nalgebra/tests/core/matrix.rs

use num::{One, Zero};
use std::cmp::Ordering;

use na::dimension::{U15, U8};
use na::{
    self, Const, DMatrix, DVector, Matrix2, Matrix2x3, Matrix2x4, Matrix3, Matrix3x2, Matrix3x4,
    Matrix4, Matrix4x3, Matrix4x5, Matrix5, Matrix6, OMatrix, RowVector3, RowVector4, RowVector5,
    Vector1, Vector2, Vector3, Vector4, Vector5, Vector6,
};

#[test]
fn iter() {
    let a = Matrix2x3::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);

    let mut it = a.iter();
    assert_eq!(*it.next().unwrap(), 1.0);
    assert_eq!(*it.next().unwrap(), 4.0);
    assert_eq!(*it.next().unwrap(), 2.0);
    assert_eq!(*it.next().unwrap(), 5.0);
    assert_eq!(*it.next().unwrap(), 3.0);
    assert_eq!(*it.next().unwrap(), 6.0);
    assert!(it.next().is_none());

    let mut it = a.iter();
    assert_eq!(*it.next().unwrap(), 1.0);
    assert_eq!(*it.next_back().unwrap(), 6.0);
    assert_eq!(*it.next_back().unwrap(), 3.0);
    assert_eq!(*it.next_back().unwrap(), 5.0);
    assert_eq!(*it.next().unwrap(), 4.0);
    assert_eq!(*it.next().unwrap(), 2.0);
    assert!(it.next().is_none());

    let mut it = a.iter().rev();
    assert_eq!(*it.next().unwrap(), 6.0);
    assert_eq!(*it.next().unwrap(), 3.0);
    assert_eq!(*it.next().unwrap(), 5.0);
    assert_eq!(*it.next().unwrap(), 2.0);
    assert_eq!(*it.next().unwrap(), 4.0);
    assert_eq!(*it.next().unwrap(), 1.0);
    assert!(it.next().is_none());

    let row = a.row(0);
    let mut it = row.iter();
    assert_eq!(*it.next().unwrap(), 1.0);
    assert_eq!(*it.next().unwrap(), 2.0);
    assert_eq!(*it.next().unwrap(), 3.0);
    assert!(it.next().is_none());

    let row = a.row(1);
    let mut it = row.iter();
    assert_eq!(*it.next().unwrap(), 4.0);
    assert_eq!(*it.next().unwrap(), 5.0);
    assert_eq!(*it.next().unwrap(), 6.0);
    assert!(it.next().is_none());

    let m22 = row.column(1);
    let mut it = m22.iter();
    assert_eq!(*it.next().unwrap(), 5.0);
    assert!(it.next().is_none());

    let col = a.column(0);
    let mut it = col.iter();
    assert_eq!(*it.next().unwrap(), 1.0);
    assert_eq!(*it.next().unwrap(), 4.0);
    assert!(it.next().is_none());

    let col = a.column(1);
    let mut it = col.iter();
    assert_eq!(*it.next().unwrap(), 2.0);
    assert_eq!(*it.next().unwrap(), 5.0);
    assert!(it.next().is_none());

    let col = a.column(2);
    let mut it = col.iter();
    assert_eq!(*it.next().unwrap(), 3.0);
    assert_eq!(*it.next().unwrap(), 6.0);
    assert!(it.next().is_none());
}

#[test]
fn debug_output_semicolon_delimited_rowwise() {
    let m = Matrix2::new(1.0, 2.0, 3.0, 4.0);
    let expected_output = "[1.0, 2.0; 3.0, 4.0]";
    let current_output = format!("{:?}", m);
    dbg!(expected_output);
    dbg!(&current_output);

    assert!(current_output == expected_output);
}

#[test]
fn format_empty_matrix() {
    let empty_row: [f32; 0] = [];
    let m = na::DMatrix::from_row_slice(0, 0, &empty_row);
    let expected_output_display = "[ ]";
    let expected_output_debug = "[]";
    let current_output_display = format!("{}", m);
    let current_output_debug = format!("{:?}", m);
    dbg!(expected_output_display);
    dbg!(expected_output_debug);
    dbg!(&current_output_debug);
    dbg!(&current_output_display);

    assert!(
        current_output_display == expected_output_display
            && current_output_debug == expected_output_debug
    );
}

#[test]
fn is_column_major() {
    let a = Matrix2x3::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);

    let expected = &[1.0, 4.0, 2.0, 5.0, 3.0, 6.0];

    assert_eq!(a.as_slice(), expected);

    let a = Matrix2x3::from_row_slice(&[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]);

    assert_eq!(a.as_slice(), expected);

    let a = Matrix2x3::from_column_slice(&[1.0, 4.0, 2.0, 5.0, 3.0, 6.0]);

    assert_eq!(a.as_slice(), expected);
}

#[test]
fn linear_index() {
    let a = Matrix2x3::new(1, 2, 3, 4, 5, 6);

    assert_eq!(a[0], 1);
    assert_eq!(a[1], 4);
    assert_eq!(a[2], 2);
    assert_eq!(a[3], 5);
    assert_eq!(a[4], 3);
    assert_eq!(a[5], 6);

    let b = Vector4::new(1, 2, 3, 4);

    assert_eq!(b[0], 1);
    assert_eq!(b[1], 2);
    assert_eq!(b[2], 3);
    assert_eq!(b[3], 4);

    let c = RowVector4::new(1, 2, 3, 4);

    assert_eq!(c[0], 1);
    assert_eq!(c[1], 2);
    assert_eq!(c[2], 3);
    assert_eq!(c[3], 4);
}

#[test]
fn identity() {
    let id1 = Matrix3::<f64>::identity();
    let id2 = Matrix3x4::new(1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
    let id2bis = Matrix3x4::identity();
    let id3 = Matrix4x3::new(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0);
    let id3bis = Matrix4x3::identity();

    let not_id1 = Matrix3::identity() * 2.0;
    let not_id2 = Matrix3x4::new(1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0);
    let not_id3 = Matrix4x3::new(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0);

    assert_eq!(id2, id2bis);
    assert_eq!(id3, id3bis);
    assert!(id1.is_identity(0.0));
    assert!(id2.is_identity(0.0));
    assert!(id3.is_identity(0.0));
    assert!(!not_id1.is_identity(0.0));
    assert!(!not_id2.is_identity(0.0));
    assert!(!not_id3.is_identity(0.0));
}

#[test]
fn coordinates() {
    let a = Matrix3x4::new(11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34);

    assert_eq!(a.m11, 11);
    assert_eq!(a.m12, 12);
    assert_eq!(a.m13, 13);
    assert_eq!(a.m14, 14);

    assert_eq!(a.m21, 21);
    assert_eq!(a.m22, 22);
    assert_eq!(a.m23, 23);
    assert_eq!(a.m24, 24);

    assert_eq!(a.m31, 31);
    assert_eq!(a.m32, 32);
    assert_eq!(a.m33, 33);
    assert_eq!(a.m34, 34);
}

#[test]
fn from_diagonal() {
    let diag = Vector3::new(1, 2, 3);
    let expected = Matrix3::new(1, 0, 0, 0, 2, 0, 0, 0, 3);
    let a = Matrix3::from_diagonal(&diag);

    assert_eq!(a, expected);
}

#[test]
fn from_rows() {
    let rows = &[
        RowVector4::new(11, 12, 13, 14),
        RowVector4::new(21, 22, 23, 24),
        RowVector4::new(31, 32, 33, 34),
    ];

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

    let a = Matrix3x4::from_rows(rows);

    assert_eq!(a, expected);
}

#[test]
fn from_columns() {
    let columns = &[
        Vector3::new(11, 21, 31),
        Vector3::new(12, 22, 32),
        Vector3::new(13, 23, 33),
        Vector3::new(14, 24, 34),
    ];

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

    let a = Matrix3x4::from_columns(columns);

    assert_eq!(a, expected);
}

#[test]
fn from_columns_dynamic() {
    let columns = &[
        DVector::from_row_slice(&[11, 21, 31]),
        DVector::from_row_slice(&[12, 22, 32]),
        DVector::from_row_slice(&[13, 23, 33]),
        DVector::from_row_slice(&[14, 24, 34]),
    ];

    let expected = DMatrix::from_row_slice(3, 4, &[11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34]);

    let a = DMatrix::from_columns(columns);

    assert_eq!(a, expected);
}

#[test]
#[should_panic]
fn from_too_many_rows() {
    let rows = &[
        RowVector4::new(11, 12, 13, 14),
        RowVector4::new(21, 22, 23, 24),
        RowVector4::new(31, 32, 33, 34),
        RowVector4::new(31, 32, 33, 34),
    ];

    let _ = Matrix3x4::from_rows(rows);
}

#[test]
#[should_panic]
fn from_not_enough_columns() {
    let columns = &[Vector3::new(11, 21, 31), Vector3::new(14, 24, 34)];

    let _ = Matrix3x4::from_columns(columns);
}

#[test]
#[should_panic]
fn from_rows_with_different_dimensions() {
    let columns = &[
        DVector::from_row_slice(&[11, 21, 31]),
        DVector::from_row_slice(&[12, 22, 32, 33]),
    ];

    let _ = DMatrix::from_columns(columns);
}

#[test]
fn copy_from_slice() {
    let mut a = Matrix3::zeros();
    let data = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0];
    let expected_a = Matrix3::new(1.0, 4.0, 7.0, 2.0, 5.0, 8.0, 3.0, 6.0, 9.0);

    a.copy_from_slice(&data);

    assert_eq!(a, expected_a);
}

#[should_panic]
#[test]
fn copy_from_slice_too_small() {
    let mut a = Matrix3::zeros();
    let data = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0];
    a.copy_from_slice(&data);
}

#[should_panic]
#[test]
fn copy_from_slice_too_large() {
    let mut a = Matrix3::zeros();
    let data = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0];
    a.copy_from_slice(&data);
}

#[test]
fn to_homogeneous() {
    let a = Vector3::new(1.0, 2.0, 3.0);
    let expected_a = Vector4::new(1.0, 2.0, 3.0, 0.0);

    let b = DVector::from_row_slice(&[1.0, 2.0, 3.0]);
    let expected_b = DVector::from_row_slice(&[1.0, 2.0, 3.0, 0.0]);

    let c = Matrix2::new(1.0, 2.0, 3.0, 4.0);
    let expected_c = Matrix3::new(1.0, 2.0, 0.0, 3.0, 4.0, 0.0, 0.0, 0.0, 1.0);

    let d = DMatrix::from_row_slice(2, 2, &[1.0, 2.0, 3.0, 4.0]);
    let expected_d = DMatrix::from_row_slice(3, 3, &[1.0, 2.0, 0.0, 3.0, 4.0, 0.0, 0.0, 0.0, 1.0]);

    assert_eq!(a.to_homogeneous(), expected_a);
    assert_eq!(b.to_homogeneous(), expected_b);
    assert_eq!(c.to_homogeneous(), expected_c);
    assert_eq!(d.to_homogeneous(), expected_d);
}

#[test]
fn push() {
    let a = Vector3::new(1.0, 2.0, 3.0);
    let expected_a = Vector4::new(1.0, 2.0, 3.0, 4.0);

    let b = DVector::from_row_slice(&[1.0, 2.0, 3.0]);
    let expected_b = DVector::from_row_slice(&[1.0, 2.0, 3.0, 4.0]);

    assert_eq!(a.push(4.0), expected_a);
    assert_eq!(b.push(4.0), expected_b);
}

#[test]
fn simple_add() {
    let a = Matrix2x3::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);

    let b = Matrix2x3::new(10.0, 20.0, 30.0, 40.0, 50.0, 60.0);
    let c = DMatrix::from_row_slice(2, 3, &[10.0, 20.0, 30.0, 40.0, 50.0, 60.0]);

    let expected = Matrix2x3::new(11.0, 22.0, 33.0, 44.0, 55.0, 66.0);

    assert_eq!(expected, &a + &b);
    assert_eq!(expected, &a + b);
    assert_eq!(expected, a + &b);
    assert_eq!(expected, a + b);

    // Sum of a static matrix with a dynamic one.
    assert_eq!(expected, &a + &c);
    assert_eq!(expected, a + &c);
    assert_eq!(expected, &c + &a);
    assert_eq!(expected, &c + a);
}

#[test]
fn simple_sum() {
    type M = Matrix2x3<f32>;

    let a = M::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
    let b = M::new(10.0, 20.0, 30.0, 40.0, 50.0, 60.0);
    let c = M::new(100.0, 200.0, 300.0, 400.0, 500.0, 600.0);

    assert_eq!(M::zero(), Vec::<M>::new().iter().sum());
    assert_eq!(M::zero(), Vec::<M>::new().into_iter().sum());
    assert_eq!(a + b, vec![a, b].iter().sum());
    assert_eq!(a + b, vec![a, b].into_iter().sum());
    assert_eq!(a + b + c, vec![a, b, c].iter().sum());
    assert_eq!(a + b + c, vec![a, b, c].into_iter().sum());
}

#[test]
fn simple_scalar_mul() {
    let a = Matrix2x3::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);

    let expected = Matrix2x3::new(10.0, 20.0, 30.0, 40.0, 50.0, 60.0);

    assert_eq!(expected, a * 10.0);
    assert_eq!(expected, &a * 10.0);
    assert_eq!(expected, 10.0 * a);
    assert_eq!(expected, 10.0 * &a);
}

#[test]
fn simple_mul() {
    let a = Matrix2x3::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);

    let b = Matrix3x4::new(
        10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0, 100.0, 110.0, 120.0,
    );

    let expected = Matrix2x4::new(380.0, 440.0, 500.0, 560.0, 830.0, 980.0, 1130.0, 1280.0);

    assert_eq!(expected, &a * &b);
    assert_eq!(expected, a * &b);
    assert_eq!(expected, &a * b);
    assert_eq!(expected, a * b);
}

#[test]
fn simple_product() {
    type M = Matrix3<f32>;

    let a = M::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0);
    let b = M::new(10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0);
    let c = M::new(
        100.0, 200.0, 300.0, 400.0, 500.0, 600.0, 700.0, 800.0, 900.0,
    );

    assert_eq!(M::one(), Vec::<M>::new().iter().product());
    assert_eq!(M::one(), Vec::<M>::new().into_iter().product());
    assert_eq!(a * b, vec![a, b].iter().product());
    assert_eq!(a * b, vec![a, b].into_iter().product());
    assert_eq!(a * b * c, vec![a, b, c].iter().product());
    assert_eq!(a * b * c, vec![a, b, c].into_iter().product());
}

#[test]
fn cross_product_vector_and_row_vector() {
    let v1 = Vector3::new(1.0, 2.0, 3.0);
    let v2 = Vector3::new(1.0, 5.0, 7.0);
    let column_cross = v1.cross(&v2);
    assert_eq!(column_cross, Vector3::new(-1.0, -4.0, 3.0));

    let v1 = RowVector3::new(1.0, 2.0, 3.0);
    let v2 = RowVector3::new(1.0, 5.0, 7.0);
    let row_cross = v1.cross(&v2);
    assert_eq!(row_cross, RowVector3::new(-1.0, -4.0, 3.0));

    assert_eq!(
        Vector3::new(1.0, 1.0, 0.0)
            .cross(&Vector3::new(-0.5, 17.0, 0.0))
            .transpose(),
        RowVector3::new(1.0, 1.0, 0.0).cross(&RowVector3::new(-0.5, 17.0, 0.0))
    );
}

#[test]
fn simple_scalar_conversion() {
    let a = Matrix2x3::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
    let expected = Matrix2x3::new(1, 2, 3, 4, 5, 6);

    let a_u32: Matrix2x3<u32> = na::try_convert(a).unwrap(); // f32 -> u32
    let a_f32: Matrix2x3<f32> = na::convert(a_u32); // u32 -> f32

    assert_eq!(a, a_f32);
    assert_eq!(expected, a_u32);
}

#[test]
fn apply() {
    let mut a = Matrix4::new(
        1.1f32, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9, 8.8, 7.7, 6.6, 5.5, 4.4, 3.3, 2.2,
    );

    let expected = Matrix4::new(
        1.0, 2.0, 3.0, 4.0, 6.0, 7.0, 8.0, 9.0, 10.0, 9.0, 8.0, 7.0, 6.0, 4.0, 3.0, 2.0,
    );

    a.apply(|e| *e = e.round());

    assert_eq!(a, expected);
}

#[test]
fn map() {
    let a = Matrix4::new(
        1.1f64, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9, 8.8, 7.7, 6.6, 5.5, 4.4, 3.3, 2.2,
    );

    let expected = Matrix4::new(1, 2, 3, 4, 6, 7, 8, 9, 10, 9, 8, 7, 6, 4, 3, 2);

    let computed = a.map(|e| e.round() as i64);

    assert_eq!(computed, expected);
}

#[test]
fn map_with_location() {
    let a = Matrix4::new(1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4);

    let expected = Matrix4::new(1, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10);

    let computed = a.map_with_location(|i, j, e| e + i + j);

    assert_eq!(computed, expected);
}

#[test]
fn zip_map() {
    let a = Matrix3::new(11i32, 12, 13, 21, 22, 23, 31, 32, 33);

    let b = Matrix3::new(11u32, 12, 13, 21, 22, 23, 31, 32, 33);

    let expected = Matrix3::new(22.0f32, 24.0, 26.0, 42.0, 44.0, 46.0, 62.0, 64.0, 66.0);

    let computed = a.zip_map(&b, |ea, eb| ea as f32 + eb as f32);

    assert_eq!(computed, expected);
}

#[test]
#[should_panic]
fn trace_panic() {
    let m = DMatrix::<f32>::new_random(2, 3);
    let _ = m.trace();
}

#[test]
fn trace() {
    let m = Matrix2::new(1.0, 20.0, 30.0, 4.0);
    assert_eq!(m.trace(), 5.0);
}

#[test]
fn simple_transpose() {
    let a = Matrix2x3::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
    let expected = Matrix3x2::new(1.0, 4.0, 2.0, 5.0, 3.0, 6.0);

    assert_eq!(a.transpose(), expected);
}

#[test]
fn simple_transpose_mut() {
    let mut a = Matrix3::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0);
    let expected = Matrix3::new(1.0, 4.0, 7.0, 2.0, 5.0, 8.0, 3.0, 6.0, 9.0);

    a.transpose_mut();
    assert_eq!(a, expected);
}

#[test]
fn vector_index_mut() {
    let mut v = Vector3::new(1, 2, 3);

    assert_eq!(v[0], 1);
    assert_eq!(v[1], 2);
    assert_eq!(v[2], 3);

    v[0] = 10;
    v[1] = 20;
    v[2] = 30;

    assert_eq!(v, Vector3::new(10, 20, 30));
}

#[test]
fn components_mut() {
    let mut m2 = Matrix2::from_element(1.0);
    let mut m3 = Matrix3::from_element(1.0);
    let mut m4 = Matrix4::from_element(1.0);
    let mut m5 = Matrix5::from_element(1.0);
    let mut m6 = Matrix6::from_element(1.0);

    m2.m11 = 0.0;
    m2.m12 = 0.0;
    m2.m21 = 0.0;
    m2.m22 = 0.0;

    m3.m11 = 0.0;
    m3.m12 = 0.0;
    m3.m13 = 0.0;
    m3.m21 = 0.0;
    m3.m22 = 0.0;
    m3.m23 = 0.0;
    m3.m31 = 0.0;
    m3.m32 = 0.0;
    m3.m33 = 0.0;

    m4.m11 = 0.0;
    m4.m12 = 0.0;
    m4.m13 = 0.0;
    m4.m14 = 0.0;
    m4.m21 = 0.0;
    m4.m22 = 0.0;
    m4.m23 = 0.0;
    m4.m24 = 0.0;
    m4.m31 = 0.0;
    m4.m32 = 0.0;
    m4.m33 = 0.0;
    m4.m34 = 0.0;
    m4.m41 = 0.0;
    m4.m42 = 0.0;
    m4.m43 = 0.0;
    m4.m44 = 0.0;

    m5.m11 = 0.0;
    m5.m12 = 0.0;
    m5.m13 = 0.0;
    m5.m14 = 0.0;
    m5.m15 = 0.0;
    m5.m21 = 0.0;
    m5.m22 = 0.0;
    m5.m23 = 0.0;
    m5.m24 = 0.0;
    m5.m25 = 0.0;
    m5.m31 = 0.0;
    m5.m32 = 0.0;
    m5.m33 = 0.0;
    m5.m34 = 0.0;
    m5.m35 = 0.0;
    m5.m41 = 0.0;
    m5.m42 = 0.0;
    m5.m43 = 0.0;
    m5.m44 = 0.0;
    m5.m45 = 0.0;
    m5.m51 = 0.0;
    m5.m52 = 0.0;
    m5.m53 = 0.0;
    m5.m54 = 0.0;
    m5.m55 = 0.0;

    m6.m11 = 0.0;
    m6.m12 = 0.0;
    m6.m13 = 0.0;
    m6.m14 = 0.0;
    m6.m15 = 0.0;
    m6.m16 = 0.0;
    m6.m21 = 0.0;
    m6.m22 = 0.0;
    m6.m23 = 0.0;
    m6.m24 = 0.0;
    m6.m25 = 0.0;
    m6.m26 = 0.0;
    m6.m31 = 0.0;
    m6.m32 = 0.0;
    m6.m33 = 0.0;
    m6.m34 = 0.0;
    m6.m35 = 0.0;
    m6.m36 = 0.0;
    m6.m41 = 0.0;
    m6.m42 = 0.0;
    m6.m43 = 0.0;
    m6.m44 = 0.0;
    m6.m45 = 0.0;
    m6.m46 = 0.0;
    m6.m51 = 0.0;
    m6.m52 = 0.0;
    m6.m53 = 0.0;
    m6.m54 = 0.0;
    m6.m55 = 0.0;
    m6.m56 = 0.0;
    m6.m61 = 0.0;
    m6.m62 = 0.0;
    m6.m63 = 0.0;
    m6.m64 = 0.0;
    m6.m65 = 0.0;
    m6.m66 = 0.0;

    assert!(m2.is_zero());
    assert!(m3.is_zero());
    assert!(m4.is_zero());
    assert!(m5.is_zero());
    assert!(m6.is_zero());

    let mut v1 = Vector1::from_element(1.0);
    let mut v2 = Vector2::from_element(1.0);
    let mut v3 = Vector3::from_element(1.0);
    let mut v4 = Vector4::from_element(1.0);
    let mut v5 = Vector5::from_element(1.0);
    let mut v6 = Vector6::from_element(1.0);

    v1.x = 0.0;
    v2.x = 0.0;
    v2.y = 0.0;
    v3.x = 0.0;
    v3.y = 0.0;
    v3.z = 0.0;
    v4.x = 0.0;
    v4.y = 0.0;
    v4.z = 0.0;
    v4.w = 0.0;
    v5.x = 0.0;
    v5.y = 0.0;
    v5.z = 0.0;
    v5.w = 0.0;
    v5.a = 0.0;
    v6.x = 0.0;
    v6.y = 0.0;
    v6.z = 0.0;
    v6.w = 0.0;
    v6.a = 0.0;
    v6.b = 0.0;

    assert!(v1.is_zero());
    assert!(v2.is_zero());
    assert!(v3.is_zero());
    assert!(v4.is_zero());
    assert!(v5.is_zero());
    assert!(v6.is_zero());

    // Check that the components order is correct.
    m3.m11 = 11.0;
    m3.m12 = 12.0;
    m3.m13 = 13.0;
    m3.m21 = 21.0;
    m3.m22 = 22.0;
    m3.m23 = 23.0;
    m3.m31 = 31.0;
    m3.m32 = 32.0;
    m3.m33 = 33.0;

    let expected_m3 = Matrix3::new(11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0);
    assert_eq!(expected_m3, m3);
}

#[test]
fn kronecker() {
    let a = Matrix2x3::new(11, 12, 13, 21, 22, 23);

    let b = Matrix4x5::new(
        110, 120, 130, 140, 150, 210, 220, 230, 240, 250, 310, 320, 330, 340, 350, 410, 420, 430,
        440, 450,
    );

    let expected = OMatrix::<_, U8, U15>::from_row_slice(&[
        1210, 1320, 1430, 1540, 1650, 1320, 1440, 1560, 1680, 1800, 1430, 1560, 1690, 1820, 1950,
        2310, 2420, 2530, 2640, 2750, 2520, 2640, 2760, 2880, 3000, 2730, 2860, 2990, 3120, 3250,
        3410, 3520, 3630, 3740, 3850, 3720, 3840, 3960, 4080, 4200, 4030, 4160, 4290, 4420, 4550,
        4510, 4620, 4730, 4840, 4950, 4920, 5040, 5160, 5280, 5400, 5330, 5460, 5590, 5720, 5850,
        2310, 2520, 2730, 2940, 3150, 2420, 2640, 2860, 3080, 3300, 2530, 2760, 2990, 3220, 3450,
        4410, 4620, 4830, 5040, 5250, 4620, 4840, 5060, 5280, 5500, 4830, 5060, 5290, 5520, 5750,
        6510, 6720, 6930, 7140, 7350, 6820, 7040, 7260, 7480, 7700, 7130, 7360, 7590, 7820, 8050,
        8610, 8820, 9030, 9240, 9450, 9020, 9240, 9460, 9680, 9900, 9430, 9660, 9890, 10120, 10350,
    ]);

    let computed = a.kronecker(&b);

    assert_eq!(computed, expected);

    let a = Vector2::new(1, 2);
    let b = Vector3::new(10, 20, 30);
    let expected = Vector6::new(10, 20, 30, 20, 40, 60);

    assert_eq!(a.kronecker(&b), expected);

    let a = Vector2::new(1, 2);
    let b = RowVector4::new(10, 20, 30, 40);
    let expected = Matrix2x4::new(10, 20, 30, 40, 20, 40, 60, 80);

    assert_eq!(a.kronecker(&b), expected);
}

#[test]
fn set_row_column() {
    let a = Matrix4x5::new(
        11, 12, 13, 14, 15, 21, 22, 23, 24, 25, 31, 32, 33, 34, 35, 41, 42, 43, 44, 45,
    );

    let expected1 = Matrix4x5::new(
        11, 12, 13, 14, 15, 42, 43, 44, 45, 46, 31, 32, 33, 34, 35, 41, 42, 43, 44, 45,
    );

    let expected2 = Matrix4x5::new(
        11, 12, 100, 14, 15, 42, 43, 101, 45, 46, 31, 32, 102, 34, 35, 41, 42, 103, 44, 45,
    );

    let row = RowVector5::new(42, 43, 44, 45, 46);
    let col = Vector4::new(100, 101, 102, 103);

    let mut computed = a;

    computed.set_row(1, &row);
    assert_eq!(expected1, computed);

    computed.set_column(2, &col);
    assert_eq!(expected2, computed);
}

#[test]
fn partial_clamp() {
    // NOTE: from #401.
    let n = Vector2::new(1.5, 0.0);
    let min = Vector2::new(-75.0, -0.0);
    let max = Vector2::new(75.0, 0.0);
    let inter = na::partial_clamp(&n, &min, &max);
    assert_eq!(*inter.unwrap(), n);
}

#[test]
fn partial_cmp() {
    let a = Vector2::new(1.0, 6.0);
    let b = Vector2::new(1.0, 3.0);
    let c = Vector2::new(2.0, 7.0);
    let d = Vector2::new(0.0, 7.0);
    assert_eq!(a.partial_cmp(&a), Some(Ordering::Equal));
    assert_eq!(a.partial_cmp(&b), Some(Ordering::Greater));
    assert_eq!(a.partial_cmp(&c), Some(Ordering::Less));
    assert_eq!(a.partial_cmp(&d), None);
}

#[test]
fn swizzle() {
    let a = Vector2::new(1.0f32, 2.0);
    let b = Vector3::new(1.0f32, 2.0, 3.0);
    let c = Vector4::new(1.0f32, 2.0, 3.0, 4.0);

    assert_eq!(a.xy(), Vector2::new(1.0, 2.0));
    assert_eq!(a.yx(), Vector2::new(2.0, 1.0));
    assert_eq!(a.xx(), Vector2::new(1.0, 1.0));
    assert_eq!(a.yy(), Vector2::new(2.0, 2.0));

    assert_eq!(a.xxx(), Vector3::new(1.0, 1.0, 1.0));
    assert_eq!(a.yyy(), Vector3::new(2.0, 2.0, 2.0));
    assert_eq!(a.xyx(), Vector3::new(1.0, 2.0, 1.0));
    assert_eq!(a.yxy(), Vector3::new(2.0, 1.0, 2.0));

    assert_eq!(b.xy(), Vector2::new(1.0, 2.0));
    assert_eq!(b.yx(), Vector2::new(2.0, 1.0));
    assert_eq!(b.xx(), Vector2::new(1.0, 1.0));
    assert_eq!(b.yy(), Vector2::new(2.0, 2.0));

    assert_eq!(b.xz(), Vector2::new(1.0, 3.0));
    assert_eq!(b.zx(), Vector2::new(3.0, 1.0));
    assert_eq!(b.yz(), Vector2::new(2.0, 3.0));
    assert_eq!(b.zy(), Vector2::new(3.0, 2.0));
    assert_eq!(b.zz(), Vector2::new(3.0, 3.0));

    assert_eq!(b.xyz(), Vector3::new(1.0, 2.0, 3.0));
    assert_eq!(b.xxx(), Vector3::new(1.0, 1.0, 1.0));
    assert_eq!(b.yyy(), Vector3::new(2.0, 2.0, 2.0));
    assert_eq!(b.zzz(), Vector3::new(3.0, 3.0, 3.0));
    assert_eq!(b.zxy(), Vector3::new(3.0, 1.0, 2.0));
    assert_eq!(b.zxz(), Vector3::new(3.0, 1.0, 3.0));
    assert_eq!(b.zyz(), Vector3::new(3.0, 2.0, 3.0));

    assert_eq!(c.xy(), Vector2::new(1.0, 2.0));
    assert_eq!(c.yx(), Vector2::new(2.0, 1.0));
    assert_eq!(c.xx(), Vector2::new(1.0, 1.0));
    assert_eq!(c.yy(), Vector2::new(2.0, 2.0));

    assert_eq!(c.xz(), Vector2::new(1.0, 3.0));
    assert_eq!(c.zx(), Vector2::new(3.0, 1.0));
    assert_eq!(c.yz(), Vector2::new(2.0, 3.0));
    assert_eq!(c.zy(), Vector2::new(3.0, 2.0));
    assert_eq!(c.zz(), Vector2::new(3.0, 3.0));

    assert_eq!(c.xyz(), Vector3::new(1.0, 2.0, 3.0));
    assert_eq!(c.xxx(), Vector3::new(1.0, 1.0, 1.0));
    assert_eq!(c.yyy(), Vector3::new(2.0, 2.0, 2.0));
    assert_eq!(c.zzz(), Vector3::new(3.0, 3.0, 3.0));
    assert_eq!(c.zxy(), Vector3::new(3.0, 1.0, 2.0));
    assert_eq!(c.zxz(), Vector3::new(3.0, 1.0, 3.0));
    assert_eq!(c.zyz(), Vector3::new(3.0, 2.0, 3.0));
}

#[cfg(feature = "proptest-support")]
mod transposition_tests {
    use super::*;
    use crate::proptest::{dmatrix, matrix, vector4, PROPTEST_F64};
    use proptest::{prop_assert, prop_assert_eq, proptest};

    proptest! {
        #[test]
        fn transpose_transpose_is_self(m in matrix(PROPTEST_F64, Const::<2>, Const::<3>)) {
            prop_assert_eq!(m.transpose().transpose(), m)
        }

        #[test]
        fn transpose_mut_transpose_mut_is_self(m in matrix(PROPTEST_F64, Const::<3>, Const::<3>)) {
            let mut mm = m;
            mm.transpose_mut();
            mm.transpose_mut();
            prop_assert_eq!(m, mm)
        }

        #[test]
        fn transpose_transpose_is_id_dyn(m in dmatrix()) {
            prop_assert_eq!(m.transpose().transpose(), m)
        }

        #[test]
        fn check_transpose_components_dyn(m in dmatrix()) {
            let tr = m.transpose();
            let (nrows, ncols) = m.shape();

            prop_assert!(nrows == tr.shape().1 && ncols == tr.shape().0);

            for i in 0 .. nrows {
                for j in 0 .. ncols {
                    prop_assert_eq!(m[(i, j)], tr[(j, i)]);
                }
            }
        }

        #[test]
        fn tr_mul_is_transpose_then_mul(m in matrix(PROPTEST_F64, Const::<4>, Const::<6>), v in vector4()) {
            prop_assert!(relative_eq!(m.transpose() * v, m.tr_mul(&v), epsilon = 1.0e-7))
        }
    }
}

#[cfg(feature = "proptest-support")]
mod inversion_tests {
    use super::*;
    use crate::proptest::*;
    use na::Matrix1;
    use proptest::{prop_assert, proptest};

    proptest! {
        #[test]
        fn self_mul_inv_is_id_dim1(m in matrix1()) {
            if let Some(im) = m.try_inverse() {
                let id = Matrix1::one();
                prop_assert!(relative_eq!(im * m, id, epsilon = 1.0e-7));
                prop_assert!(relative_eq!(m * im, id, epsilon = 1.0e-7));
            }
        }

        #[test]
        fn self_mul_inv_is_id_dim2(m in matrix2()) {
            if let Some(im) = m.try_inverse() {
                let id = Matrix2::one();
                prop_assert!(relative_eq!(im * m, id, epsilon = 1.0e-7));
                prop_assert!(relative_eq!(m * im, id, epsilon = 1.0e-7));
            }
        }

        #[test]
        fn self_mul_inv_is_id_dim3(m in matrix3()) {
            if let Some(im) = m.try_inverse() {
                let id = Matrix3::one();
                prop_assert!(relative_eq!(im * m, id, epsilon = 1.0e-7));
                prop_assert!(relative_eq!(m * im, id, epsilon = 1.0e-7));
            }
        }

        #[test]
        fn self_mul_inv_is_id_dim4(m in matrix4()) {
            if let Some(im) = m.try_inverse() {
                let id = Matrix4::one();
                prop_assert!(relative_eq!(im * m, id, epsilon = 1.0e-7));
                prop_assert!(relative_eq!(m * im, id, epsilon = 1.0e-7));
            }
        }

        #[test]
        fn self_mul_inv_is_id_dim6(m in matrix6()) {
            if let Some(im) = m.try_inverse() {
                let id = Matrix6::one();
                prop_assert!(relative_eq!(im * m, id, epsilon = 1.0e-7));
                prop_assert!(relative_eq!(m * im, id, epsilon = 1.0e-7));
            }
        }
    }
}

#[cfg(feature = "proptest-support")]
mod normalization_tests {
    use crate::proptest::*;
    use proptest::{prop_assert, proptest};

    proptest! {
        #[test]
        fn normalized_vec_norm_is_one(v in vector3()) {
            if let Some(nv) = v.try_normalize(1.0e-10) {
                prop_assert!(relative_eq!(nv.norm(), 1.0, epsilon = 1.0e-7));
            }
        }

        #[test]
        fn normalized_vec_norm_is_one_dyn(v in dvector()) {
            if let Some(nv) = v.try_normalize(1.0e-10) {
                prop_assert!(relative_eq!(nv.norm(), 1.0, epsilon = 1.0e-7));
            }
        }
    }
}

#[cfg(all(feature = "proptest-support", feature = "alga"))]
// TODO: move this to alga ?
mod finite_dim_inner_space_tests {
    use super::*;
    use crate::proptest::*;
    use alga::linear::FiniteDimInnerSpace;
    use proptest::collection::vec;
    use proptest::{prop_assert, proptest};
    use std::fmt::Display;

    macro_rules! finite_dim_inner_space_test(
        ($($Vector: ident, $vstrategy: ident, $orthonormal_subspace: ident, $orthonormalization: ident);* $(;)*) => {$(
            proptest! {
                #[test]
                fn $orthonormal_subspace(vs in vec($vstrategy(), 0..10)) {
                    let mut given_basis = vs.clone();
                    let given_basis_dim = $Vector::orthonormalize(&mut given_basis[..]);
                    let mut ortho_basis = Vec::new();
                    $Vector::orthonormal_subspace_basis(
                        &given_basis[.. given_basis_dim],
                        |e| { ortho_basis.push(*e); true }
                    );

                    prop_assert!(is_subspace_basis(&ortho_basis[..]));

                    for v in vs {
                        for b in &ortho_basis {
                            prop_assert!(relative_eq!(v.dot(b), 0.0, epsilon = 1.0e-7));
                        }
                    }
                }

                #[test]
                fn $orthonormalization(vs in vec($vstrategy(), 0..10)) {
                    let mut basis = vs.clone();
                    let subdim = $Vector::orthonormalize(&mut basis[..]);

                    prop_assert!(is_subspace_basis(&basis[.. subdim]));

                    for mut e in vs {
                        for b in &basis[.. subdim] {
                            e -= e.dot(b) * b
                        }

                        // Any element of `e` must be a linear combination of the basis elements.
                        prop_assert!(relative_eq!(e.norm(), 0.0, epsilon = 1.0e-7));
                    }
                }
            }
        )*}
    );

    finite_dim_inner_space_test!(
        Vector1, vector1, orthonormal_subspace_basis1, orthonormalize1;
        Vector2, vector2, orthonormal_subspace_basis2, orthonormalize2;
        Vector3, vector3, orthonormal_subspace_basis3, orthonormalize3;
        Vector4, vector4, orthonormal_subspace_basis4, orthonormalize4;
        Vector5, vector5, orthonormal_subspace_basis5, orthonormalize5;
        Vector6, vector6, orthonormal_subspace_basis6, orthonormalize6;
    );

    /*
     *
     * Helper functions.
     *
     */
    fn is_subspace_basis<T: FiniteDimInnerSpace<RealField = f64, ComplexField = f64> + Display>(
        vs: &[T],
    ) -> bool {
        for i in 0..vs.len() {
            // Basis elements must be normalized.
            if !relative_eq!(vs[i].norm(), 1.0, epsilon = 1.0e-7) {
                println!("Non-zero basis element norm: {}", vs[i].norm());
                return false;
            }

            for j in 0..i {
                // Basis elements must be orthogonal.
                if !relative_eq!(vs[i].dot(&vs[j]), 0.0, epsilon = 1.0e-7) {
                    println!(
                        "Non-orthogonal basis elements: {} · {} = {}",
                        vs[i],
                        vs[j],
                        vs[i].dot(&vs[j])
                    );
                    return false;
                }
            }
        }

        true
    }
}

#[test]
fn partial_eq_shape_mismatch() {
    let a = Matrix2::new(1, 2, 3, 4);
    let b = Matrix2x3::new(1, 2, 3, 4, 5, 6);
    assert_ne!(a, b);
    assert_ne!(b, a);
}

#[test]
fn partial_eq_different_types() {
    // Ensure comparability of several types of Matrices
    let dynamic_mat = DMatrix::from_row_slice(2, 4, &[1, 2, 3, 4, 5, 6, 7, 8]);
    let static_mat = Matrix2x4::new(1, 2, 3, 4, 5, 6, 7, 8);

    let mut typenum_static_mat = OMatrix::<u8, Const<1024>, Const<4>>::zeros();
    let mut slice = typenum_static_mat.slice_mut((0, 0), (2, 4));
    slice += static_mat;

    let fslice_of_dmat = dynamic_mat.fixed_slice::<2, 2>(0, 0);
    let dslice_of_dmat = dynamic_mat.slice((0, 0), (2, 2));
    let fslice_of_smat = static_mat.fixed_slice::<2, 2>(0, 0);
    let dslice_of_smat = static_mat.slice((0, 0), (2, 2));

    assert_eq!(dynamic_mat, static_mat);
    assert_eq!(static_mat, dynamic_mat);

    assert_eq!(dynamic_mat, slice);
    assert_eq!(slice, dynamic_mat);

    assert_eq!(static_mat, slice);
    assert_eq!(slice, static_mat);

    assert_eq!(fslice_of_dmat, dslice_of_dmat);
    assert_eq!(dslice_of_dmat, fslice_of_dmat);

    assert_eq!(fslice_of_dmat, fslice_of_smat);
    assert_eq!(fslice_of_smat, fslice_of_dmat);

    assert_eq!(fslice_of_dmat, dslice_of_smat);
    assert_eq!(dslice_of_smat, fslice_of_dmat);

    assert_eq!(dslice_of_dmat, fslice_of_smat);
    assert_eq!(fslice_of_smat, dslice_of_dmat);

    assert_eq!(dslice_of_dmat, dslice_of_smat);
    assert_eq!(dslice_of_smat, dslice_of_dmat);

    assert_eq!(fslice_of_smat, dslice_of_smat);
    assert_eq!(dslice_of_smat, fslice_of_smat);

    assert_ne!(dynamic_mat, dslice_of_smat);
    assert_ne!(dslice_of_smat, dynamic_mat);

    // TODO - implement those comparisons
    // assert_ne!(static_mat, typenum_static_mat);
    //assert_ne!(typenum_static_mat, static_mat);
}

fn generic_omatrix_to_string<D>(
    vector: &nalgebra::OVector<f64, D>,
    matrix: &nalgebra::OMatrix<f64, D, D>,
) -> (String, String)
where
    D: nalgebra::Dim,
    nalgebra::DefaultAllocator: nalgebra::base::allocator::Allocator<f64, D>,
    nalgebra::DefaultAllocator: nalgebra::base::allocator::Allocator<f64, D, D>,
{
    (vector.to_string(), matrix.to_string())
}

#[test]
fn omatrix_to_string() {
    let dvec: nalgebra::DVector<f64> = nalgebra::dvector![1.0, 2.0];
    let dmatr: nalgebra::DMatrix<f64> = nalgebra::dmatrix![1.0, 2.0; 3.0, 4.0];
    let svec: nalgebra::SVector<f64, 2> = nalgebra::vector![1.0, 2.0];
    let smatr: nalgebra::SMatrix<f64, 2, 2> = nalgebra::matrix![1.0, 2.0; 3.0, 4.0];
    assert_eq!(
        generic_omatrix_to_string(&dvec, &dmatr),
        (dvec.to_string(), dmatr.to_string())
    );
    assert_eq!(
        generic_omatrix_to_string(&svec, &smatr),
        (svec.to_string(), smatr.to_string())
    );
}