1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171

//! Implements necessary methods on *square* matrices.

use std::{
    ops::{
        Add,
        Index,
        IndexMut,
    },
};

use super::Vector;

#[derive(Clone, Copy, PartialEq, Debug)]
/// Abstracts over a square matrix of arbitrary dimension.
pub struct Matrix<const N: usize> {
    /// Contains the values of this matrix.
    values: [[f64; N]; N],
}

/// Implements necessary behaviors of a matrix.
impl<const N: usize> Matrix<N> {
    /// Constructs a zero matrix.
    pub fn zero() -> Self {
        Self {
            values: [[0.0; N]; N],
        }
    }

    /// Constructs an identity matrix.
    pub fn identity() -> Self {
        let mut values = [[0.0; N]; N];

        for i in 0..N {
            values[i][i] = 1.0;
        }

        Self {
            values
        }
    }

    /// Constructs a matrix of provided values.
    pub fn new(values: [[f64; N]; N]) -> Self {
        Self {
            values,
        }
    }

    /// Right-multiplies this matrix by the provided vector, returning the result.
    pub fn mult(&self, vector: Vector<N>) -> Vector<N> {
        let mut output = Vector::<N>::zero();

        for i in 0..N {
            for j in 0..N {
                output[i] += self[(i, j)] * vector[j];
            }
        }

        output
    }

    /// Swap rows `i` and `j`.
    fn swaprow(&mut self, i: usize, j: usize) {
        let temp = self.values[i];
        self.values[i] = self.values[j];
        self.values[j] = temp;
    }

    /// Scale row `i` by factor `s`.
    fn scalerow(&mut self, i: usize, s: f64) {
        for j in 0..N {
            self[(i, j)] *= s;
        }
    }

    /// Subtract `s` times row `j` from row `i`.
    fn subrow(&mut self, i: usize, j: usize, s: f64) {
        for k in 0..N {
            self[(i, k)] -= s * self[(j, k)];
        }
    }

    /// Returns the inverse of this matrix.
    pub fn inverse(&self) -> Self {
        let mut output = *self;
        let mut inverse = Self::identity();

        for i in 0..N {
            // Determine the index of the row with the largest pivot
            // Start from the working row
            let mut j = i;
            for k in i..N {
                if output[(k, i)] > output[(i, i)] {
                    j = k;
                }
            }

            // Swap largest pivot to working row
            output.swaprow(i, j);
            inverse.swaprow(i, j);

            // Normalize this row
            let s = 1.0 / output[(i, i)];
            output.scalerow(i, s);
            inverse.scalerow(i, s);

            // Subtract this row from all lower rows
            for k in (i + 1)..N {
                let s = output[(k, i)];
                output.subrow(k, i, s);
                inverse.subrow(k, i, s);
            }
        }

        // We're now in upper triangular, let's get to GJ normal form

        for i in 0..N {
            for j in (i + 1)..N {
                let s = output[(i, j)];
                output.subrow(i, j, s);
                inverse.subrow(i, j, s);
            }
        }

        inverse
    }

    /// Scales a matrix by a provided scalar, returning the new matrix.
    pub fn scale(&self, scalar: f64) -> Self {
        let mut newvalues = [[0.0; N]; N];
        for i in 0..N {
            for j in 0..N {
                newvalues[i][j] = scalar * self[(i, j)];
            }
        }

        Self {
            values: newvalues,
        }
    }
}

impl<const N: usize> Index<(usize, usize)> for Matrix<N> {
    type Output = f64;

    fn index(&self, idx: (usize, usize)) -> &Self::Output {
        &self.values[idx.0][idx.1]
    }
}

impl<const N: usize> IndexMut<(usize, usize)> for Matrix<N> {
    fn index_mut(&mut self, idx: (usize, usize)) -> &mut Self::Output {
        &mut self.values[idx.0][idx.1]
    }
}

impl<const N: usize> Add for Matrix<N> {
    type Output = Self;

    fn add(self, other: Self) -> Self {
        let mut new = Self::zero();
    
        for i in 0..N {
            for j in 0..N {
                new[(i, j)] = self[(i, j)] + other[(i, j)];   
            }
        }

        new
    }
}