PeerStreamer

/*

 * 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 "common.h"

#include "pca.h"

PCA *ff_pca_init(int n){

    PCA *pca;

    if(n<=0)

        return NULL;

    pca= av_mallocz(sizeof(PCA));

    pca->n= n;

    pca->count=0;

    pca->covariance= av_mallocz(sizeof(double)*n*n);

    pca->mean= av_mallocz(sizeof(double)*n);

    return pca;

}

void ff_pca_free(PCA *pca){

    av_freep(&pca->covariance);

    av_freep(&pca->mean);

    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, 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;

}

#ifdef TEST

#undef printf

#undef random

#include <stdio.h>

#include <stdlib.h>

int main(){

    PCA *pca;

    int i, j, k;

#define LEN 8

    double eigenvector[LEN*LEN];

    double eigenvalue[LEN];

    pca= ff_pca_init(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