z*z*(3-2*z) + $ +d*z*z1*(spl%fs1(ix,1:spl%nqty)*z1 + $ -spl%fs1(ix+1,1:spl%nqty)*z) c----------------------------------------------------------------------- c evaluate first derivatives. c----------------------------------------------------------------------- - IF(PRESENT(s_f1))THEN - s_f1=6*(spl%fs(s_ix+1,1:spl%nqty) - $ -spl%fs(s_ix,1:spl%nqty))*z*z1/d - $ +spl%fs1(s_ix,1:spl%nqty)*z1*(3*z1-2) - $ +spl%fs1(s_ix+1,1:spl%nqty)*z*(3*z-2) - ENDIF + if(present(s_f1))then + s_f1=6*(spl%fs(ix+1,1:spl%nqty) + $ -spl%fs(ix,1:spl%nqty))*z*z1/d + $ +spl%fs1(ix,1:spl%nqty)*z1*(3*z1-2) + $ +spl%fs1(ix+1,1:spl%nqty)*z*(3*z-2) + endif c----------------------------------------------------------------------- c evaluate second derivatives. c----------------------------------------------------------------------- - IF(PRESENT(s_f2))THEN - s_f2=(6*(spl%fs(s_ix+1,1:spl%nqty) - $ -spl%fs(s_ix,1:spl%nqty))*(z1-z)/d - $ -spl%fs1(s_ix,1:spl%nqty)*(6*z1-2) - $ +spl%fs1(s_ix+1,1:spl%nqty)*(6*z-2))/d - ENDIF + if(present(s_f2))then + s_f2=(6*(spl%fs(ix+1,1:spl%nqty) + $ -spl%fs(ix,1:spl%nqty))*(z1-z)/d + $ -spl%fs1(ix,1:spl%nqty)*(6*z1-2) + $ +spl%fs1(ix+1,1:spl%nqty)*(6*z-2))/d + endif c----------------------------------------------------------------------- c evaluate third derivatives. c----------------------------------------------------------------------- - IF(PRESENT(s_f3))THEN - s_f3=(12*(spl%fs(s_ix,1:spl%nqty) - $ -spl%fs(s_ix+1,1:spl%nqty))/d - $ +6*(spl%fs1(s_ix,1:spl%nqty) - $ +spl%fs1(s_ix+1,1:spl%nqty)))/(d*d) - ENDIF + if(present(s_f3))then + s_f3=(12*(spl%fs(ix,1:spl%nqty) + $ -spl%fs(ix+1,1:spl%nqty))/d + $ +6*(spl%fs1(ix,1:spl%nqty) + $ +spl%fs1(ix+1,1:spl%nqty)))/(d*d) + endif c----------------------------------------------------------------------- c restore powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dx=x-spl%x0(iside) - DO iqty=1,spl%nqty - IF(spl%xpower(iside,iqty) == 0)CYCLE + do iqty=1,spl%nqty + if(spl%xpower(iside,iqty) == 0)cycle xfac=ABS(dx)**spl%xpower(iside,iqty) g=s_f(iqty)*xfac - IF(PRESENT(s_f1))g1=(s_f1(iqty)+s_f(iqty) + if(present(s_f1))g1=(s_f1(iqty)+s_f(iqty) $ *spl%xpower(iside,iqty)/dx)*xfac - IF(PRESENT(s_f2))g2=(s_f2(iqty)+spl%xpower(iside,iqty)/dx + if(present(s_f2))g2=(s_f2(iqty)+spl%xpower(iside,iqty)/dx $ *(2*s_f1(iqty)+(spl%xpower(iside,iqty)-1) $ *s_f(iqty)/dx))*xfac - IF(PRESENT(s_f3))g3=(s_f3(iqty)+spl%xpower(iside,iqty)/dx + if(present(s_f3))g3=(s_f3(iqty)+spl%xpower(iside,iqty)/dx $ *(3*s_f2(iqty)+(spl%xpower(iside,iqty)-1)/dx $ *(3*s_f1(iqty)+(spl%xpower(iside,iqty)-2)/dx $ *s_f(iqty))))*xfac s_f(iqty)=g - IF(PRESENT(s_f1))s_f1(iqty)=g1 - IF(PRESENT(s_f2))s_f2(iqty)=g2 - IF(PRESENT(s_f3))s_f3(iqty)=g3 - ENDDO - ENDDO + if(present(s_f1))s_f1(iqty)=g1 + if(present(s_f2))s_f2(iqty)=g2 + if(present(s_f3))s_f3(iqty)=g3 + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_eval_external + return + end subroutine spline_eval_external c----------------------------------------------------------------------- c subprogram 10. spline_all_eval. c evaluates cubic spline function. @@ -997,17 +1010,17 @@ END SUBROUTINE spline_eval_external c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_all_eval(spl,z,f,f1,f2,f3,mode) + subroutine spline_all_eval(spl,z,f,f1,f2,f3,mode) - TYPE(spline_type), INTENT(INOUT) :: spl - REAL(r8), INTENT(IN) :: z - REAL(r8), DIMENSION(spl%mx,spl%nqty), INTENT(OUT) :: f,f1,f2,f3 - INTEGER, INTENT(IN) :: mode + type(spline_type), intent(inout) :: spl + real(r8), intent(in) :: z + real(r8), dimension(spl%mx,spl%nqty), intent(out) :: f,f1,f2,f3 + integer, intent(in) :: mode - INTEGER :: iqty,nqty,n,iside - REAL(r8) :: z1 - REAL(r8), DIMENSION(spl%mx) :: d,xfac,dx - REAL(r8), DIMENSION(spl%mx) :: g,g1,g2,g3 + integer :: iqty,nqty,n,iside + real(r8) :: z1 + real(r8), dimension(spl%mx) :: d,xfac,dx + real(r8), dimension(spl%mx) :: g,g1,g2,g3 c----------------------------------------------------------------------- c evaluate offset and related quantities. c----------------------------------------------------------------------- @@ -1018,70 +1031,70 @@ SUBROUTINE spline_all_eval(spl,z,f,f1,f2,f3,mode) c----------------------------------------------------------------------- c evaluate functions. c----------------------------------------------------------------------- - DO iqty=1,nqty + do iqty=1,nqty f(:,iqty)=spl%fs(0:n-1,iqty)*z1*z1*(3-2*z1) $ +spl%fs(1:n,iqty)*z*z*(3-2*z) $ +d*z*z1*(spl%fs1(0:n-1,iqty)*z1-spl%fs1(1:n,iqty)*z) - ENDDO + enddo c----------------------------------------------------------------------- c evaluate first derivatives. c----------------------------------------------------------------------- - IF(mode > 0)THEN - DO iqty=1,nqty + if(mode > 0)then + do iqty=1,nqty f1(:,iqty)=6*(spl%fs(1:n,iqty)-spl%fs(0:n-1,iqty))*z*z1/d $ +spl%fs1(0:n-1,iqty)*z1*(3*z1-2) $ +spl%fs1(1:n,iqty)*z*(3*z-2) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c evaluate second derivatives. c----------------------------------------------------------------------- - IF(mode > 1)THEN - DO iqty=1,nqty + if(mode > 1)then + do iqty=1,nqty f2(:,iqty)=(6*(spl%fs(1:n,iqty)-spl%fs(0:n-1,iqty))*(z1-z)/d $ -spl%fs1(0:n-1,iqty)*(6*z1-2) $ +spl%fs1(1:n,iqty)*(6*z-2))/d - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c evaluate third derivatives. c----------------------------------------------------------------------- - IF(mode > 2)THEN - DO iqty=1,nqty + if(mode > 2)then + do iqty=1,nqty f3(:,iqty)=(12*(spl%fs(0:n-1,iqty)-spl%fs(1:n,iqty))/d $ +6*(spl%fs1(0:n-1,iqty)+spl%fs1(1:n,iqty)))/(d*d) - ENDDO - ENDIF + enddo + endif c----------------------------------------------------------------------- c restore powers. c----------------------------------------------------------------------- - DO iside=1,2 + do iside=1,2 dx=(spl%xs(0:spl%mx-1)+z*d(1:spl%mx))-spl%x0(iside) - DO iqty=1,spl%nqty - IF(spl%xpower(iside,iqty) == 0)CYCLE + do iqty=1,spl%nqty + if(spl%xpower(iside,iqty) == 0)cycle xfac=ABS(dx)**spl%xpower(iside,iqty) g=f(:,iqty)*xfac - IF(mode > 0)g1=(f1(:,iqty) + if(mode > 0)g1=(f1(:,iqty) $ +f(:,iqty)*spl%xpower(iside,iqty)/dx)*xfac - IF(mode > 1)g2=(f2(:,iqty)+spl%xpower(iside,iqty)/dx + if(mode > 1)g2=(f2(:,iqty)+spl%xpower(iside,iqty)/dx $ *(2*f1(:,iqty)+(spl%xpower(iside,iqty)-1) $ *f(:,iqty)/dx))*xfac $ - IF(mode > 2)g3=(f3(:,iqty)+spl%xpower(iside,iqty)/dx + if(mode > 2)g3=(f3(:,iqty)+spl%xpower(iside,iqty)/dx $ *(3*f2(:,iqty)+(spl%xpower(iside,iqty)-1)/dx $ *(3*f1(:,iqty)+(spl%xpower(iside,iqty)-2)/dx $ *f(:,iqty))))*xfac f(:,iqty)=g - IF(mode > 0)f1(:,iqty)=g1 - IF(mode > 1)f2(:,iqty)=g2 - IF(mode > 2)f3(:,iqty)=g3 - ENDDO - ENDDO + if(mode > 0)f1(:,iqty)=g1 + if(mode > 1)f2(:,iqty)=g2 + if(mode > 2)f3(:,iqty)=g3 + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_all_eval + return + end subroutine spline_all_eval c----------------------------------------------------------------------- c subprogram 11. spline_write1. c produces ascii and binary output for real cubic spline fits. @@ -1089,81 +1102,81 @@ END SUBROUTINE spline_all_eval c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_write1(spl,out,bin,iua,iub,interp) + subroutine spline_write1(spl,out,bin,iua,iub,interp) - TYPE(spline_type), INTENT(INOUT) :: spl - LOGICAL, INTENT(IN) :: out,bin - INTEGER, INTENT(IN) :: iua,iub - LOGICAL, INTENT(IN) :: interp + type(spline_type), intent(inout) :: spl + logical, intent(in) :: out,bin + integer, intent(in) :: iua,iub + logical, intent(in) :: interp - CHARACTER(30) :: format1,format2 - INTEGER :: i,j - REAL(r8) :: x,dx + character(30) :: format1,format2 + integer :: i,j + real(r8) :: x,dx c----------------------------------------------------------------------- c formats. c----------------------------------------------------------------------- - 10 FORMAT('(/3x,"ix",',i2.2,'(4x,a6,1x)/)') - 20 FORMAT('(i5,1p,',i2.2,'e11.3)') -! 30 FORMAT('(/3x,"ix",2x,"j",',i2.2,'(4x,a6,1x)/)') + 10 format('(/3x,"ix",',i2.2,'(4x,a6,1x)/)') + 20 format('(i5,1p,',i2.2,'e11.3)') +! 30 format('(/3x,"ix",2x,"j",',i2.2,'(4x,a6,1x)/)') c----------------------------------------------------------------------- c abort. c----------------------------------------------------------------------- - IF(.NOT.out.AND..NOT.bin)RETURN + if(.not.out.and..not.bin)return c----------------------------------------------------------------------- c print node values. c----------------------------------------------------------------------- - IF(out)THEN - WRITE(format1,10)spl%nqty+1 - WRITE(format2,20)spl%nqty+1 - WRITE(iua,'(/1x,a)')'node values:' - WRITE(iua,format1)spl%title(0:spl%nqty) - ENDIF - DO i=0,spl%mx - CALL spline_eval(spl,spl%xs(i),0) - IF(out)WRITE(iua,format2)i,spl%xs(i),spl%f - IF(bin)WRITE(iub)REAL(spl%xs(i),4),REAL(spl%f,4) - ENDDO - IF(out)WRITE(iua,format1)spl%title(0:spl%nqty) - IF(bin)WRITE(iub) - IF(.NOT. interp)RETURN + if(out)then + write(format1,10)spl%nqty+1 + write(format2,20)spl%nqty+1 + write(iua,'(/1x,a)')'node values:' + write(iua,format1)spl%title(0:spl%nqty) + endif + do i=0,spl%mx + call spline_eval(spl,spl%xs(i),0) + if(out)write(iua,format2)i,spl%xs(i),spl%f + if(bin)write(iub)real(spl%xs(i),4),real(spl%f,4) + enddo + if(out)write(iua,format1)spl%title(0:spl%nqty) + if(bin)write(iub) + if(.not. interp)return c----------------------------------------------------------------------- c print header for interpolated values. c----------------------------------------------------------------------- - IF(out)THEN - WRITE(iua,'(/1x,a)')'interpolated values:' - WRITE(iua,format1)spl%title(0:spl%nqty) - ENDIF + if(out)then + write(iua,'(/1x,a)')'interpolated values:' + write(iua,format1)spl%title(0:spl%nqty) + endif c----------------------------------------------------------------------- c print interpolated values. c----------------------------------------------------------------------- - DO i=0,spl%mx-1 + do i=0,spl%mx-1 dx=(spl%xs(i+1)-spl%xs(i))/4 - DO j=0,4 + do j=0,4 x=spl%xs(i)+j*dx - CALL spline_eval(spl,x,0) - IF(out)WRITE(iua,format2)i,x,spl%f - IF(bin)WRITE(iub)REAL(x,4),REAL(spl%f,4) - ENDDO - ENDDO + call spline_eval(spl,x,0) + if(out)write(iua,format2)i,x,spl%f + if(bin)write(iub)real(x,4),real(spl%f,4) + enddo + enddo c----------------------------------------------------------------------- c print final interpolated values. c----------------------------------------------------------------------- x=spl%xs(spl%mx) - CALL spline_eval(spl,x,0) - IF(out)THEN - WRITE(iua,format2)i,x,spl%f - WRITE(iua,format1)spl%title - ENDIF - IF(bin)THEN - WRITE(iub)REAL(x,4),REAL(spl%f,4) - WRITE(iub) - CALL bin_close(bin_unit) - ENDIF + call spline_eval(spl,x,0) + if(out)then + write(iua,format2)i,x,spl%f + write(iua,format1)spl%title + endif + if(bin)then + write(iub)real(x,4),real(spl%f,4) + write(iub) + call bin_close(bin_unit) + endif c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_write1 + return + end subroutine spline_write1 c----------------------------------------------------------------------- c subprogram 12. spline_write2. c produces ascii and binary output for real cubic spline fits. @@ -1171,87 +1184,87 @@ END SUBROUTINE spline_write1 c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_write2(spl,out,bin,iua,iub,interp) + subroutine spline_write2(spl,out,bin,iua,iub,interp) - TYPE(spline_type), INTENT(INOUT) :: spl - LOGICAL, INTENT(IN) :: out,bin - INTEGER, INTENT(IN) :: iua,iub - LOGICAL, INTENT(IN) :: interp + type(spline_type), intent(inout) :: spl + logical, intent(in) :: out,bin + integer, intent(in) :: iua,iub + logical, intent(in) :: interp - CHARACTER(30) :: format1,format2 - INTEGER :: i,j,iz - REAL(r8) :: x,dx,z - REAL(r8), DIMENSION(spl%mx,spl%nqty) :: f, f1,f2,f3 - REAL(r8), DIMENSION(0:4*spl%mx,spl%nqty) :: g + character(30) :: format1,format2 + integer :: i,j,iz + real(r8) :: x,dx,z + real(r8), dimension(spl%mx,spl%nqty) :: f, f1,f2,f3 + real(r8), dimension(0:4*spl%mx,spl%nqty) :: g c----------------------------------------------------------------------- c formats. c----------------------------------------------------------------------- - 10 FORMAT('(/4x,"i",',i2.2,'(4x,a6,1x)/)') - 20 FORMAT('(i5,1p,',i2.2,'e11.3)') -! 30 FORMAT('(/4x,"i",2x,"j",',i2.2,'(4x,a6,1x)/)') + 10 format('(/4x,"i",',i2.2,'(4x,a6,1x)/)') + 20 format('(i5,1p,',i2.2,'e11.3)') +! 30 format('(/4x,"i",2x,"j",',i2.2,'(4x,a6,1x)/)') c----------------------------------------------------------------------- c compute values. c----------------------------------------------------------------------- z=0 - DO iz=0,3 - CALL spline_all_eval(spl,z,f,f1,f2,f3,0) + do iz=0,3 + call spline_all_eval(spl,z,f,f1,f2,f3,0) g(iz:4*spl%mx-1:4,:)=f z=z+.25_r8 - ENDDO - CALL spline_eval(spl,spl%xs(spl%mx),0) + enddo + call spline_eval(spl,spl%xs(spl%mx),0) g(4*spl%mx,:)=spl%f c----------------------------------------------------------------------- c print node values. c----------------------------------------------------------------------- - IF(.NOT.out.AND..NOT.bin)RETURN - IF(out)THEN - WRITE(format1,10)spl%nqty+1 - WRITE(format2,20)spl%nqty+1 - WRITE(iua,'(/1x,a)')'node values:' - WRITE(iua,format1)spl%title(0:spl%nqty) - ENDIF - DO i=0,spl%mx - IF(out)WRITE(iua,format2)i,spl%xs(i),g(4*i,:) - IF(bin)WRITE(iub)REAL(spl%xs(i),4),REAL(g(4*i,:),4) - ENDDO - IF(out)WRITE(iua,format1)spl%title(0:spl%nqty) - IF(bin)WRITE(iub) + if(.not.out.and..not.bin)return + if(out)then + write(format1,10)spl%nqty+1 + write(format2,20)spl%nqty+1 + write(iua,'(/1x,a)')'node values:' + write(iua,format1)spl%title(0:spl%nqty) + endif + do i=0,spl%mx + if(out)write(iua,format2)i,spl%xs(i),g(4*i,:) + if(bin)write(iub)real(spl%xs(i),4),real(g(4*i,:),4) + enddo + if(out)write(iua,format1)spl%title(0:spl%nqty) + if(bin)write(iub) c----------------------------------------------------------------------- c print header for interpolated values. c----------------------------------------------------------------------- - IF(.NOT. interp)RETURN - IF(out)THEN - WRITE(iua,'(/1x,a)')'interpolated values:' - WRITE(iua,format1)spl%title(0:spl%nqty) - ENDIF + if(.not. interp)return + if(out)then + write(iua,'(/1x,a)')'interpolated values:' + write(iua,format1)spl%title(0:spl%nqty) + endif c----------------------------------------------------------------------- c print interpolated values. c----------------------------------------------------------------------- - DO i=0,spl%mx-1 + do i=0,spl%mx-1 dx=(spl%xs(i+1)-spl%xs(i))/4 - DO j=0,4 + do j=0,4 x=spl%xs(i)+j*dx - IF(out)WRITE(iua,format2)i,x,g(4*i+j,:) - IF(bin)WRITE(iub)REAL(x,4),REAL(g(4*i+j,:),4) - ENDDO - IF(out)WRITE(iua,'(1x)') - ENDDO + if(out)write(iua,format2)i,x,g(4*i+j,:) + if(bin)write(iub)real(x,4),real(g(4*i+j,:),4) + enddo + if(out)write(iua,'(1x)') + enddo c----------------------------------------------------------------------- c print final interpolated values. c----------------------------------------------------------------------- - IF(out)THEN - WRITE(iua,format2)i,x,g(spl%mx*4,:) - WRITE(iua,format1)spl%title(0:spl%nqty) - ENDIF - IF(bin)THEN - WRITE(iub)REAL(x,4),REAL(g(spl%mx*4,:),4) - WRITE(iub) - ENDIF + if(out)then + write(iua,format2)i,x,g(spl%mx*4,:) + write(iua,format1)spl%title(0:spl%nqty) + endif + if(bin)then + write(iub)real(x,4),real(g(spl%mx*4,:),4) + write(iub) + endif c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_write2 + return + end subroutine spline_write2 c----------------------------------------------------------------------- c subprogram 13. spline_int. c integrates real cubic splines. @@ -1259,54 +1272,54 @@ END SUBROUTINE spline_write2 c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_int(spl) + subroutine spline_int(spl) - TYPE(spline_type), INTENT(INOUT) :: spl + type(spline_type), intent(inout) :: spl - INTEGER :: ix,iqty,ig - REAL(r8), DIMENSION(spl%mx) :: dx - REAL(r8), DIMENSION(spl%mx,spl%nqty) :: term,f,f1,f2,f3 + integer :: ix,iqty,ig + real(r8), dimension(spl%mx) :: dx + real(r8), dimension(spl%mx,spl%nqty) :: term,f,f1,f2,f3 - INTEGER, PARAMETER :: mg=4 - REAL(r8), DIMENSION(mg) :: xg=(1+(/-0.861136311594053_r8, + integer, PARAMETER :: mg=4 + real(r8), dimension(mg) :: xg=(1+(/-0.861136311594053_r8, $ -0.339981043584856_r8,0.339981043584856_r8, $ 0.861136311594053_r8/))/2 - REAL(r8), DIMENSION(mg) :: wg=(/0.347854845137454_r8, + real(r8), dimension(mg) :: wg=(/0.347854845137454_r8, $ 0.652145154862546_r8,0.652145154862546_r8, $ 0.347854845137454_r8/)/2 c----------------------------------------------------------------------- c preliminary computations. c----------------------------------------------------------------------- - IF(.NOT.ALLOCATED(spl%fsi))ALLOCATE(spl%fsi(0:spl%mx,spl%nqty)) + if(.not.allocated(spl%fsi))allocate(spl%fsi(0:spl%mx,spl%nqty)) dx=spl%xs(1:spl%mx)-spl%xs(0:spl%mx-1) term=0 c----------------------------------------------------------------------- c compute integrals over intervals. c----------------------------------------------------------------------- - DO iqty=1,spl%nqty - IF(spl%xpower(1,iqty) == 0 .AND. spl%xpower(2,iqty) == 0)THEN + do iqty=1,spl%nqty + if(spl%xpower(1,iqty) == 0 .and. spl%xpower(2,iqty) == 0)then term(:,iqty)=dx/12 $ *(6*(spl%fs(0:spl%mx-1,iqty)+spl%fs(1:spl%mx,iqty)) $ +dx*(spl%fs1(0:spl%mx-1,iqty)-spl%fs1(1:spl%mx,iqty))) - ELSE - DO ig=1,mg - CALL spline_all_eval(spl,xg(ig),f,f1,f2,f3,0) + else + do ig=1,mg + call spline_all_eval(spl,xg(ig),f,f1,f2,f3,0) term(:,iqty)=term(:,iqty)+dx*wg(ig)*f(:,iqty) - ENDDO - ENDIF - ENDDO + enddo + endif + enddo c----------------------------------------------------------------------- c accumulate over intervals. c----------------------------------------------------------------------- spl%fsi(0,:)=0 - DO ix=1,spl%mx + do ix=1,spl%mx spl%fsi(ix,:)=spl%fsi(ix-1,:)+term(ix,:) - ENDDO + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_int + return + end subroutine spline_int c----------------------------------------------------------------------- c subprogram 14. spline_triluf. c performs tridiagonal LU factorization. @@ -1314,40 +1327,40 @@ END SUBROUTINE spline_int c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_triluf(a) + subroutine spline_triluf(a) - REAL(r8), DIMENSION(-1:,:), INTENT(INOUT) :: a + real(r8), dimension(-1:,:), intent(inout) :: a - INTEGER :: i,j,k,jmin,jmax,n + integer :: i,j,k,jmin,jmax,n c----------------------------------------------------------------------- c begin loop over rows and define limits. c----------------------------------------------------------------------- n=SIZE(a,2) - DO i=1,n + do i=1,n jmin=MAX(1-i,-1) - jmax=MIN(n-i,1) + jmax=Min(n-i,1) c----------------------------------------------------------------------- c compute lower elements. c----------------------------------------------------------------------- - DO j=jmin,-1 - DO k=MAX(jmin,j-1),j-1 + do j=jmin,-1 + do k=MAX(jmin,j-1),j-1 a(j,i)=a(j,i)-a(k,i)*a(j-k,i+k) - ENDDO + enddo a(j,i)=a(j,i)*a(0,i+j) - ENDDO + enddo c----------------------------------------------------------------------- c compute diagonal element c----------------------------------------------------------------------- - DO k=MAX(jmin,-1),-1 + do k=MAX(jmin,-1),-1 a(0,i)=a(0,i)-a(k,i)*a(-k,i+k) - ENDDO + enddo a(0,i)=1/a(0,i) - ENDDO + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_triluf + return + end subroutine spline_triluf c----------------------------------------------------------------------- c subprogram 15. spline_trilus. c performs tridiagonal LU solution. @@ -1355,35 +1368,35 @@ END SUBROUTINE spline_triluf c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_trilus(a,x) + subroutine spline_trilus(a,x) - REAL(r8), DIMENSION(-1:,:), INTENT(IN) :: a - REAL(r8), DIMENSION(:,:), INTENT(INOUT) :: x + real(r8), dimension(-1:,:), intent(in) :: a + real(r8), dimension(:,:), intent(inout) :: x - INTEGER :: i,j,n + integer :: i,j,n c----------------------------------------------------------------------- c down sweep. c----------------------------------------------------------------------- n=SIZE(a,2) - DO i=1,n - DO j=MAX(1-i,-1),-1 + do i=1,n + do j=MAX(1-i,-1),-1 x(i,:)=x(i,:)-a(j,i)*x(i+j,:) - ENDDO - ENDDO + enddo + enddo c----------------------------------------------------------------------- c up sweep. c----------------------------------------------------------------------- - DO i=n,1,-1 - DO j=1,MIN(n-i,1) + do i=n,1,-1 + do j=1,Min(n-i,1) x(i,:)=x(i,:)-a(j,i)*x(i+j,:) - ENDDO + enddo x(i,:)=x(i,:)*a(0,i) - ENDDO + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_trilus + return + end subroutine spline_trilus c----------------------------------------------------------------------- c subprogram 16. spline_sherman. c uses Sherman-Morrison formula to factor periodic matrix. @@ -1391,12 +1404,12 @@ END SUBROUTINE spline_trilus c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_sherman(a) + subroutine spline_sherman(a) - REAL(r8), DIMENSION(-1:,:), INTENT(INOUT) :: a + real(r8), dimension(-1:,:), intent(inout) :: a - INTEGER :: j,n - REAL(r8), DIMENSION(SIZE(a,2),1) :: u + integer :: j,n + real(r8), dimension(SIZE(a,2),1) :: u c----------------------------------------------------------------------- c prepare matrices. c----------------------------------------------------------------------- @@ -1404,14 +1417,14 @@ SUBROUTINE spline_sherman(a) a(0,1)=a(0,1)-a(-1,1) a(0,n)=a(0,n)-a(-1,1) u=RESHAPE((/one,(zero,j=2,n-1),one/),SHAPE(u)) - CALL spline_triluf(a) - CALL spline_trilus(a,u) + call spline_triluf(a) + call spline_trilus(a,u) a(-1,1)=a(-1,1)/(1+a(-1,1)*(u(1,1)+u(n,1))) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_sherman + return + end subroutine spline_sherman c----------------------------------------------------------------------- c subprogram 17. spline_morrison. c uses Sherman-Morrison formula to solve periodic matrix. @@ -1419,27 +1432,27 @@ END SUBROUTINE spline_sherman c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_morrison(a,x) + subroutine spline_morrison(a,x) - REAL(r8), DIMENSION(-1:,:), INTENT(IN) :: a - REAL(r8), DIMENSION(:,:), INTENT(INOUT) :: x + real(r8), dimension(-1:,:), intent(in) :: a + real(r8), dimension(:,:), intent(inout) :: x - INTEGER :: n - REAL(r8), DIMENSION(SIZE(x,1),SIZE(x,2)) :: y + integer :: n + real(r8), dimension(SIZE(x,1),SIZE(x,2)) :: y c----------------------------------------------------------------------- c solve for x. c----------------------------------------------------------------------- n=SIZE(a,2) y=x - CALL spline_trilus(a,y) + call spline_trilus(a,y) x(1,:)=x(1,:)-a(-1,1)*(y(1,:)+y(n,:)) x(n,:)=x(n,:)-a(-1,1)*(y(1,:)+y(n,:)) - CALL spline_trilus(a,x) + call spline_trilus(a,x) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_morrison + return + end subroutine spline_morrison c----------------------------------------------------------------------- c subprogram 18. spline_copy. c copies one spline_type to another. @@ -1447,15 +1460,15 @@ END SUBROUTINE spline_morrison c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_copy(spl1,spl2) + subroutine spline_copy(spl1,spl2) - TYPE(spline_type), INTENT(IN) :: spl1 - TYPE(spline_type), INTENT(INOUT) :: spl2 + type(spline_type), intent(in) :: spl1 + type(spline_type), intent(inout) :: spl2 c----------------------------------------------------------------------- c computations. c----------------------------------------------------------------------- - IF(ALLOCATED(spl2%xs))CALL spline_dealloc(spl2) - CALL spline_alloc(spl2,spl1%mx,spl1%nqty) + if(allocated(spl2%xs))call spline_dealloc(spl2) + call spline_alloc(spl2,spl1%mx,spl1%nqty) spl2%xs=spl1%xs spl2%fs=spl1%fs spl2%fs1=spl1%fs1 @@ -1467,8 +1480,8 @@ SUBROUTINE spline_copy(spl1,spl2) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_copy + return + end subroutine spline_copy c----------------------------------------------------------------------- c subprogram 19. spline_fill_matrix. c fill local matrix into global matrix. @@ -1476,28 +1489,28 @@ END SUBROUTINE spline_copy c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_fill_matrix(mat,locmat,istart,jstart,kl,ku) - INTEGER :: istart,jstart,itot,jtot,i,j,kl,ku,m,n,offset - REAL(r8), DIMENSION(:,:), ALLOCATABLE,INTENT(INOUT) :: mat - REAL(r8), DIMENSION(:,:), ALLOCATABLE,INTENT(IN) :: locmat + subroutine spline_fill_matrix(mat,locmat,istart,jstart,kl,ku) + integer :: istart,jstart,itot,jtot,i,j,kl,ku,m,n,offset + real(r8), dimension(:,:), allocatable,intent(inout) :: mat + real(r8), dimension(:,:), allocatable,intent(in) :: locmat c----------------------------------------------------------------------- c fill matrix. c----------------------------------------------------------------------- itot=SIZE(locmat,1) jtot=SIZE(locmat,2) offset=kl+ku+1 - DO m=1, itot + do m=1, itot i=m+istart-1 - DO n=1, jtot + do n=1, jtot j=n+jstart-1 mat(offset+i-j,j)=mat(offset+i-j,j)+locmat(m,n) - ENDDO - ENDDO + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_fill_matrix + return + end subroutine spline_fill_matrix c----------------------------------------------------------------------- c subprogram 20. spline_get_yp. c get yi' with four points for spline boundary condtion . @@ -1505,17 +1518,17 @@ END SUBROUTINE spline_fill_matrix c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_get_yp(x,y,xi,yip,nqty) - INTEGER, INTENT(IN) :: nqty - INTEGER :: n,nrhs,lda,info,ldb,i - INTEGER, DIMENSION(4) :: ipiv - REAL(r8) :: dx - REAL(r8), INTENT(IN) :: xi - REAL(r8), DIMENSION(nqty),INTENT(OUT) :: yip - REAL(r8), DIMENSION(4), INTENT(IN) :: x - REAL(r8), DIMENSION(4,nqty), INTENT(IN) :: y - REAL(r8), DIMENSION(4,nqty) :: b - REAL(r8), DIMENSION(4,4) :: a + subroutine spline_get_yp(x,y,xi,yip,nqty) + integer, intent(in) :: nqty + integer :: n,nrhs,lda,info,ldb,i + integer, dimension(4) :: ipiv + real(r8) :: dx + real(r8), intent(in) :: xi + real(r8), dimension(nqty),intent(out) :: yip + real(r8), dimension(4), intent(in) :: x + real(r8), dimension(4,nqty), intent(in) :: y + real(r8), dimension(4,nqty) :: b + real(r8), dimension(4,4) :: a n=4 nrhs=nqty lda=N @@ -1525,22 +1538,22 @@ SUBROUTINE spline_get_yp(x,y,xi,yip,nqty) a(1,4)=1 b(1,:)=y(1,:) - DO i=2,n + do i=2,n dx=x(i)-x(1) a(i,1)=dx*dx*dx a(i,2)=dx*dx a(i,3)=dx a(i,4)=1 b(i,:)=y(i,:) - ENDDO - CALL dgesv(n,nrhs,a,lda,ipiv,b,ldb,info) + enddo + call dgesv(n,nrhs,a,lda,ipiv,b,ldb,info) dx=xi-x(1) yip=(3*b(1,:)*dx+2*b(2,:))*dx+b(3,:) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_get_yp + return + end subroutine spline_get_yp c----------------------------------------------------------------------- c subprogram 21. spline_thomas. c thomas method to solve tri-diagnol matrix. @@ -1548,13 +1561,13 @@ END SUBROUTINE spline_get_yp c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_thomas(l,d,u,b,n,m) + subroutine spline_thomas(l,d,u,b,n,m) - INTEGER, INTENT(IN):: n,m - REAL(r8), DIMENSION(n), INTENT(INOUT):: d - REAL(r8), DIMENSION(n-1), INTENT(INOUT):: l,u - REAL(r8), DIMENSION(n,m), INTENT(INOUT):: b - INTEGER:: i + integer, intent(in):: n,m + real(r8), dimension(n), intent(inout):: d + real(r8), dimension(n-1), intent(inout):: l,u + real(r8), dimension(n,m), intent(inout):: b + integer:: i c----------------------------------------------------------------------- c calculate tri-diagno matrix c l=[A(1,2),A(2,3),...,A(n-1,n)]; @@ -1562,21 +1575,21 @@ SUBROUTINE spline_thomas(l,d,u,b,n,m) c u=[A(2,1),A(3,2),...,A(n,n-1)]; c b is n row m column matrix c----------------------------------------------------------------------- - DO i = 2, n + do i = 2, n l(i-1) = l(i-1)/d(i-1) d(i) = d(i) - u(i-1) * l(i-1) b(i,:) = b(i,:) - b(i-1,:) * l(i-1) - ENDDO + enddo b(n,:) = b(n,:) / d(n); - DO i = n-1, 1, -1 + do i = n-1, 1, -1 b(i,:) = (b(i,:) - u(i) * b(i+1,:)) / d(i); - ENDDO + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_thomas + return + end subroutine spline_thomas c----------------------------------------------------------------------- c subprogram 22. spline_roots. c Calculate all the roots of a cubic spline. @@ -1589,41 +1602,41 @@ END SUBROUTINE spline_thomas c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_roots(spl, iqty, nroots, roots,op_extrap,op_eps) + subroutine spline_roots(spl, iqty, nroots, roots,op_extrap,op_eps) - TYPE(spline_type), INTENT(INOUT) :: spl - INTEGER, INTENT(IN):: iqty - INTEGER, INTENT(OUT) :: nroots - REAL(r8), DIMENSION(*), INTENT(OUT):: roots - !^^^^ should be DIMENSION(1:spl%mx*3) ^^^^ - LOGICAL, INTENT(IN), OPTIONAL :: op_extrap - REAL(r8), INTENT(IN), OPTIONAL :: op_eps + type(spline_type), intent(inout) :: spl + integer, intent(in):: iqty + integer, intent(out) :: nroots + real(r8), dimension(*), intent(out):: roots + !^^^^ should be dimension(1:spl%mx*3) ^^^^ + logical, intent(in), optional :: op_extrap + real(r8), intent(in), optional :: op_eps - LOGICAL, PARAMETER :: debug = .FALSE. + logical, PARAMETER :: debug = .false. - LOGICAL :: extrap - INTEGER:: ix, jroot, lx, nzvalid - REAL(r8):: f_0, f1_0, f_1, f1_1, + logical :: extrap + integer:: ix, jroot, lx, nzvalid + real(r8):: f_0, f1_0, f_1, f1_1, $ c3, c2, c1, c0, a, b, c, q, r, m, s, t, theta, $ z1, z2, z3, x1, x2, x3, last1, last2, last3, $ dx, eps, tol - INTEGER, DIMENSION(:), ALLOCATABLE :: index - REAL(r8), DIMENSION(:), ALLOCATABLE :: tmproots + integer, dimension(:), allocatable :: index + real(r8), dimension(:), allocatable :: tmproots ! allow optional accuracy manipulation repeated solutions ! within eps*stepsize are rejected - IF(PRESENT(op_eps))THEN + if(present(op_eps))then eps = op_eps - ELSE + else eps = 1e-6 - ENDIF + endif ! allow optional extrapolation beyond ends of the spline - IF(PRESENT(op_extrap))THEN + if(present(op_extrap))then extrap = op_extrap - ELSE - extrap = .FALSE. - ENDIF + else + extrap = .false. + endif roots(1:spl%mx*3) = spl%xs(0) - HUGE(last1) last1 = spl%xs(0) - HUGE(last1) @@ -1632,7 +1645,7 @@ SUBROUTINE spline_roots(spl, iqty, nroots, roots,op_extrap,op_eps) lx = spl%mx-1 jroot = 0 ! find the analytic roots of a cubic polynomial between each knot - DO ix=0, lx + do ix=0, lx nzvalid = 0 ! step size and associated tolerance for repeated roots dx=spl%xs(ix+1)-spl%xs(ix) @@ -1657,31 +1670,31 @@ SUBROUTINE spline_roots(spl, iqty, nroots, roots,op_extrap,op_eps) c1 = dx*f1_0 c0 = f_0 ! we have to watch out for secret reductions! - IF(c3==0)THEN - IF(debug) PRINT *, " >> Spline quadratic @",spl%xs(ix) + if(c3==0)then + if(debug) PRinT *, " >> Spline quadratic @",spl%xs(ix) a = c2 b = c1 c = c0 - IF(b**2 - 4.0*a*c >= 0)THEN + if(b**2 - 4.0*a*c >= 0)then z1 = (-b + sqrt(b**2 - 4.0*a*c)) / (2.0 * a) z2 = (-b - sqrt(b**2 - 4.0*a*c)) / (2.0 * a) nzvalid = 2 - ELSEIF(a==0)THEN - IF(debug) PRINT *, " >> Spline linear @",spl%xs(ix) + elseif(a==0)then + if(debug) PRinT *, " >> Spline linear @",spl%xs(ix) z1 = -c / b z2 = -huge(z2) nzvalid = 1 - ELSEIF(a==0 .and. b==0 .and. c==0)THEN - IF(debug) PRINT *, " >> Spline all 0 @",spl%xs(ix) + elseif(a==0 .and. b==0 .and. c==0)then + if(debug) PRinT *, " >> Spline all 0 @",spl%xs(ix) z1 = 0 nzvalid = 1 - ELSE + else z1 = -huge(z1) z2 = -huge(z2) nzvalid = 0 - ENDIF + endif z3 = -huge(z3) - ELSE + else ! truely a cubic case ! since we want f = 0 we can normalize out the c3 ! so 0 = z^3 + a z^2 + b z + c @@ -1692,22 +1705,22 @@ SUBROUTINE spline_roots(spl, iqty, nroots, roots,op_extrap,op_eps) q = (a * a - 3.0 * b) / 9.0 r = (2.0 * a * a * a - 9.0 * a * b + 27.0 * c) / 54.0 m = r**2 - q**3 ! discrimenent - IF(m > 0)THEN ! one real root + if(m > 0)then ! one real root s = -sign(1.0_r8, r) * (abs(r) + sqrt(m))**(1.0/3.0) t = q / s z1 = s + t - (a / 3.0) z2 = -huge(z2) z3 = -huge(z3) nzvalid = 1 - ELSE ! three real roots (watch out for repeates) + else ! three real roots (watch out for repeates) theta = acos(r / sqrt(q**3)) z1 = -2*sqrt(q)*cos(theta/3.0) - a/3.0 z2 = -2*sqrt(q)*cos((theta+twopi)/3.0) - a/3.0 z3 = -2*sqrt(q)*cos((theta-twopi)/3.0) - a/3.0 nzvalid = 3 - IF(abs(z2-z3) f zero crossing between",spl%xs(ix),spl%xs(ix+1) - PRINT *," >> f_0, f_1 =",f_0,f_1 - PRINT *," >> nzvalid =",nzvalid - PRINT *," >> z1, z2, z3 = ",z1,z2,z3 - PRINT *," >> c3,c2,c1,c0 =",c3,c2,c1,c0 - ENDIF - IF(nzvalid>0 .AND. (z1>-eps .OR. (ix==0 .AND. extrap)))THEN - IF(z1<=1+eps .OR. (ix==lx .AND. extrap)) THEN - IF(debug) PRINT '(a12,es17.8e3,a4,es17.8e3,a15,'// + if(debug .and. (f_0*f_1 <= 0))then + PRinT *," > f zero crossing between",spl%xs(ix),spl%xs(ix+1) + PRinT *," >> f_0, f_1 =",f_0,f_1 + PRinT *," >> nzvalid =",nzvalid + PRinT *," >> z1, z2, z3 = ",z1,z2,z3 + PRinT *," >> c3,c2,c1,c0 =",c3,c2,c1,c0 + endif + if(nzvalid>0 .and. (z1>-eps .OR. (ix==0 .and. extrap)))then + if(z1<=1+eps .OR. (ix==lx .and. extrap)) then + if(debug) PRinT '(a12,es17.8e3,a4,es17.8e3,a15,'// $ 'I3,a1,I3,a11,es13.4e3,a1,es13.4)', $ " > Found z1",z1,", x1",x1," between knots ",ix,",", $ ix+1," where x =",spl%xs(ix),",",spl%xs(ix+1) - ! refine solution numerically + ! refine solution numerically ! (analytics vs reality of interp) - CALL spline_refine_root(spl,iqty,x1) + call spline_refine_root(spl,iqty,x1) ! avoid repeated left/right solutions at a f=0 knot - IF(abs(last1-x1)>tol .AND. abs(last2-x1)>tol .AND. - $ abs(last3-x1)>tol) THEN + if(abs(last1-x1)>tol .and. abs(last2-x1)>tol .and. + $ abs(last3-x1)>tol) then jroot = jroot + 1 roots(jroot) = x1 - ENDIF - ENDIF - ENDIF - IF(nzvalid>1 .AND. (z2>-eps .OR. (ix==0 .AND. extrap)))THEN - IF(z2<=1+eps .OR. (ix==lx .AND. extrap)) THEN - IF(debug) PRINT '(a12,es17.8e3,a4,es17.8e3,a15,'// + endif + endif + endif + if(nzvalid>1 .and. (z2>-eps .OR. (ix==0 .and. extrap)))then + if(z2<=1+eps .OR. (ix==lx .and. extrap)) then + if(debug) PRinT '(a12,es17.8e3,a4,es17.8e3,a15,'// $ 'I3,a1,I3,a11,es13.4e3,a1,es13.4)', $ " > Found z2",z2,", x2",x2," between knots ",ix, $ ",",ix+1," where x =",spl%xs(ix),",",spl%xs(ix+1) ! refine solution numerically ! (analytics vs reality of interp) - CALL spline_refine_root(spl,iqty,x2) + call spline_refine_root(spl,iqty,x2) ! avoid double roots or repeats right at a knot location - IF(abs(last1-x2)>tol .AND. abs(last2-x2)>tol .AND. - $ abs(last3-x2)>tol .AND. abs(x1-x2)>tol) THEN + if(abs(last1-x2)>tol .and. abs(last2-x2)>tol .and. + $ abs(last3-x2)>tol .and. abs(x1-x2)>tol) then jroot = jroot + 1 roots(jroot) = x2 - ENDIF - ENDIF - ENDIF - IF(nzvalid>2 .AND. (z3>-eps .OR. (ix==0 .AND. extrap)))THEN - IF(z3<=1+eps .OR. (ix==lx .AND. extrap)) THEN - IF(debug) PRINT '(a12,es17.8e3,a4,es17.8e3,a15,'// + endif + endif + endif + if(nzvalid>2 .and. (z3>-eps .OR. (ix==0 .and. extrap)))then + if(z3<=1+eps .OR. (ix==lx .and. extrap)) then + if(debug) PRinT '(a12,es17.8e3,a4,es17.8e3,a15,'// $ 'I3,a1,I3,a11,es13.4e3,a1,es13.4)', $ " > Found z3",z3,", x3",x3," between knots ",ix, $ ",",ix+1," where x =",spl%xs(ix),",",spl%xs(ix+1) ! refine solution numerically ! (analytics vs reality of interp) - CALL spline_refine_root(spl,iqty,x3) + call spline_refine_root(spl,iqty,x3) ! avoid double roots or repeats right at a knot location - IF(abs(last1-x3)>tol .AND. abs(last2-x3)>tol .AND. - $ abs(last3-x3)>tol .AND. abs(x1-x3)>tol .AND. - $ abs(x2-x3)>tol) THEN + if(abs(last1-x3)>tol .and. abs(last2-x3)>tol .and. + $ abs(last3-x3)>tol .and. abs(x1-x3)>tol .and. + $ abs(x2-x3)>tol) then jroot = jroot + 1 roots(jroot) = x3 - ENDIF - ENDIF - ENDIF + endif + endif + endif last1 = roots(max(1,jroot)) last2 = roots(max(1,jroot-1)) last3 = roots(max(1,jroot-2)) - ENDDO + enddo nroots = jroot ! sort the roots lowest to highest - ALLOCATE(index(nroots), tmproots(nroots)) + allocate(index(nroots), tmproots(nroots)) index=(/(ix,ix=1,nroots)/) tmproots(1:nroots) = roots(1:nroots) - CALL bubble_sort(tmproots,index,1,nroots) - DO ix=1,nroots + call bubble_sort(tmproots,index,1,nroots) + do ix=1,nroots tmproots(ix) = roots(index(nroots + 1 - ix)) - ENDDO + enddo roots(1:nroots) = tmproots(1:nroots) - IF(nroots>0 .AND. debug) - $ PRINT *," > Sorted roots are",roots(1:nroots) - DEALLOCATE(index, tmproots) + if(nroots>0 .and. debug) + $ PRinT *," > Sorted roots are",roots(1:nroots) + deallocate(index, tmproots) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_roots + return + end subroutine spline_roots c----------------------------------------------------------------------- c subprogram 23. spline_refine_root. @@ -1806,54 +1819,54 @@ END SUBROUTINE spline_roots c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE spline_refine_root(spl, iqty, x, op_tol) + subroutine spline_refine_root(spl, iqty, x, op_tol) - TYPE(spline_type), INTENT(INOUT) :: spl - INTEGER, INTENT(IN):: iqty - REAL(r8), INTENT(INOUT) :: x - REAL(r8), INTENT(IN), OPTIONAL :: op_tol + type(spline_type), intent(inout) :: spl + integer, intent(in):: iqty + real(r8), intent(inout) :: x + real(r8), intent(in), optional :: op_tol ! declare variables - INTEGER :: it - INTEGER, PARAMETER :: itmax=500 - REAL(r8) :: tol=1e-12 - REAL(r8) :: dx,lx,lf,f,df + integer :: it + integer, PARAMETER :: itmax=500 + real(r8) :: tol=1e-12 + real(r8) :: dx,lx,lf,f,df ! set optional tolerance tol = 1e-12 - IF(PRESENT(op_tol)) tol = op_tol + if(present(op_tol)) tol = op_tol ! if its exact, we don't need to do anything - CALL spline_eval(spl,x,1) - IF(spl%f(iqty) == 0) RETURN + call spline_eval(spl,x,1) + if(spl%f(iqty) == 0) return ! otherwise, we'll iterate lx=spl%xs(spl%ix+1)-spl%xs(spl%ix) ! note ix set in above eval lf = maxval(spl%fs(:,iqty))-minval(spl%fs(:,iqty)) dx=lx f=huge(f) it=0 - DO - CALL spline_eval(spl,x,1) + do + call spline_eval(spl,x,1) df=spl%f(iqty)-f - !IF(abs(dx) < tol*lx .OR. abs(df) < tol*lf .OR. it >= itmax)EXIT - IF(abs(dx) <= abs(tol*lx) .OR. it >= itmax)EXIT + !if(abs(dx) < tol*lx .OR. abs(df) < tol*lf .OR. it >= itmax)EXIT + if(abs(dx) <= abs(tol*lx) .OR. it >= itmax)EXIT it=it+1 f=spl%f(iqty) dx=-spl%f(iqty)/spl%f1(iqty) x=x+dx - ENDDO + enddo ! abort on failure. - IF(it >= itmax)THEN - WRITE(*,*) - WRITE(*,*) "!! WARNING: root refining convergence failure" - WRITE(*,*) " -> estimated root ",x, + if(it >= itmax)then + write(*,*) + write(*,*) "!! WARNinG: root refining convergence failure" + write(*,*) " -> estimated root ",x, $ " has error/tol ",abs(dx)/(tol*lx),abs(df)/(tol*lf) - WRITE(*,*) - ENDIF + write(*,*) + endif c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE spline_refine_root + return + end subroutine spline_refine_root c----------------------------------------------------------------------- c subprogram 24. bubble_sort. c performs a bubble sort in decreasing order of value. @@ -1861,33 +1874,33 @@ END SUBROUTINE spline_refine_root c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - SUBROUTINE bubble_sort(key,index,mmin,mmax) + subroutine bubble_sort(key,index,mmin,mmax) - REAL(r8), DIMENSION(:), INTENT(IN) :: key - INTEGER, DIMENSION(:), INTENT(INOUT) :: index - INTEGER :: mmin,mmax + real(r8), dimension(:), intent(in) :: key + integer, dimension(:), intent(inout) :: index + integer :: mmin,mmax - LOGICAL :: switch - INTEGER :: i,temp + logical :: switch + integer :: i,temp c----------------------------------------------------------------------- c computations. c----------------------------------------------------------------------- - switch= .TRUE. - DO while(switch) - switch= .FALSE. - DO i=mmin,mmax-1 - IF(key(index(i)) < key(index(i+1)))THEN + switch= .true. + do while(switch) + switch= .false. + do i=mmin,mmax-1 + if(key(index(i)) < key(index(i+1)))then temp=index(i) index(i)=index(i+1) index(i+1)=temp - switch= .TRUE. - ENDIF - ENDDO - ENDDO + switch= .true. + endif + enddo + enddo c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- - RETURN - END SUBROUTINE bubble_sort + return + end subroutine bubble_sort c----------------------------------------------------------------------- - END MODULE spline_mod + end module spline_mod diff --git a/src/Splines/fortran/spline_c_api.f b/src/Splines/fortran/spline_c_api.f index 5bc1eade3..cb1c4c5e7 100644 --- a/src/Splines/fortran/spline_c_api.f +++ b/src/Splines/fortran/spline_c_api.f @@ -14,21 +14,31 @@ c 6. spline_c_eval_deriv c 7. spline_c_eval_deriv2 c 8. spline_c_eval_deriv3 -c 9. cspline_c_create -c 10. cspline_c_destroy -c 11. cspline_c_setup -c 12. cspline_c_fit -c 13. cspline_c_eval -c 14. cspline_c_eval_deriv -c 15. cspline_c_eval_deriv2 -c 16. cspline_c_eval_deriv3 -c 17. bicube_c_create -c 18. bicube_c_destroy -c 19. bicube_c_setup -c 20. bicube_c_fit -c 21. bicube_c_eval -c 22. bicube_c_eval_deriv -c 23. bicube_c_eval_deriv2 +c 9. spline_c_int +c 10. cspline_c_create +c 11. cspline_c_destroy +c 12. cspline_c_setup +c 13. cspline_c_fit +c 14. cspline_c_eval +c 15. cspline_c_eval_deriv +c 16. cspline_c_eval_deriv2 +c 17. cspline_c_eval_deriv3 +c 18. cspline_c_int +c 19. bicube_c_create +c 20. bicube_c_destroy +c 21. bicube_c_setup +c 22. bicube_c_fit +c 23. bicube_c_eval +c 24. bicube_c_eval_deriv +c 25. bicube_c_eval_deriv2 +c 26. fspline_c_create +c 27. fspline_c_destroy +c 28. fspline_c_setup +c 29. fspline_c_fit_1 +c 30. fspline_c_fit_2 +c 31. fspline_c_eval +c 32. fspline_c_eval_deriv +c 33. fspline_c_eval_deriv2 c----------------------------------------------------------------------- c subprogram 0. spline_c_api_mod c module declarations. @@ -38,6 +48,7 @@ module spline_c_api_mod use spline_mod use cspline_mod use bicube_mod + use fspline_mod implicit none c----------------------------------------------------------------------- c declarations. @@ -87,14 +98,14 @@ subroutine spline_c_destroy(handle) bind(C) c----------------------------------------------------------------------- type(spline_handle), value :: handle type(spline_type), pointer :: spl - + call c_f_pointer(handle%obj, spl) if (associated(spl)) then call spline_dealloc(spl) deallocate(spl) else print *, "spline_c_destroy: handle is not associated " - $ // "with a valid spline object." + $ // "with a valid spline object." end if c----------------------------------------------------------------------- c terminate. @@ -153,21 +164,23 @@ subroutine spline_c_setup(handle, xs, fs) bind(C) c------------------------------------------------------------------------ c terminate. c------------------------------------------------------------------------ - return + return end subroutine spline_c_setup c----------------------------------------------------------------------- c subprogram 4. spline_c_fit c fits the spline to the data. c----------------------------------------------------------------------- - subroutine spline_c_fit(handle, endmode) bind(C) + subroutine spline_c_fit(handle, endmode, fs1_out) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle integer(c_int), value :: endmode - type(spline_type), pointer :: spl + type(c_ptr), value :: fs1_out - character(10) :: endmode_str + type(spline_type), pointer :: spl + real(c_double), pointer :: fs1_out_fort(:,:) + integer :: mx, nqty c----------------------------------------------------------------------- c work. c----------------------------------------------------------------------- @@ -178,21 +191,23 @@ subroutine spline_c_fit(handle, endmode) bind(C) return end if - select case(endmode) - case(1) - endmode_str = "natural" - case(2) - endmode_str = "periodic" - case(3) - endmode_str = "extrap" - case(4) - endmode_str = "not-a-knot" - end select + + call spline_fit(spl, endmode) + + + mx = spl%mx + nqty = spl%nqty + + call c_f_pointer(fs1_out, fs1_out_fort, [mx+1, nqty]) + + fs1_out_fort = spl%fs1 + if (debug) then - print *, "spline_c_fit: fitting spline with endmode = " - $ // TRIM(endmode_str) + print '(A,*(I0,1X))', "fs1_out_fort dims :", + $ size(fs1_out_fort,1), size(fs1_out_fort,2) + print '(A,*(I0,1X))', "spl%fs1 dims :", + $ size(spl%fs1,1), size(spl%fs1,2) end if - call spline_fit(spl, TRIM(endmode_str)) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- @@ -202,16 +217,15 @@ end subroutine spline_c_fit c subprogram 5. spline_c_eval c evaluates the spline at a given point. c----------------------------------------------------------------------- - subroutine spline_c_eval(handle, x, f, ix_op) bind(C) + subroutine spline_c_eval(handle, x, f) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x type(c_ptr), value :: f - integer(c_int), intent(in), optional :: ix_op - integer(i4) :: ix ! index of x position in the spline + real(c_double), pointer :: fi(:) type(spline_type), pointer :: spl c----------------------------------------------------------------------- @@ -226,17 +240,8 @@ subroutine spline_c_eval(handle, x, f, ix_op) bind(C) call c_f_pointer(f, fi, [spl%nqty]) - if (present(ix_op)) then - ix = ix_op - else - ix = 0 - end if - call spline_eval_external(spl, x, ix, fi) -c----------------------------------------------------------------------- -c copy results back to the C pointer. -c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [spl%nqty]) + call spline_eval_external(spl, x, fi) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- @@ -246,16 +251,14 @@ end subroutine spline_c_eval c subprogram 6. spline_c_eval_deriv c evaluates the spline and its first derivative at a given point. c----------------------------------------------------------------------- - subroutine spline_c_eval_deriv(handle, x, f, f1, ix_op) bind(C) + subroutine spline_c_eval_deriv(handle, x, f, f1) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x type(c_ptr), value :: f, f1 - integer(c_int), intent(in), optional :: ix_op - integer(i4) :: ix ! index of x position in the spline real(c_double), pointer :: fi(:), f1i(:) type(spline_type), pointer :: spl c----------------------------------------------------------------------- @@ -271,40 +274,26 @@ subroutine spline_c_eval_deriv(handle, x, f, f1, ix_op) bind(C) call c_f_pointer(f, fi, [spl%nqty]) call c_f_pointer(f1, f1i, [spl%nqty]) - if (present(ix_op)) then - ix = ix_op - else - ix = 0 - end if - - call spline_eval_external(spl, x, ix, fi, f1i) -c----------------------------------------------------------------------- -c copy results back to the C pointer. -c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [spl%nqty]) - call c_f_pointer(f1, f1i, [spl%nqty]) - + call spline_eval_external(spl, x, fi, f1i) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return end subroutine spline_c_eval_deriv c----------------------------------------------------------------------- -c subprogram 7. spline_c_eval_deriv_2 +c subprogram 7. spline_c_eval_deriv2 c evaluates the spline and its first and\ c second derivatives at a given point. c----------------------------------------------------------------------- - subroutine spline_c_eval_deriv_2(handle, x, f, f1, - $ f2, ix_op) bind(C) + subroutine spline_c_eval_deriv2(handle, x, f, f1, + $ f2) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x type(c_ptr), value :: f, f1, f2 - integer(c_int), intent(in), optional :: ix_op - integer(i4) :: ix ! index of x position in the spline real(c_double), pointer :: fi(:), f1i(:), f2i(:) type(spline_type), pointer :: spl c----------------------------------------------------------------------- @@ -321,40 +310,27 @@ subroutine spline_c_eval_deriv_2(handle, x, f, f1, call c_f_pointer(f1, f1i, [spl%nqty]) call c_f_pointer(f2, f2i, [spl%nqty]) - if (present(ix_op)) then - ix = ix_op - else - ix = 0 - end if - - call spline_eval_external(spl, x, ix, fi, f1i, f2i) -c----------------------------------------------------------------------- -c copy results back to the C pointer. -c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [spl%nqty]) - call c_f_pointer(f1, f1i, [spl%nqty]) - call c_f_pointer(f2, f2i, [spl%nqty]) + call spline_eval_external(spl, x, fi, f1i, f2i) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return - end subroutine spline_c_eval_deriv_2 + end subroutine spline_c_eval_deriv2 c----------------------------------------------------------------------- -c subprogram 8. spline_c_eval_deriv_3 +c subprogram 8. spline_c_eval_deriv3 c evaluates the spline and its first derivative at a given point. c----------------------------------------------------------------------- - subroutine spline_c_eval_deriv_3(handle, x, f, f1, - $ f2, f3, ix_op) bind(C) + subroutine spline_c_eval_deriv3(handle, x, f, f1, + $ f2, f3) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x type(c_ptr), value :: f, f1, f2, f3 - integer(c_int), intent(in), optional :: ix_op - integer(i4) :: ix ! index of x position in the spline + real(c_double), pointer :: fi(:), f1i(:), f2i(:), f3i(:) type(spline_type), pointer :: spl c----------------------------------------------------------------------- @@ -372,27 +348,50 @@ subroutine spline_c_eval_deriv_3(handle, x, f, f1, call c_f_pointer(f2, f2i, [spl%nqty]) call c_f_pointer(f3, f3i, [spl%nqty]) - if (present(ix_op)) then - ix = ix_op - else - ix = 0 - end if - call spline_eval_external(spl, x, ix, fi, f1i, f2i, f3i) + call spline_eval_external(spl, x, fi, f1i, f2i, f3i) + c----------------------------------------------------------------------- -c copy results back to the C pointer. +c terminate. c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [spl%nqty]) - call c_f_pointer(f1, f1i, [spl%nqty]) - call c_f_pointer(f2, f2i, [spl%nqty]) - call c_f_pointer(f3, f3i, [spl%nqty]) + return + end subroutine spline_c_eval_deriv3 +c----------------------------------------------------------------------- +c subprogram 9. spline_c_int +c integrates the spline and returns the results. +c----------------------------------------------------------------------- + subroutine spline_c_int(handle, fsi_out) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + type(spline_handle), value :: handle + type(c_ptr), value :: fsi_out + + type(spline_type), pointer :: spl + real(c_double), pointer :: fsi_out_fort(:,:) + integer :: mx, nqty, i, j +c----------------------------------------------------------------------- +c work. +c----------------------------------------------------------------------- + call c_f_pointer(handle%obj, spl) + if (.not. associated(spl)) then + print *, "spline_c_int: handle is not associated." + return + end if + + call spline_int(spl) + + mx = spl%mx + nqty = spl%nqty + call c_f_pointer(fsi_out, fsi_out_fort, [mx+1, nqty]) + + fsi_out_fort = spl%fsi c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return - end subroutine spline_c_eval_deriv_3 - + end subroutine spline_c_int c----------------------------------------------------------------------- c Complex Cubic Spline API @@ -401,7 +400,7 @@ end subroutine spline_c_eval_deriv_3 c----------------------------------------------------------------------- -c subprogram 9. cspline_c_create +c subprogram 10. cspline_c_create c allocates a spline object c----------------------------------------------------------------------- subroutine cspline_c_create(mx, nqty, handle) bind(C) @@ -421,7 +420,7 @@ subroutine cspline_c_create(mx, nqty, handle) bind(C) return end subroutine cspline_c_create c----------------------------------------------------------------------- -c subprogram 10. cspline_c_destroy +c subprogram 11. cspline_c_destroy c deallocates a spline object c----------------------------------------------------------------------- subroutine cspline_c_destroy(handle) bind(C) @@ -437,7 +436,7 @@ subroutine cspline_c_destroy(handle) bind(C) deallocate(cspl) else print *, "cspline_c_destroy: handle is not associated " - $ // "with a valid cspline object." + $ // "with a valid cspline object." end if c----------------------------------------------------------------------- c terminate. @@ -445,7 +444,7 @@ subroutine cspline_c_destroy(handle) bind(C) return end subroutine cspline_c_destroy c----------------------------------------------------------------------- -c subprogram 11. cspline_c_setup +c subprogram 12. cspline_c_setup c sets up the spline object with data. c----------------------------------------------------------------------- subroutine cspline_c_setup(handle, xs, fs) bind(C) @@ -492,24 +491,27 @@ subroutine cspline_c_setup(handle, xs, fs) bind(C) c------------------------------------------------------------------------ c terminate. c------------------------------------------------------------------------ - return + return end subroutine cspline_c_setup c----------------------------------------------------------------------- -c subprogram 12. spline_c_fit +c subprogram 13. cspline_c_fit c fits the spline to the data. c----------------------------------------------------------------------- - subroutine cspline_c_fit(handle, endmode) bind(C) + subroutine cspline_c_fit(handle, endmode,fs1_out) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle integer(c_int), value :: endmode - type(cspline_type), pointer :: cspl + type(c_ptr), value :: fs1_out - character(10) :: endmode_str + type(cspline_type), pointer :: cspl + complex(c_double), pointer :: fs1_out_fort(:,:) + integer :: mx, nqty c----------------------------------------------------------------------- c work. c----------------------------------------------------------------------- + call c_f_pointer(handle%obj, cspl) if (.not. associated(cspl)) then print *, "cspline_c_fit: handle is not associated " @@ -517,40 +519,31 @@ subroutine cspline_c_fit(handle, endmode) bind(C) return end if - select case(endmode) - case(1) - endmode_str = "natural" - case(2) - endmode_str = "periodic" - case(3) - endmode_str = "extrap" - case(4) - endmode_str = "not-a-knot" - end select - if (debug) then - print *, "cspline_c_fit: fitting spline with endmode = " - $ // TRIM(endmode_str) - end if - call cspline_fit(cspl, TRIM(endmode_str)) + call cspline_fit(cspl, endmode) + + mx = cspl%mx + nqty = cspl%nqty + + call c_f_pointer(fs1_out, fs1_out_fort, [mx+1, nqty]) + + fs1_out_fort = cspl%fs1 c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return end subroutine cspline_c_fit c----------------------------------------------------------------------- -c subprogram 13. cspline_c_eval +c subprogram 14. cspline_c_eval c evaluates the spline at a given point. c----------------------------------------------------------------------- - subroutine cspline_c_eval(handle, x, f, ix_op) bind(C) + subroutine cspline_c_eval(handle, x, f) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x type(c_ptr), value :: f - integer(c_int), intent(in), optional :: ix_op - integer(i4) :: ix ! index of x position in the spline complex(c_double), pointer :: fi(:) type(cspline_type), pointer :: cspl c----------------------------------------------------------------------- @@ -565,36 +558,24 @@ subroutine cspline_c_eval(handle, x, f, ix_op) bind(C) call c_f_pointer(f, fi, [cspl%nqty]) - if (present(ix_op)) then - ix = ix_op - else - ix = 0 - end if - - call cspline_eval_external(cspl, x, ix, fi) -c----------------------------------------------------------------------- -c copy results back to the C pointer. -c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [cspl%nqty]) + call cspline_eval_external(cspl, x, fi) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return end subroutine cspline_c_eval c----------------------------------------------------------------------- -c subprogram 14. cspline_c_eval_deriv +c subprogram 15. cspline_c_eval_deriv c evaluates the spline and its first derivative at a given point. c----------------------------------------------------------------------- - subroutine cspline_c_eval_deriv(handle, x, f, f1, ix_op) bind(C) + subroutine cspline_c_eval_deriv(handle, x, f, f1) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x type(c_ptr), value :: f, f1 - integer(c_int), intent(in), optional :: ix_op - integer(i4) :: ix ! index of x position in the spline complex(c_double), pointer :: fi(:), f1i(:) type(cspline_type), pointer :: cspl c----------------------------------------------------------------------- @@ -610,40 +591,28 @@ subroutine cspline_c_eval_deriv(handle, x, f, f1, ix_op) bind(C) call c_f_pointer(f, fi, [cspl%nqty]) call c_f_pointer(f1, f1i, [cspl%nqty]) - if (present(ix_op)) then - ix = ix_op - else - ix = 0 - end if - call cspline_eval_external(cspl, x, ix, fi, f1i) -c----------------------------------------------------------------------- -c copy results back to the C pointer. -c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [cspl%nqty]) - call c_f_pointer(f1, f1i, [cspl%nqty]) + call cspline_eval_external(cspl, x, fi, f1i) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return end subroutine cspline_c_eval_deriv c----------------------------------------------------------------------- -c subprogram 15. cspline_c_eval_deriv_2 +c subprogram 16. cspline_c_eval_deriv2 c evaluates the spline and its first and\ c second derivatives at a given point. c----------------------------------------------------------------------- - subroutine cspline_c_eval_deriv_2(handle, x, f, f1, - $ f2, ix_op) bind(C) + subroutine cspline_c_eval_deriv2(handle, x, f, f1, + $ f2) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x type(c_ptr), value :: f, f1, f2 - integer(c_int), intent(in), optional :: ix_op - integer(i4) :: ix ! index of x position in the spline complex(c_double), pointer :: fi(:), f1i(:), f2i(:) type(cspline_type), pointer :: cspl c----------------------------------------------------------------------- @@ -660,40 +629,26 @@ subroutine cspline_c_eval_deriv_2(handle, x, f, f1, call c_f_pointer(f1, f1i, [cspl%nqty]) call c_f_pointer(f2, f2i, [cspl%nqty]) - if (present(ix_op)) then - ix = ix_op - else - ix = 0 - end if - - call cspline_eval_external(cspl, x, ix, fi, f1i, f2i) -c----------------------------------------------------------------------- -c copy results back to the C pointer. -c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [cspl%nqty]) - call c_f_pointer(f1, f1i, [cspl%nqty]) - call c_f_pointer(f2, f2i, [cspl%nqty]) + call cspline_eval_external(cspl, x, fi, f1i, f2i) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return - end subroutine cspline_c_eval_deriv_2 + end subroutine cspline_c_eval_deriv2 c----------------------------------------------------------------------- -c subprogram 16. cspline_c_eval_deriv_3 +c subprogram 17. cspline_c_eval_deriv3 c evaluates the spline and its first derivative at a given point. c----------------------------------------------------------------------- - subroutine cspline_c_eval_deriv_3(handle, x, f, f1, - $ f2, f3, ix_op) bind(C) + subroutine cspline_c_eval_deriv3(handle, x, f, f1, + $ f2, f3) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x type(c_ptr), value :: f, f1, f2, f3 - integer(c_int), intent(in), optional :: ix_op - integer(i4) :: ix ! index of x position in the spline complex(c_double), pointer :: fi(:), f1i(:), f2i(:), f3i(:) type(cspline_type), pointer :: cspl c----------------------------------------------------------------------- @@ -711,26 +666,50 @@ subroutine cspline_c_eval_deriv_3(handle, x, f, f1, call c_f_pointer(f2, f2i, [cspl%nqty]) call c_f_pointer(f3, f3i, [cspl%nqty]) - if (present(ix_op)) then - ix = ix_op - else - ix = 0 - end if + call cspline_eval_external(cspl, x, fi, f1i, f2i, f3i) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine cspline_c_eval_deriv3 +c----------------------------------------------------------------------- +c subprogram 18. cspline_c_int +c integrates the complex spline and returns the results. +c----------------------------------------------------------------------- + subroutine cspline_c_int(handle, fsi_out) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + use iso_c_binding, only: c_ptr, c_f_pointer, c_double_complex + type(spline_handle), value :: handle + type(c_ptr), value :: fsi_out - call cspline_eval_external(cspl, x, ix, fi, f1i, f2i, f3i) + type(cspline_type), pointer :: cspl + complex(c_double_complex), pointer :: fsi_out_fort(:,:) + integer :: mx, nqty, i, j c----------------------------------------------------------------------- -c copy results back to the C pointer. +c work. c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [cspl%nqty]) - call c_f_pointer(f1, f1i, [cspl%nqty]) - call c_f_pointer(f2, f2i, [cspl%nqty]) - call c_f_pointer(f3, f3i, [cspl%nqty]) + call c_f_pointer(handle%obj, cspl) + if (.not. associated(cspl)) then + print *, "cspline_c_int: handle is not associated." + return + end if + + call cspline_int(cspl) + + mx = cspl%mx + nqty = cspl%nqty + + call c_f_pointer(fsi_out, fsi_out_fort, [mx+1, nqty]) + fsi_out_fort = cspl%fsi c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return - end subroutine cspline_c_eval_deriv_3 + end subroutine cspline_c_int + c----------------------------------------------------------------------- c Bicubic Spline API @@ -738,7 +717,7 @@ end subroutine cspline_c_eval_deriv_3 c----------------------------------------------------------------------- c----------------------------------------------------------------------- -c subprogram 17. bicube_c_create +c subprogram 19. bicube_c_create c allocates a bicubic spline object c----------------------------------------------------------------------- subroutine bicube_c_create(mx, my, nqty, handle) bind(C) @@ -758,7 +737,7 @@ subroutine bicube_c_create(mx, my, nqty, handle) bind(C) return end subroutine bicube_c_create c----------------------------------------------------------------------- -c subprogram 18. bicube_c_destroy +c subprogram 20. bicube_c_destroy c deallocates a bicubic spline object c----------------------------------------------------------------------- subroutine bicube_c_destroy(handle) bind(C) @@ -782,7 +761,7 @@ subroutine bicube_c_destroy(handle) bind(C) return end subroutine bicube_c_destroy c----------------------------------------------------------------------- -c subprogram 19. bicube_c_setup +c subprogram 21. bicube_c_setup c sets up the bicubic spline object with data. c----------------------------------------------------------------------- subroutine bicube_c_setup(handle, xs, ys, fs) bind(C) @@ -840,18 +819,23 @@ subroutine bicube_c_setup(handle, xs, ys, fs) bind(C) return end subroutine bicube_c_setup c----------------------------------------------------------------------- -c subprogram 20. bicube_c_fit +c subprogram 22. bicube_c_fit c fits the bicubic spline to the data. c----------------------------------------------------------------------- - subroutine bicube_c_fit(handle, endmode1, endmode2) bind(C) + subroutine bicube_c_fit(handle, endmode1, endmode2 + $ , fsx, fsy, fsxy) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle integer(c_int), value :: endmode1, endmode2 - type(bicube_type), pointer :: bicube + type(c_ptr), value :: fsx,fsy,fsxy - character(10) :: endmode1_str, endmode2_str + type(bicube_type), pointer :: bicube + real(c_double), pointer :: fsx_f(:,:,:) + real(c_double), pointer :: fsy_f(:,:,:) + real(c_double), pointer :: fsxy_f(:,:,:) + integer(i8) :: mx, my, nqty c----------------------------------------------------------------------- c work. c----------------------------------------------------------------------- @@ -862,53 +846,46 @@ subroutine bicube_c_fit(handle, endmode1, endmode2) bind(C) return end if - select case(endmode1) - case(1) - endmode1_str = "natural" - case(2) - endmode1_str = "periodic" - case(3) - endmode1_str = "extrap" - case(4) - endmode1_str = "not-a-knot" - end select - select case(endmode2) - case(1) - endmode2_str = "natural" - case(2) - endmode2_str = "periodic" - case(3) - endmode2_str = "extrap" - case(4) - endmode2_str = "not-a-knot" - end select + call bicube_fit(bicube, endmode1, endmode2) + + mx = bicube%mx + my = bicube%my + nqty = bicube%nqty + call c_f_pointer(fsx, fsx_f, [mx+1, my+1, nqty]) + call c_f_pointer(fsy, fsy_f, [mx+1, my+1, nqty]) + call c_f_pointer(fsxy, fsxy_f, [mx+1, my+1, nqty]) if (debug) then - print *, "bicube_c_fit: fitting spline with endmode1 = " - $ // TRIM(endmode1_str) // " and endmode2 = " - $ // TRIM(endmode2_str) + print *, "Pointer shapes" + print *, "shape(fsx_f) =", shape(fsx_f) + print *, "shape(fsy_f) =", shape(fsy_f) + print *, "shape(fsxy_f) =", shape(fsxy_f) + + print *, "== Field shapes in bicube type ==" + print *, "shape(bicube%fsx) =", shape(bicube%fsx) + print *, "shape(bicube%fsy) =", shape(bicube%fsy) + print *, "shape(bicube%fsxy) =", shape(bicube%fsxy) end if - call bicube_fit(bicube, TRIM(endmode1_str), TRIM(endmode2_str)) + fsx_f = bicube%fsx + fsy_f = bicube%fsy + fsxy_f = bicube%fsxy c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return end subroutine bicube_c_fit c----------------------------------------------------------------------- -c subprogram 21. bicube_c_eval +c subprogram 23. bicube_c_eval c evaluates the bicubic spline at a given point. c----------------------------------------------------------------------- - subroutine bicube_c_eval(handle, x, y, f, ix_op, iy_op) bind(C) + subroutine bicube_c_eval(handle, x, y, f) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x, y type(c_ptr), value :: f - integer(c_int), intent(in), optional :: ix_op, iy_op - integer(i4) :: ix ! index of x position in the spline - integer(i4) :: iy ! index of y position in the spline real(c_double), pointer :: fi(:) real(r8), pointer :: fix(:), fiy(:), fxy(:), fxx(:), fyy(:) type(bicube_type), pointer :: bicube @@ -923,48 +900,27 @@ subroutine bicube_c_eval(handle, x, y, f, ix_op, iy_op) bind(C) end if call c_f_pointer(f, fi, [bicube%nqty]) - allocate(fix(bicube%nqty), fiy(bicube%nqty)) - allocate(fxy(bicube%nqty), fxx(bicube%nqty), fyy(bicube%nqty)) - if (present(ix_op)) then - ix = ix_op - else - ix = 0 - end if - if (present(iy_op)) then - iy = iy_op - else - iy = 0 - end if + call bicube_eval_external(bicube, x, y, 0, fi) - call bicube_eval_external(bicube, x, y, 0, ix, iy, fi, fix, fiy, - $ fxy, fxx, fyy) - deallocate(fix, fiy) -c----------------------------------------------------------------------- -c copy results back to the C pointer. -c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [bicube%nqty]) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return end subroutine bicube_c_eval c----------------------------------------------------------------------- -c subprogram 22. bicube_c_eval_deriv +c subprogram 24. bicube_c_eval_deriv c evaluates the bicube and its first derivative at a given point. c----------------------------------------------------------------------- subroutine bicube_c_eval_deriv(handle, x, y, - $ f, f1x, f1y, ix_op, iy_op) bind(C) + $ f, f1x, f1y) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x, y type(c_ptr), value :: f, f1x, f1y - integer(c_int), intent(in), optional :: ix_op, iy_op - integer(i4) :: ix ! index of x position in the spline - integer(i4) :: iy ! index of y position in the spline real(c_double), pointer :: fi(:), f1xi(:), f1yi(:) real(r8), pointer :: fxy(:), fxx(:), fyy(:) type(bicube_type), pointer :: bicube @@ -983,27 +939,8 @@ subroutine bicube_c_eval_deriv(handle, x, y, call c_f_pointer(f1y, f1yi, [bicube%nqty]) allocate(fxy(bicube%nqty), fxx(bicube%nqty), fyy(bicube%nqty)) - if (present(ix_op)) then - ix = ix_op - else - ix = 0 - end if - - if (present(iy_op)) then - iy = iy_op - else - iy = 0 - end if - call bicube_eval_external(bicube, x, y, 1, ix, iy, fi, f1xi, f1yi, - $ fxy, fxx, fyy) - deallocate(fxy, fxx, fyy) -c----------------------------------------------------------------------- -c copy results back to the C pointer. -c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [bicube%nqty]) - call c_f_pointer(f1x, f1xi, [bicube%nqty]) - call c_f_pointer(f1y, f1yi, [bicube%nqty]) + call bicube_eval_external(bicube, x, y, 1, fi, f1xi, f1yi) c----------------------------------------------------------------------- c terminate. @@ -1011,21 +948,18 @@ subroutine bicube_c_eval_deriv(handle, x, y, return end subroutine bicube_c_eval_deriv c----------------------------------------------------------------------- -c subprogram 23. bicube_c_eval_deriv2 +c subprogram 25. bicube_c_eval_deriv2 c evaluates the bicube and its derivatives at a given point. c----------------------------------------------------------------------- subroutine bicube_c_eval_deriv2(handle, x, y, f, f1x, f1y, - $ f2xx, f2xy, f2yy, ix_op, iy_op) bind(C) + $ f2xx, f2xy, f2yy) bind(C) c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- type(spline_handle), value :: handle real(c_double), value :: x, y type(c_ptr), value :: f, f1x, f1y, f2xx, f2xy, f2yy - integer(c_int), intent(in), optional :: ix_op, iy_op - integer(i4) :: ix ! index of x position in the spline - integer(i4) :: iy ! index of y position in the spline real(c_double), pointer :: fi(:), f1xi(:), f1yi(:) real(c_double), pointer :: f2xxi(:), f2xyi(:), f2yyi(:) type(bicube_type), pointer :: bicube @@ -1046,35 +980,344 @@ subroutine bicube_c_eval_deriv2(handle, x, y, f, f1x, f1y, call c_f_pointer(f2xy, f2xyi, [bicube%nqty]) call c_f_pointer(f2yy, f2yyi, [bicube%nqty]) - if (present(ix_op)) then - ix = ix_op + + call bicube_eval_external(bicube, x, y, 2, fi, f1xi, f1yi, + $ f2xxi, f2xyi, f2yyi) + +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine bicube_c_eval_deriv2 + + + +c----------------------------------------------------------------------- +c Fourier Spline API +c This section includes the C API for fspline.f. +c----------------------------------------------------------------------- + +c----------------------------------------------------------------------- +c subprogram 26. fspline_c_create +c allocates a fourier spline object +c----------------------------------------------------------------------- + subroutine fspline_c_create(mx, my, mband, nqty, handle) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + integer(c_int), value :: mx, my, mband, nqty + type(spline_handle), intent(out) :: handle + type(fspline_type), pointer :: fst + + allocate(fst) + call fspline_alloc(fst, mx, my, mband, nqty) + handle%obj = c_loc(fst) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_c_create + +c----------------------------------------------------------------------- +c subprogram 27. fspline_c_destroy +c deallocates a fourier spline object +c----------------------------------------------------------------------- + subroutine fspline_c_destroy(handle) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + type(spline_handle), value :: handle + type(fspline_type), pointer :: fst + + call c_f_pointer(handle%obj, fst) + if (associated(fst)) then + call fspline_dealloc(fst) + deallocate(fst) else - ix = 0 + print *, "fspline_c_destroy: handle is not associated " + $ // "with a valid fourier spline object." end if +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_c_destroy - if (present(iy_op)) then - iy = iy_op - else - iy = 0 +c----------------------------------------------------------------------- +c subprogram 28. fspline_c_setup +c sets up the fourier spline object with data. +c----------------------------------------------------------------------- + subroutine fspline_c_setup(handle, xs, ys, fs) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + type(spline_handle), value :: handle + type(c_ptr), value :: xs, ys, fs + + type(fspline_type), pointer :: fst + real(c_double), pointer :: x_c(:), y_c(:) + real(c_double), pointer :: f_c(:, :, :) + integer :: mx, my, nqty +c----------------------------------------------------------------------- +c work. +c----------------------------------------------------------------------- + call c_f_pointer(handle%obj, fst) + if (.not. associated(fst)) then + print *, "fspline_c_setup: handle is not associated." + return end if - call bicube_eval_external(bicube, x, y, 2, ix, iy, fi, f1xi, f1yi, - $ f2xxi, f2xyi, f2yyi) + mx = fst%mx + my = fst%my + nqty = fst%nqty + + call c_f_pointer(xs, x_c, [mx+1]) + call c_f_pointer(ys, y_c, [my+1]) + call c_f_pointer(fs, f_c, [mx+1, my+1, nqty]) + + ! notE: The data is COPIED from the C pointers to the Fortran + ! allocated arrays. This is the safe and correct way to handle memory, + ! preventing crashes on deallocation. + fst%xs(0:mx) = x_c(1:mx+1) + fst%ys(0:my) = y_c(1:my+1) + fst%fs(0:mx, 0:my, 1:nqty) = f_c(1:mx+1, 1:my+1, 1:nqty) +c------------------------------------------------------------------------ +c terminate. +c------------------------------------------------------------------------ + return + end subroutine fspline_c_setup + c----------------------------------------------------------------------- -c copy results back to the C pointer. +c subprogram 29. fspline_c_fit_1 +c fits the fourier spline using method 1. c----------------------------------------------------------------------- - call c_f_pointer(f, fi, [bicube%nqty]) - call c_f_pointer(f1x, f1xi, [bicube%nqty]) - call c_f_pointer(f1y, f1yi, [bicube%nqty]) - call c_f_pointer(f2xx, f2xxi, [bicube%nqty]) - call c_f_pointer(f2xy, f2xyi, [bicube%nqty]) - call c_f_pointer(f2yy, f2yyi, [bicube%nqty]) + subroutine fspline_c_fit_1(handle, endmode, fit_flag_c) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + type(spline_handle), value :: handle + integer(c_int), value :: endmode + logical(c_bool), value :: fit_flag_c + type(fspline_type), pointer :: fst + logical :: fit_flag +c----------------------------------------------------------------------- +c work. +c----------------------------------------------------------------------- + call c_f_pointer(handle%obj, fst) + if (.not. associated(fst)) then + print *, "fspline_c_fit_1: handle is not associated." + return + end if + + fit_flag = fit_flag_c + call fspline_fit_1(fst, endmode, fit_flag) c----------------------------------------------------------------------- c terminate. c----------------------------------------------------------------------- return - end subroutine bicube_c_eval_deriv2 + end subroutine fspline_c_fit_1 + +c----------------------------------------------------------------------- +c subprogram 30. fspline_c_fit_2 +c fits the fourier spline using method 2 (FFT). +c----------------------------------------------------------------------- + subroutine fspline_c_fit_2(handle, endmode, fit_flag_c) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + type(spline_handle), value :: handle + integer(c_int), value :: endmode + logical(c_bool), value :: fit_flag_c + + type(fspline_type), pointer :: fst + logical :: fit_flag +c----------------------------------------------------------------------- +c work. +c----------------------------------------------------------------------- + call c_f_pointer(handle%obj, fst) + if (.not. associated(fst)) then + print *, "fspline_c_fit_2: handle is not associated." + return + end if + + fit_flag = fit_flag_c + call fspline_fit_2(fst, endmode, fit_flag) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_c_fit_2 +c----------------------------------------------------------------------- +c subprogram 31. fspline_c_eval +c evaluates the fourier spline at a given point. +c----------------------------------------------------------------------- + subroutine fspline_c_eval(handle, x, y, f_out) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + type(spline_handle), value :: handle + real(c_double), value :: x, y + type(c_ptr), value :: f_out + + + real(c_double), pointer :: f_f(:) + type(fspline_type), pointer :: fst +c----------------------------------------------------------------------- +c work. +c----------------------------------------------------------------------- + call c_f_pointer(handle%obj, fst) + if (.not. associated(fst)) then + print *, "fspline_c_eval: handle is not associated." + return + end if + + call c_f_pointer(f_out, f_f, [fst%nqty]) + + + call fspline_eval_external(fst, x, y, 0, f_f) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_c_eval +c----------------------------------------------------------------------- +c subprogram 32. fspline_c_eval_deriv +c evaluates the fourier spline and its first derivatives. +c----------------------------------------------------------------------- + subroutine fspline_c_eval_deriv(handle, x, y, f_out, + $ fx_out, fy_out) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + type(spline_handle), value :: handle + real(c_double), value :: x, y + type(c_ptr), value :: f_out, fx_out, fy_out + + type(fspline_type), pointer :: fst + real(c_double), pointer :: f_f(:), f_fx(:), f_fy(:) +c----------------------------------------------------------------------- +c work. +c----------------------------------------------------------------------- + call c_f_pointer(handle%obj, fst) + if (.not. associated(fst)) then + print *, "fspline_c_eval_deriv: handle is not associated." + return + end if + + call c_f_pointer(f_out, f_f, [fst%nqty]) + call c_f_pointer(fx_out, f_fx, [fst%nqty]) + call c_f_pointer(fy_out, f_fy, [fst%nqty]) + + + call fspline_eval_external(fst, x, y, 1, f_f, f_fx, f_fy) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_c_eval_deriv + +c----------------------------------------------------------------------- +c subprogram 33. fspline_c_eval_deriv2 +c evaluates the fourier spline and its second derivatives. +c----------------------------------------------------------------------- + subroutine fspline_c_eval_deriv2(handle, x, y, f_out, + $ fx_out, fy_out, fxx_out, fxy_out, fyy_out) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + type(spline_handle), value :: handle + real(c_double), value :: x, y + type(c_ptr), value :: f_out, fx_out, fy_out + type(c_ptr), value :: fxx_out, fxy_out, fyy_out + + integer(i4) :: s_ix + real(c_double), pointer :: f_f(:), f_fx(:), f_fy(:) + real(c_double), pointer :: f_fxx(:), f_fxy(:), f_fyy(:) + type(fspline_type), pointer :: fst +c----------------------------------------------------------------------- +c work. +c----------------------------------------------------------------------- + call c_f_pointer(handle%obj, fst) + if (.not. associated(fst)) then + print *, "fspline_c_eval_deriv2: handle is not associated." + return + end if + + call c_f_pointer(f_out, f_f, [fst%nqty]) + call c_f_pointer(fx_out, f_fx, [fst%nqty]) + call c_f_pointer(fy_out, f_fy, [fst%nqty]) + call c_f_pointer(fxx_out, f_fxx, [fst%nqty]) + call c_f_pointer(fxy_out, f_fxy, [fst%nqty]) + call c_f_pointer(fyy_out, f_fyy, [fst%nqty]) + + call fspline_eval_external(fst, x, y, 2, f_f, f_fx, f_fy, + $ f_fxx, f_fxy, f_fyy) +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_c_eval_deriv2 +c----------------------------------------------------------------------- +c subprogram 34. fspline_c_get_cspline_handle +c gets a handle to the internal cspline object. +c----------------------------------------------------------------------- + subroutine fspline_c_get_cspline_handle(handle, + $ cs_handle_out) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + type(spline_handle), value, intent(in) :: handle + type(spline_handle), intent(out) :: cs_handle_out + + type(fspline_type), pointer :: fst +c----------------------------------------------------------------------- +c work. +c----------------------------------------------------------------------- + + call c_f_pointer(handle%obj, fst) + + ! Return the C address of the cspline_type component + cs_handle_out%obj = c_loc(fst%cs) + +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_c_get_cspline_handle +c----------------------------------------------------------------------- +c subprogram 35. fspline_c_get_cspline_fs +c gets a copy of the fourier coefficients (fs from cspline). +c----------------------------------------------------------------------- + subroutine fspline_c_get_cspline_fs(handle, fs_out) bind(C) +c----------------------------------------------------------------------- +c declarations. +c----------------------------------------------------------------------- + type(spline_handle), value, intent(in) :: handle + type(c_ptr), value, intent(in) :: fs_out + + type(fspline_type), pointer :: fst + complex(c_double_complex), pointer :: fs_out_fort(:,:) + integer :: cs_mx, cs_nqty +c----------------------------------------------------------------------- +c work. +c----------------------------------------------------------------------- + call c_f_pointer(handle%obj, fst) + if (.not. associated(fst)) then + print *, "fspline_c_get_cspline_fs: invalid handle." + return + end if + + cs_mx = fst%cs%mx + cs_nqty = fst%cs%nqty + call c_f_pointer(fs_out, fs_out_fort, [cs_mx+1, cs_nqty]) + + fs_out_fort = fst%cs%fs +c----------------------------------------------------------------------- +c terminate. +c----------------------------------------------------------------------- + return + end subroutine fspline_c_get_cspline_fs c----------------------------------------------------------------------- end module spline_c_api_mod diff --git a/src/Vacuum/Vacuum.jl b/src/Vacuum/Vacuum.jl index bc555fea7..6aa7383f6 100644 --- a/src/Vacuum/Vacuum.jl +++ b/src/Vacuum/Vacuum.jl @@ -117,7 +117,8 @@ function mscvac( farwal_flag::Bool, grrio::Array{Float64,2}, xzptso::Array{Float64,2}, - op_ahgfile::Union{Nothing,String}=nothing + op_ahgfile::Union{Nothing,String}=nothing, + folder::String="." ) ahgfile_ptr = if op_ahgfile === nothing @@ -126,9 +127,12 @@ function mscvac( Base.cconvert(Ptr{UInt8}, op_ahgfile) end - ccall((:__vacuum_mod_MOD_mscvac, libvac), - Nothing, - (Ptr{ComplexF64}, # wv(mpert,mpert) + # TODO: this allows VACUUM to be called from a specified folder, like the rest of the Julia DCON + # vac.in is hardcoded in the fortran, so this just changes the working directory temporarily for VACUUM + cd(folder) do + ccall((:__vacuum_mod_MOD_mscvac, libvac), + Nothing, + (Ptr{ComplexF64}, # wv(mpert,mpert) Ref{Cint}, # mpert Ref{Cint}, # mtheta Ref{Cint}, # mthvac @@ -139,18 +143,19 @@ function mscvac( Ptr{Cdouble}, # grrio(:,:) Ptr{Cdouble}, # xzptso(:,:) Ptr{UInt8}), # op_ahgfile (optional) - pointer(wv), - Ref(Int32(mpert)), - Ref(Int32(mtheta)), - Ref(Int32(mthvac)), - Ref(Int32(complex_flag)), - Ref(kernelsignin), - Ref(Int32(wall_flag)), - Ref(Int32(farwal_flag)), - pointer(grrio), - pointer(xzptso), - ahgfile_ptr - ) + pointer(wv), + Ref(Int32(mpert)), + Ref(Int32(mtheta)), + Ref(Int32(mthvac)), + Ref(Int32(complex_flag)), + Ref(kernelsignin), + Ref(Int32(wall_flag)), + Ref(Int32(farwal_flag)), + pointer(grrio), + pointer(xzptso), + ahgfile_ptr + ) + end return wv end diff --git a/src/Vacuum/fortran/bzio.c b/src/Vacuum/fortran/bzio.c index 76ec04300..e57951b4f 100644 --- a/src/Vacuum/fortran/bzio.c +++ b/src/Vacuum/fortran/bzio.c @@ -46,7 +46,7 @@ int zop_(int *ioc, char *name, int *nsize, int *idisk, return 0; } - + int zcl_(int *ioc) { close(ofp[*ioc]); @@ -75,7 +75,7 @@ int zrd_(int *ioc, char *a, int *nwords, int *adres, int *lgivup, int *irr) int num_read, ncurr, offsets, nbytes; nbytes = *nwords * WORD_LENGTH; -/* ncurr = ftell(ofp[*ioc]); */ +/* ncurr = ftell(ofp[*ioc]); */ offsets = (*adres - 0 ) * WORD_LENGTH; /* printf("In zrdc: offsets = %d ioc=%d ncurr=%d\n", offsets, *ioc, ncurr); */ @@ -123,7 +123,7 @@ int ZOP_(int *ioc, char *name, int *nsize, int *idisk, return 0; } - + int ZCL_(int *ioc) { close(ofp[*ioc]); @@ -152,7 +152,7 @@ int ZRD_(int *ioc, char *a, int *nwords, int *adres, int *lgivup, int *irr) int num_read, ncurr, offsets, nbytes; nbytes = *nwords * WORD_LENGTH; -/* ncurr = ftell(ofp[*ioc]); */ +/* ncurr = ftell(ofp[*ioc]); */ offsets = (*adres - 0 ) * WORD_LENGTH; /* printf("In zrdc: offsets = %d ioc=%d ncurr=%d\n", offsets, *ioc, ncurr); */ @@ -199,7 +199,7 @@ int zop(int *ioc, char *name, int *nsize, int *idisk, return 0; } - + int zcl(int *ioc) { close(ofp[*ioc]); @@ -228,7 +228,7 @@ int zrd(int *ioc, char *a, int *nwords, int *adres, int *lgivup, int *irr) int num_read, ncurr, offsets, nbytes; nbytes = *nwords * WORD_LENGTH; -/* ncurr = ftell(ofp[*ioc]); */ +/* ncurr = ftell(ofp[*ioc]); */ offsets = (*adres - 0 ) * WORD_LENGTH; /* printf("In zrdc: offsets = %d ioc=%d ncurr=%d\n", offsets, *ioc, ncurr); */ @@ -276,7 +276,7 @@ int ZOP(int *ioc, char *name, int *nsize, int *idisk, return 0; } - + int ZCL(int *ioc) { close(ofp[*ioc]); @@ -305,7 +305,7 @@ int ZRD(int *ioc, char *a, int *nwords, int *adres, int *lgivup, int *irr) int num_read, ncurr, offsets, nbytes; nbytes = *nwords * WORD_LENGTH; -/* ncurr = ftell(ofp[*ioc]); */ +/* ncurr = ftell(ofp[*ioc]); */ offsets = (*adres - 0 ) * WORD_LENGTH; /* printf("In zrdc: offsets = %d ioc=%d ncurr=%d\n", offsets, *ioc, ncurr); */ diff --git a/src/Vacuum/fortran/vacuum_global.f b/src/Vacuum/fortran/vacuum_global.f index 8e62a1eee..ca2371a24 100644 --- a/src/Vacuum/fortran/vacuum_global.f +++ b/src/Vacuum/fortran/vacuum_global.f @@ -279,7 +279,7 @@ SUBROUTINE global_dealloc DEALLOCATE(bxpwr,bxpwi,bzpwr,bzpwi,bnpwr,bnpwi) DEALLOCATE(bxpwtr,bxpwti,bzpwtr,bzpwti,bnpwtr,bnpwti) DEALLOCATE(xilr,xili,xigr,xigi,bnkr,bnki,bthpr,bthpi, - $ gpsjp,bnpptr,bnppti,chipr,chipi) + $ gpsjp,bnpptr,bnppti,chipr,chipi) DEALLOCATE(lfm,bnlr,bnli) c----------------------------------------------------------------------- c terminate. diff --git a/src/Vacuum/fortran/vacuum_io.f b/src/Vacuum/fortran/vacuum_io.f index cdf2fd05e..4d8fb60ba 100644 --- a/src/Vacuum/fortran/vacuum_io.f +++ b/src/Vacuum/fortran/vacuum_io.f @@ -59,7 +59,7 @@ subroutine cardmo USE vglobal_mod implicit real(r8) (a-h,o-z) implicit integer (i-n) - + logical, save :: warned = .false. character(8) under @@ -116,7 +116,7 @@ subroutine cardmo $ " > Vacuum code overriding r",r," from vac.in, to be",0 r=0.0 warned = .true. - endif + endif c----------------------------------------------------------------------- c subsidiary computations. c----------------------------------------------------------------------- diff --git a/src/Vacuum/fortran/vacuum_ma.f b/src/Vacuum/fortran/vacuum_ma.f index b9c110704..a43bfef33 100644 --- a/src/Vacuum/fortran/vacuum_ma.f +++ b/src/Vacuum/fortran/vacuum_ma.f @@ -502,7 +502,7 @@ subroutine funint zork1(i+2) = dlenth(i) enddo zork1(1) = dlenth(mth-1) - zork1(2) = dlenth(mth) + zork1(2) = dlenth(mth) zork1(mth3) = dlenth(1) zork1(mth4) = dlenth(2) zork1(mth5) = dlenth(3) @@ -860,9 +860,9 @@ subroutine pickup(blr,bli,lx,lz,vgdl,vgdx,vgdz,vbx,vbz,vbp) cwrkr(nsew,i) = 0.0 cwrki(nsew,i) = 0.0 end do - + isg = 1 - + call chi ( xwal,zwal,xwalp,zwalp,isg,chiwc,chiws, ns,0, $ cwrkr,cwrki,nsew, blr,bli,rwall ) diff --git a/src/Vacuum/fortran/vacuum_math.f b/src/Vacuum/fortran/vacuum_math.f index 48e2ada34..8b4355d79 100644 --- a/src/Vacuum/fortran/vacuum_math.f +++ b/src/Vacuum/fortran/vacuum_math.f @@ -1118,7 +1118,7 @@ subroutine shft ( i0,i, axi, ax, m, dax ) c termination. c----------------------------------------------------------------------- return - end + end c----------------------------------------------------------------------- c subprogram 15. lagpe4. c routine used by trans and transdx. @@ -1281,7 +1281,7 @@ subroutine eigen(a,r,n,mv) 36 continue if(anorm .LE. 0) then goto 165 - else + else goto 40 endif 40 anorm=1.414*sqrt(anorm) @@ -1356,7 +1356,7 @@ subroutine eigen(a,r,n,mv) 140 if(l-(n-1) == 0) goto 150 145 l=l+1 go to 55 - 150 if(ind-1 .ne. 0) goto 160 + 150 if(ind-1 .ne. 0) goto 160 155 ind=0 go to 50 160 if(thr-anrmx .gt. 0) go to 45 diff --git a/src/Vacuum/fortran/vacuum_penn.f b/src/Vacuum/fortran/vacuum_penn.f index 12f5083ff..c1fffc1c4 100644 --- a/src/Vacuum/fortran/vacuum_penn.f +++ b/src/Vacuum/fortran/vacuum_penn.f @@ -38,7 +38,7 @@ subroutine cleanup return end c----------------------------------------------------------------------- -c subprogram 3. shellb. +c subprogram 3. shellb. c----------------------------------------------------------------------- subroutine shellb USE vglobal_mod, ONLY: r8 diff --git a/src/Vacuum/fortran/vacuum_sprk2.f b/src/Vacuum/fortran/vacuum_sprk2.f index b52c658ad..c75ee26be 100644 --- a/src/Vacuum/fortran/vacuum_sprk2.f +++ b/src/Vacuum/fortran/vacuum_sprk2.f @@ -21,7 +21,7 @@ c----------------------------------------------------------------------- c declarations. c----------------------------------------------------------------------- - subroutine testvec + subroutine testvec USE vglobal_mod implicit real(r8) (a-h,o-z) implicit integer (i-n) @@ -153,8 +153,8 @@ subroutine vecpot ( xobs,zobs,nobs, xsce,zsce,xscp,zscp,nsce, $ isg,cplar,cplai,cslth,snlth, 1,1, $ cpwr,cpwi, dchxr,dchxi,dchzr,dchzi) if ( abs(n) .lt. 1.e-10 ) then - write ( outmod, 11 ) - write ( iotty, 11 ) + write ( outmod, 11 ) + write ( iotty, 11 ) return endif do iobs = 1, nobs @@ -217,7 +217,7 @@ subroutine grchi(xobs,zobs,nobs, xsce,zsce,xscp,zscp,ns, do io5 = 1, 5 xs = yes1*(xobs(io) + (io5-3)*delx) + yes2*xobs(io) zs = yes2*(zobs(io) + (io5-3)*delz) + yes1*zobs(io) - $ + $ if ( (io5 .ne. 3) .or. (ixz .ne. 2) ) then do is = 1, ns xt = xsce(is) @@ -243,8 +243,8 @@ subroutine grchi(xobs,zobs,nobs, xsce,zsce,xscp,zscp,ns, enddo enddo do l1 = 1, jmax1 - chrl(io5,l1) = 0.5 * isg*dtpw * chrl(io5,l1) - chil(io5,l1) = 0.5 * isg*dtpw * chil(io5,l1) + chrl(io5,l1) = 0.5 * isg*dtpw * chrl(io5,l1) + chil(io5,l1) = 0.5 * isg*dtpw * chil(io5,l1) enddo endif enddo diff --git a/src/Vacuum/fortran/vacuum_ut.f b/src/Vacuum/fortran/vacuum_ut.f index f036be944..20c7d07c4 100644 --- a/src/Vacuum/fortran/vacuum_ut.f +++ b/src/Vacuum/fortran/vacuum_ut.f @@ -560,9 +560,9 @@ subroutine nwvgti ( cdfid, vid, start, count,nd, val0, vals, c----------------------------------------------------------------------- do i2 = 1, count(2) do i1 = 1, count(1) - vals(i1,i2) = val0( i1+(i2-1)*count(1) ) + vals(i1,i2) = val0( i1+(i2-1)*count(1) ) enddo - enddo + enddo if ( rcode .gt. 0 ) call errnc ( "ncvgt", rcode, nout ) do io = 1, 3 if ( nout(io) .gt. 0 ) then @@ -690,7 +690,7 @@ subroutine nwainq ( cdfid, vid, attnam, attype, attlen, rcode, c----------------------------------------------------------------------- c print message. c----------------------------------------------------------------------- - if ( rcode .gt. 0 ) call errnc ( "ncainq", rcode, nout ) + if ( rcode .gt. 0 ) call errnc ( "ncainq", rcode, nout ) do io = 1, 3 if ( nout(io) .gt. 0 ) then write ( nout(io), 100 ) cdfid, vid, attnam, @@ -856,7 +856,7 @@ subroutine writn1 ( mesage, n, nout ) c----------------------------------------------------------------------- c format statements. c----------------------------------------------------------------------- - 100 format ( a, i5 ) + 100 format ( a, i5 ) c----------------------------------------------------------------------- c print message. c----------------------------------------------------------------------- @@ -886,7 +886,7 @@ subroutine writnn ( mesage, n, nd, nout ) c----------------------------------------------------------------------- c format statements. c----------------------------------------------------------------------- - 100 format ( a, 5i5 ) + 100 format ( a, 5i5 ) c----------------------------------------------------------------------- c print message. c----------------------------------------------------------------------- @@ -917,7 +917,7 @@ subroutine writa1 ( mesage, string1, nout ) c----------------------------------------------------------------------- c format statements. c----------------------------------------------------------------------- - 100 format ( a, a ) + 100 format ( a, a ) c----------------------------------------------------------------------- c print message. c----------------------------------------------------------------------- @@ -947,7 +947,7 @@ subroutine writv1 ( mesage, a, nout ) c----------------------------------------------------------------------- c format statements. c----------------------------------------------------------------------- - 100 format ( a, 1pe12.4 ) + 100 format ( a, 1pe12.4 ) c----------------------------------------------------------------------- c print message. c----------------------------------------------------------------------- @@ -1190,7 +1190,7 @@ subroutine boundsi ( x1,z1, n1,n2, xmin,xmax, zmin,zmax, xmin = 1.0e30 zmin = 1.0e30 do i = n1, n2 - if ( xmin .gt. x1(i) ) then + if ( xmin .gt. x1(i) ) then xmin = x1(i) ixn = i endif diff --git a/src/Vacuum/fortran/vacuum_vac.f b/src/Vacuum/fortran/vacuum_vac.f index c816839c5..aee597b62 100644 --- a/src/Vacuum/fortran/vacuum_vac.f +++ b/src/Vacuum/fortran/vacuum_vac.f @@ -129,9 +129,9 @@ END SUBROUTINE kernel call kernel(xpla,zpla,xpla,zpla,grdgre,grwp,j1,j2,ksgn,1,1,0) if ( checkd .and. (lfele .eq. 0) ) then call matwrtn ( grwp,nths,nths,1,1,mth,mth,16,8, - $ "grwp at 1,1", outmod, iotty ) + $ "grwp at 1,1", outmod, iotty ) call matwrtn ( grdgre,nths2,nths2,1,1,mth,mth,mth,mth, - $ "grdgre at 1,1", outmod, iotty ) + $ "grdgre at 1,1", outmod, iotty ) endif do i = 1, mth2 grwp(i,mth1) = grwp(i,1) @@ -225,9 +225,9 @@ END SUBROUTINE kernel endif if ( checkd .and. (lfele .eq. 0) ) then call matwrtn ( grwp,nths,nths,1,1,mth,mth,16,8, - $ "grwp at end", outmod, iotty ) + $ "grwp at end", outmod, iotty ) call matwrtn ( grdgre,nths2,nths2,1,1,mth12,mth12,16,8, - $ "grdgre at end", outmod, iotty ) + $ "grdgre at end", outmod, iotty ) endif write ( iotty, '(/, $ "Sum of first COLUMN in each block of GRDGRE:",/)') @@ -288,7 +288,7 @@ END SUBROUTINE kernel write ( outmod,8050 ) ier write ( iotty, 8050 ) ier if ( lspark .ne. 0 ) then - write ( iodsk, 8312 ) + write ( iodsk, 8312 ) write ( iodsk, 8311 ) jmax1, mth12 do jwdsk = 1, lmax2 write ( iodsk, 8313 ) ( grri(iwdsk,jwdsk),iwdsk=1,mth12 ) @@ -405,7 +405,7 @@ END SUBROUTINE kernel do j1 = 1, jmax1 do j2 = 1, jmax1 vacmat(j1,j2) = arr(j1,j2) + aii(j1,j2) - vacmti(j1,j2) = air(j1,j2) - ari(j1,j2) + vacmti(j1,j2) = air(j1,j2) - ari(j1,j2) enddo enddo endif @@ -427,11 +427,11 @@ END SUBROUTINE kernel call gatonorm ( vacmat, gatovac, nfm, rgato,mfel,mth, $ qa1,twopi ) call matwrtn ( gatovac,nfm,nfm,ln,ln,jmax1,jmax1,8,8, - $ "GATOVAC", outmod,iotty ) + $ "GATOVAC", outmod,iotty ) endif if ( check1 ) $ call msctimer ( outmod, "end of vacmat" ) - if ( lgato .eq. 2 ) then + if ( lgato .eq. 2 ) then call orchek ( air, ari, rmatr, rmati, work, work1 ) do j1 = 1, jmax1 do j2 = 1, jmax1 @@ -457,7 +457,7 @@ END SUBROUTINE kernel call gatonorm ( rmatr, gatovac, nfm, rgato,mfel,mth, $ qa1,twopi ) call matwrtn ( gatovac,nfm,nfm,1,1,mfel,mfel,8,8, - $ "GATOVAC", outmod,iotty ) + $ "GATOVAC", outmod,iotty ) endif deallocate(arr,ari,air,aii) write ( outmod, 500 ) n,q, nj,mj,lj @@ -576,7 +576,7 @@ END SUBROUTINE kernel call zop (iovac,"vacout",len,ndsk,iiff,999) lgivup=1 call zwr(iovac,rmatr,mtots,1,lgivup,999) - call zcl ( iovac, 999 ) + call zcl ( iovac, 999 ) else j12 = 1 do j2 = 1, jmax1 @@ -675,7 +675,7 @@ SUBROUTINE kernel(xobs,zobs,xsce,zsce,grdgre,gren, IF(lfele /= 0)THEN wsimpb1=dth/two wsimpb2=dth - wsimpb4=dth + wsimpb4=dth ELSE wsimpb1=dth/three wsimpb2=two*dth/three @@ -2088,7 +2088,7 @@ subroutine fanal1 ( gi,ndi1,ndi2,mi1, gor,goi,ndo1,ndo2 ) do l2 = 1, jmax1 ll2 = l2 - 1 + lmin(1) do i = 1, mth - elth = ll2*(i-1)*dth + elth = ll2*(i-1)*dth gor(l1,l2) = gor(l1,l2) $ + cos(elth) * gi(mi1+i,l1) $ + sin(elth) * gi(mi1+i,jmax1+l1) @@ -2199,8 +2199,8 @@ subroutine felanv ( gil, gll, cs, m00,l00 ) zwt1 = 0.5 * dth * znorm zwt2 = dth * znorm zws1 = dth * znorm /3.0 - zws2 = 2.0 * zws1 - zws4 = 2.0 * zws2 + zws2 = 2.0 * zws1 + zws4 = 2.0 * zws2 nzdel = ndfel nzdel1 = nzdel + 1 q = qa1 @@ -2235,7 +2235,7 @@ subroutine felanv ( gil, gll, cs, m00,l00 ) if ( jth1 .ne. mth ) then gll(l1,l2) = gll(l1,l2) + $ zwt * gil(m00+jth1,l00+l2) * cs(jth1) * twopi - else + else gll(l1,l2) = gll(l1,l2) $ + zwt * gil(m00+1,l00+l2) * cs(jth1) * twopi endif @@ -2269,7 +2269,7 @@ subroutine fotofi ( vin,vout, scnlth, wrk1, wrk2, iopsc ) c----------------------------------------------------------------------- jmax1 = lmax(1) - lmin(1) + 1 call tmat ( scnlth, wrk1, iopsc ) - call matmul3 ( wrk1, vin, nfm,nfm, mfel,jmax1,jmax1, wrk2,nfm ) + call matmul3 ( wrk1, vin, nfm,nfm, mfel,jmax1,jmax1, wrk2,nfm ) call mtrans ( wrk1, nfm, nfm ) call matmul3 ( wrk2, wrk1, nfm,nfm, mfel,jmax1,mfel, vout,nfm ) c----------------------------------------------------------------------- @@ -2336,7 +2336,7 @@ end subroutine orchek c----------------------------------------------------------------------- c subprogram 21. tmat. c calculates the matrix for transforming from Fourier to finite -c elements. +c elements. c----------------------------------------------------------------------- c----------------------------------------------------------------------- c declarations. @@ -2356,7 +2356,7 @@ subroutine tmat ( sil, tll, iop ) pi = pye do i = 1, nfm do j = 1, nfm - tll(i,j) = 0.0 + tll(i,j) = 0.0 end do end do if ( iop .eq. 0 ) then diff --git a/test/runtests.jl b/test/runtests.jl index 86426429c..fc69e0437 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -17,4 +17,6 @@ else include("./runtests_build.jl") include("./runtests_spline.jl") include("./runtests_vacuum_fortran.jl") + include("./runtests_ode.jl") + include("./runtests_sing.jl") end \ No newline at end of file diff --git a/test/runtests_ode.jl b/test/runtests_ode.jl new file mode 100644 index 000000000..b8581f4e8 --- /dev/null +++ b/test/runtests_ode.jl @@ -0,0 +1,131 @@ +using LinearAlgebra + +# TODO: perhaps this isn't the best place for this function? +# Should I do include("../dcon/utils.jl") instead? or maybe save these functions in a separate file? +# associated TODO: come up with Gaussian reduction test that doesn't rely on external data + +function load_u_matrix(filename) + lines = readlines(filename) + data = [parse.(Float64, split(l)) for l in lines[2:end]] + i_vals = Int.(getindex.(data, 1)) + j_vals = Int.(getindex.(data, 2)) + ncols = (length(data[1]) - 2) ÷ 2 + imax = maximum(i_vals) + jmax = maximum(j_vals) + mat = zeros(ComplexF64, imax, jmax, ncols) + for row in data + i = Int(row[1]) + j = Int(row[2]) + for k in 1:ncols + re = Float64(row[2*k+1]) + im = Float64(row[2*k+2]) + mat[i, j, k] = complex(re, im) + end + end + return mat +end + +@testset "ODE Tests" begin + @testset "ode_fixup!" begin + # Initialize to random u + msol = 5 + ifix = 1 + odet = JPEC.DCON.OdeState(msol, msol, 10, 10, 10) + odet.u = randn(ComplexF64, msol, msol, 2) + odet.unorm = [norm(odet.u[:,i,1]) for i in 1:msol] + odet.ifix = ifix + odet.fixfac = zeros(ComplexF64, odet.msol, odet.msol, ifix) + intr = JPEC.DCON.DconInternal() + intr.mpert = msol + outp = JPEC.DCON.DconOutput(; write_crit_out = false, write_dcon_out = false, write_euler_h5 = false, write_eqdata_h5 = false) + + # Save copy of original u and run + u_orig = copy(odet.u) + JPEC.DCON.ode_fixup!(odet, intr, outp, false, false) + + # Very simple tests + @test !all(odet.u .== u_orig) # u should have changed + @test all(abs.(diag(odet.fixfac[:, :, ifix])) .≈ 1) # diagonal of fixfac = 1 + + # TODO: come up with triangularization check + # --- Triangularization check (primary solutions) --- + # for isol in 1:intr.mpert + # ksol = isol + # kpert = findmax(abs.(odet.u[:, ksol, 1]))[2] + # for jsol in 1:odet.msol + # if jsol != ksol + # println("kpert, jsol = ", kpert, ", ", jsol) + # @test isapprox(abs(odet.u[kpert, jsol, 1]), 0.0; atol=1e-12) + # end + # end + # end + + # --- Real Fortran data check --- + msol = 31 + odet = JPEC.DCON.OdeState(msol, msol, 10, 10, 10) + # We'll load in Fortran data for u pulled before and after a fixup + # Note that this was generated by manually setting + # unorm = [norm(odet.u[:,i,1]) for i in 1:msol] in the Fortran to avoid + # also having to save unorm0 + odet.u = load_u_matrix(joinpath(@__DIR__, "test_data", "u_prefixup.dat")) + odet.unorm = [norm(odet.u[:,i,1]) for i in 1:msol] + odet.ifix = ifix + odet.fixfac = zeros(ComplexF64, odet.msol, odet.msol, ifix) + intr = JPEC.DCON.DconInternal(mpert=msol) + + JPEC.DCON.ode_fixup!(odet, intr, outp, false, false) + + u_fortran = load_u_matrix(joinpath(@__DIR__, "test_data", "u_postfixup.dat")) + # test that the outputs are approximately equivalent (1e-3 seems ok to account for loading differences) + @test all(abs.(odet.u .- u_fortran) .< 1e-3) + + end + + @testset "ode_unorm!" begin + msol = 2 + odet = JPEC.DCON.OdeState(msol, msol, 10, 10, 10) + intr = JPEC.DCON.DconInternal() + intr.mpert = msol + ctrl = JPEC.DCON.DconControl() + ctrl.ucrit = 10.0 + outp = JPEC.DCON.DconOutput(; write_crit_out = false, write_dcon_out = false, write_euler_h5 = false, write_eqdata_h5 = false) + + # Case 1: Basic norm computation + odet.u = zeros(ComplexF64, 2, 2, 2) + odet.u[:,1,1] .= [3, 4] # norm = 5 + odet.u[:,2,1] .= [0, 2] # norm = 2 + + JPEC.DCON.ode_unorm!(odet, intr, ctrl, outp, false) + # After the first run with new=True (default), unorm0 should be set to unorm + # and new should be false + @test odet.unorm[1:intr.mpert] ≈ [5, 2] + @test odet.unorm0 == odet.unorm + @test odet.new == false + + # Case 2: Error on zero norm + odet.u[:,1,1] .= 0 + odet.new = true + @test_throws ErrorException JPEC.DCON.ode_unorm!(odet, intr, ctrl, outp, false) + + # Case 3: Normalization on second call + odet.u[:,1,1] .= [3,4] # norm = 5 + odet.u[:,2,1] .= [0,2] # norm = 2 + odet.new = false + JPEC.DCON.ode_unorm!(odet, intr, ctrl, outp, false) + @test odet.unorm[1:intr.mpert] ≈ [1,1] + + # Case 4: Trigger fixup via ucrit + odet.unorm0 = ones(2*intr.mpert) + odet.u[:,1,1] .= [1000,0] # large norm + odet.u[:,2,1] .= [1,0] # small norm + JPEC.DCON.ode_unorm!(odet, intr, ctrl, outp, false) + @test odet.new == true # implies fixup ran + + # Case 5: Trigger fixup via sing_flag + odet.new = false + odet.u[:,1,1] .= [1,0] + odet.u[:,2,1] .= [1,0] + JPEC.DCON.ode_unorm!(odet, intr, ctrl, outp, true) + @test odet.new == true # fixup triggered + end +end \ No newline at end of file diff --git a/test/runtests_sing.jl b/test/runtests_sing.jl new file mode 100644 index 000000000..8fecc2311 --- /dev/null +++ b/test/runtests_sing.jl @@ -0,0 +1,22 @@ +@testset "Test Sing Functions" begin + @testset " Test sing_der " begin + # du = zeros(ComplexF64, intr.mpert, odet.msol, 2) + # Initialize u with some value, e.g., ones + # odet.u .= ones(ComplexF64, size(odet.u)) + # Initialize structs with relevant data, can do something like + # ffit = FourfitVars() + # amat = load in from test_data folder + # ffit.amats = SplinesMod.CubicSpline("some psi", reshape(amats, mpsi+1, :); bctype="extrap") + # if using one psi values causes issues, can make a psi array and just fill it all with amat + # repeat for other matrices, equil data, other relevant constants, etc. + + # params = (ctrl, equil, intr, odet, ffit) + # sing_der!(du, odet.u, params, odet.psifac) + + # load in du from fortran + # @test du == expected_du (to within some error) + end + + @testset " Test sing_find " begin # continue with other functions + end +end \ No newline at end of file diff --git a/test/runtests_spline.jl b/test/runtests_spline.jl index 678908745..7ec7193f7 100644 --- a/test/runtests_spline.jl +++ b/test/runtests_spline.jl @@ -1,55 +1,93 @@ @testset "Test Spline Module" begin +# TODO: add Fourier spline unit test, test against a theoretical error limit for splines? +# testing for all boundary conditions try # Test the spline setup and evaluation functions @info "Testing spline setup and evaluation" - # Make sine and cosine spline - xs = range(0.0; stop=2 * pi, length=21) - xs = collect(xs) - fs = sin.(xs) - fc = cos.(xs) - # Make a vector of vectors of (100,2) for the spline - fs_matrix = hcat(fs, fc) - # print(xs) - spline = JPEC.SplinesMod.spline_setup(xs, fs_matrix, 2) + # Make x^3 spline (a polynomial spline should be highly accurate) + xs = collect(range(1, stop=2, length=21)) + fx3 = xs .^ 3 + fs_matrix = hcat(fx3) + spline = JPEC.Spl.CubicSpline(xs, fs_matrix, bctype="extrap"); + + # Interpolate + extrapolate the spline on a finer grid + xs_fine = collect(range(0.9, stop=2.1, length=100)); + fs_fine, fsx_fine, fsxx_fine, fsxxx_fine = JPEC.SplinesMod.spline_eval(spline, xs_fine, 3); + # Check accuracy of spline for x^3 and its derivatives + @test maximum(abs.(fs_fine .- xs_fine .^ 3)) < 1e-8 + @test maximum(abs.(fsx_fine .- 3 .* xs_fine .^ 2)) < 1e-7 + @test maximum(abs.(fsxx_fine .- 6 .* xs_fine)) < 1e-7 + @test maximum(abs.(fsxxx_fine .- 6.0)) < 1e-6 + + # Make sine spline + xs = collect(range(π/8, stop=3π/8, length=50)) + fs = sin.(xs) + spline = JPEC.Spl.CubicSpline(xs, fs, bctype="extrap"); - xs_fine = collect(range(0.0; stop=2 * pi, length=100)) - fs_fine = JPEC.SplinesMod.spline_eval(spline, xs_fine) + # Interpolate the spline on a finer grid + xs_fine = collect(range(π/6, stop=π/3, length=100)); + fs_fine, fsx_fine, fsxx_fine, fsxxx_fine = JPEC.SplinesMod.spline_eval(spline, xs_fine, 3); + # Check accuracy of spline (higher tolerances for higher derivatives) + @test maximum(abs.(fs_fine .- sin.(xs_fine))) < 1e-6 + @test maximum(abs.(fsx_fine .- cos.(xs_fine))) < 1e-4 + @test maximum(abs.(fsxx_fine .+ sin.(xs_fine))) < 1e-3 + @test maximum(abs.(fsxxx_fine .+ cos.(xs_fine))) < 1e-2 # Make e^-ix and e^ix complex valued spline - xs = range(0.0; stop=2 * pi, length=20) - xs = collect(xs) + xs = collect(range(0, stop=6, length=100)) fm = exp.(-im .* xs) fp = exp.(im .* xs) - # Make a vector of vectors of (100,2) for the spline fs_matrix = hcat(fm, fp) + spline = JPEC.Spl.CubicSpline(xs, fs_matrix, bctype="extrap") + + xs_fine = collect(range(2, stop=2.5, length=100)) + fs_fine, fsx_fine, fsxx_fine, fsxxx_fine = JPEC.SplinesMod.spline_eval(spline, xs_fine, 3) + + # Check accuracy for e^-ix and e^ix and their derivatives + # Note: third derivative begins to lose accuracy due to oscillatory nature + @test maximum(abs.(fs_fine[:,1] .- exp.(-im .* xs_fine))) < 1e-7 + @test maximum(abs.(fsx_fine[:,1] .+ im .* exp.(-im .* xs_fine))) < 1e-5 + @test maximum(abs.(fsxx_fine[:,1] .- (-1) .* exp.(-im .* xs_fine))) < 1e-3 + @test maximum(abs.(fsxxx_fine[:,1] .- im .* exp.(-im .* xs_fine))) < 5e-2 + @test maximum(abs.(fs_fine[:,2] .- exp.(im .* xs_fine))) < 1e-7 + @test maximum(abs.(fsx_fine[:,2] .- im .* exp.(im .* xs_fine))) < 1e-5 + @test maximum(abs.(fsxx_fine[:,2] .- (-1) .* exp.(im .* xs_fine))) < 1e-3 + @test maximum(abs.(fsxxx_fine[:,2] .+ im .* exp.(im .* xs_fine))) < 5e-2 + + # Test bicubic spline setup and evaluation for a 2D function + xs = collect(range(0, stop=2π, length=100)) + ys = collect(range(0, stop=2π, length=100)) + + f1(x, y) = sin(x) * cos(y) + 1 + f2(x, y) = cos(x) * sin(y) + 1 + fvals = Array{Float64}(undef, length(xs), length(ys), 2) + for (ix, x) in enumerate(xs), (iy, y) in enumerate(ys) + fvals[ix, iy, 1] = f1(x, y) + fvals[ix, iy, 2] = f2(x, y) + end + + bcspline = JPEC.Spl.BicubicSpline(xs, ys, fvals) + + xs_fine = collect(range(π/2, stop=π, length=100)) + ys_fine = collect(range(0, stop=π/2, length=100)) + fs_fine, fsx_fine, fsy_fine = JPEC.Spl.bicube_eval(bcspline, xs_fine, ys_fine, 1) + + X, Y = [x for x in xs_fine, y in ys_fine], [y for x in xs_fine, y in ys_fine] + f1_true = sin.(X) .* cos.(Y) .+ 1 + f1x_true = cos.(X) .* cos.(Y) + f1y_true = -sin.(X) .* sin.(Y) + f2_true = cos.(X) .* sin.(Y) .+ 1 + f2x_true = -sin.(X) .* sin.(Y) + f2y_true = cos.(X) .* cos.(Y) - spline = JPEC.SplinesMod.spline_setup(xs, fs_matrix, 2) - - xs_fine = collect(range(0.0; stop=2 * pi, length=100)) - fs_fine = JPEC.SplinesMod.spline_eval(spline, xs_fine) - - # make a bicubic spline of a 2d periodic function - xs = range(0.0; stop=2 * pi, length=20) - ys = range(0.0; stop=2 * pi, length=20) - xs = collect(xs) - ys = collect(ys) - fs1 = sin.(xs') .* cos.(ys) .+ 1.0 - fs2 = cos.(xs') .* sin.(ys) .+ 1.0 - fs = zeros(20, 20, 2) - # fs is a 20x20x2 array - fs[:, :, 1] = fs1 - fs[:, :, 2] = fs2 - - bcspline = JPEC.SplinesMod.bicube_setup(xs, ys, fs, 2, 2) - - # Evaluate the bicubic spline - xs_fine = collect(range(0.0; stop=2 * pi, length=100)) - ys_fine = collect(range(0.0; stop=2 * pi, length=100)) - # fs_fine, fsx_fine, fsy_fine, fsxx_fine, fsxy_fine, fsyy_fine = JPEC.SplinesMod.bicube_eval(bcspline, xs_fine, ys_fine, 2) - fs_fine, fsx_fine, fsy_fine = JPEC.SplinesMod.bicube_eval(bcspline, xs_fine, ys_fine, 1) - @test true - @info "All spline tests passed successfully" + # Check accuracy + @test maximum(abs.(fs_fine[:, :, 1] .- f1_true)) < 1e-6 + @test maximum(abs.(fsx_fine[:, :, 1] .- f1x_true)) < 1e-5 + @test maximum(abs.(fsy_fine[:, :, 1] .- f1y_true)) < 1e-4 + @test maximum(abs.(fs_fine[:, :, 2] .- f2_true)) < 1e-6 + @test maximum(abs.(fsx_fine[:, :, 2] .- f2x_true)) < 1e-5 + @test maximum(abs.(fsy_fine[:, :, 2] .- f2y_true)) < 1e-4 catch e @test false @error "Spline tests failed: $e" diff --git a/test/runtests_vacuum_fortran.jl b/test/runtests_vacuum_fortran.jl index 8e0b60520..9e4647fc8 100644 --- a/test/runtests_vacuum_fortran.jl +++ b/test/runtests_vacuum_fortran.jl @@ -29,7 +29,7 @@ wv, mpert, mtheta, mthvac, complex_flag, kernelsignin, wall_flag, farwal_flag, - grrio, xzptso, op_ahgfile + grrio, xzptso, op_ahgfile, joinpath(@__DIR__, ".") ) @info "mscvac OK!" catch e diff --git a/test/test_data/README_test_data.md b/test/test_data/README_test_data.md new file mode 100644 index 000000000..8b5395317 --- /dev/null +++ b/test/test_data/README_test_data.md @@ -0,0 +1,3 @@ +Put relevant data for various tests here, most likely outputs from the Fortran code used to validate Julia outputs + +# TODO: store as hdf5 files instead? \ No newline at end of file diff --git a/test/test_data/u_postfixup.dat b/test/test_data/u_postfixup.dat new file mode 100644 index 000000000..b43262248 --- /dev/null +++ b/test/test_data/u_postfixup.dat @@ -0,0 +1,962 @@ + i j Re(u1) Im(u1) Re(u2) Im(u2) + 1 1 -1.01296208E-02 9.84199592E-03 -2.07928660E-02 3.51437374E-02 + 1 2 -3.79698452E-03 -1.22595189E-03 -1.14944457E-02 -1.37415297E-02 + 1 3 2.40132449E-03 6.87572092E-04 3.28300317E-03 2.46442243E-03 + 1 4 1.76530756E-06 1.30028703E-03 -7.03571181E-04 1.80212277E-03 + 1 5 1.19590141E-04 -4.31672493E-04 -3.30654545E-04 -3.58881563E-04 + 1 6 5.80809915E-04 3.44724140E-04 5.08978832E-04 2.70016104E-04 + 1 7 1.58223003E+03 1.96761581E-03 1.77699110E+03 2.46791423E-03 + 1 8 -4.30402653E-05 9.42704535E-05 -1.34003505E-04 2.15509005E-04 + 1 9 -1.78910298E+01 -2.54240845E-04 -2.46288585E+01 -3.75350291E-04 + 1 10 2.49492596E-04 -2.59295216E-04 2.48955196E-04 -2.93911704E-04 + 1 11 2.29944896E+02 -6.98804065E-05 2.58237838E+02 -1.18485873E-04 + 1 12 -1.36692676E-04 2.69425471E-04 -1.07850089E-04 2.92187514E-04 + 1 13 -7.92928499E+00 2.19114365E-05 -9.63281047E+00 2.85568290E-05 + 1 14 -3.39905072E-05 -4.20404659E-05 -2.45131495E-05 -3.27835147E-05 + 1 15 1.18292082E+02 3.31875324E-05 1.32847421E+02 3.49138237E-05 + 1 16 7.58716058E-05 -1.96615311E-05 -2.35040007E-05 -1.76017113E-05 + 1 17 0.00000000E+00 0.00000000E+00 -3.44259664E-01 -3.72066221E-06 + 1 18 1.40728790E-04 -1.11271834E-05 1.54741485E-04 -2.09726295E-06 + 1 19 0.00000000E+00 0.00000000E+00 6.73383614E-03 2.33222266E-06 + 1 20 1.01333793E-03 -2.34082120E-05 1.14231798E-03 -2.49181520E-05 + 1 21 0.00000000E+00 0.00000000E+00 3.63156226E-04 8.06603317E-07 + 1 22 0.00000000E+00 0.00000000E+00 8.46489723E-06 8.07575438E-07 + 1 23 0.00000000E+00 0.00000000E+00 1.57106095E-03 -1.39449291E-07 + 1 24 -2.09785925E-03 -2.50325829E-06 -2.36190869E-03 -2.63297777E-06 + 1 25 0.00000000E+00 0.00000000E+00 3.99384281E-05 3.70762783E-08 + 1 26 0.00000000E+00 0.00000000E+00 -1.50842469E-05 1.93087382E-08 + 1 27 0.00000000E+00 0.00000000E+00 -1.87642201E-04 -3.94309953E-08 + 1 28 2.43663843E-05 9.46433839E-06 -3.01317903E-04 3.84703806E-05 + 1 29 0.00000000E+00 0.00000000E+00 -7.98658783E-06 2.23460659E-08 + 1 30 0.00000000E+00 0.00000000E+00 -6.63661147E-06 -5.96867366E-09 + 1 31 0.00000000E+00 0.00000000E+00 -2.61411972E-11 -2.91090315E-13 + 2 1 -2.77405328E-04 -2.40491759E-03 -3.07898136E-02 -2.88639091E-02 + 2 2 2.05783495E-02 -1.54875106E-03 -4.74715502E-03 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