2 * Principal component analysis
3 * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
5 * This file is part of FFmpeg.
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.
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.
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
24 * Principal component analysis
37 PCA *ff_pca_init(int n){
42 pca= av_mallocz(sizeof(PCA));
45 pca->covariance= av_mallocz(sizeof(double)*n*n);
46 pca->mean= av_mallocz(sizeof(double)*n);
51 void ff_pca_free(PCA *pca){
52 av_freep(&pca->covariance);
57 void ff_pca_add(PCA *pca, double *v){
64 pca->covariance[j + i*n] += v[i]*v[j];
69 int ff_pca(PCA *pca, double *eigenvector, double *eigenvalue){
74 memset(eigenvector, 0, sizeof(double)*n*n);
77 pca->mean[j] /= pca->count;
78 eigenvector[j + j*n] = 1.0;
80 pca->covariance[j + i*n] /= pca->count;
81 pca->covariance[j + i*n] -= pca->mean[i] * pca->mean[j];
82 pca->covariance[i + j*n] = pca->covariance[j + i*n];
84 eigenvalue[j]= pca->covariance[j + j*n];
88 for(pass=0; pass < 50; pass++){
93 sum += fabs(pca->covariance[j + i*n]);
99 if(eigenvalue[j] > maxvalue){
100 maxvalue= eigenvalue[j];
104 eigenvalue[k]= eigenvalue[i];
105 eigenvalue[i]= maxvalue;
107 double tmp= eigenvector[k + j*n];
108 eigenvector[k + j*n]= eigenvector[i + j*n];
109 eigenvector[i + j*n]= tmp;
116 for(j=i+1; j<n; j++){
117 double covar= pca->covariance[j + i*n];
118 double t,c,s,tau,theta, h;
120 if(pass < 3 && fabs(covar) < sum / (5*n*n)) //FIXME why pass < 3
122 if(fabs(covar) == 0.0) //FIXME shouldnt be needed
124 if(pass >=3 && fabs((eigenvalue[j]+z[j])/covar) > (1LL<<32) && fabs((eigenvalue[i]+z[i])/covar) > (1LL<<32)){
125 pca->covariance[j + i*n]=0.0;
129 h= (eigenvalue[j]+z[j]) - (eigenvalue[i]+z[i]);
131 t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
132 if(theta < 0.0) t = -t;
140 #define ROTATE(a,i,j,k,l) {\
141 double g=a[j + i*n];\
142 double h=a[l + k*n];\
143 a[j + i*n]=g-s*(h+g*tau);\
144 a[l + k*n]=h+s*(g-h*tau); }
147 ROTATE(pca->covariance,FFMIN(k,i),FFMAX(k,i),FFMIN(k,j),FFMAX(k,j))
149 ROTATE(eigenvector,k,i,k,j)
151 pca->covariance[j + i*n]=0.0;
154 for (i=0; i<n; i++) {
155 eigenvalue[i] += z[i];
174 double eigenvector[LEN*LEN];
175 double eigenvalue[LEN];
177 pca= ff_pca_init(LEN);
179 for(i=0; i<9000000; i++){
182 int pos= random()%LEN;
183 int v2= (random()%101) - 50;
184 v[0]= (random()%101) - 50;
186 if(j<=pos) v[j]= v[0];
190 /* for(j=0; j<LEN; j++){
193 // sum += random()%10;
194 /* for(j=0; j<LEN; j++){
197 // lbt1(v+100,v+100,LEN);
202 ff_pca(pca, eigenvector, eigenvalue);
203 for(i=0; i<LEN; i++){
207 // (0.5^|x|)^2 = 0.5^2|x| = 0.25^|x|
210 // pca.covariance[i + i*LEN]= pow(0.5, fabs
211 for(j=i; j<LEN; j++){
212 printf("%f ", pca->covariance[i + j*LEN]);
218 for(i=0; i<LEN; i++){
221 memset(v, 0, sizeof(v));
222 for(j=0; j<LEN; j++){
223 for(k=0; k<LEN; k++){
224 v[j] += pca->covariance[FFMIN(k,j) + FFMAX(k,j)*LEN] * eigenvector[i + k*LEN];
226 v[j] /= eigenvalue[i];
227 error += fabs(v[j] - eigenvector[i + j*LEN]);
229 printf("%f ", error);
233 for(i=0; i<LEN; i++){
234 for(j=0; j<LEN; j++){
235 printf("%9.6f ", eigenvector[i + j*LEN]);
237 printf(" %9.1f %f\n", eigenvalue[i], eigenvalue[i]/eigenvalue[0]);