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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 "lls2.h"
  34.  
  35. static void update_lls(LLSModel2 *m, double *var)
  36. {
  37.     int i, j;
  38.  
  39.     for (i = 0; i <= m->indep_count; i++) {
  40.         for (j = i; j <= m->indep_count; j++) {
  41.             m->covariance[i][j] += var[i] * var[j];
  42.         }
  43.     }
  44. }
  45.  
  46. void avpriv_solve_lls2(LLSModel2 *m, double threshold, unsigned short min_order)
  47. {
  48.     int i, j, k;
  49.     double (*factor)[MAX_VARS_ALIGN] = (void *) &m->covariance[1][0];
  50.     double (*covar) [MAX_VARS_ALIGN] = (void *) &m->covariance[1][1];
  51.     double *covar_y                = m->covariance[0];
  52.     int count                      = m->indep_count;
  53.  
  54.     for (i = 0; i < count; i++) {
  55.         for (j = i; j < count; j++) {
  56.             double sum = covar[i][j];
  57.  
  58.             for (k = i - 1; k >= 0; k--)
  59.                 sum -= factor[i][k] * factor[j][k];
  60.  
  61.             if (i == j) {
  62.                 if (sum < threshold)
  63.                     sum = 1.0;
  64.                 factor[i][i] = sqrt(sum);
  65.             } else {
  66.                 factor[j][i] = sum / factor[i][i];
  67.             }
  68.         }
  69.     }
  70.  
  71.     for (i = 0; i < count; i++) {
  72.         double sum = covar_y[i + 1];
  73.  
  74.         for (k = i - 1; k >= 0; k--)
  75.             sum -= factor[i][k] * m->coeff[0][k];
  76.  
  77.         m->coeff[0][i] = sum / factor[i][i];
  78.     }
  79.  
  80.     for (j = count - 1; j >= min_order; j--) {
  81.         for (i = j; i >= 0; i--) {
  82.             double sum = m->coeff[0][i];
  83.  
  84.             for (k = i + 1; k <= j; k++)
  85.                 sum -= factor[k][i] * m->coeff[j][k];
  86.  
  87.             m->coeff[j][i] = sum / factor[i][i];
  88.         }
  89.  
  90.         m->variance[j] = covar_y[0];
  91.  
  92.         for (i = 0; i <= j; i++) {
  93.             double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1];
  94.  
  95.             for (k = 0; k < i; k++)
  96.                 sum += 2 * m->coeff[j][k] * covar[k][i];
  97.  
  98.             m->variance[j] += m->coeff[j][i] * sum;
  99.         }
  100.     }
  101. }
  102.  
  103. static double evaluate_lls(LLSModel2 *m, double *param, int order)
  104. {
  105.     int i;
  106.     double out = 0;
  107.  
  108.     for (i = 0; i <= order; i++)
  109.         out += param[i] * m->coeff[order][i];
  110.  
  111.     return out;
  112. }
  113.  
  114. av_cold void avpriv_init_lls2(LLSModel2 *m, int indep_count)
  115. {
  116.     memset(m, 0, sizeof(LLSModel2));
  117.     m->indep_count = indep_count;
  118.     m->update_lls = update_lls;
  119.     m->evaluate_lls = evaluate_lls;
  120.     if (ARCH_X86)
  121.         ff_init_lls_x86(m);
  122. }
  123.  
  124. #ifdef TEST
  125.  
  126. #include <stdio.h>
  127. #include <limits.h>
  128. #include "lfg.h"
  129.  
  130. int main(void)
  131. {
  132.     LLSModel2 m;
  133.     int i, order;
  134.     AVLFG lfg;
  135.  
  136.     av_lfg_init(&lfg, 1);
  137.     avpriv_init_lls2(&m, 3);
  138.  
  139.     for (i = 0; i < 100; i++) {
  140.         LOCAL_ALIGNED(32, double, var, [4]);
  141.         double eval;
  142.  
  143.         var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2;
  144.         var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
  145.         var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
  146.         var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
  147.         m.update_lls(&m, var);
  148.         avpriv_solve_lls2(&m, 0.001, 0);
  149.         for (order = 0; order < 3; order++) {
  150.             eval = m.evaluate_lls(&m, var + 1, order);
  151.             printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n",
  152.                    var[0], order, eval, sqrt(m.variance[order] / (i + 1)),
  153.                    m.coeff[order][0], m.coeff[order][1],
  154.                    m.coeff[order][2]);
  155.         }
  156.     }
  157.     return 0;
  158. }
  159.  
  160. #endif
  161.