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 lls.c
  25  * linear least squares model
  26  */
  27
  28 #include <math.h>
  29 #include <string.h>
  30
  31 #include "lls.h"
  32
  33 #ifdef TEST
  34 #define av_log(a,b,...) printf(__VA_ARGS__)
  35 #endif
  36
  37 void av_init_lls(LLSModel *m, int indep_count){
  38     memset(m, 0, sizeof(LLSModel));
  39
  40     m->indep_count= indep_count;
  41 }
  42
  43 void av_update_lls(LLSModel *m, double *var, double decay){
  44     int i,j;
  45
  46     for(i=0; i<=m->indep_count; i++){
  47         for(j=i; j<=m->indep_count; j++){
  48             m->covariance[i][j] *= decay;
  49             m->covariance[i][j] += var[i]*var[j];
  50         }
  51     }
  52 }
  53
  54 void av_solve_lls(LLSModel *m, double threshold, int min_order){
  55     int i,j,k;
  56     double (*factor)[MAX_VARS+1]= (void*)&m->covariance[1][0];
  57     double (*covar )[MAX_VARS+1]= (void*)&m->covariance[1][1];
  58     double  *covar_y            =  m->covariance[0];
  59     int count= m->indep_count;
  60
  61     for(i=0; i<count; i++){
  62         for(j=i; j<count; j++){
  63             double sum= covar[i][j];
  64
  65             for(k=i-1; k>=0; k--)
  66                 sum -= factor[i][k]*factor[j][k];
  67
  68             if(i==j){
  69                 if(sum < threshold)
  70                     sum= 1.0;
  71                 factor[i][i]= sqrt(sum);
  72             }else
  73                 factor[j][i]= sum / factor[i][i];
  74         }
  75     }
  76     for(i=0; i<count; i++){
  77         double sum= covar_y[i+1];
  78         for(k=i-1; k>=0; k--)
  79             sum -= factor[i][k]*m->coeff[0][k];
  80         m->coeff[0][i]= sum / factor[i][i];
  81     }
  82
  83     for(j=count-1; j>=min_order; j--){
  84         for(i=j; i>=0; i--){
  85             double sum= m->coeff[0][i];
  86             for(k=i+1; k<=j; k++)
  87                 sum -= factor[k][i]*m->coeff[j][k];
  88             m->coeff[j][i]= sum / factor[i][i];
  89         }
  90
  91         m->variance[j]= covar_y[0];
  92         for(i=0; i<=j; i++){
  93             double sum= m->coeff[j][i]*covar[i][i] - 2*covar_y[i+1];
  94             for(k=0; k<i; k++)
  95                 sum += 2*m->coeff[j][k]*covar[k][i];
  96             m->variance[j] += m->coeff[j][i]*sum;
  97         }
  98     }
  99 }
 100
 101 double av_evaluate_lls(LLSModel *m, double *param, int order){
 102     int i;
 103     double out= 0;
 104
 105     for(i=0; i<=order; i++)
 106         out+= param[i]*m->coeff[order][i];
 107
 108     return out;
 109 }
 110
 111 #ifdef TEST
 112
 113 #include <stdlib.h>
 114 #include <stdio.h>
 115
 116 int main(void){
 117     LLSModel m;
 118     int i, order;
 119
 120     av_init_lls(&m, 3);
 121
 122     for(i=0; i<100; i++){
 123         double var[4];
 124         double eval;
 125 #if 0
 126         var[1] = rand() / (double)RAND_MAX;
 127         var[2] = rand() / (double)RAND_MAX;
 128         var[3] = rand() / (double)RAND_MAX;
 129
 130         var[2]= var[1] + var[3]/2;
 131
 132         var[0] = var[1] + var[2] + var[3] +  var[1]*var[2]/100;
 133 #else
 134         var[0] = (rand() / (double)RAND_MAX - 0.5)*2;
 135         var[1] = var[0] + rand() / (double)RAND_MAX - 0.5;
 136         var[2] = var[1] + rand() / (double)RAND_MAX - 0.5;
 137         var[3] = var[2] + rand() / (double)RAND_MAX - 0.5;
 138 #endif
 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             av_log(NULL, AV_LOG_DEBUG, "real:%f order:%d pred:%f var:%f coeffs:%f %f %f\n",
 144                 var[0], order, eval, sqrt(m.variance[order] / (i+1)),
 145                 m.coeff[order][0], m.coeff[order][1], m.coeff[order][2]);
 146         }
 147     }
 148     return 0;
 149 }
 150
 151 #endif