mirror of https://github.com/FFmpeg/FFmpeg.git
Signed-off-by: Mans Rullgard <mans@mansr.com>pull/2/head
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5dd514af93
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cfa68a3381
3 changed files with 1 additions and 281 deletions
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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 |
@ -1,35 +0,0 @@ |
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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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/**
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* @file |
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* principal component analysis (PCA) |
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*/ |
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#ifndef AVUTIL_PCA_H |
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#define AVUTIL_PCA_H |
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struct PCA *ff_pca_init(int n); |
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void ff_pca_free(struct PCA *pca); |
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void ff_pca_add(struct PCA *pca, double *v); |
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int ff_pca(struct PCA *pca, double *eigenvector, double *eigenvalue); |
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#endif /* AVUTIL_PCA_H */ |
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