Function russell_lab::solve_lin_sys

pub fn solve_lin_sys(b: &mut Vector, a: &mut Matrix) -> Result<(), StrError>

Solves a general linear system (real numbers)

For a general matrix a (square, symmetric, non-symmetric, dense, sparse), find x such that:

  a   ⋅  x  =  b
(m,m)   (m)   (m)

However, the right-hand-side will hold the solution:

b := a⁻¹⋅b == x

The solution is obtained via LU decomposition using Lapack dgesv routine.

Note

1. The matrix a will be modified
2. The right-hand-side b will contain the solution x

use russell_lab::{solve_lin_sys, Matrix, Vector, StrError};

fn main() -> Result<(), StrError> {
    // set matrix and right-hand side
    let mut a = Matrix::from(&[
        [1.0,  3.0, -2.0],
        [3.0,  5.0,  6.0],
        [2.0,  4.0,  3.0],
    ]);
    let mut b = Vector::from(&[5.0, 7.0, 8.0]);

    // solve linear system b := a⁻¹⋅b
    solve_lin_sys(&mut b, &mut a)?;

    // check
    let x_correct = "┌         ┐\n\
                     │ -15.000 │\n\
                     │   8.000 │\n\
                     │   2.000 │\n\
                     └         ┘";
    assert_eq!(format!("{:.3}", b), x_correct);
    Ok(())
}