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 "lls2.h" 34 35static void update_lls(LLSModel2 *m, double *var) 36{ 37 int i, j; 38 39 for (i = 0; i <= m->indep_count; i++) { 40 for (j = i; j <= m->indep_count; j++) { 41 m->covariance[i][j] += var[i] * var[j]; 42 } 43 } 44} 45 46void avpriv_solve_lls2(LLSModel2 *m, double threshold, unsigned short min_order) 47{ 48 int i, j, k; 49 double (*factor)[MAX_VARS_ALIGN] = (void *) &m->covariance[1][0]; 50 double (*covar) [MAX_VARS_ALIGN] = (void *) &m->covariance[1][1]; 51 double *covar_y = m->covariance[0]; 52 int count = m->indep_count; 53 54 for (i = 0; i < count; i++) { 55 for (j = i; j < count; j++) { 56 double sum = covar[i][j]; 57 58 for (k = i - 1; k >= 0; k--) 59 sum -= factor[i][k] * factor[j][k]; 60 61 if (i == j) { 62 if (sum < threshold) 63 sum = 1.0; 64 factor[i][i] = sqrt(sum); 65 } else { 66 factor[j][i] = sum / factor[i][i]; 67 } 68 } 69 } 70 71 for (i = 0; i < count; i++) { 72 double sum = covar_y[i + 1]; 73 74 for (k = i - 1; k >= 0; k--) 75 sum -= factor[i][k] * m->coeff[0][k]; 76 77 m->coeff[0][i] = sum / factor[i][i]; 78 } 79 80 for (j = count - 1; j >= min_order; j--) { 81 for (i = j; i >= 0; i--) { 82 double sum = m->coeff[0][i]; 83 84 for (k = i + 1; k <= j; k++) 85 sum -= factor[k][i] * m->coeff[j][k]; 86 87 m->coeff[j][i] = sum / factor[i][i]; 88 } 89 90 m->variance[j] = covar_y[0]; 91 92 for (i = 0; i <= j; i++) { 93 double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1]; 94 95 for (k = 0; k < i; k++) 96 sum += 2 * m->coeff[j][k] * covar[k][i]; 97 98 m->variance[j] += m->coeff[j][i] * sum; 99 } 100 } 101} 102 103static double evaluate_lls(LLSModel2 *m, double *param, int order) 104{ 105 int i; 106 double out = 0; 107 108 for (i = 0; i <= order; i++) 109 out += param[i] * m->coeff[order][i]; 110 111 return out; 112} 113 114av_cold void avpriv_init_lls2(LLSModel2 *m, int indep_count) 115{ 116 memset(m, 0, sizeof(LLSModel2)); 117 m->indep_count = indep_count; 118 m->update_lls = update_lls; 119 m->evaluate_lls = evaluate_lls; 120 if (ARCH_X86) 121 ff_init_lls_x86(m); 122} 123 124#ifdef TEST 125 126#include <stdio.h> 127#include <limits.h> 128#include "lfg.h" 129 130int main(void) 131{ 132 LLSModel2 m; 133 int i, order; 134 AVLFG lfg; 135 136 av_lfg_init(&lfg, 1); 137 avpriv_init_lls2(&m, 3); 138 139 for (i = 0; i < 100; i++) { 140 LOCAL_ALIGNED(32, double, var, [4]); 141 double eval; 142 143 var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2; 144 var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; 145 var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; 146 var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; 147 m.update_lls(&m, var); 148 avpriv_solve_lls2(&m, 0.001, 0); 149 for (order = 0; order < 3; order++) { 150 eval = m.evaluate_lls(&m, var + 1, order); 151 printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n", 152 var[0], order, eval, sqrt(m.variance[order] / (i + 1)), 153 m.coeff[order][0], m.coeff[order][1], 154 m.coeff[order][2]); 155 } 156 } 157 return 0; 158} 159 160#endif 161