Russell Lab - Matrix-vector laboratory including linear algebra tools

This crate is part of Russell - Rust Scientific Library

This repository is a "rust laboratory" for vectors and matrices.

Documentation:

• API reference (docs.rs)

Installation

Install some libraries:

bash sudo apt-get install \ liblapacke-dev \ libopenblas-dev

Add this to your Cargo.toml (choose the right version):

toml [dependencies] russell_lab = "*"

Number of threads

By default OpenBLAS will use all available threads, including Hyper-Threads that make the performance worse. Thus, it is best to set the following environment variable:

bash export OPENBLAS_NUM_THREADS=<real-core-count>

Furthermore, if working on a multi-threaded application, it is recommended to set:

bash export OPENBLAS_NUM_THREADS=1

Examples

Compute the pseudo-inverse matrix

```rust use russell_lab::*;

fn main() -> Result<(), &'static str> { // set matrix let mut a = Matrix::from(&[ [1.0, 0.0], [0.0, 1.0], [0.0, 1.0], ]); let acopy = a.getcopy();

// compute pseudo-inverse matrix (because it's square)
let mut ai = Matrix::new(2, 3);
pseudo_inverse(&mut ai, &mut a)?;

// compare with solution
let ai_correct = "┌                ┐\n\
                  │ 1.00 0.00 0.00 │\n\
                  │ 0.00 0.50 0.50 │\n\
                  └                ┘";
assert_eq!(format!("{:.2}", ai), ai_correct);

// compute a⋅ai
let (m, n) = a.dims();
let mut a_ai = Matrix::new(m, m);
for i in 0..m {
    for j in 0..m {
        for k in 0..n {
            a_ai[i][j] += a_copy[i][k] * ai[k][j];
        }
    }
}

// check if a⋅ai⋅a == a
let mut a_ai_a = Matrix::new(m, n);
for i in 0..m {
    for j in 0..n {
        for k in 0..m {
            a_ai_a[i][j] += a_ai[i][k] * a_copy[k][j];
        }
    }
}
let a_ai_a_correct = "┌           ┐\n\
                      │ 1.00 0.00 │\n\
                      │ 0.00 1.00 │\n\
                      │ 0.00 1.00 │\n\
                      └           ┘";
assert_eq!(format!("{:.2}", a_ai_a), a_ai_a_correct);
Ok(())

} ```

Compute eigenvalues

```rust use russelllab::*; use russellchk::*;

fn main() -> Result<(), &'static str> { // set matrix let data = [ [2.0, 0.0, 0.0], [0.0, 3.0, 4.0], [0.0, 4.0, 9.0], ]; let mut a = Matrix::from(&data);

// allocate output arrays
let m = a.nrow();
let mut l_real = vec![0.0; m];
let mut l_imag = vec![0.0; m];
let mut v_real = Matrix::new(m, m);
let mut v_imag = Matrix::new(m, m);

// perform the eigen-decomposition
eigen_decomp(
    &mut l_real,
    &mut l_imag,
    &mut v_real,
    &mut v_imag,
    &mut a,
)?;

// check results
let l_real_correct = "[11.0, 1.0, 2.0]";
let l_imag_correct = "[0.0, 0.0, 0.0]";
let v_real_correct = "┌                      ┐\n\
                      │  0.000  0.000  1.000 │\n\
                      │  0.447  0.894  0.000 │\n\
                      │  0.894 -0.447  0.000 │\n\
                      └                      ┘";
let v_imag_correct = "┌       ┐\n\
                      │ 0 0 0 │\n\
                      │ 0 0 0 │\n\
                      │ 0 0 0 │\n\
                      └       ┘";
assert_eq!(format!("{:?}", l_real), l_real_correct);
assert_eq!(format!("{:?}", l_imag), l_imag_correct);
assert_eq!(format!("{:.3}", v_real), v_real_correct);
assert_eq!(format!("{}", v_imag), v_imag_correct);

// check eigen-decomposition (similarity transformation) of a
// symmetric matrix with real-only eigenvalues and eigenvectors
let a_copy = Matrix::from(&data);
let lam = Matrix::diagonal(&l_real);
let mut a_v = Matrix::new(m, m);
let mut v_l = Matrix::new(m, m);
let mut err = Matrix::filled(m, m, f64::MAX);
mat_mat_mul(&mut a_v, 1.0, &a_copy, &v_real)?;
mat_mat_mul(&mut v_l, 1.0, &v_real, &lam)?;
add_matrices(&mut err, 1.0, &a_v, -1.0, &v_l)?;
assert_approx_eq!(err.norm(EnumMatrixNorm::Max), 0.0, 1e-15);
Ok(())

} ```