/* * linear least squares model * * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at> * * This file is part of Libav. * * Libav is free software; you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public * License as published by the Free Software Foundation; either * version 2.1 of the License, or (at your option) any later version. * * Libav is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with Libav; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ /** * @file * linear least squares model */ #include <math.h> #include <string.h> #include "lls.h" void av_init_lls(LLSModel *m, int indep_count) { memset(m, 0, sizeof(LLSModel)); m->indep_count = indep_count; } void av_update_lls(LLSModel *m, double *var, double decay) { int i, j; for (i = 0; i <= m->indep_count; i++) { for (j = i; j <= m->indep_count; j++) { m->covariance[i][j] *= decay; m->covariance[i][j] += var[i] * var[j]; } } } void av_solve_lls(LLSModel *m, double threshold, int min_order) { int i, j, k; double (*factor)[MAX_VARS + 1] = (void *) &m->covariance[1][0]; double (*covar) [MAX_VARS + 1] = (void *) &m->covariance[1][1]; double *covar_y = m->covariance[0]; int count = m->indep_count; for (i = 0; i < count; i++) { for (j = i; j < count; j++) { double sum = covar[i][j]; for (k = i - 1; k >= 0; k--) sum -= factor[i][k] * factor[j][k]; if (i == j) { if (sum < threshold) sum = 1.0; factor[i][i] = sqrt(sum); } else { factor[j][i] = sum / factor[i][i]; } } } for (i = 0; i < count; i++) { double sum = covar_y[i + 1]; for (k = i - 1; k >= 0; k--) sum -= factor[i][k] * m->coeff[0][k]; m->coeff[0][i] = sum / factor[i][i]; } for (j = count - 1; j >= min_order; j--) { for (i = j; i >= 0; i--) { double sum = m->coeff[0][i]; for (k = i + 1; k <= j; k++) sum -= factor[k][i] * m->coeff[j][k]; m->coeff[j][i] = sum / factor[i][i]; } m->variance[j] = covar_y[0]; for (i = 0; i <= j; i++) { double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1]; for (k = 0; k < i; k++) sum += 2 * m->coeff[j][k] * covar[k][i]; m->variance[j] += m->coeff[j][i] * sum; } } } double av_evaluate_lls(LLSModel *m, double *param, int order) { int i; double out = 0; for (i = 0; i <= order; i++) out += param[i] * m->coeff[order][i]; return out; } #ifdef TEST #include <stdio.h> #include <limits.h> #include "lfg.h" int main(void) { LLSModel m; int i, order; AVLFG lfg; av_lfg_init(&lfg, 1); av_init_lls(&m, 3); for (i = 0; i < 100; i++) { double var[4]; double eval; var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2; var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5; av_update_lls(&m, var, 0.99); av_solve_lls(&m, 0.001, 0); for (order = 0; order < 3; order++) { eval = av_evaluate_lls(&m, var + 1, order); printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n", var[0], order, eval, sqrt(m.variance[order] / (i + 1)), m.coeff[order][0], m.coeff[order][1], m.coeff[order][2]); } } return 0; } #endif