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 double *z; 36}PCA; 37 38PCA *ff_pca_init(int n){ 39 PCA *pca; 40 if(n<=0) 41 return NULL; 42 43 pca= av_mallocz(sizeof(*pca)); 44 pca->n= n; 45 pca->z = av_malloc_array(n, sizeof(*pca->z)); 46 pca->count=0; 47 pca->covariance= av_calloc(n*n, sizeof(double)); 48 pca->mean= av_calloc(n, sizeof(double)); 49 50 return pca; 51} 52 53void ff_pca_free(PCA *pca){ 54 av_freep(&pca->covariance); 55 av_freep(&pca->mean); 56 av_freep(&pca->z); 57 av_free(pca); 58} 59 60void ff_pca_add(PCA *pca, double *v){ 61 int i, j; 62 const int n= pca->n; 63 64 for(i=0; i<n; i++){ 65 pca->mean[i] += v[i]; 66 for(j=i; j<n; j++) 67 pca->covariance[j + i*n] += v[i]*v[j]; 68 } 69 pca->count++; 70} 71 72int ff_pca(PCA *pca, double *eigenvector, double *eigenvalue){ 73 int i, j, pass; 74 int k=0; 75 const int n= pca->n; 76 double *z = pca->z; 77 78 memset(eigenvector, 0, sizeof(double)*n*n); 79 80 for(j=0; j<n; j++){ 81 pca->mean[j] /= pca->count; 82 eigenvector[j + j*n] = 1.0; 83 for(i=0; i<=j; i++){ 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]; 87 } 88 eigenvalue[j]= pca->covariance[j + j*n]; 89 z[j]= 0; 90 } 91 92 for(pass=0; pass < 50; pass++){ 93 double sum=0; 94 95 for(i=0; i<n; i++) 96 for(j=i+1; j<n; j++) 97 sum += fabs(pca->covariance[j + i*n]); 98 99 if(sum == 0){ 100 for(i=0; i<n; i++){ 101 double maxvalue= -1; 102 for(j=i; j<n; j++){ 103 if(eigenvalue[j] > maxvalue){ 104 maxvalue= eigenvalue[j]; 105 k= j; 106 } 107 } 108 eigenvalue[k]= eigenvalue[i]; 109 eigenvalue[i]= maxvalue; 110 for(j=0; j<n; j++){ 111 double tmp= eigenvector[k + j*n]; 112 eigenvector[k + j*n]= eigenvector[i + j*n]; 113 eigenvector[i + j*n]= tmp; 114 } 115 } 116 return pass; 117 } 118 119 for(i=0; i<n; i++){ 120 for(j=i+1; j<n; j++){ 121 double covar= pca->covariance[j + i*n]; 122 double t,c,s,tau,theta, h; 123 124 if(pass < 3 && fabs(covar) < sum / (5*n*n)) //FIXME why pass < 3 125 continue; 126 if(fabs(covar) == 0.0) //FIXME should not be needed 127 continue; 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; 130 continue; 131 } 132 133 h= (eigenvalue[j]+z[j]) - (eigenvalue[i]+z[i]); 134 theta=0.5*h/covar; 135 t=1.0/(fabs(theta)+sqrt(1.0+theta*theta)); 136 if(theta < 0.0) t = -t; 137 138 c=1.0/sqrt(1+t*t); 139 s=t*c; 140 tau=s/(1.0+c); 141 z[i] -= t*covar; 142 z[j] += t*covar; 143 144#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); } 149 for(k=0; k<n; k++) { 150 if(k!=i && k!=j){ 151 ROTATE(pca->covariance,FFMIN(k,i),FFMAX(k,i),FFMIN(k,j),FFMAX(k,j)) 152 } 153 ROTATE(eigenvector,k,i,k,j) 154 } 155 pca->covariance[j + i*n]=0.0; 156 } 157 } 158 for (i=0; i<n; i++) { 159 eigenvalue[i] += z[i]; 160 z[i]=0.0; 161 } 162 } 163 164 return -1; 165} 166 167#ifdef TEST 168 169#undef printf 170#include <stdio.h> 171#include <stdlib.h> 172#include "lfg.h" 173 174int main(void){ 175 PCA *pca; 176 int i, j, k; 177#define LEN 8 178 double eigenvector[LEN*LEN]; 179 double eigenvalue[LEN]; 180 AVLFG prng; 181 182 av_lfg_init(&prng, 1); 183 184 pca= ff_pca_init(LEN); 185 186 for(i=0; i<9000000; i++){ 187 double v[2*LEN+100]; 188 double sum=0; 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; 192 for(j=1; j<8; j++){ 193 if(j<=pos) v[j]= v[0]; 194 else v[j]= v2; 195 sum += v[j]; 196 } 197/* for(j=0; j<LEN; j++){ 198 v[j] -= v[pos]; 199 }*/ 200// sum += av_lfg_get(&prng) % 10; 201/* for(j=0; j<LEN; j++){ 202 v[j] -= sum/LEN; 203 }*/ 204// lbt1(v+100,v+100,LEN); 205 ff_pca_add(pca, v); 206 } 207 208 209 ff_pca(pca, eigenvector, eigenvalue); 210 for(i=0; i<LEN; i++){ 211 pca->count= 1; 212 pca->mean[i]= 0; 213 214// (0.5^|x|)^2 = 0.5^2|x| = 0.25^|x| 215 216 217// pca.covariance[i + i*LEN]= pow(0.5, fabs 218 for(j=i; j<LEN; j++){ 219 printf("%f ", pca->covariance[i + j*LEN]); 220 } 221 printf("\n"); 222 } 223 224 for(i=0; i<LEN; i++){ 225 double v[LEN]; 226 double error=0; 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]; 231 } 232 v[j] /= eigenvalue[i]; 233 error += fabs(v[j] - eigenvector[i + j*LEN]); 234 } 235 printf("%f ", error); 236 } 237 printf("\n"); 238 239 for(i=0; i<LEN; i++){ 240 for(j=0; j<LEN; j++){ 241 printf("%9.6f ", eigenvector[i + j*LEN]); 242 } 243 printf(" %9.1f %f\n", eigenvalue[i], eigenvalue[i]/eigenvalue[0]); 244 } 245 246 return 0; 247} 248#endif 249