nalgebra/tests/linalg/full_piv_lu.rs

use na::Matrix3;

#[test]
#[rustfmt::skip]
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]
#[rustfmt::skip]
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")]
mod proptest_tests {
    macro_rules! gen_tests(
    ($module: ident, $scalar: expr, $scalar_type: ty) => {
            mod $module {
                use std::cmp;
                use num::One;
                use na::{DMatrix, Matrix4x3, DVector, Vector4};
                #[allow(unused_imports)]
                use crate::core::helper::{RandScalar, RandComplex};

                use crate::proptest::*;
                use proptest::{prop_assert, proptest};

                proptest! {
                    #[test]
                    fn full_piv_lu(m in dmatrix_($scalar)) {
                        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);

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

                    #[test]
                    fn full_piv_lu_static_3_5(m in matrix3x5_($scalar)) {
                        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);

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

                    #[test]
                    fn full_piv_lu_static_5_3(m in matrix5x3_($scalar)) {
                        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);

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

                    #[test]
                    fn full_piv_lu_static_square(m in matrix4_($scalar)) {
                        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);

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

                    #[test]
                    fn full_piv_lu_solve(n in PROPTEST_MATRIX_DIM, nb in PROPTEST_MATRIX_DIM) {
                        let m  = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);

                        let lu = m.clone().full_piv_lu();
                        let b1 = DVector::<$scalar_type>::new_random(n).map(|e| e.0);
                        let b2 = DMatrix::<$scalar_type>::new_random(n, nb).map(|e| e.0);

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

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

                    #[test]
                    fn full_piv_lu_solve_static(m in matrix4_($scalar)) {
                         let lu = m.full_piv_lu();
                         let b1 = Vector4::<$scalar_type>::new_random().map(|e| e.0);
                         let b2 = Matrix4x3::<$scalar_type>::new_random().map(|e| e.0);

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

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

                    #[test]
                    fn full_piv_lu_inverse(n in PROPTEST_MATRIX_DIM) {
                        let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
                        let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);

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

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

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

                        prop_assert!(id1.is_identity(1.0e-5));
                        prop_assert!(id2.is_identity(1.0e-5));
                    }

                    #[test]
                    fn full_piv_lu_inverse_static(m in matrix4_($scalar)) {
                        let lu = m.full_piv_lu();

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

                            prop_assert!(id1.is_identity(1.0e-5));
                            prop_assert!(id2.is_identity(1.0e-5));
                        }
                    }
                }
            }
        }
    );

    gen_tests!(complex, complex_f64(), RandComplex<f64>);
    gen_tests!(f64, PROPTEST_F64, RandScalar<f64>);
}

/*
#[test]
fn swap_rows() {
    let mut m = Matrix5x3::new(
        11.0, 12.0, 13.0,
        21.0, 22.0, 23.0,
        31.0, 32.0, 33.0,
        41.0, 42.0, 43.0,
        51.0, 52.0, 53.0);

    let expected = Matrix5x3::new(
        11.0, 12.0, 13.0,
        41.0, 42.0, 43.0,
        31.0, 32.0, 33.0,
        21.0, 22.0, 23.0,
        51.0, 52.0, 53.0);

    m.swap_rows(1, 3);

    assert_eq!(m, expected);
}

#[test]
fn swap_columns() {
    let mut m = Matrix3x5::new(
        11.0, 12.0, 13.0, 14.0, 15.0,
        21.0, 22.0, 23.0, 24.0, 25.0,
        31.0, 32.0, 33.0, 34.0, 35.0);

    let expected = Matrix3x5::new(
        11.0, 14.0, 13.0, 12.0, 15.0,
        21.0, 24.0, 23.0, 22.0, 25.0,
        31.0, 34.0, 33.0, 32.0, 35.0);

    m.swap_columns(1, 3);

    assert_eq!(m, expected);
}

#[test]
fn remove_columns() {
    let m = Matrix3x5::new(
        11, 12, 13, 14, 15,
        21, 22, 23, 24, 25,
        31, 32, 33, 34, 35);

    let expected1 = Matrix3x4::new(
        12, 13, 14, 15,
        22, 23, 24, 25,
        32, 33, 34, 35);

    let expected2 = Matrix3x4::new(
        11, 12, 13, 14,
        21, 22, 23, 24,
        31, 32, 33, 34);

    let expected3 = Matrix3x4::new(
        11, 12, 14, 15,
        21, 22, 24, 25,
        31, 32, 34, 35);

    assert_eq!(m.remove_column(0), expected1);
    assert_eq!(m.remove_column(4), expected2);
    assert_eq!(m.remove_column(2), expected3);

    let expected1 = Matrix3::new(
        13, 14, 15,
        23, 24, 25,
        33, 34, 35);

    let expected2 = Matrix3::new(
        11, 12, 13,
        21, 22, 23,
        31, 32, 33);

    let expected3 = Matrix3::new(
        11, 12, 15,
        21, 22, 25,
        31, 32, 35);

    assert_eq!(m.remove_fixed_columns::<U2>(0), expected1);
    assert_eq!(m.remove_fixed_columns::<U2>(3), expected2);
    assert_eq!(m.remove_fixed_columns::<U2>(2), expected3);

    // The following is just to verify that the return type dimensions is correctly inferred.
    let computed: Matrix<_, U3, Dyn, _> = m.remove_columns(3, 2);
    assert!(computed.eq(&expected2));
}


#[test]
fn remove_rows() {
    let m = Matrix5x3::new(
        11, 12, 13,
        21, 22, 23,
        31, 32, 33,
        41, 42, 43,
        51, 52, 53);

    let expected1 = Matrix4x3::new(
        21, 22, 23,
        31, 32, 33,
        41, 42, 43,
        51, 52, 53);

    let expected2 = Matrix4x3::new(
        11, 12, 13,
        21, 22, 23,
        31, 32, 33,
        41, 42, 43);

    let expected3 = Matrix4x3::new(
        11, 12, 13,
        21, 22, 23,
        41, 42, 43,
        51, 52, 53);

    assert_eq!(m.remove_row(0), expected1);
    assert_eq!(m.remove_row(4), expected2);
    assert_eq!(m.remove_row(2), expected3);

    let expected1 = Matrix3::new(
        31, 32, 33,
        41, 42, 43,
        51, 52, 53);

    let expected2 = Matrix3::new(
        11, 12, 13,
        21, 22, 23,
        31, 32, 33);

    let expected3 = Matrix3::new(
        11, 12, 13,
        21, 22, 23,
        51, 52, 53);

    assert_eq!(m.remove_fixed_rows::<U2>(0), expected1);
    assert_eq!(m.remove_fixed_rows::<U2>(3), expected2);
    assert_eq!(m.remove_fixed_rows::<U2>(2), expected3);

    // The following is just to verify that the return type dimensions is correctly inferred.
    let computed: Matrix<_, Dyn, U3, _> = m.remove_rows(3, 2);
    assert!(computed.eq(&expected2));
}


#[test]
fn insert_columns() {
    let m = Matrix5x3::new(
        11, 12, 13,
        21, 22, 23,
        31, 32, 33,
        41, 42, 43,
        51, 52, 53);

    let expected1 = Matrix5x4::new(
        0, 11, 12, 13,
        0, 21, 22, 23,
        0, 31, 32, 33,
        0, 41, 42, 43,
        0, 51, 52, 53);

    let expected2 = Matrix5x4::new(
        11, 12, 13, 0,
        21, 22, 23, 0,
        31, 32, 33, 0,
        41, 42, 43, 0,
        51, 52, 53, 0);

    let expected3 = Matrix5x4::new(
        11, 12, 0, 13,
        21, 22, 0, 23,
        31, 32, 0, 33,
        41, 42, 0, 43,
        51, 52, 0, 53);

    assert_eq!(m.insert_column(0, 0), expected1);
    assert_eq!(m.insert_column(3, 0), expected2);
    assert_eq!(m.insert_column(2, 0), expected3);

    let expected1 = Matrix5::new(
        0, 0, 11, 12, 13,
        0, 0, 21, 22, 23,
        0, 0, 31, 32, 33,
        0, 0, 41, 42, 43,
        0, 0, 51, 52, 53);

    let expected2 = Matrix5::new(
        11, 12, 13, 0, 0,
        21, 22, 23, 0, 0,
        31, 32, 33, 0, 0,
        41, 42, 43, 0, 0,
        51, 52, 53, 0, 0);

    let expected3 = Matrix5::new(
        11, 12, 0, 0, 13,
        21, 22, 0, 0, 23,
        31, 32, 0, 0, 33,
        41, 42, 0, 0, 43,
        51, 52, 0, 0, 53);

    assert_eq!(m.insert_fixed_columns::<U2>(0, 0), expected1);
    assert_eq!(m.insert_fixed_columns::<U2>(3, 0), expected2);
    assert_eq!(m.insert_fixed_columns::<U2>(2, 0), expected3);

    // The following is just to verify that the return type dimensions is correctly inferred.
    let computed: Matrix<_, U5, Dyn, _> = m.insert_columns(3, 2, 0);
    assert!(computed.eq(&expected2));
}


#[test]
fn insert_rows() {
    let m = Matrix3x5::new(
        11, 12, 13, 14, 15,
        21, 22, 23, 24, 25,
        31, 32, 33, 34, 35);

    let expected1 = Matrix4x5::new(
         0,  0,  0,  0,  0,
        11, 12, 13, 14, 15,
        21, 22, 23, 24, 25,
        31, 32, 33, 34, 35);

    let expected2 = Matrix4x5::new(
        11, 12, 13, 14, 15,
        21, 22, 23, 24, 25,
        31, 32, 33, 34, 35,
         0,  0,  0,  0,  0);

    let expected3 = Matrix4x5::new(
        11, 12, 13, 14, 15,
        21, 22, 23, 24, 25,
         0,  0,  0,  0,  0,
        31, 32, 33, 34, 35);

    assert_eq!(m.insert_row(0, 0), expected1);
    assert_eq!(m.insert_row(3, 0), expected2);
    assert_eq!(m.insert_row(2, 0), expected3);

    let expected1 = Matrix5::new(
         0,  0,  0,  0,  0,
         0,  0,  0,  0,  0,
        11, 12, 13, 14, 15,
        21, 22, 23, 24, 25,
        31, 32, 33, 34, 35);

    let expected2 = Matrix5::new(
        11, 12, 13, 14, 15,
        21, 22, 23, 24, 25,
        31, 32, 33, 34, 35,
         0,  0,  0,  0,  0,
         0,  0,  0,  0,  0);

    let expected3 = Matrix5::new(
        11, 12, 13, 14, 15,
        21, 22, 23, 24, 25,
         0,  0,  0,  0,  0,
         0,  0,  0,  0,  0,
        31, 32, 33, 34, 35);

    assert_eq!(m.insert_fixed_rows::<2>(0, 0), expected1);
    assert_eq!(m.insert_fixed_rows::<2>(3, 0), expected2);
    assert_eq!(m.insert_fixed_rows::<2>(2, 0), expected3);

    // The following is just to verify that the return type dimensions is correctly inferred.
    let computed: Matrix<_, Dyn, U5, _> = m.insert_rows(3, 2, 0);
    assert!(computed.eq(&expected2));
}

#[test]
fn resize() {
    let m = Matrix3x5::new(
        11, 12, 13, 14, 15,
        21, 22, 23, 24, 25,
        31, 32, 33, 34, 35);

    let add_add = DMatrix::from_row_slice(5, 6, &[
        11, 12, 13, 14, 15, 42,
        21, 22, 23, 24, 25, 42,
        31, 32, 33, 34, 35, 42,
        42, 42, 42, 42, 42, 42,
        42, 42, 42, 42, 42, 42]);

    let del_del = DMatrix::from_row_slice(1, 2, &[11, 12]);

    let add_del = DMatrix::from_row_slice(5, 2, &[
        11, 12,
        21, 22,
        31, 32,
        42, 42,
        42, 42]);

    let del_add = DMatrix::from_row_slice(1, 8, &[
        11, 12, 13, 14, 15, 42, 42, 42]);

    assert_eq!(del_del, m.resize(1, 2, 42));
    assert_eq!(add_add, m.resize(5, 6, 42));
    assert_eq!(add_del, m.resize(5, 2, 42));
    assert_eq!(del_add, m.resize(1, 8, 42));
}
*/