yading@11: /*
yading@11:  * principal component analysis (PCA)
yading@11:  * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
yading@11:  *
yading@11:  * This file is part of FFmpeg.
yading@11:  *
yading@11:  * FFmpeg is free software; you can redistribute it and/or
yading@11:  * modify it under the terms of the GNU Lesser General Public
yading@11:  * License as published by the Free Software Foundation; either
yading@11:  * version 2.1 of the License, or (at your option) any later version.
yading@11:  *
yading@11:  * FFmpeg is distributed in the hope that it will be useful,
yading@11:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
yading@11:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
yading@11:  * Lesser General Public License for more details.
yading@11:  *
yading@11:  * You should have received a copy of the GNU Lesser General Public
yading@11:  * License along with FFmpeg; if not, write to the Free Software
yading@11:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
yading@11:  */
yading@11: 
yading@11: /**
yading@11:  * @file
yading@11:  * principal component analysis (PCA)
yading@11:  */
yading@11: 
yading@11: #include "common.h"
yading@11: #include "pca.h"
yading@11: 
yading@11: typedef struct PCA{
yading@11:     int count;
yading@11:     int n;
yading@11:     double *covariance;
yading@11:     double *mean;
yading@11:     double *z;
yading@11: }PCA;
yading@11: 
yading@11: PCA *ff_pca_init(int n){
yading@11:     PCA *pca;
yading@11:     if(n<=0)
yading@11:         return NULL;
yading@11: 
yading@11:     pca= av_mallocz(sizeof(*pca));
yading@11:     pca->n= n;
yading@11:     pca->z = av_malloc(sizeof(*pca->z) * n);
yading@11:     pca->count=0;
yading@11:     pca->covariance= av_calloc(n*n, sizeof(double));
yading@11:     pca->mean= av_calloc(n, sizeof(double));
yading@11: 
yading@11:     return pca;
yading@11: }
yading@11: 
yading@11: void ff_pca_free(PCA *pca){
yading@11:     av_freep(&pca->covariance);
yading@11:     av_freep(&pca->mean);
yading@11:     av_freep(&pca->z);
yading@11:     av_free(pca);
yading@11: }
yading@11: 
yading@11: void ff_pca_add(PCA *pca, double *v){
yading@11:     int i, j;
yading@11:     const int n= pca->n;
yading@11: 
yading@11:     for(i=0; i<n; i++){
yading@11:         pca->mean[i] += v[i];
yading@11:         for(j=i; j<n; j++)
yading@11:             pca->covariance[j + i*n] += v[i]*v[j];
yading@11:     }
yading@11:     pca->count++;
yading@11: }
yading@11: 
yading@11: int ff_pca(PCA *pca, double *eigenvector, double *eigenvalue){
yading@11:     int i, j, pass;
yading@11:     int k=0;
yading@11:     const int n= pca->n;
yading@11:     double *z = pca->z;
yading@11: 
yading@11:     memset(eigenvector, 0, sizeof(double)*n*n);
yading@11: 
yading@11:     for(j=0; j<n; j++){
yading@11:         pca->mean[j] /= pca->count;
yading@11:         eigenvector[j + j*n] = 1.0;
yading@11:         for(i=0; i<=j; i++){
yading@11:             pca->covariance[j + i*n] /= pca->count;
yading@11:             pca->covariance[j + i*n] -= pca->mean[i] * pca->mean[j];
yading@11:             pca->covariance[i + j*n] = pca->covariance[j + i*n];
yading@11:         }
yading@11:         eigenvalue[j]= pca->covariance[j + j*n];
yading@11:         z[j]= 0;
yading@11:     }
yading@11: 
yading@11:     for(pass=0; pass < 50; pass++){
yading@11:         double sum=0;
yading@11: 
yading@11:         for(i=0; i<n; i++)
yading@11:             for(j=i+1; j<n; j++)
yading@11:                 sum += fabs(pca->covariance[j + i*n]);
yading@11: 
yading@11:         if(sum == 0){
yading@11:             for(i=0; i<n; i++){
yading@11:                 double maxvalue= -1;
yading@11:                 for(j=i; j<n; j++){
yading@11:                     if(eigenvalue[j] > maxvalue){
yading@11:                         maxvalue= eigenvalue[j];
yading@11:                         k= j;
yading@11:                     }
yading@11:                 }
yading@11:                 eigenvalue[k]= eigenvalue[i];
yading@11:                 eigenvalue[i]= maxvalue;
yading@11:                 for(j=0; j<n; j++){
yading@11:                     double tmp= eigenvector[k + j*n];
yading@11:                     eigenvector[k + j*n]= eigenvector[i + j*n];
yading@11:                     eigenvector[i + j*n]= tmp;
yading@11:                 }
yading@11:             }
yading@11:             return pass;
yading@11:         }
yading@11: 
yading@11:         for(i=0; i<n; i++){
yading@11:             for(j=i+1; j<n; j++){
yading@11:                 double covar= pca->covariance[j + i*n];
yading@11:                 double t,c,s,tau,theta, h;
yading@11: 
yading@11:                 if(pass < 3 && fabs(covar) < sum / (5*n*n)) //FIXME why pass < 3
yading@11:                     continue;
yading@11:                 if(fabs(covar) == 0.0) //FIXME should not be needed
yading@11:                     continue;
yading@11:                 if(pass >=3 && fabs((eigenvalue[j]+z[j])/covar) > (1LL<<32) && fabs((eigenvalue[i]+z[i])/covar) > (1LL<<32)){
yading@11:                     pca->covariance[j + i*n]=0.0;
yading@11:                     continue;
yading@11:                 }
yading@11: 
yading@11:                 h= (eigenvalue[j]+z[j]) - (eigenvalue[i]+z[i]);
yading@11:                 theta=0.5*h/covar;
yading@11:                 t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
yading@11:                 if(theta < 0.0) t = -t;
yading@11: 
yading@11:                 c=1.0/sqrt(1+t*t);
yading@11:                 s=t*c;
yading@11:                 tau=s/(1.0+c);
yading@11:                 z[i] -= t*covar;
yading@11:                 z[j] += t*covar;
yading@11: 
yading@11: #define ROTATE(a,i,j,k,l) {\
yading@11:     double g=a[j + i*n];\
yading@11:     double h=a[l + k*n];\
yading@11:     a[j + i*n]=g-s*(h+g*tau);\
yading@11:     a[l + k*n]=h+s*(g-h*tau); }
yading@11:                 for(k=0; k<n; k++) {
yading@11:                     if(k!=i && k!=j){
yading@11:                         ROTATE(pca->covariance,FFMIN(k,i),FFMAX(k,i),FFMIN(k,j),FFMAX(k,j))
yading@11:                     }
yading@11:                     ROTATE(eigenvector,k,i,k,j)
yading@11:                 }
yading@11:                 pca->covariance[j + i*n]=0.0;
yading@11:             }
yading@11:         }
yading@11:         for (i=0; i<n; i++) {
yading@11:             eigenvalue[i] += z[i];
yading@11:             z[i]=0.0;
yading@11:         }
yading@11:     }
yading@11: 
yading@11:     return -1;
yading@11: }
yading@11: 
yading@11: #ifdef TEST
yading@11: 
yading@11: #undef printf
yading@11: #include <stdio.h>
yading@11: #include <stdlib.h>
yading@11: #include "lfg.h"
yading@11: 
yading@11: int main(void){
yading@11:     PCA *pca;
yading@11:     int i, j, k;
yading@11: #define LEN 8
yading@11:     double eigenvector[LEN*LEN];
yading@11:     double eigenvalue[LEN];
yading@11:     AVLFG prng;
yading@11: 
yading@11:     av_lfg_init(&prng, 1);
yading@11: 
yading@11:     pca= ff_pca_init(LEN);
yading@11: 
yading@11:     for(i=0; i<9000000; i++){
yading@11:         double v[2*LEN+100];
yading@11:         double sum=0;
yading@11:         int pos = av_lfg_get(&prng) % LEN;
yading@11:         int v2  = av_lfg_get(&prng) % 101 - 50;
yading@11:         v[0]    = av_lfg_get(&prng) % 101 - 50;
yading@11:         for(j=1; j<8; j++){
yading@11:             if(j<=pos) v[j]= v[0];
yading@11:             else       v[j]= v2;
yading@11:             sum += v[j];
yading@11:         }
yading@11: /*        for(j=0; j<LEN; j++){
yading@11:             v[j] -= v[pos];
yading@11:         }*/
yading@11: //        sum += av_lfg_get(&prng) % 10;
yading@11: /*        for(j=0; j<LEN; j++){
yading@11:             v[j] -= sum/LEN;
yading@11:         }*/
yading@11: //        lbt1(v+100,v+100,LEN);
yading@11:         ff_pca_add(pca, v);
yading@11:     }
yading@11: 
yading@11: 
yading@11:     ff_pca(pca, eigenvector, eigenvalue);
yading@11:     for(i=0; i<LEN; i++){
yading@11:         pca->count= 1;
yading@11:         pca->mean[i]= 0;
yading@11: 
yading@11: //        (0.5^|x|)^2 = 0.5^2|x| = 0.25^|x|
yading@11: 
yading@11: 
yading@11: //        pca.covariance[i + i*LEN]= pow(0.5, fabs
yading@11:         for(j=i; j<LEN; j++){
yading@11:             printf("%f ", pca->covariance[i + j*LEN]);
yading@11:         }
yading@11:         printf("\n");
yading@11:     }
yading@11: 
yading@11:     for(i=0; i<LEN; i++){
yading@11:         double v[LEN];
yading@11:         double error=0;
yading@11:         memset(v, 0, sizeof(v));
yading@11:         for(j=0; j<LEN; j++){
yading@11:             for(k=0; k<LEN; k++){
yading@11:                 v[j] += pca->covariance[FFMIN(k,j) + FFMAX(k,j)*LEN] * eigenvector[i + k*LEN];
yading@11:             }
yading@11:             v[j] /= eigenvalue[i];
yading@11:             error += fabs(v[j] - eigenvector[i + j*LEN]);
yading@11:         }
yading@11:         printf("%f ", error);
yading@11:     }
yading@11:     printf("\n");
yading@11: 
yading@11:     for(i=0; i<LEN; i++){
yading@11:         for(j=0; j<LEN; j++){
yading@11:             printf("%9.6f ", eigenvector[i + j*LEN]);
yading@11:         }
yading@11:         printf("  %9.1f %f\n", eigenvalue[i], eigenvalue[i]/eigenvalue[0]);
yading@11:     }
yading@11: 
yading@11:     return 0;
yading@11: }
yading@11: #endif