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