rsparse

A Rust library for solving sparse linear systems using direct methods.

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Data structures

• CSC matrix (Sprs)
• Triplet matrix (Trpl)

Features

• Convert from dense [Vec<T>] or Vec<Vec<T>> matrix to CSC sparse matrix Sprs
• Convert from sparse to dense Vec<Vec<T>>
• Convert from a triplet format matrix Trpl to CSC Sprs
• Sparse matrix addition [C=A+B]
• Sparse matrix multiplication [C=A*B]
• Transpose sparse matrices
• Solve sparse linear systems

Solvers

• lsolve: Solve a lower triangular system. Solves Lx=b where x and b are dense.
• ltsolve: Solve L’x=b where x and b are dense.
• usolve: Solve an upper triangular system. Solves Ux=b where x and b are dense
• utsolve: Solve U’x=b where x and b are dense
• cholsol: A\b solver using Cholesky factorization. Where A is a defined positive Sprs matrix and b is a dense vector
• lusol: A\b solver using LU factorization. Where A is a square Sprs matrix and b is a dense vector
• qrsol: A\b solver using QR factorization. Where A is a rectangular Sprs matrix and b is a dense vector

Examples

Basic matrix operations

use rsparse;fnmain(){// Create a CSC sparse matrix Alet a = rsparse::data::Sprs{// Maximum number of entriesnzmax:5,// number of rowsm:3,// number of columnsn:3,// Valuesx:vec![1.,9.,9.,2.,9.],// Indicesi:vec![1,2,2,0,2],// Pointersp:vec![0,2,3,5]};// Import the same matrix from a dense structureletmut a2 = rsparse::data::Sprs::new_from_vec(&[vec![0.,0.,2.],vec![1.,0.,0.],vec![9.,9.,9.]]);// Check if they are the sameassert_eq!(a.nzmax, a2.nzmax);assert_eq!(a.m,a2.m);assert_eq!(a.n,a2.n);assert_eq!(a.x,a2.x);assert_eq!(a.i,a2.i);assert_eq!(a.p,a2.p);// Transform A to dense and print resultprintln!("\nA");print_matrix(&a.to_dense());// Transpose Alet at = rsparse::transpose(&a);// Transform to dense and print resultprintln!("\nAt");print_matrix(&at.to_dense());// B = A + A'let b = &a + &at;// Transform to dense and print resultprintln!("\nB");print_matrix(&b.to_dense());// C = A * Blet c = &a *&b;// Transform to dense and print resultprintln!("\nC");print_matrix(&c.to_dense());}fnprint_matrix(vec:&[Vec<f64>]){for row in vec {println!("{:?}", row);}}

Output:

A
0	0	2
1	0	0
9	9	9
At
0	1	9
0	0	9
2	0	9
B
0	1	11
1	0	9
11	9	18
C
22	18	36
0	1	11
108	90	342

Solve a linear system

use rsparse;fnmain(){// Arbitrary A matrix (dense)let a = [vec![8.2541e-01,9.5622e-01,4.6698e-01,8.4410e-03,6.3193e-01,7.5741e-01,5.3584e-01,3.9448e-01],vec![7.4808e-01,2.0403e-01,9.4649e-01,2.5086e-01,2.6931e-01,5.5866e-01,3.1827e-01,2.9819e-02],vec![6.3980e-01,9.1615e-01,8.5515e-01,9.5323e-01,7.8323e-01,8.6003e-01,7.5761e-01,8.9255e-01],vec![1.8726e-01,8.9339e-01,9.9796e-01,5.0506e-01,6.1439e-01,4.3617e-01,7.3369e-01,1.5565e-01],vec![2.8015e-02,6.3404e-01,8.4771e-01,8.6419e-01,2.7555e-01,3.5909e-01,7.6644e-01,8.9905e-02],vec![9.1817e-01,8.6629e-01,5.9917e-01,1.9346e-01,2.1960e-01,1.8676e-01,8.7020e-01,2.7891e-01],vec![3.1999e-01,5.9988e-01,8.7402e-01,5.5710e-01,2.4707e-01,7.5652e-01,8.3682e-01,6.3145e-01],vec![9.3807e-01,7.5985e-02,7.8758e-01,3.6881e-01,4.4553e-01,5.5005e-02,3.3908e-01,3.4573e-01],];// Convert A to sparseletmut a_sparse = rsparse::data::Sprs::new();
a_sparse.from_vec(&a);// Generate arbitrary b vectorletmut b = [0.4377,0.7328,0.1227,0.1817,0.2634,0.6876,0.8711,0.4201];// Known solution:/* 0.264678, -1.228118, -0.035452, -0.676711, -0.066194, 0.761495, 1.852384, -0.282992 */// A*x=b -> solve for x -> place x in b
rsparse::lusol(&a_sparse,&mut b,1,1e-6);println!("\nX");println!("{:?}",&b);}

Output:

X
[0.2646806068156303, -1.2280777288645675, -0.035491404094236435, -0.6766064748053932, -0.06619898266432682, 0.7615102544801993, 1.8522970972589123, -0.2830302118359591]

Documentation

Documentation is available at docs.rs.

Sources

• Davis, T. (2006). Direct Methods for Sparse Linear Systems. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9780898718881
• CSparse: A Concise Sparse Matrix Package in C