libavutil/lls.c

   1 /*
   2  * linear least squares model
   3  *
   4  * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
   5  *
   6  * This file is part of Libav.
   7  *
   8  * Libav is free software; you can redistribute it and/or
   9  * modify it under the terms of the GNU Lesser General Public
  10  * License as published by the Free Software Foundation; either
  11  * version 2.1 of the License, or (at your option) any later version.
  12  *
  13  * Libav is distributed in the hope that it will be useful,
  14  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  16  * Lesser General Public License for more details.
  17  *
  18  * You should have received a copy of the GNU Lesser General Public
  19  * License along with Libav; if not, write to the Free Software
  20  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
  21  */
  22
  23 /**
  24  * @file
  25  * linear least squares model
  26  */
  27
  28 #include <math.h>
  29 #include <string.h>
  30
  31 #include "lls.h"
  32
  33 void av_init_lls(LLSModel *m, int indep_count)
  34 {
  35     memset(m, 0, sizeof(LLSModel));
  36     m->indep_count = indep_count;
  37 }
  38
  39 void av_update_lls(LLSModel *m, double *var, double decay)
  40 {
  41     int i, j;
  42
  43     for (i = 0; i <= m->indep_count; i++) {
  44         for (j = i; j <= m->indep_count; j++) {
  45             m->covariance[i][j] *= decay;
  46             m->covariance[i][j] += var[i] * var[j];
  47         }
  48     }
  49 }
  50
  51 void av_solve_lls(LLSModel *m, double threshold, int min_order)
  52 {
  53     int i, j, k;
  54     double (*factor)[MAX_VARS + 1] = (void *) &m->covariance[1][0];
  55     double (*covar) [MAX_VARS + 1] = (void *) &m->covariance[1][1];
  56     double *covar_y                = m->covariance[0];
  57     int count                      = m->indep_count;
  58
  59     for (i = 0; i < count; i++) {
  60         for (j = i; j < count; j++) {
  61             double sum = covar[i][j];
  62
  63             for (k = i - 1; k >= 0; k--)
  64                 sum -= factor[i][k] * factor[j][k];
  65
  66             if (i == j) {
  67                 if (sum < threshold)
  68                     sum = 1.0;
  69                 factor[i][i] = sqrt(sum);
  70             } else {
  71                 factor[j][i] = sum / factor[i][i];
  72             }
  73         }
  74     }
  75
  76     for (i = 0; i < count; i++) {
  77         double sum = covar_y[i + 1];
  78
  79         for (k = i - 1; k >= 0; k--)
  80             sum -= factor[i][k] * m->coeff[0][k];
  81
  82         m->coeff[0][i] = sum / factor[i][i];
  83     }
  84
  85     for (j = count - 1; j >= min_order; j--) {
  86         for (i = j; i >= 0; i--) {
  87             double sum = m->coeff[0][i];
  88
  89             for (k = i + 1; k <= j; k++)
  90                 sum -= factor[k][i] * m->coeff[j][k];
  91
  92             m->coeff[j][i] = sum / factor[i][i];
  93         }
  94
  95         m->variance[j] = covar_y[0];
  96
  97         for (i = 0; i <= j; i++) {
  98             double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1];
  99
 100             for (k = 0; k < i; k++)
 101                 sum += 2 * m->coeff[j][k] * covar[k][i];
 102
 103             m->variance[j] += m->coeff[j][i] * sum;
 104         }
 105     }
 106 }
 107
 108 double av_evaluate_lls(LLSModel *m, double *param, int order)
 109 {
 110     int i;
 111     double out = 0;
 112
 113     for (i = 0; i <= order; i++)
 114         out += param[i] * m->coeff[order][i];
 115
 116     return out;
 117 }
 118
 119 #ifdef TEST
 120
 121 #include <stdlib.h>
 122 #include <stdio.h>
 123
 124 int main(void)
 125 {
 126     LLSModel m;
 127     int i, order;
 128
 129     av_init_lls(&m, 3);
 130
 131     for (i = 0; i < 100; i++) {
 132         double var[4];
 133         double eval;
 134
 135         var[0] = (rand() / (double) RAND_MAX - 0.5) * 2;
 136         var[1] = var[0] + rand() / (double) RAND_MAX - 0.5;
 137         var[2] = var[1] + rand() / (double) RAND_MAX - 0.5;
 138         var[3] = var[2] + rand() / (double) RAND_MAX - 0.5;
 139         av_update_lls(&m, var, 0.99);
 140         av_solve_lls(&m, 0.001, 0);
 141         for (order = 0; order < 3; order++) {
 142             eval = av_evaluate_lls(&m, var + 1, order);
 143             printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n",
 144                    var[0], order, eval, sqrt(m.variance[order] / (i + 1)),
 145                    m.coeff[order][0], m.coeff[order][1],
 146                    m.coeff[order][2]);
 147         }
 148     }
 149     return 0;
 150 }
 151
 152 #endif