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			/* | 
		
		
	
		
			
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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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			    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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			    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 |