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
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
//! Module to scale vectors and matrices.
extern crate num;
use gaussian::{Gaussian, GaussianFunctions};
use matrix::Matrix;
use math::{Dimension, Normalization, Mean, Var};
use ops_inplace::VectorVectorOpsInPlace;
/// Trait to scale a matrix.
pub trait ScaleMatrix<T> {
/// Scales the values of the matrix and returns the scaled
/// matrix and the parameters that were used for scaling.
///
/// First the mean and the standard deviation of the values for
/// each column is computed. Then, a new matrix is computed where
/// the element at row `i` and column `j` is the result of
/// `(m(i,j) - mu(j)) / std(j)` where
///
/// * m(i,j) is the element at row `i` and column `j` in the original matrix `m`
/// * mu(j) is the mean of the elements in column `j` of `m`
/// * std(j) is the standard deviation of the elements in column `j` of `m`
///
/// If the standard deviation is smaller than 0.0001 then 1.0 is used
/// in the denominator.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate rustml;
/// use rustml::*;
/// use rustml::scaling::*;
///
/// # fn main() {
/// let m = mat![
/// 1.0, 100.0;
/// 2.0, 150.0;
/// 0.6, 110.0
/// ];
///
/// let (scaled, gaussians) = m.scale();
///
/// // mean and standard deviation of first column
/// assert_eq!(gaussians[0].mean(), 1.2);
/// assert!(gaussians[0].std() - 0.721 < 0.001);
/// // mean and standard deviation of second column
/// assert_eq!(gaussians[1].mean(), 120.0);
/// assert!(gaussians[1].std() - 26.458 < 0.001);
///
/// let e = mat![
/// -0.27735, -0.75593;
/// 1.10940, 1.13389;
/// -0.83205, -0.37796
/// ];
///
/// assert!(scaled.similar(&e, 0.0001))
/// # }
/// ```
fn scale(&self) -> (Box<Self>, Vec<Gaussian<T>>);
}
macro_rules! scale_mat_impl {
($($t:ty)*) => ($(
impl ScaleMatrix<$t> for Matrix<$t> {
// TODO normalization, dimension
fn scale(&self) -> (Box<Matrix<$t>>, Vec<Gaussian<$t>>) {
let mean_vec = self.mean(Dimension::Column);
let var_vec = self.var(Dimension::Column, Normalization::MinusOne);
let std_vec: Vec<$t> = var_vec.iter().
map(|&x| x.sqrt()).map(|x| if num::abs(x) < 0.0001 { 1 as $t } else { x }).collect();
// TODO 0.000001 is hard coded
let r = mean_vec.iter().zip(var_vec.iter()).map(|(&x, &y)| Gaussian::new(x, y)).collect();
let mut mr = self.clone();
for i in 0..mr.rows() {
let r = mr.row_mut(i).unwrap();
r.isub(&mean_vec);
r.idiv(&std_vec);
}
(Box::new(mr), r)
}
}
)*)
}
scale_mat_impl!{ f32 f64 }
// ----------------------------------------------------------------------------
/// Trait to scale a vector.
pub trait ScaleVector<T> {
/// Scales the values of the vector by the parameters provided
/// by the vector `g`.
///
/// For each value the following is done: the value at index `i` is
/// subtracted by the mean
/// of the `Gaussian` at index `i` and the result is divided by the
/// standard deviation of the `Gaussian` at index `i`. This is done
/// for each value in the vector and a new vector is returned with
/// the result.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate rustml;
/// use rustml::scaling::*;
/// use rustml::gaussian::*;
///
/// # fn main() {
/// let gaussians = vec![
/// Gaussian::new(2.0, 4.0),
/// Gaussian::new(5.0, 16.0)
/// ];
///
/// assert_eq!(
/// [4.0, 7.0].scale_by(&gaussians),
/// vec![
/// (4.0 - 2.0) / 2.0,
/// (7.0 - 5.0) / 4.0
/// ]
/// );
/// # }
/// ```
fn scale_by(&self, g: &Vec<Gaussian<T>>) -> Vec<T>;
}
macro_rules! scaling_vec_impl {
($($t:ty)*) => ($(
impl ScaleVector<$t> for Vec<$t> {
fn scale_by(&self, g: &Vec<Gaussian<$t>>) -> Vec<$t> {
(self[..]).scale_by(g)
}
}
impl ScaleVector<$t> for [$t] {
fn scale_by(&self, g: &Vec<Gaussian<$t>>) -> Vec<$t> {
self.iter().zip(g.iter()).map(|(&x, ref y)| (x - y.mean()) / y.std()).collect()
}
}
)*)
}
scaling_vec_impl!{ f32 f64 }
// ----------------------------------------------------------------------------
#[cfg(test)]
mod tests {
extern crate num;
use super::*;
use matrix::Matrix;
use gaussian::{Gaussian, GaussianFunctions};
#[test]
fn test_scale_mat() {
let m = mat![
1.0, 2.0;
3.0, 5.0;
4.0, 10.0
];
let (x, g) = m.scale();
assert!(g[0].mean() - 2.6667 < 0.001);
assert!(g[1].mean() - 5.6667 < 0.001);
assert!(g[0].var() - 2.3333 < 0.001);
assert!(g[1].var() - 16.3333 < 0.001);
assert!(g[0].std() - 1.5275 < 0.001);
assert!(g[1].std() - 4.0415 < 0.001);
assert!(x.get(0, 0).unwrap() - (-1.09109) < 0.001);
assert!(x.get(0, 1).unwrap() - (-0.90726) < 0.001);
assert!(x.get(1, 0).unwrap() - (0.21822) < 0.001);
assert!(x.get(1, 1).unwrap() - (-0.16496) < 0.001);
assert!(x.get(2, 0).unwrap() - (0.87287) < 0.001);
assert!(x.get(2, 1).unwrap() - (1.07222) < 0.001);
}
#[test]
fn test_scale_mat2() {
let m = mat![
1.0, 50.0, 1000.0;
0.3, 45.0, 1200.0;
1.9, 44.0, 1150.0;
0.7, 60.0, 1300.0
];
let (s, _g) = m.scale();
let r = mat![
0.036761, 0.034153, -1.300000;
-0.992540, -0.648901, 0.300000;
1.360147, -0.785512, -0.100000;
-0.404368, 1.400261, 1.100000
];
assert!(s.buf().iter().zip(r.buf().iter()).all(|(&a, &b)| num::abs(a - b) < 0.01));
}
#[test]
fn test_scale_vec() {
let x = vec![1.0, 2.0, 3.0, 4.0];
let g = vec![
Gaussian::new(2.0, 16.0),
Gaussian::new(3.0, 4.0),
Gaussian::new(9.0, 64.0),
Gaussian::new(5.0, 25.0)
];
let y = x.scale_by(&g);
assert_eq!(y, vec![-0.25, -0.5, -0.75, -0.2]);
}
}