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 25 * linear least squares model 26 */ 27 28#include <math.h> 29#include <string.h> 30 31#include "lls.h" 32 33void av_init_lls(LLSModel *m, int indep_count){ 34 memset(m, 0, sizeof(LLSModel)); 35 36 m->indep_count= indep_count; 37} 38 39void 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 50void 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 97double 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 112int 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 var[0] = (rand() / (double)RAND_MAX - 0.5)*2; 122 var[1] = var[0] + rand() / (double)RAND_MAX - 0.5; 123 var[2] = var[1] + rand() / (double)RAND_MAX - 0.5; 124 var[3] = var[2] + rand() / (double)RAND_MAX - 0.5; 125 av_update_lls(&m, var, 0.99); 126 av_solve_lls(&m, 0.001, 0); 127 for(order=0; order<3; order++){ 128 eval= av_evaluate_lls(&m, var+1, order); 129 printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n", 130 var[0], order, eval, sqrt(m.variance[order] / (i+1)), 131 m.coeff[order][0], m.coeff[order][1], m.coeff[order][2]); 132 } 133 } 134 return 0; 135} 136 137#endif 138