483 lines
12 KiB
Rust
483 lines
12 KiB
Rust
#[macro_use]
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extern crate approx;
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use structs::Tuple;
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use std::ops::Index;
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#[derive(Debug)]
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pub struct Matrix {
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matrix: Vec<Vec<f32>>,
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}
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impl Matrix {
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pub fn default(width: usize, height: usize) -> Self {
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Matrix {
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matrix: vec![vec![0.0f32; width]; height],
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}
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}
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pub fn from_array<const H: usize, const W: usize>(array: [[f32; W]; H]) -> Matrix {
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let mut matrix: Vec<Vec<f32>> = Vec::with_capacity(H);
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for r in array.iter() {
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let mut row: Vec<f32> = Vec::with_capacity(W);
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for v in r.iter() {
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row.push(*v);
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}
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matrix.push(row);
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}
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Matrix {
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matrix,
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}
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}
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pub fn from_vec(matrix: Vec<Vec<f32>>) -> Matrix {
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Matrix {
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matrix,
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}
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}
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pub fn identity(size: usize) -> Matrix {
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let mut m = Self::default(size, size);
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for i in 0..m.matrix.len() {
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m.matrix[i][i] = 1.0;
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}
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m
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}
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pub fn transpose(&mut self) {
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for i in 0..self.matrix.len() {
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for j in i..self.matrix[0].len() {
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let v = self.matrix[i][j];
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self.matrix[i][j] = self.matrix[j][i];
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self.matrix[j][i] = v;
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}
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}
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}
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pub fn determinant(&self) -> f32 {
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if self.matrix[0].len() == 2 {
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self.matrix[0][0] * self.matrix[1][1] - self.matrix[0][1] * self.matrix[1][0]
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} else {
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let mut sum = 0.0;
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for (col, val) in self.matrix[0].iter().enumerate().take(self.matrix[0].len()) {
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sum += val * self.cofactor(0, col);
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}
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sum
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}
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}
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pub fn minor(&self, row: usize, col: usize) -> f32 {
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let m = self.sub_matrix(row, col);
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let det = m.determinant();
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det
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}
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pub fn cofactor(&self, row: usize, col: usize) -> f32 {
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let minor = self.minor(row, col);
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if (row + col) & 0x1 == 0 {
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minor
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} else {
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minor * -1.0
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}
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}
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pub fn sub_matrix(&self, skip_row: usize, skip_col: usize) -> Matrix
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{
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let mut m = Vec::<Vec<f32>>::with_capacity(self.matrix.len() - 1);
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for (i, row) in self.matrix.iter().enumerate().take(self.matrix.len()) {
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if i == skip_row { continue; }
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let mut r = Vec::<f32>::with_capacity(row.len() - 1);
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for (j, col) in row.iter().enumerate().take(row.len()) {
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if j == skip_col { continue; }
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r.push(*col);
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}
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m.push(r);
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}
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Matrix::from_vec(m)
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}
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}
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impl Index<usize> for Matrix {
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type Output = Vec<f32>;
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fn index(&self, index: usize) -> &Self::Output {
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&self.matrix[index]
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}
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}
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impl PartialEq for Matrix {
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fn eq(&self, _rhs: &Self) -> bool {
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if self.matrix.len() != _rhs.matrix.len() {
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return false;
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}
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for row_idx in 0..self.matrix.len() {
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if self.matrix[row_idx].len() != _rhs.matrix[row_idx].len() {
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return false;
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}
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for col_idx in 0..self.matrix[row_idx].len() {
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if !relative_eq!(self.matrix[row_idx][col_idx], _rhs.matrix[row_idx][col_idx]) {
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return false;
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}
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}
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}
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true
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}
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}
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impl Matrix {
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fn calc_val_for_mul(&self, row: usize, rhs: &Matrix, col: usize) -> f32 {
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let mut sum = 0.0;
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for i in 0..self.matrix.len() {
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sum += self.matrix[row][i] * rhs.matrix[i][col];
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}
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sum
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}
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fn calc_val_for_mul_tuple(&self, row: usize, tuple: &Tuple) -> f32 {
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(self.matrix[row][0] * tuple.x()) +
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(self.matrix[row][1] * tuple.y()) +
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(self.matrix[row][2] * tuple.z()) +
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(self.matrix[row][3] * tuple.w())
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}
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}
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impl std::ops::Mul<Matrix> for Matrix {
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type Output = Matrix;
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fn mul(self, _rhs: Matrix) -> Matrix {
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let mut result: Vec<Vec<f32>> = Vec::with_capacity(self.matrix.len());
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for row in 0..self.matrix.len() {
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let width = self.matrix[row].len();
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let mut new_col = Vec::with_capacity(width);
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for col in 0..width {
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new_col.push( self.calc_val_for_mul(row, &_rhs, col));
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}
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result.push(new_col);
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}
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Matrix::from_vec(result)
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}
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}
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impl std::ops::Mul<Tuple> for Matrix {
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type Output = Tuple;
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fn mul(self, _rhs: Tuple) -> Tuple {
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Tuple::new(
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self.calc_val_for_mul_tuple(0, &_rhs),
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self.calc_val_for_mul_tuple(1, &_rhs),
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self.calc_val_for_mul_tuple(2, &_rhs),
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self.calc_val_for_mul_tuple(3, &_rhs),
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)
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn matrix_4x4() {
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let m = [
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[1.0, 2.0, 3.0, 4.0],
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[5.5, 6.5, 7.5, 8.5],
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[9.0, 10.0, 11.0, 12.0],
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[13.5, 14.5, 15.5, 16.5],
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];
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let matrix = Matrix::from_array(m);
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assert_eq!(1.0, matrix[0][0]);
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assert_eq!(4.0, matrix[0][3]);
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assert_eq!(5.5, matrix[1][0]);
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assert_eq!(7.5, matrix[1][2]);
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assert_eq!(11.0, matrix[2][2]);
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assert_eq!(13.5, matrix[3][0]);
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assert_eq!(15.5, matrix[3][2]);
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}
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#[test]
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fn matrix_4x4_array() {
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let m = [
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[1.0, 2.0, 3.0, 4.0],
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[5.5, 6.5, 7.5, 8.5],
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[9.0, 10.0, 11.0, 12.0],
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[13.5, 14.5, 15.5, 16.5],
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];
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let matrix = Matrix::from_array(m);
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assert_eq!(1.0, matrix[0][0]);
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assert_eq!(4.0, matrix[0][3]);
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assert_eq!(5.5, matrix[1][0]);
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assert_eq!(7.5, matrix[1][2]);
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assert_eq!(11.0, matrix[2][2]);
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assert_eq!(13.5, matrix[3][0]);
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assert_eq!(15.5, matrix[3][2]);
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}
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#[test]
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fn matrix_2x2() {
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let m = [
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[-3.0, 5.0,],
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[1.0, 2.0,],
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];
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let matrix = Matrix::from_array(m);
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assert_eq!(-3.0, matrix[0][0]);
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assert_eq!(5.0, matrix[0][1]);
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assert_eq!(1.0, matrix[1][0]);
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assert_eq!(2.0, matrix[1][1]);
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}
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#[test]
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fn matrix_3x3() {
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let m = [
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[-3.0, 5.0, 0.0],
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[1.0, -2.0, -7.0],
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[0.0, 1.0, 1.0],
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];
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let matrix = Matrix::from_array(m);
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assert_eq!(-3.0, matrix[0][0]);
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assert_eq!(-2.0, matrix[1][1]);
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assert_eq!(1.0, matrix[2][2]);
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}
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#[test]
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fn matrix_equality_a() {
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let a = [
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[1.0, 2.0, 3.0, 4.0],
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[5.0, 6.0, 7.0, 8.0],
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[9.0, 8.0, 7.0, 6.0],
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[5.0, 4.0, 3.0, 2.0],
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];
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let m_a = Matrix::from_array(a);
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let b = [
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[1.0, 2.0, 3.0, 4.0],
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[5.0, 6.0, 7.0, 8.0],
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[9.0, 8.0, 7.0, 6.0],
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[5.0, 4.0, 3.0, 2.0],
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];
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let m_b = Matrix::from_array(b);
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assert_eq!(m_a, m_b);
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}
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#[test]
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fn matrix_equality_b() {
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let a = [
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[1.0, 2.0, 3.0, 4.0],
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[5.0, 6.0, 7.0, 8.0],
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[9.0, 8.0, 7.0, 6.0],
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[5.0, 4.0, 3.0, 2.0],
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];
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let m_a = Matrix::from_array(a);
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let b = [
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[2.0, 3.0, 4.0, 5.0],
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[6.0, 7.0, 8.0, 9.0],
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[8.0, 7.0, 6.0, 5.0],
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[4.0, 3.0, 2.0, 1.0],
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];
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let m_b = Matrix::from_array(b);
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assert_ne!(m_a, m_b);
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}
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#[test]
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fn multiply() {
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let matrix_a = Matrix::from_array([
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[1.0, 2.0, 3.0, 4.0,],
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[5.0, 6.0, 7.0, 8.0,],
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[9.0, 8.0, 7.0, 6.0,],
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[5.0, 4.0, 3.0, 2.0,],
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]);
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let matrix_b = Matrix::from_array([
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[-2.0, 1.0, 2.0, 3.0,],
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[3.0, 2.0, 1.0, -1.0,],
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[4.0, 3.0, 6.0, 5.0,],
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[1.0, 2.0, 7.0, 8.0,],
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]);
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let expected = Matrix::from_array([
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[20.0, 22.0, 50.0, 48.0],
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[44.0, 54.0, 114.0, 108.0],
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[40.0, 58.0, 110.0, 102.0,],
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[16.0, 26.0, 46.0, 42.0],
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]);
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assert_eq!(matrix_a * matrix_b, expected);
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}
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#[test]
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fn multiply_by_tuple() {
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let matrix = Matrix::from_array([
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[1.0, 2.0, 3.0, 4.0],
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[2.0, 4.0, 4.0, 2.0],
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[8.0, 6.0, 4.0, 1.0],
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[0.0, 0.0, 0.0, 1.0],
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]);
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let tuple = Tuple::new(1.0, 2.0, 3.0, 1.0);
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let expected = Tuple::new(18.0, 24.0, 33.0, 1.0);
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assert_eq!(matrix * tuple, expected);
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}
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#[test]
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fn matrix_by_identity() {
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let matrix = Matrix::from_array([
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[0.0, 1.0, 2.0, 4.0,],
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[1.0, 2.0, 4.0, 8.0,],
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[2.0, 4.0, 8.0, 16.0],
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[4.0, 8.0, 16.0, 32.0,]
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]);
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let expected = Matrix::from_array([
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[0.0, 1.0, 2.0, 4.0,],
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[1.0, 2.0, 4.0, 8.0,],
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[2.0, 4.0, 8.0, 16.0],
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[4.0, 8.0, 16.0, 32.0,]
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]);
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assert_eq!(matrix * Matrix::identity(4), expected);
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}
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#[test]
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fn tuple_by_identity() {
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let t = Tuple::new(1.0, 2.0, 3.0, 4.0);
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let expected = Tuple::new(1.0, 2.0, 3.0, 4.0);
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assert_eq!(Matrix::identity(4) * t, expected);
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}
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#[test]
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fn transposition() {
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let mut m = Matrix::from_array([
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[0.0, 9.0, 3.0, 0.0],
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[9.0, 8.0, 0.0, 8.0],
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[1.0, 8.0, 5.0, 3.0],
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[0.0, 0.0, 5.0, 8.0],
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]);
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let expected = Matrix::from_array([
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[0.0, 9.0, 1.0, 0.0],
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[9.0, 8.0, 8.0, 0.0],
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[3.0, 0.0, 5.0, 5.0],
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[0.0, 8.0, 3.0, 8.0],
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]);
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m.transpose();
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assert_eq!(m, expected);
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}
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#[test]
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fn transpose_identity() {
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let mut m = Matrix::identity(4);
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m.transpose();
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assert_eq!(m, Matrix::identity(4));
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}
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#[test]
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fn determinant_2x2() {
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let m = Matrix::from_array([
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[1.0, 5.0],
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[-3.0, 2.0],
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]);
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assert_eq!(17.0, m.determinant());
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}
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#[test]
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fn submatrix_3x3() {
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let start = Matrix::from_array([
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[1.0, 5.0, 0.0],
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[-3.0, 2.0, 7.0],
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[0.0, 6.0, -3.0],
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]);
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let expected = Matrix::from_array([
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[-3.0, 2.0],
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[0.0, 6.0],
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]);
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assert_eq!(expected, start.sub_matrix(0, 2));
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}
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#[test]
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fn submatrix_4x4() {
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let start = Matrix::from_array([
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[-6.0, 1.0, 1.0, 6.0],
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[-8.0, 5.0, 8.0, 6.0],
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[-1.0, 0.0, 8.0, 2.0],
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[-7.0, 1.0, -1.0, 1.0],
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]);
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let expected = Matrix::from_array([
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[-6.0, 1.0, 6.0],
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[-8.0, 8.0, 6.0],
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[-7.0, -1.0, 1.0],
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]);
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assert_eq!(expected, start.sub_matrix(2, 1));
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}
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#[test]
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fn minor_3x3() {
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let m = Matrix::from_array([
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[3.0, 5.0, 0.0],
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[2.0, -1.0, -7.0],
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[6.0, -1.0, 5.0],
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]);
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let s = m.sub_matrix(1, 0);
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assert_eq!(25.0, s.determinant());
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assert_eq!(25.0, m.minor(1, 0));
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}
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#[test]
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fn cofactor_3x3() {
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let m = Matrix::from_array([
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[3.0, 5.0, 0.0],
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[2.0, -1.0, -7.0],
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[6.0, -1.0, 5.0],
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]);
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assert_eq!(-12.0, m.minor(0, 0));
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assert_eq!(-12.0, m.cofactor(0, 0));
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assert_eq!(25.0, m.minor(1, 0));
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assert_eq!(-25.0, m.cofactor(1, 0));
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}
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#[test]
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fn determinant_3x3() {
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let m = Matrix::from_array([
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[1.0, 2.0, 6.0],
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[-5.0, 8.0, -4.0],
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[2.0, 6.0, 4.0],
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]);
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assert_eq!(56.0, m.cofactor(0, 0));
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assert_eq!(12.0, m.cofactor(0, 1));
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assert_eq!(-46.0, m.cofactor(0, 2));
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assert_eq!(-196.0, m.determinant());
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}
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#[test]
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fn determinant_4x4() {
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let m = Matrix::from_array([
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[-2.0, -8.0, 3.0, 5.0],
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[-3.0, 1.0, 7.0, 3.0],
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[1.0, 2.0, -9.0, 6.0],
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[-6.0, 7.0, 7.0, -9.0],
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]);
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assert_eq!(690.0, m.cofactor(0, 0));
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assert_eq!(447.0, m.cofactor(0, 1));
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assert_eq!(210.0, m.cofactor(0, 2));
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assert_eq!(51.0, m.cofactor(0, 3));
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assert_eq!(-4071.0, m.determinant());
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}
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}
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