static_math/

matrix3x3.rs

//-------------------------------------------------------------------------
// @file matrix3x3.rs
//
// @date 06/02/20 18:41:39
// @author Martin Noblia
// @email mnoblia@disroot.org
//
// @brief
//
// @detail
//
// Licence MIT:
// Copyright <2020> <Martin Noblia>
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.  THE SOFTWARE IS PROVIDED
// "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
// LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
// PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
// ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
//-------------------------------------------------------------------------
#![macro_use]
use core::fmt;
use core::ops::{Add, Mul, Div, Sub, SubAssign, AddAssign, Neg};
use core::ops::{Deref, DerefMut, Index, IndexMut};

use crate::traits::LinearAlgebra;
use crate::utils::nearly_zero;
use num::{Float, One, Zero, Num, Signed};

use crate::slices_methods::*;
use crate::vector3::*;
//-------------------------------------------------------------------------
//                        code
//-------------------------------------------------------------------------

/// A static matrix of 3x3 shape
#[derive(Copy, Clone, Debug, PartialEq)]
pub struct M33<T>([[T; 3]; 3]);

impl<T> M33<T> {
    pub const fn new(data_input: [[T; 3]; 3]) -> M33<T> {
        M33(data_input)
    }

    pub const fn rows(&self) -> usize {
        self.0.len()
    }

    pub const fn cols(&self) -> usize {
        self.rows()
    }
}

impl<T: Float + core::iter::Sum> LinearAlgebra<T> for M33<T> {
    fn rows(&self) -> usize {
        self.0.len()
    }

    fn cols(&self) -> usize {
        self.rows()
    }

    #[inline(always)]
    fn transpose(&self) -> M33<T> {
        M33::new([
            [self[(0, 0)], self[(1, 0)], self[(2, 0)]],
            [self[(0, 1)], self[(1, 1)], self[(2, 1)]],
            [self[(0, 2)], self[(1, 2)], self[(2, 2)]],
        ])
    }

    #[inline(always)]
    fn trace(&self) -> T {
        self[(0, 0)] + self[(1, 1)] + self[(2, 2)]
    }

    fn norm2(&self) -> T {
        T::sqrt(
            self[(0, 0)] * self[(0, 0)]
                + self[(1, 0)] * self[(1, 0)]
                + self[(2, 0)] * self[(2, 0)]
                + self[(0, 1)] * self[(0, 1)]
                + self[(1, 1)] * self[(1, 1)]
                + self[(2, 1)] * self[(2, 1)]
                + self[(0, 2)] * self[(0, 2)]
                + self[(1, 2)] * self[(1, 2)]
                + self[(2, 2)] * self[(2, 2)],
        )
    }

    /// Calculate the determinant of the matrix
    #[inline(always)]
    fn det(&self) -> T {
          self[(0, 0)] * (self[(1, 1)] * self[(2, 2)] - self[(2, 1)] * self[(1, 2)])
        - self[(0, 1)] * (self[(1, 0)] * self[(2, 2)] - self[(1, 2)] * self[(2, 0)])
        + self[(0, 2)] * (self[(1, 0)] * self[(2, 1)] - self[(1, 1)] * self[(2, 0)])
    }

    /// Calculate the inverse
    #[inline(always)]
    fn inverse(&self) -> Option<Self> {
        let det = self.det();
        if !nearly_zero(det) {
            let invdet = det.recip();
            let mut res = M33::zero();
            res[(0, 0)] = (self[(1, 1)] * self[(2, 2)] - self[(2, 1)] * self[(1, 2)]) * invdet;
            res[(0, 1)] = (self[(0, 2)] * self[(2, 1)] - self[(0, 1)] * self[(2, 2)]) * invdet;
            res[(0, 2)] = (self[(0, 1)] * self[(1, 2)] - self[(0, 2)] * self[(1, 1)]) * invdet;
            res[(1, 0)] = (self[(1, 2)] * self[(2, 0)] - self[(1, 0)] * self[(2, 2)]) * invdet;
            res[(1, 1)] = (self[(0, 0)] * self[(2, 2)] - self[(0, 2)] * self[(2, 0)]) * invdet;
            res[(1, 2)] = (self[(1, 0)] * self[(0, 2)] - self[(0, 0)] * self[(1, 2)]) * invdet;
            res[(2, 0)] = (self[(1, 0)] * self[(2, 1)] - self[(2, 0)] * self[(1, 1)]) * invdet;
            res[(2, 1)] = (self[(2, 0)] * self[(0, 1)] - self[(0, 0)] * self[(2, 1)]) * invdet;
            res[(2, 2)] = (self[(0, 0)] * self[(1, 1)] - self[(1, 0)] * self[(0, 1)]) * invdet;
            Some(res)
        } else {
            None
        }
    }

    /// Calculate de QR factorization of the M33 via gram-schmidt
    /// orthogonalization process
    fn qr(&self) -> Option<(Self, Self)> {
        if !nearly_zero(self.det()) {
            let cols = self.get_cols();
            let mut q: [V3<T>; 3] = *M33::zeros().get_cols();
            for i in 0..q.len() {
                let mut q_tilde = cols[i];
                for elem in q.iter().take(i) {
                    q_tilde -= *elem * project_x_over_y(&*cols[i], &**elem);
                }
                normalize(&mut *q_tilde);
                q[i] = q_tilde;
            }
            let basis = V3::new_from(q[0], q[1], q[2]);
            let q     = M33::new_from_vecs(basis);
            let r     = q.transpose() * (*self);
            Some((q, r))
        } else {
            None
        }
    }
}

impl<T: Num + Copy> M33<T> {
    /// contruct identity matrix
    pub fn identity() -> M33<T> {
        <M33<T> as One>::one()
    }

    /// construct the matrix with all zeros
    pub fn zeros() -> M33<T> {
        <M33<T> as Zero>::zero()
    }

    /// transform the matrix to a flatten vector
    pub fn as_vec(&self) -> [T; 9] {
        let mut result = [T::zero(); 9];
        for (index, element) in self.iter().flatten().enumerate() {
            result[index] = *element;
        }
        result
    }

    /// construct the matrix from columns-vectors
    pub fn new_from_vecs(cols: V3<V3<T>>) -> Self {
        let mut result = Self::zeros();

        for i in 0..result.cols() {
            result[(i, 0)] = cols[0][i];
            result[(i, 1)] = cols[1][i];
            result[(i, 2)] = cols[2][i];
        }
        result
    }

    /// get the diagonal of the matrix
    pub fn get_diagonal(&self) -> V3<T> {
        let mut result = V3::zeros();
        let mut index: usize = 0;
        for i in 0..self.rows() {
            for j in 0..self.cols() {
                if i == j {
                    result[index] = self[(i, j)];
                    index += 1;
                }
            }
        }
        result
    }

    pub fn get_upper_triagular(&self) -> [T; 3] {
        let zero = T::zero();
        let mut result: [T; 3] = [zero, zero, zero];
        let mut index = 0;
        for i in 0..self.rows() {
            for j in 0..self.cols() {
                if i < j {
                    result[index] = self[(i, j)];
                    index += 1;
                }
            }
        }
        result
    }

    pub fn get_lower_triangular(&self) -> [T; 3] {
        let zero = T::zero();
        let mut result: [T; 3] = [zero, zero, zero];
        let mut index = 0;
        for i in 0..self.rows() {
            for j in 0..self.cols() {
                if i > j {
                    result[index] = self[(i, j)];
                    index += 1;
                }
            }
        }
        result
    }


    /// Applies `f` of each element in the M33
    pub fn for_each(&self, f: impl Fn(T) -> T) -> Self {
        let mut result = Self::zeros();
        for i in 0..self.rows() {
            for j in 0..self.cols() {
                result[(i, j)] = f(self[(i, j)]);
            }
        }
        result
    }

}

impl<T: Num + Copy> M33<T> {

    /// get the rows of the matrix as a vectors
    pub fn get_rows(self) -> V3<V3<T>> {
        let mut r0 = V3::zeros();
        let mut r1 = V3::zeros();
        let mut r2 = V3::zeros();

        for j in 0..self.rows() {
            r0[j] = self[(0, j)];
            r1[j] = self[(1, j)];
            r2[j] = self[(2, j)];
        }
        V3::new([r0, r1, r2])
    }

    /// get the columns of the matrix as a vectors
    pub fn get_cols(self) -> V3<V3<T>> {
        let mut c0 = V3::zeros();
        let mut c1 = V3::zeros();
        let mut c2 = V3::zeros();

        for i in 0..self.rows() {
            c0[i] = self[(i, 0)];
            c1[i] = self[(i, 1)];
            c2[i] = self[(i, 2)];
        }
        V3::new([c0, c1, c2])
    }
}

impl<T: Num + Copy> Add for M33<T> {
    type Output = Self;

    #[inline(always)]
    fn add(self, rhs: Self) -> Self {
        M33::new([
            [
                self[(0, 0)] + rhs[(0, 0)],
                self[(0, 1)] + rhs[(0, 1)],
                self[(0, 2)] + rhs[(0, 2)],
            ],
            [
                self[(1, 0)] + rhs[(1, 0)],
                self[(1, 1)] + rhs[(1, 1)],
                self[(1, 2)] + rhs[(1, 2)],
            ],
            [
                self[(2, 0)] + rhs[(2, 0)],
                self[(2, 1)] + rhs[(2, 1)],
                self[(2, 2)] + rhs[(2, 2)],
            ],
        ])
    }
}

// M33 += M33
impl<T: Num + Copy> AddAssign for M33<T> {
    fn add_assign(&mut self, other: Self) {
        *self = *self + other
    }
}

// M33 - M33
impl<T: Num + Copy> Sub for M33<T> {
    type Output = Self;

    fn sub(self, rhs: Self) -> Self {
        M33::new([
            [
                self[(0, 0)] - rhs[(0, 0)],
                self[(0, 1)] - rhs[(0, 1)],
                self[(0, 2)] - rhs[(0, 2)],
            ],
            [
                self[(1, 0)] - rhs[(1, 0)],
                self[(1, 1)] - rhs[(1, 1)],
                self[(1, 2)] - rhs[(1, 2)],
            ],
            [
                self[(2, 0)] - rhs[(2, 0)],
                self[(2, 1)] - rhs[(2, 1)],
                self[(2, 2)] - rhs[(2, 2)],
            ],
        ])
    }
}

// M33 -= M33
impl<T: Num + Copy> SubAssign for M33<T> {
    fn sub_assign(&mut self, other: Self) {
        *self = *self - other
    }
}

// M3 * V3
impl<T: Num + Copy> Mul<V3<T>> for M33<T> {
    type Output = V3<T>;

    #[inline(always)]
    fn mul(self, rhs: V3<T>) -> V3<T> {

        let a_00 = self[(0, 0)];
        let a_01 = self[(0, 1)];
        let a_02 = self[(0, 2)];
        let a_10 = self[(1, 0)];
        let a_11 = self[(1, 1)];
        let a_12 = self[(1, 2)];
        let a_20 = self[(2, 0)];
        let a_21 = self[(2, 1)];
        let a_22 = self[(2, 2)];

        let v0 = rhs[0];
        let v1 = rhs[1];
        let v2 = rhs[2];
        V3::new([a_00 * v0 + a_01 * v1 + a_02 * v2,
                 a_10 * v0 + a_11 * v1 + a_12 * v2,
                 a_20 * v0 + a_21 * v1 + a_22 * v2])
    }
}

// M3 * constant
impl<T: Num + Copy> Mul<T> for M33<T> {
    type Output = M33<T>;

    fn mul(self, rhs: T) -> Self::Output {
        let a_00 = self[(0, 0)] * rhs;
        let a_01 = self[(0, 1)] * rhs;
        let a_02 = self[(0, 2)] * rhs;
        let a_10 = self[(1, 0)] * rhs;
        let a_11 = self[(1, 1)] * rhs;
        let a_12 = self[(1, 2)] * rhs;
        let a_20 = self[(2, 0)] * rhs;
        let a_21 = self[(2, 1)] * rhs;
        let a_22 = self[(2, 2)] * rhs;

        M33::new([[a_00, a_01, a_02], [a_10, a_11, a_12], [a_20, a_21, a_22]])
    }
}

// M33 / constant
impl<T: Num + Copy> Div<T> for M33<T> {
    type Output = Self;

    fn div(self, rhs: T) -> Self::Output {
        let a_00 = self[(0, 0)] / rhs;
        let a_01 = self[(0, 1)] / rhs;
        let a_02 = self[(0, 2)] / rhs;
        let a_10 = self[(1, 0)] / rhs;
        let a_11 = self[(1, 1)] / rhs;
        let a_12 = self[(1, 2)] / rhs;
        let a_20 = self[(2, 0)] / rhs;
        let a_21 = self[(2, 1)] / rhs;
        let a_22 = self[(2, 2)] / rhs;

        M33::new([[a_00, a_01, a_02], [a_10, a_11, a_12], [a_20, a_21, a_22]])
    }
}

// f32 * M33<f32>
impl Mul<M33<f32>> for f32 {
    type Output = M33<f32>;

    fn mul(self, rhs: M33<f32>) -> Self::Output {
        let a_00 = self * rhs[(0, 0)];
        let a_01 = self * rhs[(0, 1)];
        let a_02 = self * rhs[(0, 2)];
        let a_10 = self * rhs[(1, 0)];
        let a_11 = self * rhs[(1, 1)];
        let a_12 = self * rhs[(1, 2)];
        let a_20 = self * rhs[(2, 0)];
        let a_21 = self * rhs[(2, 1)];
        let a_22 = self * rhs[(2, 2)];

        M33::new([[a_00, a_01, a_02], [a_10, a_11, a_12], [a_20, a_21, a_22]])
    }
}

// f64 * M33<f64>
impl Mul<M33<f64>> for f64 {
    type Output = M33<f64>;

    fn mul(self, rhs: M33<f64>) -> Self::Output {
        let a_00 = self * rhs[(0, 0)];
        let a_01 = self * rhs[(0, 1)];
        let a_02 = self * rhs[(0, 2)];
        let a_10 = self * rhs[(1, 0)];
        let a_11 = self * rhs[(1, 1)];
        let a_12 = self * rhs[(1, 2)];
        let a_20 = self * rhs[(2, 0)];
        let a_21 = self * rhs[(2, 1)];
        let a_22 = self * rhs[(2, 2)];

        M33::new([[a_00, a_01, a_02], [a_10, a_11, a_12], [a_20, a_21, a_22]])
    }
}


// M3 * M3
impl<T: Num + Copy> Mul for M33<T> {
    type Output = Self;

    #[inline]
    fn mul(self, rhs: Self) -> Self {
        let m00 =
            self[(0, 0)] * rhs[(0, 0)] + self[(0, 1)] * rhs[(1, 0)] + self[(0, 2)] * rhs[(2, 0)];
        let m01 =
            self[(0, 0)] * rhs[(0, 1)] + self[(0, 1)] * rhs[(1, 1)] + self[(0, 2)] * rhs[(2, 1)];
        let m02 =
            self[(0, 0)] * rhs[(0, 2)] + self[(0, 1)] * rhs[(1, 2)] + self[(0, 2)] * rhs[(2, 2)];

        let m10 =
            self[(1, 0)] * rhs[(0, 0)] + self[(1, 1)] * rhs[(1, 0)] + self[(1, 2)] * rhs[(2, 0)];
        let m11 =
            self[(1, 0)] * rhs[(0, 1)] + self[(1, 1)] * rhs[(1, 1)] + self[(1, 2)] * rhs[(2, 1)];
        let m12 =
            self[(1, 0)] * rhs[(0, 2)] + self[(1, 1)] * rhs[(1, 2)] + self[(1, 2)] * rhs[(2, 2)];

        let m20 =
            self[(2, 0)] * rhs[(0, 0)] + self[(2, 1)] * rhs[(1, 0)] + self[(2, 2)] * rhs[(2, 0)];
        let m21 =
            self[(2, 0)] * rhs[(0, 1)] + self[(2, 1)] * rhs[(1, 1)] + self[(2, 2)] * rhs[(2, 1)];
        let m22 =
            self[(2, 0)] * rhs[(0, 2)] + self[(2, 1)] * rhs[(1, 2)] + self[(2, 2)] * rhs[(2, 2)];

        M33::new([[m00, m01, m02], [m10, m11, m12], [m20, m21, m22]])
    }
}

// -M33
impl<T: Num + Copy + Signed> Neg for M33<T> {
    type Output = Self;

    fn neg(self) -> Self {
        let a_00 = -self[(0, 0)];
        let a_01 = -self[(0, 1)];
        let a_02 = -self[(0, 2)];
        let a_10 = -self[(1, 0)];
        let a_11 = -self[(1, 1)];
        let a_12 = -self[(1, 2)];
        let a_20 = -self[(2, 0)];
        let a_21 = -self[(2, 1)];
        let a_22 = -self[(2, 2)];

        M33::new([[a_00, a_01, a_02], [a_10, a_11, a_12], [a_20, a_21, a_22]])
    }
}

impl<T: Num + Copy> Zero for M33<T> {
    fn zero() -> M33<T> {
        M33::new([[T::zero(); 3]; 3])
    }

    fn is_zero(&self) -> bool {
        *self == M33::zero()
    }
}

impl<T: Num + Copy> One for M33<T> {
    /// Create an identity matrix
    fn one() -> M33<T> {
        let one = T::one();
        let zero = T::zero();
        M33::new([[one, zero, zero], [zero, one, zero], [zero, zero, one]])
    }
}
//
impl<T> Deref for M33<T> {
    type Target = [[T; 3]; 3];
    #[inline]
    fn deref(&self) -> &Self::Target {
        &self.0
    }
}

impl<T> DerefMut for M33<T> {
    #[inline]
    fn deref_mut(&mut self) -> &mut Self::Target {
        &mut self.0
    }
}

impl<T> From<[[T; 3]; 3]> for M33<T> {
    fn from(data: [[T; 3]; 3]) -> M33<T> {
        M33(data)
    }
}

impl<T> Index<(usize, usize)> for M33<T> {
    type Output = T;
    #[inline(always)]
    fn index(&self, index: (usize, usize)) -> &T {
        &self.0[index.0][index.1]
    }
}

impl<T> IndexMut<(usize, usize)> for M33<T> {
    #[inline(always)]
    fn index_mut(&mut self, index: (usize, usize)) -> &mut T {
        &mut self.0[index.0][index.1]
    }
}

//-------------------------------------------------------------------------
//                        Display for M33
//-------------------------------------------------------------------------
impl<T: Num + fmt::Display> fmt::Display for M33<T> {
    fn fmt(&self, dest: &mut fmt::Formatter) -> fmt::Result {
        println!();
        writeln!(
            dest,
            "|{0:<7.2} {1:^7.2} {2:>7.2}|",
            self[(0, 0)],
            self[(0, 1)],
            self[(0, 2)]
        )?;
        writeln!(
            dest,
            "|{0:<7.2} {1:^7.2} {2:>7.2}|",
            self[(1, 0)],
            self[(1, 1)],
            self[(1, 2)]
        )?;
        writeln!(
            dest,
            "|{0:<7.2} {1:^7.2} {2:>7.2}|",
            self[(2, 0)],
            self[(2, 1)],
            self[(2, 2)]
        )
    }
}

//-------------------------------------------------------------------------
//                        macros
//-------------------------------------------------------------------------
#[macro_export]
macro_rules! m33_new {
    ($($first_row:expr),*;
     $($second_row:expr),*;
     $($third_row:expr),*
     ) => {
        M33::new([[$($first_row),*], [$($second_row),*], [$($third_row),*]])
    }
}

//-------------------------------------------------------------------------
//                        tests
//-------------------------------------------------------------------------

#[cfg(test)]
mod test_matrix3x3 {
    use crate::traits::LinearAlgebra;
    use crate::matrix3x3::M33;
    use crate::utils::nearly_equal;
    use crate::utils::compare_vecs;
    use crate::vector3::*;

    const EPS: f32 = 1e-8;

    #[test]
    fn create_matrix() {
        let matrix = M33::new([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]]);
        assert_eq!(matrix[(0, 0)], 0.0);
        assert_eq!(matrix[(0, 1)], 1.0);
        assert_eq!(matrix[(0, 2)], 2.0);
        assert_eq!(matrix[(1, 0)], 3.0);
        assert_eq!(matrix[(1, 1)], 4.0);
        assert_eq!(matrix[(1, 2)], 5.0);
        assert_eq!(matrix[(2, 0)], 6.0);
        assert_eq!(matrix[(2, 1)], 7.0);
        assert_eq!(matrix[(2, 2)], 8.0);
    }

    #[test]
    fn trace_test() {
        let matrix = M33::new([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]]);
        assert_eq!(matrix.trace(), 12.0);
    }

    #[test]
    fn add_matrix() {
        use super::test_matrix3x3::EPS;
        let m1 = M33::new([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]]);

        let m2 = M33::new([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]]);

        let expected = M33::new([[0.0, 2.0, 4.0], [6.0, 8.0, 10.0], [12.0, 14.0, 16.0]]);
        let result = m1 + m2;
        assert!(compare_vecs(&result.as_vec(), &expected.as_vec(), EPS));
    }

    #[test]
    fn sub_test() {
        use super::test_matrix3x3::EPS;
        let m1 = m33_new!(0.0, 1.0, 2.0;
                          3.0, 4.0, 5.0;
                          6.0, 7.0, 8.0);

        let m2 = m33_new!(0.0, 1.0, 2.0;
                          3.0, 4.0, 5.0;
                          6.0, 7.0, 8.0);

        let expected = m33_new!(0.0, 0.0, 0.0;
                          0.0, 0.0, 0.0;
                          0.0, 0.0, 0.0);

        let result = m1 - m2;
        assert!(compare_vecs(&result.as_vec(), &expected.as_vec(), EPS));
    }

    #[test]
    fn test_identity_creation() {
        use super::test_matrix3x3::EPS;
        let identity: M33<f32> = M33::identity();

        let expected = M33::new([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]);
        assert!(compare_vecs(&identity.as_vec(), &expected.as_vec(), EPS));
    }

    #[test]
    fn test_zeros_creation() {
        use super::test_matrix3x3::EPS;
        let zero: M33<f32> = M33::zeros();

        let expected = M33::new([[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]);
        assert!(compare_vecs(&zero.as_vec(), &expected.as_vec(), EPS));
    }

    #[test]
    fn test_trace() {
        let m: M33<f32> = M33::identity();
        assert_eq!(m.trace(), 3.0);
    }

    #[test]
    fn test_norm2() {
        use super::test_matrix3x3::EPS;
        let m = M33::new([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]]);
        assert!(nearly_equal(m.norm2(), 14.2828568570857, EPS));
    }

    #[test]
    fn determinant_test() {
        let m = M33::new([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 9.0]]);
        let expected = -3.0;
        let result = m.det();

        assert!(nearly_equal(result, expected, EPS));
    }

    #[test]
    fn inverse_test() {
        use super::test_matrix3x3::EPS;
        let m = M33::new([[1.0, 0.0, 3.0], [2.0, 1.0, 6.0], [1.0, 0.0, 9.0]]);
        // NOTE(elsuizo:2019-09-25): hay que buscar una que tenga una inversa mas facil jasjdfjas
        let expected = M33::new([
            [1.5, 0.0, -0.5],
            [-2.0, 1.0, 0.0],
            [-0.16666666666666666, 0.0, 0.16666666666666666],
        ]);

        if let Some(result) = m.inverse() {
            assert!(compare_vecs(&result.as_vec(), &expected.as_vec(), EPS));
        }
    }

    #[test]
    fn inverse_fail() {
        let m = M33::new([[1.0, 0.0, 3.0], [1.0, 0.0, 3.0], [10.0, 0.0, 3.0]]);
        let result = m.inverse();
        let expected = None;
        assert_eq!(result, expected);
    }

    #[test]
    fn test_mul_m33_v3() {
        let m = M33::new([[1.0,  1.0,  1.0],
                          [3.0,  2.0,  1.0],
                          [7.0,  3.0,  3.0],]);
        let v = V3::new([2.0, 7.0, 6.0]);
        let result = m * v;
        let expected = V3::new([15.0, 26.0, 53.0]);
        assert_eq!(
            &result[..],
            &expected[..],
            "\nExpected\n{:?}\nfound\n{:?}",
            &result[..],
            &expected[..]
        );
    }

    #[test]
    fn get_columns_test() {
        let m = m33_new!(0.0, 1.0, 2.0;
                         3.0, 4.0, 5.0;
                         6.0, 7.0, 8.0);

        let result = m.get_cols();

        let expected0 = V3::new([0.0, 3.0, 6.0]);
        let expected1 = V3::new([1.0, 4.0, 7.0]);
        let expected2 = V3::new([2.0, 5.0, 8.0]);

        let expected = V3::new([expected0, expected1, expected2]);
        assert_eq!(
            &result[..],
            &expected[..],
            "\nExpected\n{:?}\nfound\n{:?}",
            &result[..],
            &expected[..]
        );
    }

    #[test]
    fn get_rows_test() {
        let m = m33_new!(0.0, 1.0, 2.0;
                         3.0, 4.0, 5.0;
                         6.0, 7.0, 8.0);

        let result = m.get_rows();

        let expected0 = V3::new([0.0, 1.0, 2.0]);
        let expected1 = V3::new([3.0, 4.0, 5.0]);
        let expected2 = V3::new([6.0, 7.0, 8.0]);

        let expected = V3::new([expected0, expected1, expected2]);

        assert_eq!(
            &result[..],
            &expected[..],
            "\nExpected\n{:?}\nfound\n{:?}",
            &result[..],
            &expected[..]
        );
    }

    #[test]
    fn new_from_vecs_test() {
        let expected = m33_new!(0.0, 1.0, 2.0;
                                3.0, 4.0, 5.0;
                                6.0, 7.0, 8.0);

        let cols = expected.get_cols();

        let result = M33::new_from_vecs(cols);

        assert!(compare_vecs(&result.as_vec(), &expected.as_vec(), EPS));
    }

    #[test]
    fn qr_test() {
        let expected = m33_new!(0.0, 1.0, 2.0;
                                3.0, 4.0, 5.0;
                                6.0, 7.0, 8.0);
        if let Some((q, r)) = expected.qr() {
            let result = q * r;
            assert!(compare_vecs(&result.as_vec(), &expected.as_vec(), EPS));
            assert!(nearly_equal(q.det().abs(), 1.0, EPS));
        }
    }

    #[test]
    fn get_diagonal() {
        let m = m33_new!(0.0, 1.0, 2.0;
                         3.0, 4.0, 5.0;
                         6.0, 7.0, 8.0);
        let result = m.get_diagonal();
        let expected = V3::new([0.0, 4.0, 8.0]);
        assert_eq!(
            &result[..],
            &expected[..],
            "\nExpected\n{:?}\nfound\n{:?}",
            &result[..],
            &expected[..]
        );
    }

    #[test]
    fn get_upper_triangular_test() {
        let m = m33_new!(0.0, 1.0, 2.0;
                         3.0, 4.0, 5.0;
                         6.0, 7.0, 8.0);
        let result = m.get_upper_triagular();
        let expected = [1.0, 2.0, 5.0];
        assert_eq!(
            &result[..],
            &expected[..],
            "\nExpected\n{:?}\nfound\n{:?}",
            &result[..],
            &expected[..]
        );
    }

    #[test]
    fn get_lower_triangular_test() {
        let m = m33_new!(0.0, 1.0, 2.0;
                         3.0, 4.0, 5.0;
                         6.0, 7.0, 8.0);
        let result = m.get_lower_triangular();
        let expected = [3.0, 6.0, 7.0];
        assert_eq!(
            &result[..],
            &expected[..],
            "\nExpected\n{:?}\nfound\n{:?}",
            &result[..],
            &expected[..]
        );
    }

    #[test]
    fn for_each_test() {
        let m = m33_new!(0.0, 1.0, 2.0;
                         3.0, 4.0, 5.0;
                         6.0, 7.0, 8.0);
        let result = m.for_each(|element| element + 1.0);
        let expected = m33_new!(1.0, 2.0, 3.0;
                                4.0, 5.0, 6.0;
                                7.0, 8.0, 9.0);
        assert!(compare_vecs(&result.as_vec(), &expected.as_vec(), EPS));
    }

}