2 * principal component analysis (PCA)
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 (PCA)
38 PCA *ff_pca_init(int n){
43 pca= av_mallocz(sizeof(*pca));
45 pca->z = av_malloc(sizeof(*pca->z) * n);
47 pca->covariance= av_calloc(n*n, sizeof(double));
48 pca->mean= av_calloc(n, sizeof(double));
53 void ff_pca_free(PCA *pca){
54 av_freep(&pca->covariance);
60 void ff_pca_add(PCA *pca, double *v){
67 pca->covariance[j + i*n] += v[i]*v[j];
72 int ff_pca(PCA *pca, double *eigenvector, double *eigenvalue){
78 memset(eigenvector, 0, sizeof(double)*n*n);
81 pca->mean[j] /= pca->count;
82 eigenvector[j + j*n] = 1.0;
84 pca->covariance[j + i*n] /= pca->count;
85 pca->covariance[j + i*n] -= pca->mean[i] * pca->mean[j];
86 pca->covariance[i + j*n] = pca->covariance[j + i*n];
88 eigenvalue[j]= pca->covariance[j + j*n];
92 for(pass=0; pass < 50; pass++){
97 sum += fabs(pca->covariance[j + i*n]);
103 if(eigenvalue[j] > maxvalue){
104 maxvalue= eigenvalue[j];
108 eigenvalue[k]= eigenvalue[i];
109 eigenvalue[i]= maxvalue;
111 double tmp= eigenvector[k + j*n];
112 eigenvector[k + j*n]= eigenvector[i + j*n];
113 eigenvector[i + j*n]= tmp;
120 for(j=i+1; j<n; j++){
121 double covar= pca->covariance[j + i*n];
122 double t,c,s,tau,theta, h;
124 if(pass < 3 && fabs(covar) < sum / (5*n*n)) //FIXME why pass < 3
126 if(fabs(covar) == 0.0) //FIXME should not be needed
128 if(pass >=3 && fabs((eigenvalue[j]+z[j])/covar) > (1LL<<32) && fabs((eigenvalue[i]+z[i])/covar) > (1LL<<32)){
129 pca->covariance[j + i*n]=0.0;
133 h= (eigenvalue[j]+z[j]) - (eigenvalue[i]+z[i]);
135 t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
136 if(theta < 0.0) t = -t;
144 #define ROTATE(a,i,j,k,l) {\
145 double g=a[j + i*n];\
146 double h=a[l + k*n];\
147 a[j + i*n]=g-s*(h+g*tau);\
148 a[l + k*n]=h+s*(g-h*tau); }
151 ROTATE(pca->covariance,FFMIN(k,i),FFMAX(k,i),FFMIN(k,j),FFMAX(k,j))
153 ROTATE(eigenvector,k,i,k,j)
155 pca->covariance[j + i*n]=0.0;
158 for (i=0; i<n; i++) {
159 eigenvalue[i] += z[i];
178 double eigenvector[LEN*LEN];
179 double eigenvalue[LEN];
182 av_lfg_init(&prng, 1);
184 pca= ff_pca_init(LEN);
186 for(i=0; i<9000000; i++){
189 int pos = av_lfg_get(&prng) % LEN;
190 int v2 = av_lfg_get(&prng) % 101 - 50;
191 v[0] = av_lfg_get(&prng) % 101 - 50;
193 if(j<=pos) v[j]= v[0];
197 /* for(j=0; j<LEN; j++){
200 // sum += av_lfg_get(&prng) % 10;
201 /* for(j=0; j<LEN; j++){
204 // lbt1(v+100,v+100,LEN);
209 ff_pca(pca, eigenvector, eigenvalue);
210 for(i=0; i<LEN; i++){
214 // (0.5^|x|)^2 = 0.5^2|x| = 0.25^|x|
217 // pca.covariance[i + i*LEN]= pow(0.5, fabs
218 for(j=i; j<LEN; j++){
219 printf("%f ", pca->covariance[i + j*LEN]);
224 for(i=0; i<LEN; i++){
227 memset(v, 0, sizeof(v));
228 for(j=0; j<LEN; j++){
229 for(k=0; k<LEN; k++){
230 v[j] += pca->covariance[FFMIN(k,j) + FFMAX(k,j)*LEN] * eigenvector[i + k*LEN];
232 v[j] /= eigenvalue[i];
233 error += fabs(v[j] - eigenvector[i + j*LEN]);
235 printf("%f ", error);
239 for(i=0; i<LEN; i++){
240 for(j=0; j<LEN; j++){
241 printf("%9.6f ", eigenvector[i + j*LEN]);
243 printf(" %9.1f %f\n", eigenvalue[i], eigenvalue[i]/eigenvalue[0]);