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 "attributes.h" 32#include "version.h" 33#include "lls1.h" 34 35#if FF_API_LLS1 36 37av_cold void avpriv_init_lls(LLSModel *m, int indep_count) 38{ 39 memset(m, 0, sizeof(LLSModel)); 40 m->indep_count = indep_count; 41} 42 43void avpriv_update_lls(LLSModel *m, double *var, double decay) 44{ 45 int i, j; 46 47 for (i = 0; i <= m->indep_count; i++) { 48 for (j = i; j <= m->indep_count; j++) { 49 m->covariance[i][j] *= decay; 50 m->covariance[i][j] += var[i] * var[j]; 51 } 52 } 53} 54 55void avpriv_solve_lls(LLSModel *m, double threshold, unsigned short min_order) 56{ 57 int i, j, k; 58 double (*factor)[MAX_VARS + 1] = (void *) &m->covariance[1][0]; 59 double (*covar) [MAX_VARS + 1] = (void *) &m->covariance[1][1]; 60 double *covar_y = m->covariance[0]; 61 int count = m->indep_count; 62 63 for (i = 0; i < count; i++) { 64 for (j = i; j < count; j++) { 65 double sum = covar[i][j]; 66 67 for (k = i - 1; k >= 0; k--) 68 sum -= factor[i][k] * factor[j][k]; 69 70 if (i == j) { 71 if (sum < threshold) 72 sum = 1.0; 73 factor[i][i] = sqrt(sum); 74 } else { 75 factor[j][i] = sum / factor[i][i]; 76 } 77 } 78 } 79 80 for (i = 0; i < count; i++) { 81 double sum = covar_y[i + 1]; 82 83 for (k = i - 1; k >= 0; k--) 84 sum -= factor[i][k] * m->coeff[0][k]; 85 86 m->coeff[0][i] = sum / factor[i][i]; 87 } 88 89 for (j = count - 1; j >= min_order; j--) { 90 for (i = j; i >= 0; i--) { 91 double sum = m->coeff[0][i]; 92 93 for (k = i + 1; k <= j; k++) 94 sum -= factor[k][i] * m->coeff[j][k]; 95 96 m->coeff[j][i] = sum / factor[i][i]; 97 } 98 99 m->variance[j] = covar_y[0]; 100 101 for (i = 0; i <= j; i++) { 102 double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1]; 103 104 for (k = 0; k < i; k++) 105 sum += 2 * m->coeff[j][k] * covar[k][i]; 106 107 m->variance[j] += m->coeff[j][i] * sum; 108 } 109 } 110} 111 112double avpriv_evaluate_lls(LLSModel *m, double *param, int order) 113{ 114 int i; 115 double out = 0; 116 117 for (i = 0; i <= order; i++) 118 out += param[i] * m->coeff[order][i]; 119 120 return out; 121} 122 123#if FF_API_LLS_PRIVATE 124av_cold void av_init_lls(LLSModel *m, int indep_count) 125{ 126 avpriv_init_lls(m, indep_count); 127} 128void av_update_lls(LLSModel *m, double *param, double decay) 129{ 130 avpriv_update_lls(m, param, decay); 131} 132void av_solve_lls(LLSModel *m, double threshold, int min_order) 133{ 134 avpriv_solve_lls(m, threshold, min_order); 135} 136double av_evaluate_lls(LLSModel *m, double *param, int order) 137{ 138 return avpriv_evaluate_lls(m, param, order); 139} 140#endif /* FF_API_LLS_PRIVATE */ 141 142#endif /* FF_API_LLS1 */ 143 144#ifdef TEST 145 146#include <stdio.h> 147#include <limits.h> 148#include "lfg.h" 149 150int main(void) 151{ 152 LLSModel m; 153 int i, order; 154 AVLFG lfg; 155 156 av_lfg_init(&lfg, 1); 157 avpriv_init_lls(&m, 3); 158 159 for (i = 0; i < 100; i++) { 160 double var[4]; 161 double eval; 162 163 var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2; 164 var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; 165 var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; 166 var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; 167 avpriv_update_lls(&m, var, 0.99); 168 avpriv_solve_lls(&m, 0.001, 0); 169 for (order = 0; order < 3; order++) { 170 eval = avpriv_evaluate_lls(&m, var + 1, order); 171 printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n", 172 var[0], order, eval, sqrt(m.variance[order] / (i + 1)), 173 m.coeff[order][0], m.coeff[order][1], 174 m.coeff[order][2]); 175 } 176 } 177 return 0; 178} 179 180#endif 181