1/* 2 * linear least squares model 3 * 4 * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at> 5 * 6 * This file is part of Libav. 7 * 8 * Libav 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 * Libav 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 Libav; 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{ 35 memset(m, 0, sizeof(LLSModel)); 36 m->indep_count = indep_count; 37} 38 39void av_update_lls(LLSModel *m, double *var, double decay) 40{ 41 int i, j; 42 43 for (i = 0; i <= m->indep_count; i++) { 44 for (j = i; j <= m->indep_count; j++) { 45 m->covariance[i][j] *= decay; 46 m->covariance[i][j] += var[i] * var[j]; 47 } 48 } 49} 50 51void av_solve_lls(LLSModel *m, double threshold, int min_order) 52{ 53 int i, j, k; 54 double (*factor)[MAX_VARS + 1] = (void *) &m->covariance[1][0]; 55 double (*covar) [MAX_VARS + 1] = (void *) &m->covariance[1][1]; 56 double *covar_y = m->covariance[0]; 57 int count = m->indep_count; 58 59 for (i = 0; i < count; i++) { 60 for (j = i; j < count; j++) { 61 double sum = covar[i][j]; 62 63 for (k = i - 1; k >= 0; k--) 64 sum -= factor[i][k] * factor[j][k]; 65 66 if (i == j) { 67 if (sum < threshold) 68 sum = 1.0; 69 factor[i][i] = sqrt(sum); 70 } else { 71 factor[j][i] = sum / factor[i][i]; 72 } 73 } 74 } 75 76 for (i = 0; i < count; i++) { 77 double sum = covar_y[i + 1]; 78 79 for (k = i - 1; k >= 0; k--) 80 sum -= factor[i][k] * m->coeff[0][k]; 81 82 m->coeff[0][i] = sum / factor[i][i]; 83 } 84 85 for (j = count - 1; j >= min_order; j--) { 86 for (i = j; i >= 0; i--) { 87 double sum = m->coeff[0][i]; 88 89 for (k = i + 1; k <= j; k++) 90 sum -= factor[k][i] * m->coeff[j][k]; 91 92 m->coeff[j][i] = sum / factor[i][i]; 93 } 94 95 m->variance[j] = covar_y[0]; 96 97 for (i = 0; i <= j; i++) { 98 double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1]; 99 100 for (k = 0; k < i; k++) 101 sum += 2 * m->coeff[j][k] * covar[k][i]; 102 103 m->variance[j] += m->coeff[j][i] * sum; 104 } 105 } 106} 107 108double av_evaluate_lls(LLSModel *m, double *param, int order) 109{ 110 int i; 111 double out = 0; 112 113 for (i = 0; i <= order; i++) 114 out += param[i] * m->coeff[order][i]; 115 116 return out; 117} 118 119#ifdef TEST 120 121#include <stdio.h> 122#include <limits.h> 123#include "lfg.h" 124 125int main(void) 126{ 127 LLSModel m; 128 int i, order; 129 AVLFG lfg; 130 131 av_lfg_init(&lfg, 1); 132 av_init_lls(&m, 3); 133 134 for (i = 0; i < 100; i++) { 135 double var[4]; 136 double eval; 137 138 var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2; 139 var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; 140 var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; 141 var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; 142 av_update_lls(&m, var, 0.99); 143 av_solve_lls(&m, 0.001, 0); 144 for (order = 0; order < 3; order++) { 145 eval = av_evaluate_lls(&m, var + 1, order); 146 printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n", 147 var[0], order, eval, sqrt(m.variance[order] / (i + 1)), 148 m.coeff[order][0], m.coeff[order][1], 149 m.coeff[order][2]); 150 } 151 } 152 return 0; 153} 154 155#endif 156