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