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  1. /*
  2.  * linear least squares model
  3.  *
  4.  * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
  5.  *
  6.  * This file is part of FFmpeg.
  7.  *
  8.  * FFmpeg 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.  * FFmpeg 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 FFmpeg; 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 "attributes.h"
  32. #include "version.h"
  33. #include "lls1.h"
  34.  
  35. #if FF_API_LLS1
  36.  
  37. av_cold void avpriv_init_lls(LLSModel *m, int indep_count)
  38. {
  39.     memset(m, 0, sizeof(LLSModel));
  40.     m->indep_count = indep_count;
  41. }
  42.  
  43. void avpriv_update_lls(LLSModel *m, double *var, double decay)
  44. {
  45.     int i, j;
  46.  
  47.     for (i = 0; i <= m->indep_count; i++) {
  48.         for (j = i; j <= m->indep_count; j++) {
  49.             m->covariance[i][j] *= decay;
  50.             m->covariance[i][j] += var[i] * var[j];
  51.         }
  52.     }
  53. }
  54.  
  55. void avpriv_solve_lls(LLSModel *m, double threshold, unsigned short min_order)
  56. {
  57.     int i, j, k;
  58.     double (*factor)[MAX_VARS + 1] = (void *) &m->covariance[1][0];
  59.     double (*covar) [MAX_VARS + 1] = (void *) &m->covariance[1][1];
  60.     double *covar_y                = m->covariance[0];
  61.     int count                      = m->indep_count;
  62.  
  63.     for (i = 0; i < count; i++) {
  64.         for (j = i; j < count; j++) {
  65.             double sum = covar[i][j];
  66.  
  67.             for (k = i - 1; k >= 0; k--)
  68.                 sum -= factor[i][k] * factor[j][k];
  69.  
  70.             if (i == j) {
  71.                 if (sum < threshold)
  72.                     sum = 1.0;
  73.                 factor[i][i] = sqrt(sum);
  74.             } else {
  75.                 factor[j][i] = sum / factor[i][i];
  76.             }
  77.         }
  78.     }
  79.  
  80.     for (i = 0; i < count; i++) {
  81.         double sum = covar_y[i + 1];
  82.  
  83.         for (k = i - 1; k >= 0; k--)
  84.             sum -= factor[i][k] * m->coeff[0][k];
  85.  
  86.         m->coeff[0][i] = sum / factor[i][i];
  87.     }
  88.  
  89.     for (j = count - 1; j >= min_order; j--) {
  90.         for (i = j; i >= 0; i--) {
  91.             double sum = m->coeff[0][i];
  92.  
  93.             for (k = i + 1; k <= j; k++)
  94.                 sum -= factor[k][i] * m->coeff[j][k];
  95.  
  96.             m->coeff[j][i] = sum / factor[i][i];
  97.         }
  98.  
  99.         m->variance[j] = covar_y[0];
  100.  
  101.         for (i = 0; i <= j; i++) {
  102.             double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1];
  103.  
  104.             for (k = 0; k < i; k++)
  105.                 sum += 2 * m->coeff[j][k] * covar[k][i];
  106.  
  107.             m->variance[j] += m->coeff[j][i] * sum;
  108.         }
  109.     }
  110. }
  111.  
  112. double avpriv_evaluate_lls(LLSModel *m, double *param, int order)
  113. {
  114.     int i;
  115.     double out = 0;
  116.  
  117.     for (i = 0; i <= order; i++)
  118.         out += param[i] * m->coeff[order][i];
  119.  
  120.     return out;
  121. }
  122.  
  123. #if FF_API_LLS_PRIVATE
  124. av_cold void av_init_lls(LLSModel *m, int indep_count)
  125. {
  126.     avpriv_init_lls(m, indep_count);
  127. }
  128. void av_update_lls(LLSModel *m, double *param, double decay)
  129. {
  130.     avpriv_update_lls(m, param, decay);
  131. }
  132. void av_solve_lls(LLSModel *m, double threshold, int min_order)
  133. {
  134.     avpriv_solve_lls(m, threshold, min_order);
  135. }
  136. double av_evaluate_lls(LLSModel *m, double *param, int order)
  137. {
  138.     return avpriv_evaluate_lls(m, param, order);
  139. }
  140. #endif /* FF_API_LLS_PRIVATE */
  141.  
  142. #endif /* FF_API_LLS1 */
  143.  
  144. #ifdef TEST
  145.  
  146. #include <stdio.h>
  147. #include <limits.h>
  148. #include "lfg.h"
  149.  
  150. int main(void)
  151. {
  152.     LLSModel m;
  153.     int i, order;
  154.     AVLFG lfg;
  155.  
  156.     av_lfg_init(&lfg, 1);
  157.     avpriv_init_lls(&m, 3);
  158.  
  159.     for (i = 0; i < 100; i++) {
  160.         double var[4];
  161.         double eval;
  162.  
  163.         var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2;
  164.         var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
  165.         var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
  166.         var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
  167.         avpriv_update_lls(&m, var, 0.99);
  168.         avpriv_solve_lls(&m, 0.001, 0);
  169.         for (order = 0; order < 3; order++) {
  170.             eval = avpriv_evaluate_lls(&m, var + 1, order);
  171.             printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n",
  172.                    var[0], order, eval, sqrt(m.variance[order] / (i + 1)),
  173.                    m.coeff[order][0], m.coeff[order][1],
  174.                    m.coeff[order][2]);
  175.         }
  176.     }
  177.     return 0;
  178. }
  179.  
  180. #endif
  181.