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/*
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 * linear least squares model
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 *
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 * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
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 *
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 * This file is part of FFmpeg.
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 *
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 * FFmpeg is free software; you can redistribute it and/or
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 * modify it under the terms of the GNU Lesser General Public
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 * License as published by the Free Software Foundation; either
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 * version 2.1 of the License, or (at your option) any later version.
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 *
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 * FFmpeg is distributed in the hope that it will be useful,
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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 * Lesser General Public License for more details.
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 *
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 * You should have received a copy of the GNU Lesser General Public
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 * License along with FFmpeg; if not, write to the Free Software
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 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
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 */
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/**
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 * @file lls.c
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 * linear least squares model
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 */
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#include <math.h>
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#include <string.h>
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#include "lls.h"
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#ifdef TEST
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#define av_log(a,b,...) printf(__VA_ARGS__)
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#endif
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void av_init_lls(LLSModel *m, int indep_count){
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    memset(m, 0, sizeof(LLSModel));
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    m->indep_count= indep_count;
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}
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void av_update_lls(LLSModel *m, double *var, double decay){
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    int i,j;
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    for(i=0; i<=m->indep_count; i++){
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        for(j=i; j<=m->indep_count; j++){
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            m->covariance[i][j] *= decay;
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            m->covariance[i][j] += var[i]*var[j];
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        }
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    }
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}
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void av_solve_lls(LLSModel *m, double threshold, int min_order){
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    int i,j,k;
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    double (*factor)[MAX_VARS+1]= &m->covariance[1][0];
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    double (*covar )[MAX_VARS+1]= &m->covariance[1][1];
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    double  *covar_y            =  m->covariance[0];
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    int count= m->indep_count;
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    for(i=0; i<count; i++){
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        for(j=i; j<count; j++){
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            double sum= covar[i][j];
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            for(k=i-1; k>=0; k--)
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                sum -= factor[i][k]*factor[j][k];
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            if(i==j){
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                if(sum < threshold)
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                    sum= 1.0;
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                factor[i][i]= sqrt(sum);
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            }else
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                factor[j][i]= sum / factor[i][i];
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        }
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    }
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    for(i=0; i<count; i++){
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        double sum= covar_y[i+1];
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        for(k=i-1; k>=0; k--)
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            sum -= factor[i][k]*m->coeff[0][k];
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        m->coeff[0][i]= sum / factor[i][i];
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    }
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    for(j=count-1; j>=min_order; j--){
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        for(i=j; i>=0; i--){
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            double sum= m->coeff[0][i];
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            for(k=i+1; k<=j; k++)
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                sum -= factor[k][i]*m->coeff[j][k];
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            m->coeff[j][i]= sum / factor[i][i];
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        }
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        m->variance[j]= covar_y[0];
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        for(i=0; i<=j; i++){
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            double sum= m->coeff[j][i]*covar[i][i] - 2*covar_y[i+1];
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            for(k=0; k<i; k++)
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                sum += 2*m->coeff[j][k]*covar[k][i];
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            m->variance[j] += m->coeff[j][i]*sum;
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        }
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    }
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}
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double av_evaluate_lls(LLSModel *m, double *param, int order){
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    int i;
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    double out= 0;
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    for(i=0; i<=order; i++)
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        out+= param[i]*m->coeff[order][i];
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    return out;
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}
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#ifdef TEST
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#include <stdlib.h>
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#include <stdio.h>
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int main(){
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    LLSModel m;
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    int i, order;
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    av_init_lls(&m, 3);
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    for(i=0; i<100; i++){
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        double var[4];
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        double eval, variance;
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#if 0
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        var[1] = rand() / (double)RAND_MAX;
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        var[2] = rand() / (double)RAND_MAX;
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        var[3] = rand() / (double)RAND_MAX;
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        var[2]= var[1] + var[3]/2;
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        var[0] = var[1] + var[2] + var[3] +  var[1]*var[2]/100;
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#else
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        var[0] = (rand() / (double)RAND_MAX - 0.5)*2;
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        var[1] = var[0] + rand() / (double)RAND_MAX - 0.5;
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        var[2] = var[1] + rand() / (double)RAND_MAX - 0.5;
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        var[3] = var[2] + rand() / (double)RAND_MAX - 0.5;
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#endif
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        av_update_lls(&m, var, 0.99);
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        av_solve_lls(&m, 0.001, 0);
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        for(order=0; order<3; order++){
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            eval= av_evaluate_lls(&m, var+1, order);
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            av_log(NULL, AV_LOG_DEBUG, "real:%f order:%d pred:%f var:%f coeffs:%f %f %f\n",
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                var[0], order, eval, sqrt(m.variance[order] / (i+1)),
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                m.coeff[order][0], m.coeff[order][1], m.coeff[order][2]);
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        }
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    }
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    return 0;
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}
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#endif