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156 lines
4.0 KiB
C
156 lines
4.0 KiB
C
/*
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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 Libav.
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*
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* Libav 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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* Libav 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 Libav; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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/**
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* @file
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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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void av_init_lls(LLSModel *m, int indep_count)
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{
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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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{
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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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{
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int i, j, k;
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double (*factor)[MAX_VARS + 1] = (void *) &m->covariance[1][0];
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double (*covar) [MAX_VARS + 1] = (void *) &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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}
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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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{
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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 <stdio.h>
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#include <limits.h>
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#include "lfg.h"
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int main(void)
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{
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LLSModel m;
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int i, order;
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AVLFG lfg;
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av_lfg_init(&lfg, 1);
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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;
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var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2;
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var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
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var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
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var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
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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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printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\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],
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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
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