Module solve

Solve systems of linear equations and invert matrices

Examples

Solve A * x = b:

use ndarray::prelude::*;
use ndarray_linalg::Solve;

let a: Array2<f64> = array![[3., 2., -1.], [2., -2., 4.], [-2., 1., -2.]];
let b: Array1<f64> = array![1., -2., 0.];
let x = a.solve_into(b).unwrap();
assert!(x.abs_diff_eq(&array![1., -2., -2.], 1e-9));

There are also special functions for solving A^T * x = b and A^H * x = b.

If you are solving multiple systems of linear equations with the same coefficient matrix A, it’s faster to compute the LU factorization once at the beginning than solving directly using A:

use ndarray::prelude::*;
use ndarray_linalg::*;

/// Use fixed algorithm and seed of PRNG for reproducible test
let mut rng = rand_pcg::Mcg128Xsl64::new(0xcafef00dd15ea5e5);

let a: Array2<f64> = random_using((3, 3), &mut rng);
let f = a.factorize_into().unwrap(); // LU factorize A (A is consumed)
for _ in 0..10 {
    let b: Array1<f64> = random_using(3, &mut  rng);
    let x = f.solve_into(b).unwrap(); // Solve A * x = b using factorized L, U
}

Structs

• LUFactorized
  Represents the LU factorization of a matrix A as A = P*L*U.

Enums

• Transpose

Traits

• Determinant
  An interface for calculating determinants of matrix refs.
• DeterminantInto
  An interface for calculating determinants of matrices.
• Factorize
  An interface for computing LU factorizations of matrix refs.
• FactorizeInto
  An interface for computing LU factorizations of matrices.
• Inverse
  An interface for inverting matrix refs.
• InverseInto
  An interface for inverting matrices.
• ReciprocalConditionNum
  An interface for estimating the reciprocal condition number of matrix refs.
• ReciprocalConditionNumInto
  An interface for estimating the reciprocal condition number of matrices.
• Solve
  An interface for solving systems of linear equations.

Type Aliases

• Pivot