forked from andeya/algorithm
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathcovariance.go
More file actions
99 lines (82 loc) · 2.83 KB
/
covariance.go
File metadata and controls
99 lines (82 loc) · 2.83 KB
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
package stat
/* covariance.go
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Jim Davies, Brian Gough
* Copyright (C) 2012, 2013 G.vd.Schoot
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
import (
"math"
)
// takes a dataset and calculates the covariance
func covariance(data1, data2 Interface, mean1, mean2 float64) (res float64) {
// calculate the sum of the squares
n := data1.Len()
for i := 0; i < n; i++ {
delta1 := (data1.Get(i) - mean1)
delta2 := (data2.Get(i) - mean2)
res += (delta1*delta2 - res) / float64(i+1)
}
return
}
func CovarianceMean(data1, data2 Interface, mean1, mean2 float64) float64 {
n := data1.Len()
covariance := covariance(data1, data2, mean1, mean2)
return covariance * float64(n) / float64(n-1)
}
func Covariance(data1, data2 Interface) float64 {
mean1 := Mean(data1)
mean2 := Mean(data2)
return CovarianceMean(data1, data2, mean1, mean2)
}
/*
Correlation()
Calculate Pearson correlation = cov(X, Y) / (sigma_X * sigma_Y)
This routine efficiently computes the correlation in one pass of the
data and makes use of the algorithm described in:
B. P. Welford, "Note on a Method for Calculating Corrected Sums of
Squares and Products", Technometrics, Vol 4, No 3, 1962.
This paper derives a numerically stable recurrence to compute a sum
of products
S = sum_{i=1..N} [ (x_i - mu_x) * (y_i - mu_y) ]
with the relation
S_n = S_{n-1} + ((n-1)/n) * (x_n - mu_x_{n-1}) * (y_n - mu_y_{n-1})
*/
func Correlation(data1, data2 Interface) (res float64) {
var sum_xsq, sum_ysq, sum_cross float64
n := data1.Len()
//
// Compute:
// sum_xsq = Sum [ (x_i - mu_x)^2 ],
// sum_ysq = Sum [ (y_i - mu_y)^2 ] and
// sum_cross = Sum [ (x_i - mu_x) * (y_i - mu_y) ]
// using the above relation from Welford's paper
//
mean_x := data1.Get(0)
mean_y := data2.Get(0)
for i := 1; i < n; i++ {
ratio := float64(i) / float64(i+1)
delta_x := data1.Get(i) - mean_x
delta_y := data2.Get(i) - mean_y
sum_xsq += delta_x * delta_x * ratio
sum_ysq += delta_y * delta_y * ratio
sum_cross += delta_x * delta_y * ratio
mean_x += delta_x / float64(i+1)
mean_y += delta_y / float64(i+1)
}
res = sum_cross / (math.Sqrt(sum_xsq) * math.Sqrt(sum_ysq))
return
}