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libavutil/lls.c

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00001 /*
00002  * linear least squares model
00003  *
00004  * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
00005  *
00006  * This file is part of Libav.
00007  *
00008  * Libav is free software; you can redistribute it and/or
00009  * modify it under the terms of the GNU Lesser General Public
00010  * License as published by the Free Software Foundation; either
00011  * version 2.1 of the License, or (at your option) any later version.
00012  *
00013  * Libav is distributed in the hope that it will be useful,
00014  * but WITHOUT ANY WARRANTY; without even the implied warranty of
00015  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00016  * Lesser General Public License for more details.
00017  *
00018  * You should have received a copy of the GNU Lesser General Public
00019  * License along with Libav; if not, write to the Free Software
00020  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
00021  */
00022 
00028 #include <math.h>
00029 #include <string.h>
00030 
00031 #include "lls.h"
00032 
00033 void av_init_lls(LLSModel *m, int indep_count)
00034 {
00035     memset(m, 0, sizeof(LLSModel));
00036     m->indep_count = indep_count;
00037 }
00038 
00039 void av_update_lls(LLSModel *m, double *var, double decay)
00040 {
00041     int i, j;
00042 
00043     for (i = 0; i <= m->indep_count; i++) {
00044         for (j = i; j <= m->indep_count; j++) {
00045             m->covariance[i][j] *= decay;
00046             m->covariance[i][j] += var[i] * var[j];
00047         }
00048     }
00049 }
00050 
00051 void av_solve_lls(LLSModel *m, double threshold, int min_order)
00052 {
00053     int i, j, k;
00054     double (*factor)[MAX_VARS + 1] = (void *) &m->covariance[1][0];
00055     double (*covar) [MAX_VARS + 1] = (void *) &m->covariance[1][1];
00056     double *covar_y                = m->covariance[0];
00057     int count                      = m->indep_count;
00058 
00059     for (i = 0; i < count; i++) {
00060         for (j = i; j < count; j++) {
00061             double sum = covar[i][j];
00062 
00063             for (k = i - 1; k >= 0; k--)
00064                 sum -= factor[i][k] * factor[j][k];
00065 
00066             if (i == j) {
00067                 if (sum < threshold)
00068                     sum = 1.0;
00069                 factor[i][i] = sqrt(sum);
00070             } else {
00071                 factor[j][i] = sum / factor[i][i];
00072             }
00073         }
00074     }
00075 
00076     for (i = 0; i < count; i++) {
00077         double sum = covar_y[i + 1];
00078 
00079         for (k = i - 1; k >= 0; k--)
00080             sum -= factor[i][k] * m->coeff[0][k];
00081 
00082         m->coeff[0][i] = sum / factor[i][i];
00083     }
00084 
00085     for (j = count - 1; j >= min_order; j--) {
00086         for (i = j; i >= 0; i--) {
00087             double sum = m->coeff[0][i];
00088 
00089             for (k = i + 1; k <= j; k++)
00090                 sum -= factor[k][i] * m->coeff[j][k];
00091 
00092             m->coeff[j][i] = sum / factor[i][i];
00093         }
00094 
00095         m->variance[j] = covar_y[0];
00096 
00097         for (i = 0; i <= j; i++) {
00098             double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1];
00099 
00100             for (k = 0; k < i; k++)
00101                 sum += 2 * m->coeff[j][k] * covar[k][i];
00102 
00103             m->variance[j] += m->coeff[j][i] * sum;
00104         }
00105     }
00106 }
00107 
00108 double av_evaluate_lls(LLSModel *m, double *param, int order)
00109 {
00110     int i;
00111     double out = 0;
00112 
00113     for (i = 0; i <= order; i++)
00114         out += param[i] * m->coeff[order][i];
00115 
00116     return out;
00117 }
00118 
00119 #ifdef TEST
00120 
00121 #include <stdio.h>
00122 #include <limits.h>
00123 #include "lfg.h"
00124 
00125 int main(void)
00126 {
00127     LLSModel m;
00128     int i, order;
00129     AVLFG lfg;
00130 
00131     av_lfg_init(&lfg, 1);
00132     av_init_lls(&m, 3);
00133 
00134     for (i = 0; i < 100; i++) {
00135         double var[4];
00136         double eval;
00137 
00138         var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2;
00139         var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
00140         var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
00141         var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
00142         av_update_lls(&m, var, 0.99);
00143         av_solve_lls(&m, 0.001, 0);
00144         for (order = 0; order < 3; order++) {
00145             eval = av_evaluate_lls(&m, var + 1, order);
00146             printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n",
00147                    var[0], order, eval, sqrt(m.variance[order] / (i + 1)),
00148                    m.coeff[order][0], m.coeff[order][1],
00149                    m.coeff[order][2]);
00150         }
00151     }
00152     return 0;
00153 }
00154 
00155 #endif
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