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