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+/*

+ * 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

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+/*

+ * 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;