/*
* 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 "mem.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;
}