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 libavutil/pca.c
  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 }PCA;
  36
  37 PCA *ff_pca_init(int n){
  38     PCA *pca;
  39     if(n<=0)
  40         return NULL;
  41
  42     pca= av_mallocz(sizeof(PCA));
  43     pca->n= n;
  44     pca->count=0;
  45     pca->covariance= av_mallocz(sizeof(double)*n*n);
  46     pca->mean= av_mallocz(sizeof(double)*n);
  47
  48     return pca;
  49 }
  50
  51 void ff_pca_free(PCA *pca){
  52     av_freep(&pca->covariance);
  53     av_freep(&pca->mean);
  54     av_free(pca);
  55 }
  56
  57 void ff_pca_add(PCA *pca, double *v){
  58     int i, j;
  59     const int n= pca->n;
  60
  61     for(i=0; i<n; i++){
  62         pca->mean[i] += v[i];
  63         for(j=i; j<n; j++)
  64             pca->covariance[j + i*n] += v[i]*v[j];
  65     }
  66     pca->count++;
  67 }
  68
  69 int ff_pca(PCA *pca, double *eigenvector, double *eigenvalue){
  70     int i, j, pass;
  71     int k=0;
  72     const int n= pca->n;
  73     double z[n];
  74
  75     memset(eigenvector, 0, sizeof(double)*n*n);
  76
  77     for(j=0; j<n; j++){
  78         pca->mean[j] /= pca->count;
  79         eigenvector[j + j*n] = 1.0;
  80         for(i=0; i<=j; i++){
  81             pca->covariance[j + i*n] /= pca->count;
  82             pca->covariance[j + i*n] -= pca->mean[i] * pca->mean[j];
  83             pca->covariance[i + j*n] = pca->covariance[j + i*n];
  84         }
  85         eigenvalue[j]= pca->covariance[j + j*n];
  86         z[j]= 0;
  87     }
  88
  89     for(pass=0; pass < 50; pass++){
  90         double sum=0;
  91
  92         for(i=0; i<n; i++)
  93             for(j=i+1; j<n; j++)
  94                 sum += fabs(pca->covariance[j + i*n]);
  95
  96         if(sum == 0){
  97             for(i=0; i<n; i++){
  98                 double maxvalue= -1;
  99                 for(j=i; j<n; j++){
 100                     if(eigenvalue[j] > maxvalue){
 101                         maxvalue= eigenvalue[j];
 102                         k= j;
 103                     }
 104                 }
 105                 eigenvalue[k]= eigenvalue[i];
 106                 eigenvalue[i]= maxvalue;
 107                 for(j=0; j<n; j++){
 108                     double tmp= eigenvector[k + j*n];
 109                     eigenvector[k + j*n]= eigenvector[i + j*n];
 110                     eigenvector[i + j*n]= tmp;
 111                 }
 112             }
 113             return pass;
 114         }
 115
 116         for(i=0; i<n; i++){
 117             for(j=i+1; j<n; j++){
 118                 double covar= pca->covariance[j + i*n];
 119                 double t,c,s,tau,theta, h;
 120
 121                 if(pass < 3 && fabs(covar) < sum / (5*n*n)) //FIXME why pass < 3
 122                     continue;
 123                 if(fabs(covar) == 0.0) //FIXME should not be needed
 124                     continue;
 125                 if(pass >=3 && fabs((eigenvalue[j]+z[j])/covar) > (1LL<<32) && fabs((eigenvalue[i]+z[i])/covar) > (1LL<<32)){
 126                     pca->covariance[j + i*n]=0.0;
 127                     continue;
 128                 }
 129
 130                 h= (eigenvalue[j]+z[j]) - (eigenvalue[i]+z[i]);
 131                 theta=0.5*h/covar;
 132                 t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
 133                 if(theta < 0.0) t = -t;
 134
 135                 c=1.0/sqrt(1+t*t);
 136                 s=t*c;
 137                 tau=s/(1.0+c);
 138                 z[i] -= t*covar;
 139                 z[j] += t*covar;
 140
 141 #define ROTATE(a,i,j,k,l) {\
 142     double g=a[j + i*n];\
 143     double h=a[l + k*n];\
 144     a[j + i*n]=g-s*(h+g*tau);\
 145     a[l + k*n]=h+s*(g-h*tau); }
 146                 for(k=0; k<n; k++) {
 147                     if(k!=i && k!=j){
 148                         ROTATE(pca->covariance,FFMIN(k,i),FFMAX(k,i),FFMIN(k,j),FFMAX(k,j))
 149                     }
 150                     ROTATE(eigenvector,k,i,k,j)
 151                 }
 152                 pca->covariance[j + i*n]=0.0;
 153             }
 154         }
 155         for (i=0; i<n; i++) {
 156             eigenvalue[i] += z[i];
 157             z[i]=0.0;
 158         }
 159     }
 160
 161     return -1;
 162 }
 163
 164 #ifdef TEST
 165
 166 #undef printf
 167 #undef random
 168 #include <stdio.h>
 169 #include <stdlib.h>
 170
 171 int main(void){
 172     PCA *pca;
 173     int i, j, k;
 174 #define LEN 8
 175     double eigenvector[LEN*LEN];
 176     double eigenvalue[LEN];
 177
 178     pca= ff_pca_init(LEN);
 179
 180     for(i=0; i<9000000; i++){
 181         double v[2*LEN+100];
 182         double sum=0;
 183         int pos= random()%LEN;
 184         int v2= (random()%101) - 50;
 185         v[0]= (random()%101) - 50;
 186         for(j=1; j<8; j++){
 187             if(j<=pos) v[j]= v[0];
 188             else       v[j]= v2;
 189             sum += v[j];
 190         }
 191 /*        for(j=0; j<LEN; j++){
 192             v[j] -= v[pos];
 193         }*/
 194 //        sum += random()%10;
 195 /*        for(j=0; j<LEN; j++){
 196             v[j] -= sum/LEN;
 197         }*/
 198 //        lbt1(v+100,v+100,LEN);
 199         ff_pca_add(pca, v);
 200     }
 201
 202
 203     ff_pca(pca, eigenvector, eigenvalue);
 204     for(i=0; i<LEN; i++){
 205         pca->count= 1;
 206         pca->mean[i]= 0;
 207
 208 //        (0.5^|x|)^2 = 0.5^2|x| = 0.25^|x|
 209
 210
 211 //        pca.covariance[i + i*LEN]= pow(0.5, fabs
 212         for(j=i; j<LEN; j++){
 213             printf("%f ", pca->covariance[i + j*LEN]);
 214         }
 215         printf("\n");
 216     }
 217
 218 #if 1
 219     for(i=0; i<LEN; i++){
 220         double v[LEN];
 221         double error=0;
 222         memset(v, 0, sizeof(v));
 223         for(j=0; j<LEN; j++){
 224             for(k=0; k<LEN; k++){
 225                 v[j] += pca->covariance[FFMIN(k,j) + FFMAX(k,j)*LEN] * eigenvector[i + k*LEN];
 226             }
 227             v[j] /= eigenvalue[i];
 228             error += fabs(v[j] - eigenvector[i + j*LEN]);
 229         }
 230         printf("%f ", error);
 231     }
 232     printf("\n");
 233 #endif
 234     for(i=0; i<LEN; i++){
 235         for(j=0; j<LEN; j++){
 236             printf("%9.6f ", eigenvector[i + j*LEN]);
 237         }
 238         printf("  %9.1f %f\n", eigenvalue[i], eigenvalue[i]/eigenvalue[0]);
 239     }
 240
 241     return 0;
 242 }
 243 #endif