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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
* 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 <stdio.h>
#include <limits.h>
#include "lfg.h"
int main(void)
{
LLSModel m;
int i, order;
AVLFG lfg;
av_lfg_init(&lfg, 1);
av_init_lls(&m, 3);
for (i = 0; i < 100; i++) {
double var[4];
double eval;
var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2;
var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
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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