extended_matrix 0.9.9

A matrix calculation module.
Documentation 
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#![allow(unused_imports)]

use crate::{BasicOperationsTrait, SquareMatrix, SquareMatrixTrait, Vector, Vector3};

#[test]
fn test_determinant() {
    let sm_1 = SquareMatrix::create(2, &[1.0, 2.0, 3.0, 4.0]);
    let sm_2 = SquareMatrix::create(5, &[0.0; 25]);
    let sm_3 = SquareMatrix::create(2, &[1.0, 1e4, 1e-4, 2.0]);
    let sm_4 = SquareMatrix::create(3, &[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 10.0]);
    let sm_5 = SquareMatrix::create(3, &[2.0, 1.0, 0.0, 1.0, 3.0, 1.0, 0.0, 1.0, 2.0]);
    let sm_6 = SquareMatrix::create(
        4,
        &[
            1.0, 1.0, 3.0, 4.0, 2.0, 0.0, 0.0, 8.0, 3.0, 0.0, 0.0, 2.0, 4.0, 4.0, 7.0, 5.0,
        ],
    );
    let sm_7 = SquareMatrix::create(
        6,
        &[
            1.0, 2.0, 0.0, 0.0, 0.0, 0.0, 3.0, 4.0, 0.0, 0.0, 0.0, 0.0, 7.0, 6.0, 5.0, 4.0, 0.0,
            0.0, 2.0, 3.0, 4.0, 5.0, 0.0, 0.0, 5.0, 1.0, 2.0, 6.0, 7.0, 3.0, 2.0, 7.0, 5.0, 3.0,
            4.0, 1.0,
        ],
    );
    let sm_8 = SquareMatrix::create(
        4,
        &[
            7.0f32, 6.0, 3.0, 7.0, 3.0, 5.0, 7.0, 2.0, 5.0, 4.0, 3.0, 5.0, 5.0, 6.0, 5.0, 4.0,
        ],
    );
    assert_eq!(sm_1.determinant(1e-6), -2.0);
    assert_eq!(sm_2.determinant(1e-6), 0.0);
    assert_eq!(sm_3.determinant(1e-6), 1.0);
    assert_eq!(sm_4.determinant(1e-6), -2.9999999999999982);
    assert_eq!(sm_5.determinant(1e-6), 8.0);
    assert_eq!(sm_6.determinant(1e-6), 100.0);
    assert_eq!(sm_7.determinant(1e-6), 89.99999999999986);
    assert_eq!(sm_8.determinant(1e-6), -9.999998);
}

#[test]
fn test_gauss_gep() -> Result<(), String> {
    let a_1 = SquareMatrix::create(3, &[3.0, -0.1, -0.2, 0.1, 7.0, -0.3, 0.3, -0.2, 10.0]);
    let b_1 = Vector::create(&[7.85, -19.3, 71.4]);
    let mut x_1 = Vector3::create(&[0.0; 3]);

    let a_2 = SquareMatrix::create(
        4,
        &[
            5.0, -4.0, 1.0, 0.0, -4.0, 6.0, -4.0, 1.0, 1.0, -4.0, 6.0, -4.0, 0.0, 1.0, -4.0, 5.0,
        ],
    );
    let b_2 = Vector::create(&[0.0, 1.0, 0.0, 0.0]);
    let mut x_2 = Vector::create(&[0.0; 4]);

    let a_3 = SquareMatrix::create(
        5,
        &[
            2.0f32, -2.0, 0.0, 0.0, -1.0, -2.0, 3.0, -2.0, 0.0, 0.0, 0.0, -2.0, 5.0, -3.0, 0.0,
            0.0, 0.0, -3.0, 10.0, 4.0, -1.0, 0.0, 0.0, 4.0, 10.0,
        ],
    );
    let mut b_3 = Vector::create(&[0.0, 1.0, 0.0, 0.0, 0.0]);
    b_3 = b_3.transpose();
    let mut x_3 = Vector::create(&[0.0; 5]);

    let a_4 = SquareMatrix::create(
        6,
        &[
            0.866f32, 0.0, -0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.866, 0.0, 0.0, 0.0, -0.866, -1.0, 0.0,
            -1.0, 0.0, 0.0, -0.5, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
            -0.866, 0.0, 0.0, -1.0,
        ],
    );
    let b_4 = Vector::create(&[0.0, -1000.0, 0.0, 0.0, 0.0, 0.0]);
    let mut x_4 = Vector::create(&[0.0; 6]);

    let expected_x_1 = Vector3::create(&[3.0, -2.5, 7.000000000000002]);
    let expected_x_2 = Vector::create(&[
        1.6000000000000028,
        2.6000000000000045,
        2.400000000000004,
        1.4000000000000024,
    ]);
    let expected_x_3 = Vector::create(&[635.995, 618.9951, 291.99768, 73.99941, 33.999725]);
    let expected_x_4 = Vector::create(&[-500.022, 433.01904, -866.0381, -0.0, 250.011, 749.989]);

    a_1.gauss_gep(&b_1, &mut x_1, 1e-6)?;
    a_2.gauss_gep(&b_2, &mut x_2, 1e-6)?;
    a_3.gauss_gep(&b_3, &mut x_3, 1e-6)?;
    a_4.gauss_gep(&b_4, &mut x_4, 1e-6)?;

    assert_eq!(x_1, expected_x_1);
    assert_eq!(x_2, expected_x_2);
    assert_eq!(x_3, expected_x_3);
    assert_eq!(x_4, expected_x_4);

    Ok(())
}

#[test]
fn test_inverse() {
    let a_1 = SquareMatrix::create(3, &[3.0f32, -0.1, -0.2, 0.1, 7.0, -0.3, 0.3, -0.2, 10.0]);
    let mut x_1 = Vector3::create(&[0.0; 3]);

    let a_2 = SquareMatrix::create(2, &[1.0f32, 2.0, 3.0, 4.0]);
    let mut x_2 = Vector::create(&[0.0; 2]);

    let a_3 = SquareMatrix::create(3, &[2.0f32, 5.0, 7.0, 6.0, 3.0, 4.0, 5.0, -2.0, -3.0]);
    let mut x_3 = Vector::create(&[0.0; 3]);

    let a_4 = SquareMatrix::create(
        4,
        &[
            1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0, 1.0,
        ],
    );
    let mut x_4 = Vector::create(&[0.0; 4]);

    let expected_a_i_1 = SquareMatrix::create(
        3,
        &[
            0.33248872,
            0.0049440702,
            0.0067980965,
            -0.005181766,
            0.14290264,
            0.004183444,
            -0.010078297,
            0.0027097305,
            0.09987973,
        ],
    );

    let expected_a_i_2 = SquareMatrix::create(2, &[-2.0000002, 1.0000001, 1.5000001, -0.50000006]);

    let expected_a_i_3 = SquareMatrix::create(
        3,
        &[
            1.0000025, -1.0000013, 1.0000025, -38.00014, 41.00015, -34.000126, 27.000103,
            -29.000109, 24.000092,
        ],
    );

    let expected_a_i_4 = SquareMatrix::create(
        4,
        &[
            0.25, 0.25, 0.25, 0.25, 0.25, 0.25, -0.25, -0.25, 0.25, -0.25, 0.25, -0.25, 0.25,
            -0.25, -0.25, 0.25,
        ],
    );

    assert_eq!(a_1.inverse(&mut x_1, 1e-6), Ok(expected_a_i_1));
    assert_eq!(a_2.inverse(&mut x_2, 1e-6), Ok(expected_a_i_2));
    assert_eq!(a_3.inverse(&mut x_3, 1e-6), Ok(expected_a_i_3));
    assert_eq!(a_4.inverse(&mut x_4, 1e-6), Ok(expected_a_i_4));
}

#[test]
fn test_lup_decomp() -> Result<(), String> {
    let a_1 = SquareMatrix::create(3, &[3.0, -0.1, -0.2, 0.1, 7.0, -0.3, 0.3, -0.2, 10.0]);
    let b_1 = Vector::create(&[7.85, -19.3, 71.4]);
    let mut x_1 = Vector3::create(&[0.0; 3]);

    let a_2 = SquareMatrix::create(
        4,
        &[
            5.0, -4.0, 1.0, 0.0, -4.0, 6.0, -4.0, 1.0, 1.0, -4.0, 6.0, -4.0, 0.0, 1.0, -4.0, 5.0,
        ],
    );
    let b_2 = Vector::create(&[0.0, 1.0, 0.0, 0.0]);
    let mut x_2 = Vector::create(&[0.0; 4]);

    let a_3 = SquareMatrix::create(
        5,
        &[
            2.0f32, -2.0, 0.0, 0.0, -1.0, -2.0, 3.0, -2.0, 0.0, 0.0, 0.0, -2.0, 5.0, -3.0, 0.0,
            0.0, 0.0, -3.0, 10.0, 4.0, -1.0, 0.0, 0.0, 4.0, 10.0,
        ],
    );
    let mut b_3 = Vector::create(&[0.0, 1.0, 0.0, 0.0, 0.0]);
    b_3 = b_3.transpose();
    let mut x_3 = Vector::create(&[0.0; 5]);

    let a_4 = SquareMatrix::create(
        6,
        &[
            0.866f32, 0.0, -0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.866, 0.0, 0.0, 0.0, -0.866, -1.0, 0.0,
            -1.0, 0.0, 0.0, -0.5, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
            -0.866, 0.0, 0.0, -1.0,
        ],
    );
    let b_4 = Vector::create(&[0.0, -1000.0, 0.0, 0.0, 0.0, 0.0]);
    let mut x_4 = Vector::create(&[0.0; 6]);

    let expected_x_1 = Vector3::create(&[3.0, -2.5, 7.000000000000002]);
    let expected_x_2 = Vector::create(&[
        1.6000000000000028,
        2.6000000000000045,
        2.400000000000004,
        1.4000000000000024,
    ]);
    let expected_x_3 = Vector::create(&[635.995, 618.9951, 291.99768, 73.99941, 33.999725]);
    let expected_x_4 = Vector::create(&[-500.022, 433.01904, -866.0381, -0.0, 250.011, 749.989]);

    a_1.lup_decomp(&b_1, &mut x_1, 1e-6)?;
    a_2.lup_decomp(&b_2, &mut x_2, 1e-6)?;
    a_3.lup_decomp(&b_3, &mut x_3, 1e-6)?;
    a_4.lup_decomp(&b_4, &mut x_4, 1e-6)?;

    assert_eq!(x_1, expected_x_1);
    assert_eq!(x_2, expected_x_2);
    assert_eq!(x_3, expected_x_3);
    assert_eq!(x_4, expected_x_4);

    Ok(())
}