easy-ml 1.0.0

Matrix and linear algebra library aimed at being easy to use
Documentation 
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

extern crate easy_ml;

#[cfg(test)]
mod tests {
    use easy_ml::matrices::Matrix;
    use easy_ml::linear_algebra;

    #[test]
    fn check_determinant_2_by_2() {
        let matrix = Matrix::from(vec![vec![1.0, 2.0], vec![3.0, 4.0]]);
        let a = matrix.get(0, 0);
        let b = matrix.get(0, 1);
        let c = matrix.get(1, 0);
        let d = matrix.get(1, 1);
        let determinant = (a * d) - (b * c);
        assert_eq!(determinant, linear_algebra::determinant::<f32>(&matrix).unwrap());
    }

    #[test]
    fn check_determinant_3_by_3() {
        // use the example from wikipedia
        // https://en.wikipedia.org/wiki/Determinant#n_%C3%97_n_matrices
        let matrix = Matrix::from(vec![
            vec![-1.0,  2.0,  3.0],
            vec![ 3.0,  4.0, -5.0],
            vec![ 5.0, -2.0,  3.0]]);

        let determinant = 0.0
            + (matrix.get(0, 0) * matrix.get(1, 1) * matrix.get(2, 2))
            - (matrix.get(0, 0) * matrix.get(1, 2) * matrix.get(2, 1))
            - (matrix.get(0, 1) * matrix.get(1, 0) * matrix.get(2, 2))
            + (matrix.get(0, 1) * matrix.get(1, 2) * matrix.get(2, 0))
            + (matrix.get(0, 2) * matrix.get(1, 0) * matrix.get(2, 1))
            - (matrix.get(0, 2) * matrix.get(1, 1) * matrix.get(2, 0));

        assert_eq!(determinant, matrix.determinant().unwrap());
    }

    #[test]
    fn inverse_1_by_1() {
        let matrix = Matrix::unit(3.0);
        let inverse = linear_algebra::inverse::<f32>(&matrix).unwrap();
        let absolute_difference = inverse.scalar() - (1.0 / 3.0);
        assert!(absolute_difference <= std::f32::EPSILON);
    }

    #[test]
    fn inverse_2_by_2() {
        let matrix = Matrix::from(vec![
            vec![ 4.0, 7.0 ],
            vec![ 2.0, 6.0 ]]);
        let inverse = matrix.inverse().unwrap();
        // we use the example from https://www.mathsisfun.com/algebra/matrix-inverse.html
        let answer = Matrix::from(vec![
            vec![ 0.6, -0.7 ],
            vec![ -0.2, 0.4 ]]);
        for row in 0..answer.rows() {
            for column in 0..answer.columns() {
                let absolute_difference = inverse.get(row, column) - answer.get(row, column);
                assert!(absolute_difference <= std::f32::EPSILON);
            }
        }
        // multiplying the inverse and original should yeild the identity matrix
        let identity = &matrix * &inverse;
        let answer = Matrix::diagonal(1.0, matrix.size());
        for row in 0..answer.rows() {
            for column in 0..answer.columns() {
                let absolute_difference = identity.get(row, column) - answer.get(row, column);
                assert!(absolute_difference <= std::f32::EPSILON);
            }
        }
    }

    #[test]
    fn inverse_2_by_2_not_inversible() {
        let matrix = Matrix::from(vec![
            vec![ 3.0, 4.0 ],
            vec![ 6.0, 8.0 ]]);
        let inverse = matrix.inverse();
        assert!(inverse.is_none());
    }

    #[test]
    fn test_covariance() {
        let matrix: Matrix<f32> = Matrix::from(vec![
                vec![  1.0,  1.0, -1.0],
                vec![ -1.0, -1.0,  1.0],
                vec![ -1.0, -1.0,  1.0],
                vec![  1.0,  1.0, -1.0]]);
        assert_eq!(linear_algebra::covariance_column_features::<f32>(&matrix),
            Matrix::from(vec![
                vec![ 1.0,  1.0, -1.0 ],
                vec![ 1.0,  1.0, -1.0 ],
                vec![ -1.0, -1.0, 1.0 ]]));
    }

    #[test]
    fn test_cholesky_decomposition_3_by_3() {
        // some examples are outlined at https://rosettacode.org/wiki/Cholesky_decomposition
        // they form the test cases here
        let matrix = Matrix::from(vec![
            vec![ 25.0, 15.0, -5.0 ],
            vec![ 15.0, 18.0,  0.0 ],
            vec![ -5.0,  0.0, 11.0 ]]);
        let lower_triangular = linear_algebra::cholesky_decomposition::<f32>(&matrix).unwrap();
        let recovered = &lower_triangular * lower_triangular.transpose();
        assert_eq!(lower_triangular, Matrix::from(vec![
            vec![ 5.0, 0.0, 0.0 ],
            vec![ 3.0, 3.0, 0.0 ],
            vec![-1.0, 1.0, 3.0 ]]));
        assert_eq!(matrix, recovered);
    }

    #[test]
    fn test_cholesky_decomposition_4_by_4() {
        // some examples are outlined at https://rosettacode.org/wiki/Cholesky_decomposition
        // they form the test cases here
        // this test case requires a lot of decimal representation so
        // is checked for approximation rather than exact value
        let matrix = Matrix::from(vec![
            vec![ 18.0, 22.0,  54.0,  42.0 ],
            vec![ 22.0, 70.0,  86.0,  62.0 ],
            vec![ 54.0, 86.0, 174.0, 134.0 ],
            vec![ 42.0, 62.0, 134.0, 106.0 ]]);
        let lower_triangular = linear_algebra::cholesky_decomposition::<f64>(&matrix).unwrap();
        let recovered = &lower_triangular * lower_triangular.transpose();
        let expected = Matrix::from(vec![
            vec![  4.24264, 0.0,     0.0,     0.0     ],
            vec![  5.18545, 6.56591, 0.0,     0.0     ],
            vec![ 12.72792, 3.04604, 1.64974, 0.0     ],
            vec![  9.89949, 1.62455, 1.84971, 1.39262 ]]);
        let absolute_difference: f64 = lower_triangular.column_major_iter()
            .zip(expected.column_major_iter())
            .map(|(x, y)| (x - y).abs())
            .sum();
        println!("absolute_difference: {}", absolute_difference);
        assert!(absolute_difference < 0.0001);
        let absolute_difference: f64 = matrix.column_major_iter()
            .zip(recovered.column_major_iter())
            .map(|(x, y)| (x - y).abs())
            .sum();
        assert!(absolute_difference < 0.0001);
    }
}