cgmath/tests/matrix.rs

// Copyright 2013-2014 The CGMath Developers. For a full listing of the authors,
// refer to the Cargo.toml file at the top-level directory of this distribution.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#[macro_use]
extern crate approx;
#[macro_use]
extern crate cgmath;

pub mod matrix2 {
    use std::f64;

    use cgmath::*;

    const A: Matrix2<f64> = Matrix2 { x: Vector2 { x: 1.0f64, y: 3.0f64 },
                                      y: Vector2 { x: 2.0f64, y: 4.0f64 } };
    const B: Matrix2<f64> = Matrix2 { x: Vector2 { x: 2.0f64, y: 4.0f64 },
                                      y: Vector2 { x: 3.0f64, y: 5.0f64 } };
    const C: Matrix2<f64> = Matrix2 { x: Vector2 { x: 2.0f64, y: 1.0f64 },
                                      y: Vector2 { x: 1.0f64, y: 2.0f64 } };

    const V: Vector2<f64> = Vector2 { x: 1.0f64, y: 2.0f64 };
    const F: f64 = 0.5;

    #[test]
    fn test_neg() {
        assert_eq!(-A,
                   Matrix2::new(-1.0f64, -3.0f64,
                                -2.0f64, -4.0f64));
    }

    #[test]
    fn test_mul_scalar() {
        let result = Matrix2::new(0.5f64, 1.5f64,
                                  1.0f64, 2.0f64) ;
        assert_eq!(A * F, result);
        assert_eq!(F * A, result);
    }

    #[test]
    fn test_div_scalar() {
        assert_eq!(A / F,
                   Matrix2::new(2.0f64, 6.0f64,
                                4.0f64, 8.0f64));
        assert_eq!(4.0f64 / C,
                   Matrix2::new(2.0f64, 4.0f64,
                                4.0f64, 2.0f64));
    }

    #[test]
    fn test_rem_scalar() {
        assert_eq!(A % 3.0f64,
                   Matrix2::new(1.0f64, 0.0f64,
                                2.0f64, 1.0f64));
        assert_eq!(3.0f64 % A,
                   Matrix2::new(0.0f64, 0.0f64,
                                1.0f64, 3.0f64));
    }

    #[test]
    fn test_add_matrix() {
        assert_eq!(A + B,
                   Matrix2::new(3.0f64, 7.0f64,
                                5.0f64, 9.0f64));
    }

    #[test]
    fn test_sub_matrix() {
        assert_eq!(A - B,
                   Matrix2::new(-1.0f64, -1.0f64,
                                -1.0f64, -1.0f64));
    }

    #[test]
    fn test_mul_vector() {
        assert_eq!(A * V, Vector2::new(5.0f64, 11.0f64));
    }

    #[test]
    fn test_mul_matrix() {
        assert_eq!(A * B,
                   Matrix2::new(10.0f64, 22.0f64,
                                13.0f64, 29.0f64));

        assert_eq!(A * B, &A * &B);
    }

    #[test]
    fn test_sum_matrix() {
        let res: Matrix2<f64> = [A, B, C].iter().sum();
        assert_eq!(res, A + B + C);
    }

    #[test]
    fn test_product_matrix() {
        let res: Matrix2<f64> = [A, B, C].iter().product();
        assert_eq!(res, A * B * C);
    }

    #[test]
    fn test_determinant() {
        assert_eq!(A.determinant(), -2.0f64)
    }

    #[test]
    fn test_trace() {
        assert_eq!(A.trace(), 5.0f64);
    }

    #[test]
    fn test_transpose() {
        assert_eq!(A.transpose(),
                   Matrix2::<f64>::new(1.0f64, 2.0f64,
                                       3.0f64, 4.0f64));
    }

    #[test]
    fn test_transpose_self() {
        let mut mut_a = A;
        mut_a.transpose_self();
        assert_eq!(mut_a, A.transpose());
    }

    #[test]
    fn test_invert() {
        assert!(Matrix2::<f64>::identity().invert().unwrap().is_identity());

        assert_eq!(A.invert().unwrap(),
                   Matrix2::new(-2.0f64,  1.5f64,
                                 1.0f64, -0.5f64));
        assert!(Matrix2::new(0.0f64, 2.0f64,
                             0.0f64, 5.0f64).invert().is_none());
    }

    #[test]
    fn test_predicates() {
        assert!(Matrix2::<f64>::identity().is_identity());
        assert!(Matrix2::<f64>::identity().is_symmetric());
        assert!(Matrix2::<f64>::identity().is_diagonal());
        assert!(Matrix2::<f64>::identity().is_invertible());

        assert!(!A.is_identity());
        assert!(!A.is_symmetric());
        assert!(!A.is_diagonal());
        assert!(A.is_invertible());

        assert!(!C.is_identity());
        assert!(C.is_symmetric());
        assert!(!C.is_diagonal());
        assert!(C.is_invertible());

        assert!(Matrix2::from_value(6.0f64).is_diagonal());
    }

    #[test]
    fn test_from_angle() {
        // Rotate the vector (1, 0) by π/2 radians to the vector (0, 1)
        let rot1 = Matrix2::from_angle(Rad(0.5f64 * f64::consts::PI));
        assert_ulps_eq!(rot1 * Vector2::unit_x(), &Vector2::unit_y());

        // Rotate the vector (-1, 0) by -π/2 radians to the vector (0, 1)
        let rot2 = -rot1;
        assert_ulps_eq!(rot2 * -Vector2::unit_x(), &Vector2::unit_y());

        // Rotate the vector (1, 1) by π radians to the vector (-1, -1)
        let rot3: Matrix2<f64> = Matrix2::from_angle(Rad(f64::consts::PI));
        assert_ulps_eq!(rot3 * Vector2::new(1.0, 1.0), &Vector2::new(-1.0, -1.0));
    }
}

pub mod matrix3 {
    use cgmath::*;

    const A: Matrix3<f64> = Matrix3 { x: Vector3 { x: 1.0f64, y: 4.0f64, z:  7.0f64 },
                                      y: Vector3 { x: 2.0f64, y: 5.0f64, z:  8.0f64 },
                                      z: Vector3 { x: 3.0f64, y: 6.0f64, z:  9.0f64 } };
    const B: Matrix3<f64> = Matrix3 { x: Vector3 { x: 2.0f64, y: 5.0f64, z:  8.0f64 },
                                      y: Vector3 { x: 3.0f64, y: 6.0f64, z:  9.0f64 },
                                      z: Vector3 { x: 4.0f64, y: 7.0f64, z: 10.0f64 } };
    const C: Matrix3<f64> = Matrix3 { x: Vector3 { x: 2.0f64, y: 4.0f64, z:  6.0f64 },
                                      y: Vector3 { x: 0.0f64, y: 2.0f64, z:  4.0f64 },
                                      z: Vector3 { x: 0.0f64, y: 0.0f64, z:  1.0f64 } };
    const D: Matrix3<f64> = Matrix3 { x: Vector3 { x: 3.0f64, y: 2.0f64, z:  1.0f64 },
                                      y: Vector3 { x: 2.0f64, y: 3.0f64, z:  2.0f64 },
                                      z: Vector3 { x: 1.0f64, y: 2.0f64, z:  3.0f64 } };

    const V: Vector3<f64> = Vector3 { x: 1.0f64, y: 2.0f64, z:  3.0f64 };
    const F: f64 = 0.5;

    #[test]
    fn test_neg() {
        assert_eq!(-A,
                   Matrix3::new(-1.0f64, -4.0f64, -7.0f64,
                                -2.0f64, -5.0f64, -8.0f64,
                                -3.0f64, -6.0f64, -9.0f64));
    }

    #[test]
    fn test_mul_scalar() {
        let result = Matrix3::new(0.5f64, 2.0f64, 3.5f64,
                                  1.0f64, 2.5f64, 4.0f64,
                                  1.5f64, 3.0f64, 4.5f64);
        assert_eq!(A * F, result);
        assert_eq!(F * A, result);
    }

    #[test]
    fn test_div_scalar() {
        assert_eq!(A / F,
                   Matrix3::new(2.0f64,  8.0f64, 14.0f64,
                                4.0f64, 10.0f64, 16.0f64,
                                6.0f64, 12.0f64, 18.0f64));
        assert_eq!(6.0f64 / D,
                   Matrix3::new(2.0f64, 3.0f64, 6.0f64,
                                3.0f64, 2.0f64, 3.0f64,
                                6.0f64, 3.0f64, 2.0f64));
    }

    #[test]
    fn test_rem_scalar() {
        assert_eq!(A % 3.0f64,
                   Matrix3::new(1.0f64, 1.0f64, 1.0f64,
                                2.0f64, 2.0f64, 2.0f64,
                                0.0f64, 0.0f64, 0.0f64));
        assert_eq!(9.0f64 % A,
                   Matrix3::new(0.0f64, 1.0f64, 2.0f64,
                                1.0f64, 4.0f64, 1.0f64,
                                0.0f64, 3.0f64, 0.0f64));
    }

    #[test]
    fn test_add_matrix() {
        assert_eq!(A + B,
                   Matrix3::new(3.0f64,  9.0f64, 15.0f64,
                                5.0f64, 11.0f64, 17.0f64,
                                7.0f64, 13.0f64, 19.0f64));
    }

    #[test]
    fn test_sub_matrix() {
        assert_eq!(A - B,
                   Matrix3::new(-1.0f64, -1.0f64, -1.0f64,
                                -1.0f64, -1.0f64, -1.0f64,
                                -1.0f64, -1.0f64, -1.0f64));
    }

    #[test]
    fn test_mul_vector() {
        assert_eq!(A * V, Vector3::new(14.0f64, 32.0f64, 50.0f64));
    }

    #[test]
    fn test_mul_matrix() {
        assert_eq!(A * B,
                   Matrix3::new(36.0f64,  81.0f64, 126.0f64,
                                42.0f64,  96.0f64, 150.0f64,
                                48.0f64, 111.0f64, 174.0f64));

        assert_eq!(A * B, &A * &B);
    }

    #[test]
    fn test_sum_matrix() {
        let res: Matrix3<f64> = [A, B, C, D].iter().sum();
        assert_eq!(res, A + B + C + D);
    }

    #[test]
    fn test_product_matrix() {
        let res: Matrix3<f64> = [A, B, C, D].iter().product();
        assert_eq!(res, A * B * C * D);
    }

    #[test]
    fn test_determinant() {;
        assert_eq!(A.determinant(), 0.0f64);
    }

    #[test]
    fn test_trace() {
        assert_eq!(A.trace(), 15.0f64);
    }

    #[test]
    fn test_transpose() {
        assert_eq!(A.transpose(),
                   Matrix3::<f64>::new(1.0f64, 2.0f64, 3.0f64,
                                       4.0f64, 5.0f64, 6.0f64,
                                       7.0f64, 8.0f64, 9.0f64));
    }

    #[test]
    fn test_transpose_self() {
        let mut mut_a = A;
        mut_a.transpose_self();
        assert_eq!(mut_a, A.transpose());
    }

    #[test]
    fn test_invert() {
        assert!(Matrix3::<f64>::identity().invert().unwrap().is_identity());

        assert_eq!(A.invert(), None);

        assert_eq!(C.invert().unwrap(),
                   Matrix3::new(0.5f64, -1.0f64,  1.0f64,
                                0.0f64,  0.5f64, -2.0f64,
                                0.0f64,  0.0f64,  1.0f64));
    }

    #[test]
    fn test_predicates() {
        assert!(Matrix3::<f64>::identity().is_identity());
        assert!(Matrix3::<f64>::identity().is_symmetric());
        assert!(Matrix3::<f64>::identity().is_diagonal());
        assert!(Matrix3::<f64>::identity().is_invertible());

        assert!(!A.is_identity());
        assert!(!A.is_symmetric());
        assert!(!A.is_diagonal());
        assert!(!A.is_invertible());

        assert!(!D.is_identity());
        assert!(D.is_symmetric());
        assert!(!D.is_diagonal());
        assert!(D.is_invertible());

        assert!(Matrix3::from_value(6.0f64).is_diagonal());
    }

    mod from_axis_x {
        use cgmath::*;

        fn check_from_axis_angle_x(pitch: Rad<f32>) {
            let found = Matrix3::from_angle_x(pitch);
            let expected = Matrix3::from(Euler { x: pitch, y: Rad(0.0), z: Rad(0.0) });
            assert_relative_eq!(found, expected, epsilon = 0.001);
        }

        #[test] fn test_zero()      { check_from_axis_angle_x(Rad(0.0)); }
        #[test] fn test_pos_1()     { check_from_axis_angle_x(Rad(1.0)); }
        #[test] fn test_neg_1()     { check_from_axis_angle_x(Rad(-1.0)); }
    }

    mod from_axis_y {
        use cgmath::*;

        fn check_from_axis_angle_y(yaw: Rad<f32>) {
            let found = Matrix3::from_angle_y(yaw);
            let expected = Matrix3::from(Euler { x: Rad(0.0), y: yaw, z: Rad(0.0) });
            assert_relative_eq!(found, expected, epsilon = 0.001);
        }

        #[test] fn test_zero()      { check_from_axis_angle_y(Rad(0.0)); }
        #[test] fn test_pos_1()     { check_from_axis_angle_y(Rad(1.0)); }
        #[test] fn test_neg_1()     { check_from_axis_angle_y(Rad(-1.0)); }
    }

    mod from_axis_z {
        use cgmath::*;

        fn check_from_axis_angle_z(roll: Rad<f32>) {
            let found = Matrix3::from_angle_z(roll);
            let expected = Matrix3::from(Euler { x: Rad(0.0), y: Rad(0.0), z: roll });
            assert_relative_eq!(found, expected, epsilon = 0.001);
        }

        #[test] fn test_zero()      { check_from_axis_angle_z(Rad(0.0)); }
        #[test] fn test_pos_1()     { check_from_axis_angle_z(Rad(1.0)); }
        #[test] fn test_neg_1()     { check_from_axis_angle_z(Rad(-1.0)); }
    }

    mod from_axis_angle {
        mod axis_x {
            use cgmath::*;

            fn check_from_axis_angle_x(pitch: Rad<f32>) {
                let found = Matrix3::from_axis_angle(Vector3::unit_x(), pitch);
                let expected = Matrix3::from(Euler { x: pitch, y: Rad(0.0), z: Rad(0.0) });
                assert_relative_eq!(found, expected, epsilon = 0.001);
            }

            #[test] fn test_zero()      { check_from_axis_angle_x(Rad(0.0)); }
            #[test] fn test_pos_1()     { check_from_axis_angle_x(Rad(1.0)); }
            #[test] fn test_neg_1()     { check_from_axis_angle_x(Rad(-1.0)); }
        }

        mod axis_y {
            use cgmath::*;

            fn check_from_axis_angle_y(yaw: Rad<f32>) {
                let found = Matrix3::from_axis_angle(Vector3::unit_y(), yaw);
                let expected = Matrix3::from(Euler { x: Rad(0.0), y: yaw, z: Rad(0.0) });
                assert_relative_eq!(found, expected, epsilon = 0.001);
            }

            #[test] fn test_zero()      { check_from_axis_angle_y(Rad(0.0)); }
            #[test] fn test_pos_1()     { check_from_axis_angle_y(Rad(1.0)); }
            #[test] fn test_neg_1()     { check_from_axis_angle_y(Rad(-1.0)); }
        }

        mod axis_z {
            use cgmath::*;

            fn check_from_axis_angle_z(roll: Rad<f32>) {
                let found = Matrix3::from_axis_angle(Vector3::unit_z(), roll);
                let expected = Matrix3::from(Euler { x: Rad(0.0), y: Rad(0.0), z: roll });
                assert_relative_eq!(found, expected, epsilon = 0.001);
            }

            #[test] fn test_zero()      { check_from_axis_angle_z(Rad(0.0)); }
            #[test] fn test_pos_1()     { check_from_axis_angle_z(Rad(1.0)); }
            #[test] fn test_neg_1()     { check_from_axis_angle_z(Rad(-1.0)); }
        }
    }

    mod rotate_from_euler {
        use cgmath::*;

        #[test]
        fn test_x() {
            let vec = vec3(0.0, 0.0, 1.0);

            let rot = Matrix3::from(Euler::new(Deg(90.0), Deg(0.0), Deg(0.0)));
            assert_ulps_eq!(vec3(0.0, -1.0, 0.0), rot * vec);

            let rot = Matrix3::from(Euler::new(Deg(-90.0), Deg(0.0), Deg(0.0)));
            assert_ulps_eq!(vec3(0.0, 1.0, 0.0), rot * vec);
        }

        #[test]
        fn test_y() {
            let vec = vec3(0.0, 0.0, 1.0);

            let rot = Matrix3::from(Euler::new(Deg(0.0), Deg(90.0), Deg(0.0)));
            assert_ulps_eq!(vec3(1.0, 0.0, 0.0), rot * vec);

            let rot = Matrix3::from(Euler::new(Deg(0.0), Deg(-90.0), Deg(0.0)));
            assert_ulps_eq!(vec3(-1.0, 0.0, 0.0), rot * vec);
        }

        #[test]
        fn test_z() {
            let vec = vec3(1.0, 0.0, 0.0);

            let rot = Matrix3::from(Euler::new(Deg(0.0), Deg(0.0), Deg(90.0)));
            assert_ulps_eq!(vec3(0.0, 1.0, 0.0), rot * vec);

            let rot = Matrix3::from(Euler::new(Deg(0.0), Deg(0.0), Deg(-90.0)));
            assert_ulps_eq!(vec3(0.0, -1.0, 0.0), rot * vec);
        }


        // tests that the Y rotation is done after the X
        #[test]
        fn test_x_then_y() {
            let vec = vec3(0.0, 1.0, 0.0);

            let rot = Matrix3::from(Euler::new(Deg(90.0), Deg(90.0), Deg(0.0)));
            assert_ulps_eq!(vec3(0.0, 0.0, 1.0), rot * vec);
        }

        // tests that the Z rotation is done after the Y
        #[test]
        fn test_y_then_z() {
            let vec = vec3(0.0, 0.0, 1.0);

            let rot = Matrix3::from(Euler::new(Deg(0.0), Deg(90.0), Deg(90.0)));
            assert_ulps_eq!(vec3(1.0, 0.0, 0.0), rot * vec);
        }
    }

    mod rotate_from_axis_angle {
        use cgmath::*;

        #[test]
        fn test_x() {
            let vec = vec3(0.0, 0.0, 1.0);

            let rot = Matrix3::from_angle_x(Deg(90.0));
            println!("x mat: {:?}", rot);
            assert_ulps_eq!(vec3(0.0, -1.0, 0.0), rot * vec);
        }

        #[test]
        fn test_y() {
            let vec = vec3(0.0, 0.0, 1.0);

            let rot = Matrix3::from_angle_y(Deg(90.0));
            assert_ulps_eq!(vec3(1.0, 0.0, 0.0), rot * vec);
        }

        #[test]
        fn test_z() {
            let vec = vec3(1.0, 0.0, 0.0);

            let rot = Matrix3::from_angle_z(Deg(90.0));
            assert_ulps_eq!(vec3(0.0, 1.0, 0.0), rot * vec);
        }

        #[test]
        fn test_xy() {
            let vec = vec3(0.0, 0.0, 1.0);

            let rot = Matrix3::from_axis_angle(vec3(1.0, 1.0, 0.0).normalize(), Deg(90.0));
            assert_ulps_eq!(vec3(2.0f32.sqrt() / 2.0, -2.0f32.sqrt() / 2.0, 0.0), rot * vec);
        }

        #[test]
        fn test_yz() {
            let vec = vec3(1.0, 0.0, 0.0);

            let rot = Matrix3::from_axis_angle(vec3(0.0, 1.0, 1.0).normalize(), Deg(-90.0));
            assert_ulps_eq!(vec3(0.0, -2.0f32.sqrt() / 2.0, 2.0f32.sqrt() / 2.0), rot * vec);
        }

        #[test]
        fn test_xz() {
            let vec = vec3(0.0, 1.0, 0.0);

            let rot = Matrix3::from_axis_angle(vec3(1.0, 0.0, 1.0).normalize(), Deg(90.0));
            assert_ulps_eq!(vec3(-2.0f32.sqrt() / 2.0, 0.0, 2.0f32.sqrt() / 2.0), rot * vec);
        }
    }
}

pub mod matrix4 {
    use cgmath::*;

    const A: Matrix4<f64> = Matrix4 { x: Vector4 { x: 1.0f64, y: 5.0f64, z:  9.0f64, w: 13.0f64 },
                                      y: Vector4 { x: 2.0f64, y: 6.0f64, z: 10.0f64, w: 14.0f64 },
                                      z: Vector4 { x: 3.0f64, y: 7.0f64, z: 11.0f64, w: 15.0f64 },
                                      w: Vector4 { x: 4.0f64, y: 8.0f64, z: 12.0f64, w: 16.0f64 } };
    const B: Matrix4<f64> = Matrix4 { x: Vector4 { x: 2.0f64, y: 6.0f64, z: 10.0f64, w: 14.0f64 },
                                      y: Vector4 { x: 3.0f64, y: 7.0f64, z: 11.0f64, w: 15.0f64 },
                                      z: Vector4 { x: 4.0f64, y: 8.0f64, z: 12.0f64, w: 16.0f64 },
                                      w: Vector4 { x: 5.0f64, y: 9.0f64, z: 13.0f64, w: 17.0f64 } };
    const C: Matrix4<f64> = Matrix4 { x: Vector4 { x: 3.0f64, y: 2.0f64, z:  1.0f64, w:  1.0f64 },
                                      y: Vector4 { x: 2.0f64, y: 3.0f64, z:  2.0f64, w:  2.0f64 },
                                      z: Vector4 { x: 1.0f64, y: 2.0f64, z:  3.0f64, w:  3.0f64 },
                                      w: Vector4 { x: 0.0f64, y: 1.0f64, z:  1.0f64, w:  0.0f64 } };
    const D: Matrix4<f64> = Matrix4 { x: Vector4 { x: 4.0f64, y: 3.0f64, z:  2.0f64, w:  1.0f64 },
                                      y: Vector4 { x: 3.0f64, y: 4.0f64, z:  3.0f64, w:  2.0f64 },
                                      z: Vector4 { x: 2.0f64, y: 3.0f64, z:  4.0f64, w:  3.0f64 },
                                      w: Vector4 { x: 1.0f64, y: 2.0f64, z:  3.0f64, w:  4.0f64 } };

    const V: Vector4<f64> = Vector4 { x: 1.0f64, y: 2.0f64, z: 3.0f64, w: 4.0f64 };
    const F: f64 = 0.5;

    #[test]
    fn test_neg() {
        assert_eq!(-A,
                   Matrix4::new(-1.0f64, -5.0f64,  -9.0f64, -13.0f64,
                                -2.0f64, -6.0f64, -10.0f64, -14.0f64,
                                -3.0f64, -7.0f64, -11.0f64, -15.0f64,
                                -4.0f64, -8.0f64, -12.0f64, -16.0f64));
    }

    #[test]
    fn test_mul_scalar() {
        let result = Matrix4::new(0.5f64, 2.5f64, 4.5f64, 6.5f64,
                                  1.0f64, 3.0f64, 5.0f64, 7.0f64,
                                  1.5f64, 3.5f64, 5.5f64, 7.5f64,
                                  2.0f64, 4.0f64, 6.0f64, 8.0f64);
        assert_eq!(A * F, result);
        assert_eq!(F * A, result);
    }

    #[test]
    fn test_div_scalar() {
        assert_eq!(A / F,
                   Matrix4::new(2.0f64, 10.0f64, 18.0f64, 26.0f64,
                                4.0f64, 12.0f64, 20.0f64, 28.0f64,
                                6.0f64, 14.0f64, 22.0f64, 30.0f64,
                                8.0f64, 16.0f64, 24.0f64, 32.0f64));
        assert_eq!(12.0f64 / D,
                   Matrix4::new( 3.0f64,  4.0f64,  6.0f64, 12.0f64,
                                 4.0f64,  3.0f64,  4.0f64,  6.0f64,
                                 6.0f64,  4.0f64,  3.0f64,  4.0f64,
                                12.0f64,  6.0f64,  4.0f64,  3.0f64));
    }

    #[test]
    fn test_rem_scalar() {
        assert_eq!(A % 4.0f64,
                   Matrix4::new(1.0f64, 1.0f64, 1.0f64, 1.0f64,
                                2.0f64, 2.0f64, 2.0f64, 2.0f64,
                                3.0f64, 3.0f64, 3.0f64, 3.0f64,
                                0.0f64, 0.0f64, 0.0f64, 0.0f64));
         assert_eq!(16.0f64 % A,
                    Matrix4::new(0.0f64, 1.0f64, 7.0f64, 3.0f64,
                                 0.0f64, 4.0f64, 6.0f64, 2.0f64,
                                 1.0f64, 2.0f64, 5.0f64, 1.0f64,
                                 0.0f64, 0.0f64, 4.0f64, 0.0f64));
    }

    #[test]
    fn test_add_matrix() {
        assert_eq!(A + B,
                   Matrix4::new(3.0f64, 11.0f64, 19.0f64, 27.0f64,
                                5.0f64, 13.0f64, 21.0f64, 29.0f64,
                                7.0f64, 15.0f64, 23.0f64, 31.0f64,
                                9.0f64, 17.0f64, 25.0f64, 33.0f64));
    }

    #[test]
    fn test_sub_matrix() {
        assert_eq!(A - B,
                   Matrix4::new(-1.0f64, -1.0f64, -1.0f64, -1.0f64,
                                -1.0f64, -1.0f64, -1.0f64, -1.0f64,
                                -1.0f64, -1.0f64, -1.0f64, -1.0f64,
                                -1.0f64, -1.0f64, -1.0f64, -1.0f64));
    }

    #[test]
    fn test_mul_vector() {
        assert_eq!(A * V, Vector4::new(30.0f64, 70.0f64, 110.0f64, 150.0f64));
    }

    #[test]
    fn test_mul_matrix() {
        assert_eq!(A * B,
                   Matrix4::new(100.0f64, 228.0f64, 356.0f64, 484.0f64,
                                110.0f64, 254.0f64, 398.0f64, 542.0f64,
                                120.0f64, 280.0f64, 440.0f64, 600.0f64,
                                130.0f64, 306.0f64, 482.0f64, 658.0f64));

        assert_eq!(A * B, &A * &B);
    }

    #[test]
    fn test_sum_matrix() {
        let res: Matrix4<f64> = [A, B, C, D].iter().sum();
        assert_eq!(res, A + B + C + D);
    }

    #[test]
    fn test_product_matrix() {
        let res: Matrix4<f64> = [A, B, C, D].iter().product();
        assert_eq!(res, A * B * C * D);
    }

    #[test]
    fn test_determinant() {
        assert_eq!(A.determinant(), 0.0f64);
    }

    #[test]
    fn test_trace() {
        assert_eq!(A.trace(), 34.0f64);
    }

    #[test]
    fn test_transpose() {
        assert_eq!(A.transpose(),
                   Matrix4::<f64>::new( 1.0f64,  2.0f64,  3.0f64,  4.0f64,
                                        5.0f64,  6.0f64,  7.0f64,  8.0f64,
                                        9.0f64, 10.0f64, 11.0f64, 12.0f64,
                                       13.0f64, 14.0f64, 15.0f64, 16.0f64));
    }

    #[test]
    fn test_transpose_self() {
        let mut mut_a = A;
        mut_a.transpose_self();
        assert_eq!(mut_a, A.transpose());
    }

    #[test]
    fn test_invert() {
        assert!(Matrix4::<f64>::identity().invert().unwrap().is_identity());

        assert_ulps_eq!(&C.invert().unwrap(), &(
                Matrix4::new( 5.0f64, -4.0f64,  1.0f64,  0.0f64,
                             -4.0f64,  8.0f64, -4.0f64,  0.0f64,
                              4.0f64, -8.0f64,  4.0f64,  8.0f64,
                             -3.0f64,  4.0f64,  1.0f64, -8.0f64) * 0.125f64));

        let mat_c = Matrix4::new(-0.131917f64, -0.76871f64,   0.625846f64, 0.0f64,
                                 -0.,        0.631364f64,  0.775487f64, 0.0f64,
                                 -0.991261f64,  0.1023f64,   -0.083287f64, 0.0f64,
                                  0.,       -1.262728f64, -1.550973f64, 1.0f64);
        assert!((mat_c.invert().unwrap() * mat_c).is_identity());

        let mat_d = Matrix4::new( 0.065455f64, -0.720002f64,  0.690879f64, 0.0f64,
                                 -0.,        0.692364f64,  0.721549f64, 0.0f64,
                                 -0.997856f64, -0.047229f64,  0.045318f64, 0.0f64,
                                  0.,       -1.384727f64, -1.443098f64, 1.0f64);
        assert!((mat_d.invert().unwrap() * mat_d).is_identity());

        let mat_e = Matrix4::new( 0.409936f64,  0.683812f64, -0.603617f64, 0.0f64,
                                  0.,        0.661778f64,  0.7497f64,   0.0f64,
                                  0.912114f64, -0.307329f64,  0.271286f64, 0.0f64,
                                 -0.,       -1.323555f64, -1.499401f64, 1.0f64);
        assert!((mat_e.invert().unwrap() * mat_e).is_identity());

        let mat_f = Matrix4::new(-0.160691f64, -0.772608f64,  0.614211f64, 0.0f64,
                                 -0.,        0.622298f64,  0.78278f64,  0.0f64,
                                 -0.987005f64,  0.125786f64, -0.099998f64, 0.0f64,
                                  0.,       -1.244597f64, -1.565561f64, 1.0f64);
        assert!((mat_f.invert().unwrap() * mat_f).is_identity());
    }

    #[test]
    fn test_predicates() {
        assert!(Matrix4::<f64>::identity().is_identity());
        assert!(Matrix4::<f64>::identity().is_symmetric());
        assert!(Matrix4::<f64>::identity().is_diagonal());
        assert!(Matrix4::<f64>::identity().is_invertible());

        assert!(!A.is_identity());
        assert!(!A.is_symmetric());
        assert!(!A.is_diagonal());
        assert!(!A.is_invertible());

        assert!(!D.is_identity());
        assert!(D.is_symmetric());
        assert!(!D.is_diagonal());
        assert!(D.is_invertible());

        assert!(Matrix4::from_value(6.0f64).is_diagonal());
    }

    #[test]
    fn test_from_translation() {
        let mat = Matrix4::from_translation(Vector3::new(1.0f64, 2.0f64, 3.0f64));
        let vertex = Vector4::new(0.0f64, 0.0f64, 0.0f64, 1.0f64);
        let res = mat * vertex;
        assert_eq!(res, Vector4::new(1., 2., 3., 1.));
    }

    #[test]
    fn test_cast() {
        assert_ulps_eq!(Matrix2::new(0.2f64, 1.5, 4.7, 2.3).cast(), Matrix2::new(0.2f32, 1.5, 4.7, 2.3));
        assert_ulps_eq!(Matrix3::new(
            0.2f64, 1.5, 4.7,
            2.3,    5.7, 2.1,
            4.6,    5.2, 6.6,
        ).cast(), Matrix3::new(
            0.2f32, 1.5, 4.7,
            2.3,    5.7, 2.1,
            4.6,    5.2, 6.6,
        ));

        assert_ulps_eq!(Matrix4::new(
            0.2f64, 1.5, 4.7, 2.5,
            2.3,    5.7, 2.1, 1.1,
            4.6,    5.2, 6.6, 0.2,
            3.2,    1.8, 0.4, 2.9,
        ).cast(), Matrix4::new(
            0.2f32, 1.5, 4.7, 2.5,
            2.3,    5.7, 2.1, 1.1,
            4.6,    5.2, 6.6, 0.2,
            3.2,    1.8, 0.4, 2.9,
        ));

    }

    mod from {
        use cgmath::*;

        #[test]
        fn test_quaternion() {
            let quaternion = Quaternion::new(2f32, 3f32, 4f32, 5f32);

            let matrix_short = Matrix4::from(quaternion);

            let matrix_long = Matrix3::from(quaternion);
            let matrix_long = Matrix4::from(matrix_long);

            assert_ulps_eq!(matrix_short, matrix_long);
        }
    }
}