| /* |
| * principal component analysis (PCA) |
| * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at> |
| * |
| * This file is part of FFmpeg. |
| * |
| * FFmpeg is free software; you can redistribute it and/or |
| * modify it under the terms of the GNU Lesser General Public |
| * License as published by the Free Software Foundation; either |
| * version 2.1 of the License, or (at your option) any later version. |
| * |
| * FFmpeg is distributed in the hope that it will be useful, |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| * Lesser General Public License for more details. |
| * |
| * You should have received a copy of the GNU Lesser General Public |
| * License along with FFmpeg; if not, write to the Free Software |
| * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA |
| */ |
| |
| /** |
| * @file |
| * principal component analysis (PCA) |
| */ |
| |
| #include "common.h" |
| #include "pca.h" |
| |
| typedef struct PCA{ |
| int count; |
| int n; |
| double *covariance; |
| double *mean; |
| double *z; |
| }PCA; |
| |
| PCA *ff_pca_init(int n){ |
| PCA *pca; |
| if(n<=0) |
| return NULL; |
| |
| pca= av_mallocz(sizeof(*pca)); |
| if (!pca) |
| return NULL; |
| |
| pca->n= n; |
| pca->z = av_malloc_array(n, sizeof(*pca->z)); |
| pca->count=0; |
| pca->covariance= av_calloc(n*n, sizeof(double)); |
| pca->mean= av_calloc(n, sizeof(double)); |
| |
| if (!pca->z || !pca->covariance || !pca->mean) { |
| ff_pca_free(pca); |
| return NULL; |
| } |
| |
| return pca; |
| } |
| |
| void ff_pca_free(PCA *pca){ |
| av_freep(&pca->covariance); |
| av_freep(&pca->mean); |
| av_freep(&pca->z); |
| av_free(pca); |
| } |
| |
| void ff_pca_add(PCA *pca, const double *v){ |
| int i, j; |
| const int n= pca->n; |
| |
| for(i=0; i<n; i++){ |
| pca->mean[i] += v[i]; |
| for(j=i; j<n; j++) |
| pca->covariance[j + i*n] += v[i]*v[j]; |
| } |
| pca->count++; |
| } |
| |
| int ff_pca(PCA *pca, double *eigenvector, double *eigenvalue){ |
| int i, j, pass; |
| int k=0; |
| const int n= pca->n; |
| double *z = pca->z; |
| |
| memset(eigenvector, 0, sizeof(double)*n*n); |
| |
| for(j=0; j<n; j++){ |
| pca->mean[j] /= pca->count; |
| eigenvector[j + j*n] = 1.0; |
| for(i=0; i<=j; i++){ |
| pca->covariance[j + i*n] /= pca->count; |
| pca->covariance[j + i*n] -= pca->mean[i] * pca->mean[j]; |
| pca->covariance[i + j*n] = pca->covariance[j + i*n]; |
| } |
| eigenvalue[j]= pca->covariance[j + j*n]; |
| z[j]= 0; |
| } |
| |
| for(pass=0; pass < 50; pass++){ |
| double sum=0; |
| |
| for(i=0; i<n; i++) |
| for(j=i+1; j<n; j++) |
| sum += fabs(pca->covariance[j + i*n]); |
| |
| if(sum == 0){ |
| for(i=0; i<n; i++){ |
| double maxvalue= -1; |
| for(j=i; j<n; j++){ |
| if(eigenvalue[j] > maxvalue){ |
| maxvalue= eigenvalue[j]; |
| k= j; |
| } |
| } |
| eigenvalue[k]= eigenvalue[i]; |
| eigenvalue[i]= maxvalue; |
| for(j=0; j<n; j++){ |
| double tmp= eigenvector[k + j*n]; |
| eigenvector[k + j*n]= eigenvector[i + j*n]; |
| eigenvector[i + j*n]= tmp; |
| } |
| } |
| return pass; |
| } |
| |
| for(i=0; i<n; i++){ |
| for(j=i+1; j<n; j++){ |
| double covar= pca->covariance[j + i*n]; |
| double t,c,s,tau,theta, h; |
| |
| if(pass < 3 && fabs(covar) < sum / (5*n*n)) //FIXME why pass < 3 |
| continue; |
| if(fabs(covar) == 0.0) //FIXME should not be needed |
| continue; |
| if(pass >=3 && fabs((eigenvalue[j]+z[j])/covar) > (1LL<<32) && fabs((eigenvalue[i]+z[i])/covar) > (1LL<<32)){ |
| pca->covariance[j + i*n]=0.0; |
| continue; |
| } |
| |
| h= (eigenvalue[j]+z[j]) - (eigenvalue[i]+z[i]); |
| theta=0.5*h/covar; |
| t=1.0/(fabs(theta)+sqrt(1.0+theta*theta)); |
| if(theta < 0.0) t = -t; |
| |
| c=1.0/sqrt(1+t*t); |
| s=t*c; |
| tau=s/(1.0+c); |
| z[i] -= t*covar; |
| z[j] += t*covar; |
| |
| #define ROTATE(a,i,j,k,l) {\ |
| double g=a[j + i*n];\ |
| double h=a[l + k*n];\ |
| a[j + i*n]=g-s*(h+g*tau);\ |
| a[l + k*n]=h+s*(g-h*tau); } |
| for(k=0; k<n; k++) { |
| if(k!=i && k!=j){ |
| ROTATE(pca->covariance,FFMIN(k,i),FFMAX(k,i),FFMIN(k,j),FFMAX(k,j)) |
| } |
| ROTATE(eigenvector,k,i,k,j) |
| } |
| pca->covariance[j + i*n]=0.0; |
| } |
| } |
| for (i=0; i<n; i++) { |
| eigenvalue[i] += z[i]; |
| z[i]=0.0; |
| } |
| } |
| |
| return -1; |
| } |