libavutil/pca.c

   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
  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
  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
  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
  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 }