scirs2_linalg::matrix_functions

Function sqrtm

Source 
pub fn sqrtm<F>(
    a: &ArrayView2<'_, F>,
    max_iter: usize,
    tol: F,
) -> LinalgResult<Array2<F>>
where
    F: Float + NumAssign + Sum + One,
Expand description

Compute the matrix square root using the Denman-Beavers iteration.

The matrix square root X of matrix A satisfies X^2 = A. This function uses the Denman-Beavers iteration, which is suitable for matrices with no eigenvalues on the negative real axis.

§Arguments

  • a - Input square matrix (should be positive definite for real result)
  • max_iter - Maximum number of iterations
  • tol - Convergence tolerance

§Returns

  • Matrix square root of a

§Examples

use ndarray::array;
use scirs2_linalg::matrix_functions::sqrtm;

let a = array![[4.0_f64, 0.0], [0.0, 9.0]];
let sqrt_a = sqrtm(&a.view(), 20, 1e-10).unwrap();
// sqrt_a should be approximately [[2.0, 0.0], [0.0, 3.0]]
assert!((sqrt_a[[0, 0]] - 2.0).abs() < 1e-10);
assert!((sqrt_a[[0, 1]] - 0.0).abs() < 1e-10);
assert!((sqrt_a[[1, 0]] - 0.0).abs() < 1e-10);
assert!((sqrt_a[[1, 1]] - 3.0).abs() < 1e-10);