Expand description
§GMRES: Generalized minimum residual method
A sparse linear system solver using the GMRES iterative method.
This crates provides a solver for Ax=b
linear problems using the GMRES method.
Sparse matrices are a common representation for many real-world problems commonly
found in engineering and scientific applications. This implementation of the
GMRES method is specifically tailored to sparse matrices, making it an efficient
and effective tool for solving large linear systems arising from real-world
problems.
§Example:
§Solve a linear system
// Define an arbitrary matrix `A`
let a = rsparse::data::Sprs::new_from_vec(&[
vec![0.888641, 0.477151, 0.764081, 0.244348, 0.662542],
vec![0.695741, 0.991383, 0.800932, 0.089616, 0.250400],
vec![0.149974, 0.584978, 0.937576, 0.870798, 0.990016],
vec![0.429292, 0.459984, 0.056629, 0.567589, 0.048561],
vec![0.454428, 0.253192, 0.173598, 0.321640, 0.632031],
]);
// Define a vector `b`
let b = vec![0.104594, 0.437549, 0.040264, 0.298842, 0.254451];
// Provide an initial guess
let mut x = vec![0.; b.len()];
// Solve for `x`
gmres::gmres(&a, &b, &mut x, 100, 1e-5).unwrap();
// Check if the result is correct
gmres::test_utils::assert_eq_f_vec(
&x,
&vec![0.037919, 0.888551, -0.657575, -0.181680, 0.292447],
1e-5,
);
Modules§
- dense_
math - Basic dense matrix and vector operations
- test_
utils - Testing utilities
Functions§
- gmres
- GMRES solver for
Sprs
input matrices. Solves Ax = b. Overwrites x with the solution.