nalgebra/tests/linalg/full_piv_lu.rs

use std::cmp;
use na::{DMatrix, Matrix3, Matrix4, Matrix4x3, Matrix5x3, Matrix3x5,
         DVector, Vector4};


#[test]
fn full_piv_lu_simple() {
    let m = Matrix3::new(
        2.0, -1.0,  0.0,
       -1.0,  2.0, -1.0,
        0.0, -1.0,  2.0);

    let lu = m.full_piv_lu();
    assert_eq!(lu.determinant(), 4.0);

    let (p, l, u, q) = lu.unpack();

    let mut lu = l * u;
    p.inv_permute_rows(&mut lu);
    q.inv_permute_columns(&mut lu);

    assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
}

#[test]
fn full_piv_lu_simple_with_pivot() {
    let m = Matrix3::new(
        0.0, -1.0,  2.0,
       -1.0,  2.0, -1.0,
        2.0, -1.0,  0.0);

    let lu = m.full_piv_lu();
    assert_eq!(lu.determinant(), -4.0);

    let (p, l, u, q) = lu.unpack();

    let mut lu = l * u;
    p.inv_permute_rows(&mut lu);
    q.inv_permute_columns(&mut lu);

    assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
}

#[cfg(feature = "arbitrary")]
quickcheck! {
    fn full_piv_lu(m: DMatrix<f64>) -> bool {
        let mut m = m;
        if m.len() == 0 {
            m = DMatrix::new_random(1, 1);
        }

        let lu = m.clone().full_piv_lu();
        let (p, l, u, q) = lu.unpack();
        let mut lu = l * u;
        p.inv_permute_rows(&mut lu);
        q.inv_permute_columns(&mut lu);

        relative_eq!(m, lu, epsilon = 1.0e-7)
    }

    fn full_piv_lu_static_3_5(m: Matrix3x5<f64>) -> bool {
        let lu = m.full_piv_lu();
        let (p, l, u, q) = lu.unpack();
        let mut lu = l * u;
        p.inv_permute_rows(&mut lu);
        q.inv_permute_columns(&mut lu);

        relative_eq!(m, lu, epsilon = 1.0e-7)
    }

    fn full_piv_lu_static_5_3(m: Matrix5x3<f64>) -> bool {
        let lu = m.full_piv_lu();
        let (p, l, u, q) = lu.unpack();
        let mut lu = l * u;
        p.inv_permute_rows(&mut lu);
        q.inv_permute_columns(&mut lu);

        relative_eq!(m, lu, epsilon = 1.0e-7)
    }

    fn full_piv_lu_static_square(m: Matrix4<f64>) -> bool {
        let lu = m.full_piv_lu();
        let (p, l, u, q) = lu.unpack();
        let mut lu = l * u;
        p.inv_permute_rows(&mut lu);
        q.inv_permute_columns(&mut lu);

        relative_eq!(m, lu, epsilon = 1.0e-7)
    }

    fn full_piv_lu_solve(n: usize, nb: usize) -> bool {
        if n != 0 && nb != 0 {
            let n  = cmp::min(n, 50);  // To avoid slowing down the test too much.
            let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
            let m  = DMatrix::<f64>::new_random(n, n);

            let lu = m.clone().full_piv_lu();
            let b1 = DVector::new_random(n);
            let b2 = DMatrix::new_random(n, nb);

            let sol1 = lu.solve(&b1);
            let sol2 = lu.solve(&b2);

            return (sol1.is_none() || relative_eq!(&m * sol1.unwrap(), b1, epsilon = 1.0e-6)) &&
                   (sol2.is_none() || relative_eq!(&m * sol2.unwrap(), b2, epsilon = 1.0e-6))
        }

        return true;
    }

    fn full_piv_lu_solve_static(m: Matrix4<f64>) -> bool {
         let lu = m.full_piv_lu();
         let b1 = Vector4::new_random();
         let b2 = Matrix4x3::new_random();

         let sol1 = lu.solve(&b1);
         let sol2 = lu.solve(&b2);

         return (sol1.is_none() || relative_eq!(&m * sol1.unwrap(), b1, epsilon = 1.0e-6)) &&
                (sol2.is_none() || relative_eq!(&m * sol2.unwrap(), b2, epsilon = 1.0e-6))
    }

    fn full_piv_lu_inverse(n: usize) -> bool {
        let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
        let m = DMatrix::<f64>::new_random(n, n);

        let mut l = m.lower_triangle();
        let mut u = m.upper_triangle();

        // Ensure the matrix is well conditioned for inversion.
        l.fill_diagonal(1.0);
        u.fill_diagonal(1.0);
        let m = l * u;

        let m1  = m.clone().full_piv_lu().try_inverse().unwrap();
        let id1 = &m  * &m1;
        let id2 = &m1 * &m;

        return id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5);
    }

    fn full_piv_lu_inverse_static(m: Matrix4<f64>) -> bool {
        let lu = m.full_piv_lu();

        if let Some(m1)  = lu.try_inverse() {
            let id1 = &m  * &m1;
            let id2 = &m1 * &m;

            id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
        }
        else {
            true
        }
    }
}