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/libavutil/pca.c

http://github.com/FFmpeg/FFmpeg
C | 173 lines | 126 code | 23 blank | 24 comment | 32 complexity | b642dbbf8c954d0f76f9f01aeb809dcf MD5 | raw file
  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    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
 61void 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
 68void 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
 80int 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}