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-rw-r--r--libavutil/pca.c248
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diff --git a/libavutil/pca.c b/libavutil/pca.c
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+/*
+ * 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 "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));
+ pca->n= n;
+ pca->z = av_malloc(sizeof(*pca->z) * n);
+ pca->count=0;
+ pca->covariance= av_calloc(n*n, sizeof(double));
+ pca->mean= av_calloc(n, sizeof(double));
+
+ 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, 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;
+}
+
+#ifdef TEST
+
+#undef printf
+#include <stdio.h>
+#include <stdlib.h>
+#include "lfg.h"
+
+int main(void){
+ PCA *pca;
+ int i, j, k;
+#define LEN 8
+ double eigenvector[LEN*LEN];
+ double eigenvalue[LEN];
+ AVLFG prng;
+
+ av_lfg_init(&prng, 1);
+
+ pca= ff_pca_init(LEN);
+
+ for(i=0; i<9000000; i++){
+ double v[2*LEN+100];
+ double sum=0;
+ int pos = av_lfg_get(&prng) % LEN;
+ int v2 = av_lfg_get(&prng) % 101 - 50;
+ v[0] = av_lfg_get(&prng) % 101 - 50;
+ for(j=1; j<8; j++){
+ if(j<=pos) v[j]= v[0];
+ else v[j]= v2;
+ sum += v[j];
+ }
+/* for(j=0; j<LEN; j++){
+ v[j] -= v[pos];
+ }*/
+// sum += av_lfg_get(&prng) % 10;
+/* for(j=0; j<LEN; j++){
+ v[j] -= sum/LEN;
+ }*/
+// lbt1(v+100,v+100,LEN);
+ ff_pca_add(pca, v);
+ }
+
+
+ ff_pca(pca, eigenvector, eigenvalue);
+ for(i=0; i<LEN; i++){
+ pca->count= 1;
+ pca->mean[i]= 0;
+
+// (0.5^|x|)^2 = 0.5^2|x| = 0.25^|x|
+
+
+// pca.covariance[i + i*LEN]= pow(0.5, fabs
+ for(j=i; j<LEN; j++){
+ printf("%f ", pca->covariance[i + j*LEN]);
+ }
+ printf("\n");
+ }
+
+ for(i=0; i<LEN; i++){
+ double v[LEN];
+ double error=0;
+ memset(v, 0, sizeof(v));
+ for(j=0; j<LEN; j++){
+ for(k=0; k<LEN; k++){
+ v[j] += pca->covariance[FFMIN(k,j) + FFMAX(k,j)*LEN] * eigenvector[i + k*LEN];
+ }
+ v[j] /= eigenvalue[i];
+ error += fabs(v[j] - eigenvector[i + j*LEN]);
+ }
+ printf("%f ", error);
+ }
+ printf("\n");
+
+ for(i=0; i<LEN; i++){
+ for(j=0; j<LEN; j++){
+ printf("%9.6f ", eigenvector[i + j*LEN]);
+ }
+ printf(" %9.1f %f\n", eigenvalue[i], eigenvalue[i]/eigenvalue[0]);
+ }
+
+ return 0;
+}
+#endif
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