## rsparse

A Rust library for solving sparse linear systems using direct methods

### 15 releases(1 stable)

 new 1.0.0 Apr 12, 2024 Apr 5, 2023 Feb 4, 2023 Jan 31, 2023

#76 in Math

Used in 2 crates

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# 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<f64>]` or `Vec<Vec<64>>` 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 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;

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_from_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<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;

fn main() {
// 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 sparse
let mut a_sparse = rsparse::data::Sprs::new();
a_sparse.from_vec(&a);

// Generate arbitrary b vector
let mut 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.