1 /* statistics/variance_source.c
2 *
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Jim Davies, Brian Gough
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
14 *
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
18 */
19
20 static double
21 FUNCTION(compute,variance) (const BASE data[], const size_t stride, const size_t n, const double mean);
22
23 static double
24 FUNCTION(compute,tss) (const BASE data[], const size_t stride, const size_t n, const double mean);
25
26 static double
FUNCTION(compute,variance)27 FUNCTION(compute,variance) (const BASE data[], const size_t stride, const size_t n, const double mean)
28 {
29 /* takes a dataset and finds the variance */
30
31 long double variance = 0 ;
32
33 size_t i;
34
35 /* find the sum of the squares */
36 for (i = 0; i < n; i++)
37 {
38 const long double delta = (data[i * stride] - mean);
39 variance += (delta * delta - variance) / (i + 1);
40 }
41
42 return variance ;
43 }
44
45 static double
FUNCTION(compute,tss)46 FUNCTION(compute,tss) (const BASE data[], const size_t stride, const size_t n, const double mean)
47 {
48 /* takes a dataset and finds the sum of squares about the mean */
49
50 long double tss = 0 ;
51
52 size_t i;
53
54 /* find the sum of the squares */
55 for (i = 0; i < n; i++)
56 {
57 const long double delta = (data[i * stride] - mean);
58 tss += delta * delta;
59 }
60
61 return tss ;
62 }
63
64
65 double
FUNCTION(gsl_stats,variance_with_fixed_mean)66 FUNCTION(gsl_stats,variance_with_fixed_mean) (const BASE data[], const size_t stride, const size_t n, const double mean)
67 {
68 const double variance = FUNCTION(compute,variance) (data, stride, n, mean);
69 return variance;
70 }
71
72 double
FUNCTION(gsl_stats,sd_with_fixed_mean)73 FUNCTION(gsl_stats,sd_with_fixed_mean) (const BASE data[], const size_t stride, const size_t n, const double mean)
74 {
75 const double variance = FUNCTION(compute,variance) (data, stride, n, mean);
76 const double sd = sqrt (variance);
77
78 return sd;
79 }
80
81
82
83 double
FUNCTION(gsl_stats,variance_m)84 FUNCTION(gsl_stats,variance_m) (const BASE data[], const size_t stride, const size_t n, const double mean)
85 {
86 const double variance = FUNCTION(compute,variance) (data, stride, n, mean);
87
88 return variance * ((double)n / (double)(n - 1));
89 }
90
91 double
FUNCTION(gsl_stats,sd_m)92 FUNCTION(gsl_stats,sd_m) (const BASE data[], const size_t stride, const size_t n, const double mean)
93 {
94 const double variance = FUNCTION(compute,variance) (data, stride, n, mean);
95 const double sd = sqrt (variance * ((double)n / (double)(n - 1)));
96
97 return sd;
98 }
99
100 double
FUNCTION(gsl_stats,variance)101 FUNCTION(gsl_stats,variance) (const BASE data[], const size_t stride, const size_t n)
102 {
103 const double mean = FUNCTION(gsl_stats,mean) (data, stride, n);
104 return FUNCTION(gsl_stats,variance_m)(data, stride, n, mean);
105 }
106
107 double
FUNCTION(gsl_stats,sd)108 FUNCTION(gsl_stats,sd) (const BASE data[], const size_t stride, const size_t n)
109 {
110 const double mean = FUNCTION(gsl_stats,mean) (data, stride, n);
111 return FUNCTION(gsl_stats,sd_m) (data, stride, n, mean);
112 }
113
114
115 double
FUNCTION(gsl_stats,tss_m)116 FUNCTION(gsl_stats,tss_m) (const BASE data[], const size_t stride, const size_t n, const double mean)
117 {
118 const double tss = FUNCTION(compute,tss) (data, stride, n, mean);
119
120 return tss;
121 }
122
123 double
FUNCTION(gsl_stats,tss)124 FUNCTION(gsl_stats,tss) (const BASE data[], const size_t stride, const size_t n)
125 {
126 const double mean = FUNCTION(gsl_stats,mean) (data, stride, n);
127 return FUNCTION(gsl_stats,tss_m)(data, stride, n, mean);
128 }
129