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libavutil/pca.c

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00001 /*
00002  * principal component analysis (PCA)
00003  * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
00004  *
00005  * This file is part of FFmpeg.
00006  *
00007  * FFmpeg is free software; you can redistribute it and/or
00008  * modify it under the terms of the GNU Lesser General Public
00009  * License as published by the Free Software Foundation; either
00010  * version 2.1 of the License, or (at your option) any later version.
00011  *
00012  * FFmpeg is distributed in the hope that it will be useful,
00013  * but WITHOUT ANY WARRANTY; without even the implied warranty of
00014  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00015  * Lesser General Public License for more details.
00016  *
00017  * You should have received a copy of the GNU Lesser General Public
00018  * License along with FFmpeg; if not, write to the Free Software
00019  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
00020  */
00021 
00027 #include "common.h"
00028 #include "pca.h"
00029 
00030 typedef struct PCA{
00031     int count;
00032     int n;
00033     double *covariance;
00034     double *mean;
00035 }PCA;
00036 
00037 PCA *ff_pca_init(int n){
00038     PCA *pca;
00039     if(n<=0)
00040         return NULL;
00041 
00042     pca= av_mallocz(sizeof(PCA));
00043     pca->n= n;
00044     pca->count=0;
00045     pca->covariance= av_mallocz(sizeof(double)*n*n);
00046     pca->mean= av_mallocz(sizeof(double)*n);
00047 
00048     return pca;
00049 }
00050 
00051 void ff_pca_free(PCA *pca){
00052     av_freep(&pca->covariance);
00053     av_freep(&pca->mean);
00054     av_free(pca);
00055 }
00056 
00057 void ff_pca_add(PCA *pca, double *v){
00058     int i, j;
00059     const int n= pca->n;
00060 
00061     for(i=0; i<n; i++){
00062         pca->mean[i] += v[i];
00063         for(j=i; j<n; j++)
00064             pca->covariance[j + i*n] += v[i]*v[j];
00065     }
00066     pca->count++;
00067 }
00068 
00069 int ff_pca(PCA *pca, double *eigenvector, double *eigenvalue){
00070     int i, j, pass;
00071     int k=0;
00072     const int n= pca->n;
00073     double z[n];
00074 
00075     memset(eigenvector, 0, sizeof(double)*n*n);
00076 
00077     for(j=0; j<n; j++){
00078         pca->mean[j] /= pca->count;
00079         eigenvector[j + j*n] = 1.0;
00080         for(i=0; i<=j; i++){
00081             pca->covariance[j + i*n] /= pca->count;
00082             pca->covariance[j + i*n] -= pca->mean[i] * pca->mean[j];
00083             pca->covariance[i + j*n] = pca->covariance[j + i*n];
00084         }
00085         eigenvalue[j]= pca->covariance[j + j*n];
00086         z[j]= 0;
00087     }
00088 
00089     for(pass=0; pass < 50; pass++){
00090         double sum=0;
00091 
00092         for(i=0; i<n; i++)
00093             for(j=i+1; j<n; j++)
00094                 sum += fabs(pca->covariance[j + i*n]);
00095 
00096         if(sum == 0){
00097             for(i=0; i<n; i++){
00098                 double maxvalue= -1;
00099                 for(j=i; j<n; j++){
00100                     if(eigenvalue[j] > maxvalue){
00101                         maxvalue= eigenvalue[j];
00102                         k= j;
00103                     }
00104                 }
00105                 eigenvalue[k]= eigenvalue[i];
00106                 eigenvalue[i]= maxvalue;
00107                 for(j=0; j<n; j++){
00108                     double tmp= eigenvector[k + j*n];
00109                     eigenvector[k + j*n]= eigenvector[i + j*n];
00110                     eigenvector[i + j*n]= tmp;
00111                 }
00112             }
00113             return pass;
00114         }
00115 
00116         for(i=0; i<n; i++){
00117             for(j=i+1; j<n; j++){
00118                 double covar= pca->covariance[j + i*n];
00119                 double t,c,s,tau,theta, h;
00120 
00121                 if(pass < 3 && fabs(covar) < sum / (5*n*n)) //FIXME why pass < 3
00122                     continue;
00123                 if(fabs(covar) == 0.0) //FIXME should not be needed
00124                     continue;
00125                 if(pass >=3 && fabs((eigenvalue[j]+z[j])/covar) > (1LL<<32) && fabs((eigenvalue[i]+z[i])/covar) > (1LL<<32)){
00126                     pca->covariance[j + i*n]=0.0;
00127                     continue;
00128                 }
00129 
00130                 h= (eigenvalue[j]+z[j]) - (eigenvalue[i]+z[i]);
00131                 theta=0.5*h/covar;
00132                 t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
00133                 if(theta < 0.0) t = -t;
00134 
00135                 c=1.0/sqrt(1+t*t);
00136                 s=t*c;
00137                 tau=s/(1.0+c);
00138                 z[i] -= t*covar;
00139                 z[j] += t*covar;
00140 
00141 #define ROTATE(a,i,j,k,l) {\
00142     double g=a[j + i*n];\
00143     double h=a[l + k*n];\
00144     a[j + i*n]=g-s*(h+g*tau);\
00145     a[l + k*n]=h+s*(g-h*tau); }
00146                 for(k=0; k<n; k++) {
00147                     if(k!=i && k!=j){
00148                         ROTATE(pca->covariance,FFMIN(k,i),FFMAX(k,i),FFMIN(k,j),FFMAX(k,j))
00149                     }
00150                     ROTATE(eigenvector,k,i,k,j)
00151                 }
00152                 pca->covariance[j + i*n]=0.0;
00153             }
00154         }
00155         for (i=0; i<n; i++) {
00156             eigenvalue[i] += z[i];
00157             z[i]=0.0;
00158         }
00159     }
00160 
00161     return -1;
00162 }
00163 
00164 #ifdef TEST
00165 
00166 #undef printf
00167 #include <stdio.h>
00168 #include <stdlib.h>
00169 #include "lfg.h"
00170 
00171 int main(void){
00172     PCA *pca;
00173     int i, j, k;
00174 #define LEN 8
00175     double eigenvector[LEN*LEN];
00176     double eigenvalue[LEN];
00177     AVLFG prng;
00178 
00179     av_lfg_init(&prng, 1);
00180 
00181     pca= ff_pca_init(LEN);
00182 
00183     for(i=0; i<9000000; i++){
00184         double v[2*LEN+100];
00185         double sum=0;
00186         int pos = av_lfg_get(&prng) % LEN;
00187         int v2  = av_lfg_get(&prng) % 101 - 50;
00188         v[0]    = av_lfg_get(&prng) % 101 - 50;
00189         for(j=1; j<8; j++){
00190             if(j<=pos) v[j]= v[0];
00191             else       v[j]= v2;
00192             sum += v[j];
00193         }
00194 /*        for(j=0; j<LEN; j++){
00195             v[j] -= v[pos];
00196         }*/
00197 //        sum += av_lfg_get(&prng) % 10;
00198 /*        for(j=0; j<LEN; j++){
00199             v[j] -= sum/LEN;
00200         }*/
00201 //        lbt1(v+100,v+100,LEN);
00202         ff_pca_add(pca, v);
00203     }
00204 
00205 
00206     ff_pca(pca, eigenvector, eigenvalue);
00207     for(i=0; i<LEN; i++){
00208         pca->count= 1;
00209         pca->mean[i]= 0;
00210 
00211 //        (0.5^|x|)^2 = 0.5^2|x| = 0.25^|x|
00212 
00213 
00214 //        pca.covariance[i + i*LEN]= pow(0.5, fabs
00215         for(j=i; j<LEN; j++){
00216             printf("%f ", pca->covariance[i + j*LEN]);
00217         }
00218         printf("\n");
00219     }
00220 
00221 #if 1
00222     for(i=0; i<LEN; i++){
00223         double v[LEN];
00224         double error=0;
00225         memset(v, 0, sizeof(v));
00226         for(j=0; j<LEN; j++){
00227             for(k=0; k<LEN; k++){
00228                 v[j] += pca->covariance[FFMIN(k,j) + FFMAX(k,j)*LEN] * eigenvector[i + k*LEN];
00229             }
00230             v[j] /= eigenvalue[i];
00231             error += fabs(v[j] - eigenvector[i + j*LEN]);
00232         }
00233         printf("%f ", error);
00234     }
00235     printf("\n");
00236 #endif
00237     for(i=0; i<LEN; i++){
00238         for(j=0; j<LEN; j++){
00239             printf("%9.6f ", eigenvector[i + j*LEN]);
00240         }
00241         printf("  %9.1f %f\n", eigenvalue[i], eigenvalue[i]/eigenvalue[0]);
00242     }
00243 
00244     return 0;
00245 }
00246 #endif

Generated on Fri Sep 16 2011 17:17:51 for FFmpeg by  doxygen 1.7.1