Deprecate Banded Matrices in ForceFreeStates

[jhalpern30]

A long overdue removal of mband related terms within ForceFreeStates that clutters up the code. This PR closes#50.

Basically we decided banded matrices were untested and not applicable for perturbed equilibria, so having this functionality only added unnecessary complexity. Since mband = mpert - 1 in this case, this PR replaces this throughout the code and simplifies things where necessary.

Note that there is still some banded matrix code that exists in the Galerkin solver that I am not touching here. @matt-pharr can decide whether or not this stays since I don't know that part of the code

[jhalpern30]

@copilot review this PR

[Copilot]

Pull request overview

This PR removes the deprecated/unused “banded matrix” plumbing from the ForceFreeStates stability pipeline (closing #50) by eliminating mband/delta_mband concepts and consistently treating the coupled operators as dense over the full mpert range. It also renames the FFT coefficient container field from mband → mmax to better reflect “highest retained mode”.

Changes:

• Remove delta_mband from user configs and remove mband from ForceFreeStates internal/control structs and matrix-build paths, switching indexing/loop bounds to mpert.
• Update metric/Fourier coefficient handling (Utilities.FourierCoefficients) and all call sites/tests/docs from mband → mmax.
• Refresh examples, regression TOMLs, tests, and benchmark scripts to match the new API and parameter set.

Reviewed changes

Copilot reviewed 33 out of 33 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
test/test_data/regression_solovev_kinetic_multi_n/gpec.toml	Drops delta_mband from regression config.
test/test_data/regression_solovev_kinetic_example/gpec.toml	Drops delta_mband from regression config.
test/test_data/regression_solovev_kinetic_calculated/gpec.toml	Drops delta_mband from regression config.
test/test_data/regression_solovev_ideal_example/gpec.toml	Drops delta_mband from regression config.
test/test_data/regression_solovev_ideal_example_multi_n/gpec.toml	Drops delta_mband from regression config.
test/runtests_utilities.jl	Updates assertions to use FourierCoefficients.mmax.
test/runtests_sing.jl	Updates FourFitVars construction to remove mband kwarg.
test/runtests_riccati.jl	Removes mband usage in setup and updates make_metric call signature.
test/runtests_parallel_integration.jl	Removes mband setup/usage and updates make_metric calls.
test/runtests_fouriertransforms.jl	Updates empty FourierCoefficients test to use mmax.
src/Utilities/FourierCoefficients.jl	Renames mband → mmax and keeps Nyquist clamping logic.
src/PerturbedEquilibrium/FieldReconstruction.jl	Removes mband coupling limits and reindexes convolution buffers by mpert.
src/GeneralizedPerturbedEquilibrium.jl	Removes delta_mband/mband runtime logic and updates make_metric call + output fields.
src/ForceFreeStates/Sing.jl	Removes band-limited loop bounds; treats matrices as fully dense over mpert.
src/ForceFreeStates/Free.jl	Removes mband destructuring and reindexes jmat lookups by mpert.
src/ForceFreeStates/Fourfit.jl	Changes make_metric API to (equil, mpert) and threads mpert through Fourier/matrix assembly.
src/ForceFreeStates/ForceFreeStatesStructs.jl	Removes mband from structs and adjusts FourFitVars storage sizing to mpert.
examples/Solovev_ideal_example/gpec.toml	Drops delta_mband from example config.
examples/Solovev_ideal_example_multi_n/single_n_2/gpec.toml	Drops delta_mband from example config.
examples/Solovev_ideal_example_multi_n/single_n_1/gpec.toml	Drops delta_mband from example config.
examples/Solovev_ideal_example_multi_n/gpec.toml	Drops delta_mband from example config.
examples/Solovev_ideal_example_3D/gpec.toml	Drops delta_mband from example config.
examples/LAR_epsilon_scan/gpec.toml	Drops delta_mband from example config.
examples/LAR_beta_scan/gpec.toml	Drops delta_mband from example config.
examples/DIIID-like_ideal_example/gpec.toml	Drops delta_mband from example config.
examples/a10_kinetic_example/gpec.toml	Drops delta_mband from example config.
docs/src/utilities.md	Updates documentation to use fc.mmax.
docs/src/stability.md	Updates stability docs to remove mband and use new make_metric call.
benchmarks/benchmark_threads.jl	Updates benchmark setup to remove mband and use (equil, intr.mpert) metric call.
benchmarks/benchmark_riccati_der.jl	Updates benchmark setup to remove mband and use (equil, intr.mpert) metric call.
benchmarks/benchmark_diiid_kinetic_stability.jl	Removes delta_mband from generated TOML and updates formatting.
benchmarks/benchmark_diiid_ideal_ntv_torque.jl	Removes delta_mband from generated TOML and updates make_metric call.
benchmarks/benchmark_delta_prime_methods.jl	Updates benchmark setup to remove mband and use (equil, intr.mpert) metric call.

[Copilot]

@copilot review this PR

Addressed a high-impact PR regression in commit df57afa: legacy delta_mband in [ForceFreeStates] no longer crashes startup. I added a compatibility parser path that drops delta_mband with a deprecation warning, plus a targeted test in runtests_utilities.jl to lock this behavior.

[jhalpern30]

Regression harness (first time running this, this is very cool)

Regression Report: solovev_multi_n

Ref 1: develop @ bb3c503 (2026-06-14)
Ref 2: local @ local (2026-06-16)
Summary: 15 unchanged

Regression Report: diiid_n1

Ref 1: develop @ bb3c503 (2026-06-14)
Ref 2: local @ local (2026-06-16)
Summary: 30 unchanged

Regression Report: solovev_kinetic_calculated

Ref 1: develop @ bb3c503 (2026-06-14)
Ref 2: local @ local (2026-06-16)
Summary: 15 unchanged

Regression Report: solovev_n1

Ref 1: develop @ bb3c503 (2026-06-14)
Ref 2: local @ local (2026-06-16)
Summary: 21 unchanged

Regression Report: ggj_reference

Ref 1: develop @ bb3c503 (2026-06-14)
Ref 2: local @ local (2026-06-16)
Summary: 4 unchanged

[matt-pharr]

I support getting rid of the banded matrix functionality.

[logan-nc]

Great!