/*
  * 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

  * linear least squares model
  */
 
 #include <math.h>
 #include <string.h>
 

 #include "attributes.h"

 #include "version.h"

 #include "lls.h"

 static void update_lls(LLSModel *m, const double *var)

 {
     int i, j;

     for (i = 0; i <= m->indep_count; i++) {
         for (j = i; j <= m->indep_count; j++) {
             m->covariance[i][j] += var[i] * var[j];

         }
     }
 }
 

 void avpriv_solve_lls(LLSModel *m, double threshold, unsigned short min_order)

 {
     int i, j, k;

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

         }

     }
 }
 

 static double evaluate_lls(LLSModel *m, const double *param, int order)

 {

     int i;

     double out = 0;

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

 
     return out;
 }
 

 av_cold void avpriv_init_lls(LLSModel *m, int indep_count)

 {

     memset(m, 0, sizeof(LLSModel));

     m->indep_count = indep_count;
     m->update_lls = update_lls;
     m->evaluate_lls = evaluate_lls;

     if (ARCH_X86)
         ff_init_lls_x86(m);

 }
 

 #ifdef TEST
 
 #include <stdio.h>

 #include <limits.h>
 #include "lfg.h"

 int main(void)
 {

     LLSModel m;

     int i, order;

     AVLFG lfg;

     av_lfg_init(&lfg, 1);

     avpriv_init_lls(&m, 3);

     for (i = 0; i < 100; i++) {

         LOCAL_ALIGNED(32, double, var, [4]);

         double eval;

         var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2;
         var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
         var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
         var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;

         m.update_lls(&m, var);

         avpriv_solve_lls(&m, 0.001, 0);

         for (order = 0; order < 3; order++) {

             eval = m.evaluate_lls(&m, var + 1, order);

             printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\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