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 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 libavutil/lls.c
  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     memset(m, 0, sizeof(LLSModel));
  35
  36     m->indep_count= indep_count;
  37 }
  38
  39 void av_update_lls(LLSModel *m, double *var, double decay){
  40     int i,j;
  41
  42     for(i=0; i<=m->indep_count; i++){
  43         for(j=i; j<=m->indep_count; j++){
  44             m->covariance[i][j] *= decay;
  45             m->covariance[i][j] += var[i]*var[j];
  46         }
  47     }
  48 }
  49
  50 void av_solve_lls(LLSModel *m, double threshold, int min_order){
  51     int i,j,k;
  52     double (*factor)[MAX_VARS+1]= (void*)&m->covariance[1][0];
  53     double (*covar )[MAX_VARS+1]= (void*)&m->covariance[1][1];
  54     double  *covar_y            =  m->covariance[0];
  55     int count= m->indep_count;
  56
  57     for(i=0; i<count; i++){
  58         for(j=i; j<count; j++){
  59             double sum= covar[i][j];
  60
  61             for(k=i-1; k>=0; k--)
  62                 sum -= factor[i][k]*factor[j][k];
  63
  64             if(i==j){
  65                 if(sum < threshold)
  66                     sum= 1.0;
  67                 factor[i][i]= sqrt(sum);
  68             }else
  69                 factor[j][i]= sum / factor[i][i];
  70         }
  71     }
  72     for(i=0; i<count; i++){
  73         double sum= covar_y[i+1];
  74         for(k=i-1; k>=0; k--)
  75             sum -= factor[i][k]*m->coeff[0][k];
  76         m->coeff[0][i]= sum / factor[i][i];
  77     }
  78
  79     for(j=count-1; j>=min_order; j--){
  80         for(i=j; i>=0; i--){
  81             double sum= m->coeff[0][i];
  82             for(k=i+1; k<=j; k++)
  83                 sum -= factor[k][i]*m->coeff[j][k];
  84             m->coeff[j][i]= sum / factor[i][i];
  85         }
  86
  87         m->variance[j]= covar_y[0];
  88         for(i=0; i<=j; i++){
  89             double sum= m->coeff[j][i]*covar[i][i] - 2*covar_y[i+1];
  90             for(k=0; k<i; k++)
  91                 sum += 2*m->coeff[j][k]*covar[k][i];
  92             m->variance[j] += m->coeff[j][i]*sum;
  93         }
  94     }
  95 }
  96
  97 double av_evaluate_lls(LLSModel *m, double *param, int order){
  98     int i;
  99     double out= 0;
 100
 101     for(i=0; i<=order; i++)
 102         out+= param[i]*m->coeff[order][i];
 103
 104     return out;
 105 }
 106
 107 #ifdef TEST
 108
 109 #include <stdlib.h>
 110 #include <stdio.h>
 111
 112 int main(void){
 113     LLSModel m;
 114     int i, order;
 115
 116     av_init_lls(&m, 3);
 117
 118     for(i=0; i<100; i++){
 119         double var[4];
 120         double eval;
 121 #if 0
 122         var[1] = rand() / (double)RAND_MAX;
 123         var[2] = rand() / (double)RAND_MAX;
 124         var[3] = rand() / (double)RAND_MAX;
 125
 126         var[2]= var[1] + var[3]/2;
 127
 128         var[0] = var[1] + var[2] + var[3] +  var[1]*var[2]/100;
 129 #else
 130         var[0] = (rand() / (double)RAND_MAX - 0.5)*2;
 131         var[1] = var[0] + rand() / (double)RAND_MAX - 0.5;
 132         var[2] = var[1] + rand() / (double)RAND_MAX - 0.5;
 133         var[3] = var[2] + rand() / (double)RAND_MAX - 0.5;
 134 #endif
 135         av_update_lls(&m, var, 0.99);
 136         av_solve_lls(&m, 0.001, 0);
 137         for(order=0; order<3; order++){
 138             eval= av_evaluate_lls(&m, var+1, order);
 139             printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n",
 140                 var[0], order, eval, sqrt(m.variance[order] / (i+1)),
 141                 m.coeff[order][0], m.coeff[order][1], m.coeff[order][2]);
 142         }
 143     }
 144     return 0;
 145 }
 146
 147 #endif