| /* |
| * linear least squares model |
| * |
| * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at> |
| * |
| * This file is part of FFmpeg. |
| * |
| * FFmpeg 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. |
| * |
| * FFmpeg 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 FFmpeg; 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 |