lls.c

/*
 * 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 libavutil/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