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/*
* 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:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\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
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