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 30typedef struct PCA{ 31 int count; 32 int n; 33 double *covariance; 34 double *mean; 35}PCA; 36 37PCA *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 51void ff_pca_free(PCA *pca){ 52 av_freep(&pca->covariance); 53 av_freep(&pca->mean); 54 av_free(pca); 55} 56 57void 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 69int 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#include <stdio.h> 168#include <stdlib.h> 169#include "lfg.h" 170 171int main(void){ 172 PCA *pca; 173 int i, j, k; 174#define LEN 8 175 double eigenvector[LEN*LEN]; 176 double eigenvalue[LEN]; 177 AVLFG prng; 178 179 av_lfg_init(&prng, 1); 180 181 pca= ff_pca_init(LEN); 182 183 for(i=0; i<9000000; i++){ 184 double v[2*LEN+100]; 185 double sum=0; 186 int pos = av_lfg_get(&prng) % LEN; 187 int v2 = av_lfg_get(&prng) % 101 - 50; 188 v[0] = av_lfg_get(&prng) % 101 - 50; 189 for(j=1; j<8; j++){ 190 if(j<=pos) v[j]= v[0]; 191 else v[j]= v2; 192 sum += v[j]; 193 } 194/* for(j=0; j<LEN; j++){ 195 v[j] -= v[pos]; 196 }*/ 197// sum += av_lfg_get(&prng) % 10; 198/* for(j=0; j<LEN; j++){ 199 v[j] -= sum/LEN; 200 }*/ 201// lbt1(v+100,v+100,LEN); 202 ff_pca_add(pca, v); 203 } 204 205 206 ff_pca(pca, eigenvector, eigenvalue); 207 for(i=0; i<LEN; i++){ 208 pca->count= 1; 209 pca->mean[i]= 0; 210 211// (0.5^|x|)^2 = 0.5^2|x| = 0.25^|x| 212 213 214// pca.covariance[i + i*LEN]= pow(0.5, fabs 215 for(j=i; j<LEN; j++){ 216 printf("%f ", pca->covariance[i + j*LEN]); 217 } 218 printf("\n"); 219 } 220 221#if 1 222 for(i=0; i<LEN; i++){ 223 double v[LEN]; 224 double error=0; 225 memset(v, 0, sizeof(v)); 226 for(j=0; j<LEN; j++){ 227 for(k=0; k<LEN; k++){ 228 v[j] += pca->covariance[FFMIN(k,j) + FFMAX(k,j)*LEN] * eigenvector[i + k*LEN]; 229 } 230 v[j] /= eigenvalue[i]; 231 error += fabs(v[j] - eigenvector[i + j*LEN]); 232 } 233 printf("%f ", error); 234 } 235 printf("\n"); 236#endif 237 for(i=0; i<LEN; i++){ 238 for(j=0; j<LEN; j++){ 239 printf("%9.6f ", eigenvector[i + j*LEN]); 240 } 241 printf(" %9.1f %f\n", eigenvalue[i], eigenvalue[i]/eigenvalue[0]); 242 } 243 244 return 0; 245} 246#endif 247