Principal component analysis

(will be cleaned up in next commits)

Originally committed as revision 14802 to svn://svn.ffmpeg.org/ffmpeg/trunk

libavutil/pca.c

+/*
+ * Principal component analysis
+ * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
+ *
+ * This library 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 of the License, or (at your option) any later version.
+ *
+ * This library 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 this library; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *
+ */
+
+/**
+ * @file pca.c
+ * Principal component analysis
+ */
+
+#include <math.h>
+#include "avcodec.h"
+#include "pca.h"
+
+int ff_pca_init(PCA *pca, int n){
+    if(n<=0)
+        return -1;
+
+    pca->n= n;
+    pca->count=0;
+    pca->covariance= av_mallocz(sizeof(double)*n*n);
+    pca->mean= av_mallocz(sizeof(double)*n);
+
+    return 0;
+}
+
+void ff_pca_free(PCA *pca){
+    av_freep(&pca->covariance);
+    av_freep(&pca->mean);
+}
+
+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, k, pass;
+    const int n= pca->n;
+    double z[n];
+
+    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 shouldnt 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;
+}
+
+#if 1
+
+#undef printf
+#include <stdio.h>
+#include <stdlib.h>
+
+int main(){
+    PCA pca;
+    int i, j, k;
+#define LEN 8
+    double eigenvector[LEN*LEN];
+    double eigenvalue[LEN];
+
+    ff_pca_init(&pca, LEN);
+
+    for(i=0; i<9000000; i++){
+        double v[2*LEN+100];
+        double sum=0;
+        int pos= random()%LEN;
+        int v2= (random()%101) - 50;
+        v[0]= (random()%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 += random()%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");
+    }
+
+#if 1
+    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");
+#endif
+    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

libavutil/pca.h

+/*
+ * Principal component analysis
+ * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
+ *
+ * This library 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 of the License, or (at your option) any later version.
+ *
+ * This library 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 this library; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *
+ */
+
+/**
+ * @file pca.h
+ * Principal component analysis
+ */
+
+typedef struct PCA{
+    int count;
+    int n;
+    double *covariance;
+    double *mean;
+}PCA;