Incorrect results from pseudo_inverse about nalgebra HOT 4 CLOSED

#[test]
fn bidiagonal_regression_issue_1313() {
    let s = 6.123234e-16_f32;
    let mut m = nalgebra::dmatrix![
        10.0,   0.0, 0.0,  0.0, -10.0, 0.0, 0.0, 0.0;
        s,     10.0, 0.0, 10.0,     s, 0.0, 0.0, 0.0;
        20.0, -20.0, 0.0, 20.0,  20.0, 0.0, 0.0, 0.0;
    ];
    m.unscale_mut(m.camax());
    let bidiagonal = m.clone().bidiagonalize();
    let (u, d, v_t) = bidiagonal.unpack();
    let m2 = &u * d * &v_t;
    println!("m = {:.1}", m);
    println!("m2 = {:.1}", m2);
    assert_relative_eq!(m, m2, epsilon = 1e-6);
}

#[test]
fn test_pseudo_inverse() {
    let s = 6.123234e-16;
    // let s = 0.0;
    let m = nalgebra::DMatrix::from_column_slice(
        3,
        8,
        &[
            10.0f32, s, 20.0, 0.0, 10.0, -20.0, 0.0, 0.0, 0.0, 0.0, 10.0, 20.0, -10.0, s, 20.0,
            0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
        ],
    );
    let m_inv = m.clone().pseudo_inverse(1.0e-6).unwrap();
    println!("m: {:}", m);
    println!("m†: {:}", &m_inv);
    println!("mm†: {:}", &m * &m_inv);
    println!("mm†m: {:}", &m * &m_inv * &m);
    // Assert distance to identity matrix is small
    assert!(
        (&m * &m_inv).apply_metric_distance(&nalgebra::Matrix3::identity(), &nalgebra::UniformNorm)
            < 0.0001
    );
}

#[test]
// Exercises bug reported in issue #1313 of nalgebra (https://github.com/dimforge/nalgebra/issues/1313)
fn svd_regression_issue_1313() {
    let s = 6.123234e-16_f32;
    let m = nalgebra::dmatrix![
        10.0,   0.0, 0.0,  0.0, -10.0, 0.0, 0.0, 0.0;
           s,  10.0, 0.0, 10.0,     s, 0.0, 0.0, 0.0;
        20.0, -20.0, 0.0, 20.0,  20.0, 0.0, 0.0, 0.0;
    ];
    let svd = m.clone().svd(true, true);
    let m2 = svd.recompose().unwrap();
    assert_relative_eq!(&m, &m2, epsilon = 1e-5);
}