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148 lines
4.0 KiB
C
148 lines
4.0 KiB
C
/*
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* linear least squares model
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*
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* Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
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*
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* This file is part of FFmpeg.
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*
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* FFmpeg is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* FFmpeg is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with FFmpeg; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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/**
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* @file lls.c
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* linear least squares model
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*/
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#include <math.h>
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#include <string.h>
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#include "lls.h"
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void av_init_lls(LLSModel *m, int indep_count){
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memset(m, 0, sizeof(LLSModel));
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m->indep_count= indep_count;
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}
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void av_update_lls(LLSModel *m, double *var, double decay){
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int i,j;
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for(i=0; i<=m->indep_count; i++){
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for(j=i; j<=m->indep_count; j++){
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m->covariance[i][j] *= decay;
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m->covariance[i][j] += var[i]*var[j];
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}
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}
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}
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void av_solve_lls(LLSModel *m, double threshold, int min_order){
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int i,j,k;
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double (*factor)[MAX_VARS+1]= (void*)&m->covariance[1][0];
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double (*covar )[MAX_VARS+1]= (void*)&m->covariance[1][1];
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double *covar_y = m->covariance[0];
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int count= m->indep_count;
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for(i=0; i<count; i++){
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for(j=i; j<count; j++){
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double sum= covar[i][j];
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for(k=i-1; k>=0; k--)
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sum -= factor[i][k]*factor[j][k];
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if(i==j){
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if(sum < threshold)
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sum= 1.0;
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factor[i][i]= sqrt(sum);
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}else
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factor[j][i]= sum / factor[i][i];
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}
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}
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for(i=0; i<count; i++){
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double sum= covar_y[i+1];
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for(k=i-1; k>=0; k--)
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sum -= factor[i][k]*m->coeff[0][k];
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m->coeff[0][i]= sum / factor[i][i];
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}
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for(j=count-1; j>=min_order; j--){
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for(i=j; i>=0; i--){
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double sum= m->coeff[0][i];
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for(k=i+1; k<=j; k++)
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sum -= factor[k][i]*m->coeff[j][k];
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m->coeff[j][i]= sum / factor[i][i];
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}
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m->variance[j]= covar_y[0];
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for(i=0; i<=j; i++){
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double sum= m->coeff[j][i]*covar[i][i] - 2*covar_y[i+1];
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for(k=0; k<i; k++)
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sum += 2*m->coeff[j][k]*covar[k][i];
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m->variance[j] += m->coeff[j][i]*sum;
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}
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}
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}
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double av_evaluate_lls(LLSModel *m, double *param, int order){
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int i;
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double out= 0;
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for(i=0; i<=order; i++)
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out+= param[i]*m->coeff[order][i];
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return out;
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}
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#ifdef TEST
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#include <stdlib.h>
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#include <stdio.h>
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int main(void){
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LLSModel m;
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int i, order;
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av_init_lls(&m, 3);
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for(i=0; i<100; i++){
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double var[4];
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double eval;
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#if 0
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var[1] = rand() / (double)RAND_MAX;
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var[2] = rand() / (double)RAND_MAX;
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var[3] = rand() / (double)RAND_MAX;
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var[2]= var[1] + var[3]/2;
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var[0] = var[1] + var[2] + var[3] + var[1]*var[2]/100;
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#else
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var[0] = (rand() / (double)RAND_MAX - 0.5)*2;
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var[1] = var[0] + rand() / (double)RAND_MAX - 0.5;
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var[2] = var[1] + rand() / (double)RAND_MAX - 0.5;
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var[3] = var[2] + rand() / (double)RAND_MAX - 0.5;
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#endif
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av_update_lls(&m, var, 0.99);
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av_solve_lls(&m, 0.001, 0);
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for(order=0; order<3; order++){
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eval= av_evaluate_lls(&m, var+1, order);
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printf("real:%f order:%d pred:%f var:%f coeffs:%f %f %f\n",
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var[0], order, eval, sqrt(m.variance[order] / (i+1)),
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m.coeff[order][0], m.coeff[order][1], m.coeff[order][2]);
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}
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}
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return 0;
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}
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#endif
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