Module ndarray_linalg::solve

Solve systems of linear equations and invert matrices

Examples

Solve A * x = b:

#[macro_use]
extern crate ndarray;
extern crate ndarray_linalg;

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.all_close(&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::*;

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

Re-exports

pub use crate::lapack::Pivot;

pub use crate::lapack::Transpose;

Structs

LUFactorized

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

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.