rsparse

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

Data structures

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

Features

• Convert from dense Vec<Vec<f64>> matrix to CSC sparse matrix Sprs
• Convert from sparse to dense Vec<Vec<f64>>
• 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

```rust use rsparse;

fn main(){ // Create a CSC sparse matrix A let a = rsparse::data::Sprs{ // Maximum number of entries nzmax: 5, // number of rows m: 3, //number of columns n: 3, // Values x: vec![1., 9., 9., 2., 9.], // Indices
i: vec![1, 2, 2, 0, 2], // Pointers p: vec![0, 2, 3, 5] };

// Import the same matrix from a dense structure
let mut a2 = rsparse::data::Sprs::new();
a2.from_vec(
    &vec![
        vec![0., 0., 2.], 
        vec![1., 0., 0.], 
        vec![9., 9., 9.]
    ]
);

// Check if they are the same
assert_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 result
println!("\nA");
print_matrix(&a.to_dense());


// Transpose A
let at = rsparse::transpose(&a);
// Transform to dense and print result
println!("\nAt");
print_matrix(&at.to_dense());

// B = A + A'
let b = &a + &at;
// Transform to dense and print result
println!("\nB");
print_matrix(&b.to_dense());

// C = A * B
let c = &a * &b;
// Transform to dense and print result
println!("\nC");
print_matrix(&c.to_dense());

}

fn print_matrix(vec: &Vec>) { 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

```rust use rsparse;

fn main(){ // Arbitrary A matrix (dense) let a = vec![ 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 sparse
let mut a_sparse = rsparse::data::Sprs::new();
a_sparse.from_vec(&a);

// Generate arbitrary b vector
let mut b = vec![
    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