PeerStreamer

/*

 * linear least squares model

 *

 * Copyright (c) 2006 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 lls.c

 * linear least squares model

 */

#include <math.h>

#include <string.h>

#include "lls.h"

void av_init_lls(LLSModel *m, int indep_count){

    memset(m, 0, sizeof(LLSModel));

    m->indep_count= indep_count;

}

void av_update_lls(LLSModel *m, double *var, double decay){

    int i,j;

    for(i=0; i<=m->indep_count; i++){

        for(j=i; j<=m->indep_count; j++){

            m->covariance[i][j] *= decay;

            m->covariance[i][j] += var[i]*var[j];

        }

    }

}

void av_solve_lls(LLSModel *m, double threshold, int min_order){

    int i,j,k;

    double (*factor)[MAX_VARS+1]= (void*)&m->covariance[1][0];

    double (*covar )[MAX_VARS+1]= (void*)&m->covariance[1][1];

    double  *covar_y            =  m->covariance[0];

    int count= m->indep_count;

    for(i=0; i<count; i++){

        for(j=i; j<count; j++){

            double sum= covar[i][j];

            for(k=i-1; k>=0; k--)

                sum -= factor[i][k]*factor[j][k];

            if(i==j){

                if(sum < threshold)

                    sum= 1.0;

                factor[i][i]= sqrt(sum);

            }else

                factor[j][i]= sum / factor[i][i];

        }

    }

    for(i=0; i<count; i++){

        double sum= covar_y[i+1];

        for(k=i-1; k>=0; k--)

            sum -= factor[i][k]*m->coeff[0][k];

        m->coeff[0][i]= sum / factor[i][i];

    }

    for(j=count-1; j>=min_order; j--){

        for(i=j; i>=0; i--){

            double sum= m->coeff[0][i];

            for(k=i+1; k<=j; k++)

                sum -= factor[k][i]*m->coeff[j][k];

            m->coeff[j][i]= sum / factor[i][i];

        }

        m->variance[j]= covar_y[0];

        for(i=0; i<=j; i++){

            double sum= m->coeff[j][i]*covar[i][i] - 2*covar_y[i+1];

            for(k=0; k<i; k++)

                sum += 2*m->coeff[j][k]*covar[k][i];

            m->variance[j] += m->coeff[j][i]*sum;

        }

    }

}

double av_evaluate_lls(LLSModel *m, double *param, int order){

    int i;

    double out= 0;

    for(i=0; i<=order; i++)

        out+= param[i]*m->coeff[order][i];

    return out;

}

#ifdef TEST

#include <stdlib.h>

#include <stdio.h>

int main(void){

    LLSModel m;

    int i, order;

    av_init_lls(&m, 3);

    for(i=0; i<100; i++){

        double var[4];

        double eval;

#if 0

        var[1] = rand() / (double)RAND_MAX;

        var[2] = rand() / (double)RAND_MAX;

        var[3] = rand() / (double)RAND_MAX;

        var[2]= var[1] + var[3]/2;

        var[0] = var[1] + var[2] + var[3] +  var[1]*var[2]/100;

#else

        var[0] = (rand() / (double)RAND_MAX - 0.5)*2;

        var[1] = var[0] + rand() / (double)RAND_MAX - 0.5;

        var[2] = var[1] + rand() / (double)RAND_MAX - 0.5;

        var[3] = var[2] + rand() / (double)RAND_MAX - 0.5;

#endif

        av_update_lls(&m, var, 0.99);

        av_solve_lls(&m, 0.001, 0);

        for(order=0; order<3; order++){

            eval= av_evaluate_lls(&m, var+1, order);

            printf("real:%f order:%d pred:%f var:%f coeffs:%f %f %f\n",

                var[0], order, eval, sqrt(m.variance[order] / (i+1)),

                m.coeff[order][0], m.coeff[order][1], m.coeff[order][2]);

        }

    }

    return 0;

}

#endif