/*
  * linear least squares model
  *
  * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
  *

  * This file is part of FFmpeg.
  *
  * FFmpeg is free software; you can redistribute it and/or

  * modify it under the terms of the GNU Lesser General Public
  * License as published by the Free Software Foundation; either

  * version 2.1 of the License, or (at your option) any later version.

  *

  * FFmpeg is distributed in the hope that it will be useful,

  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  * Lesser General Public License for more details.
  *
  * You should have received a copy of the GNU Lesser General Public

  * License along with FFmpeg; if not, write to the Free Software

  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

  */
 
 /**

  * @file libavutil/lls.c

  * linear least squares model
  */
 
 #include <math.h>
 #include <string.h>
 
 #include "lls.h"
 
 void av_init_lls(LLSModel *m, int indep_count){
     memset(m, 0, sizeof(LLSModel));
 
     m->indep_count= indep_count;
 }
 
 void av_update_lls(LLSModel *m, double *var, double decay){
     int i,j;
 
     for(i=0; i<=m->indep_count; i++){
         for(j=i; j<=m->indep_count; j++){
             m->covariance[i][j] *= decay;
             m->covariance[i][j] += var[i]*var[j];
         }
     }
 }
 

 void av_solve_lls(LLSModel *m, double threshold, int min_order){

     int i,j,k;

     double (*factor)[MAX_VARS+1]= (void*)&m->covariance[1][0];
     double (*covar )[MAX_VARS+1]= (void*)&m->covariance[1][1];

     double  *covar_y            =  m->covariance[0];
     int count= m->indep_count;
 
     for(i=0; i<count; i++){
         for(j=i; j<count; j++){
             double sum= covar[i][j];
 
             for(k=i-1; k>=0; k--)
                 sum -= factor[i][k]*factor[j][k];
 
             if(i==j){
                 if(sum < threshold)
                     sum= 1.0;
                 factor[i][i]= sqrt(sum);
             }else
                 factor[j][i]= sum / factor[i][i];
         }
     }
     for(i=0; i<count; i++){
         double sum= covar_y[i+1];
         for(k=i-1; k>=0; k--)

             sum -= factor[i][k]*m->coeff[0][k];
         m->coeff[0][i]= sum / factor[i][i];

     }
 

     for(j=count-1; j>=min_order; j--){
         for(i=j; i>=0; i--){
             double sum= m->coeff[0][i];
             for(k=i+1; k<=j; k++)
                 sum -= factor[k][i]*m->coeff[j][k];
             m->coeff[j][i]= sum / factor[i][i];
         }

         m->variance[j]= covar_y[0];
         for(i=0; i<=j; i++){
             double sum= m->coeff[j][i]*covar[i][i] - 2*covar_y[i+1];
             for(k=0; k<i; k++)
                 sum += 2*m->coeff[j][k]*covar[k][i];
             m->variance[j] += m->coeff[j][i]*sum;
         }

     }
 }
 

 double av_evaluate_lls(LLSModel *m, double *param, int order){

     int i;
     double out= 0;
 

     for(i=0; i<=order; i++)
         out+= param[i]*m->coeff[order][i];

 
     return out;
 }
 
 #ifdef TEST
 
 #include <stdlib.h>
 #include <stdio.h>
 

 int main(void){

     LLSModel m;

     int i, order;

 
     av_init_lls(&m, 3);
 
     for(i=0; i<100; i++){
         double var[4];

         double eval;

 #if 0

         var[1] = rand() / (double)RAND_MAX;
         var[2] = rand() / (double)RAND_MAX;
         var[3] = rand() / (double)RAND_MAX;
 

         var[2]= var[1] + var[3]/2;

 
         var[0] = var[1] + var[2] + var[3] +  var[1]*var[2]/100;

 #else
         var[0] = (rand() / (double)RAND_MAX - 0.5)*2;
         var[1] = var[0] + rand() / (double)RAND_MAX - 0.5;
         var[2] = var[1] + rand() / (double)RAND_MAX - 0.5;
         var[3] = var[2] + rand() / (double)RAND_MAX - 0.5;
 #endif

         av_update_lls(&m, var, 0.99);

         av_solve_lls(&m, 0.001, 0);
         for(order=0; order<3; order++){
             eval= av_evaluate_lls(&m, var+1, order);

             printf("real:%f order:%d pred:%f var:%f coeffs:%f %f %f\n",

                 var[0], order, eval, sqrt(m.variance[order] / (i+1)),
                 m.coeff[order][0], m.coeff[order][1], m.coeff[order][2]);
         }

     }
     return 0;
 }
 
 #endif