1 /*
2 * principal component analysis (PCA)
3 * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
4 *
5 * This file is part of FFmpeg.
6 *
7 * FFmpeg is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU Lesser General Public
9 * License as published by the Free Software Foundation; either
10 * version 2.1 of the License, or (at your option) any later version.
11 *
12 * FFmpeg is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 * Lesser General Public License for more details.
16 *
17 * You should have received a copy of the GNU Lesser General Public
18 * License along with FFmpeg; if not, write to the Free Software
19 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
20 */
21
22 /**
23 * @file
24 * principal component analysis (PCA)
25 */
26
27 #include "common.h"
28 #include "pca.h"
29
30 typedef struct PCA{
31 int count;
32 int n;
33 double *covariance;
34 double *mean;
35 double *z;
36 }PCA;
37
ff_pca_init(int n)38 PCA *ff_pca_init(int n){
39 PCA *pca;
40 if(n<=0)
41 return NULL;
42
43 pca= av_mallocz(sizeof(*pca));
44 if (!pca)
45 return NULL;
46
47 pca->n= n;
48 pca->z = av_malloc_array(n, sizeof(*pca->z));
49 pca->count=0;
50 pca->covariance= av_calloc(n*n, sizeof(double));
51 pca->mean= av_calloc(n, sizeof(double));
52
53 if (!pca->z || !pca->covariance || !pca->mean) {
54 ff_pca_free(pca);
55 return NULL;
56 }
57
58 return pca;
59 }
60
ff_pca_free(PCA * pca)61 void ff_pca_free(PCA *pca){
62 av_freep(&pca->covariance);
63 av_freep(&pca->mean);
64 av_freep(&pca->z);
65 av_free(pca);
66 }
67
ff_pca_add(PCA * pca,const double * v)68 void ff_pca_add(PCA *pca, const double *v){
69 int i, j;
70 const int n= pca->n;
71
72 for(i=0; i<n; i++){
73 pca->mean[i] += v[i];
74 for(j=i; j<n; j++)
75 pca->covariance[j + i*n] += v[i]*v[j];
76 }
77 pca->count++;
78 }
79
ff_pca(PCA * pca,double * eigenvector,double * eigenvalue)80 int ff_pca(PCA *pca, double *eigenvector, double *eigenvalue){
81 int i, j, pass;
82 int k=0;
83 const int n= pca->n;
84 double *z = pca->z;
85
86 memset(eigenvector, 0, sizeof(double)*n*n);
87
88 for(j=0; j<n; j++){
89 pca->mean[j] /= pca->count;
90 eigenvector[j + j*n] = 1.0;
91 for(i=0; i<=j; i++){
92 pca->covariance[j + i*n] /= pca->count;
93 pca->covariance[j + i*n] -= pca->mean[i] * pca->mean[j];
94 pca->covariance[i + j*n] = pca->covariance[j + i*n];
95 }
96 eigenvalue[j]= pca->covariance[j + j*n];
97 z[j]= 0;
98 }
99
100 for(pass=0; pass < 50; pass++){
101 double sum=0;
102
103 for(i=0; i<n; i++)
104 for(j=i+1; j<n; j++)
105 sum += fabs(pca->covariance[j + i*n]);
106
107 if(sum == 0){
108 for(i=0; i<n; i++){
109 double maxvalue= -1;
110 for(j=i; j<n; j++){
111 if(eigenvalue[j] > maxvalue){
112 maxvalue= eigenvalue[j];
113 k= j;
114 }
115 }
116 eigenvalue[k]= eigenvalue[i];
117 eigenvalue[i]= maxvalue;
118 for(j=0; j<n; j++){
119 double tmp= eigenvector[k + j*n];
120 eigenvector[k + j*n]= eigenvector[i + j*n];
121 eigenvector[i + j*n]= tmp;
122 }
123 }
124 return pass;
125 }
126
127 for(i=0; i<n; i++){
128 for(j=i+1; j<n; j++){
129 double covar= pca->covariance[j + i*n];
130 double t,c,s,tau,theta, h;
131
132 if(pass < 3 && fabs(covar) < sum / (5*n*n)) //FIXME why pass < 3
133 continue;
134 if(fabs(covar) == 0.0) //FIXME should not be needed
135 continue;
136 if(pass >=3 && fabs((eigenvalue[j]+z[j])/covar) > (1LL<<32) && fabs((eigenvalue[i]+z[i])/covar) > (1LL<<32)){
137 pca->covariance[j + i*n]=0.0;
138 continue;
139 }
140
141 h= (eigenvalue[j]+z[j]) - (eigenvalue[i]+z[i]);
142 theta=0.5*h/covar;
143 t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
144 if(theta < 0.0) t = -t;
145
146 c=1.0/sqrt(1+t*t);
147 s=t*c;
148 tau=s/(1.0+c);
149 z[i] -= t*covar;
150 z[j] += t*covar;
151
152 #define ROTATE(a,i,j,k,l) {\
153 double g=a[j + i*n];\
154 double h=a[l + k*n];\
155 a[j + i*n]=g-s*(h+g*tau);\
156 a[l + k*n]=h+s*(g-h*tau); }
157 for(k=0; k<n; k++) {
158 if(k!=i && k!=j){
159 ROTATE(pca->covariance,FFMIN(k,i),FFMAX(k,i),FFMIN(k,j),FFMAX(k,j))
160 }
161 ROTATE(eigenvector,k,i,k,j)
162 }
163 pca->covariance[j + i*n]=0.0;
164 }
165 }
166 for (i=0; i<n; i++) {
167 eigenvalue[i] += z[i];
168 z[i]=0.0;
169 }
170 }
171
172 return -1;
173 }
174