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
pub struct Numeric;
pub type Matrix = Vec<Vec<f64>>;
impl Numeric {
pub fn dim(x: &Matrix) -> Vec<usize> {
return vec![x.len(), x[0].len()];
}
pub fn clone(x: &Matrix) -> Matrix {
let mut yy = Vec::new();
for xx in x.iter() {
yy.push(xx.clone());
}
yy
}
pub fn identity(n: usize) -> Matrix {
let mut x = Vec::new();
for i in 0..n {
let mut yy = Vec::new();
for j in 0..n {
yy.push(if i == j {1.0} else {0.0});
}
x.push(yy);
}
x
}
pub fn transpose(x: &Matrix) -> Matrix {
let mut yy = Vec::new();
for _j in 0..x[0].len() {
yy.push(Vec::new());
}
for j in 0..x[0].len() {
for i in 0..x.len() {
yy[j].push(x[i][j]);
}
}
yy
}
pub fn inv(mx: &Matrix) -> Option<Matrix> {
let dim = Self::dim(mx);
let m = dim[0];
let n = dim[1];
let mut mx = Self::clone(mx);
let mut ii = Self::identity(m);
for j in 0..n {
let mut i0 = 0;
let mut v0 = -1.0;
for i in j..m {
let k = (mx[i][j]).abs();
if k > v0 {
i0 = i;
v0 = k;
}
}
mx.swap(i0, j);
ii.swap(i0, j);
let x = mx[j][j];
if x == 0.0 {
return None;
}
for k in j..n {
mx[j][k] /= x;
}
for k in (0..n).rev() {
ii[j][k] /= x;
}
for i in (0..m).rev() {
if i != j {
let x = mx[i][j];
for k in j+1..n {
mx[i][k] -= mx[j][k]*x;
}
let mut k = n as i32 - 1;
while k > 0 {
ii[i][k as usize] -= ii[j][k as usize]*x;
k -= 1;
ii[i][k as usize] -= ii[j][k as usize]*x;
k -= 1;
}
if k == 0 {
ii[i][0] -= ii[j][0]*x;
}
}
}
}
Some(ii)
}
pub fn dot_mm_small(x: &Matrix, y: &Matrix) -> Matrix {
let p = x.len(); let q = y.len(); let r = y[0].len();
let mut ret = vec![Vec::new(); p];
for i in (0..p).rev() {
let mut foo = vec![0.0; r];
let bar = &x[i];
for k in (0..r).rev() {
let mut woo = bar[q-1]*y[q-1][k];
let mut j = q as i32 - 2;
while j >= 1 {
let i0 = j-1;
woo += bar[j as usize]*y[j as usize][k] + bar[i0 as usize]*y[i0 as usize][k];
j -= 2;
}
if j == 0 {
woo += bar[0]*y[0][k];
}
foo[k] = woo;
}
ret[i] = foo;
}
ret
}
pub fn dot_mv(x: &Matrix, y: &[f64]) -> Vec<f64> {
let p = x.len();
let mut ret = vec![0.0; p];
for i in (0..p).rev() {
ret[i] = Self::dot_vv(&x[i], y);
}
ret
}
pub fn dot_vv(x: &[f64], y: &[f64]) -> f64 {
let n = x.len();
let mut ret = x[n-1]*y[n-1];
let mut i = n as i32 - 2;
while i >= 1 {
let i1 = i-1;
ret += x[i as usize]*y[i as usize] + x[i1 as usize]*y[i1 as usize];
i -= 2;
}
if i == 0 {
ret += x[0]*y[0];
}
ret
}
}