/* * 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;}