1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
|
/*
* 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 "attributes.h"
#include "version.h"
#include "lls.h"
av_cold void avpriv_init_lls(LLSModel *m, int indep_count)
{
memset(m, 0, sizeof(LLSModel));
m->indep_count = indep_count;
}
void avpriv_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 avpriv_solve_lls(LLSModel *m, double threshold, unsigned short 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 avpriv_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;
}
#if FF_API_LLS_PRIVATE
av_cold void av_init_lls(LLSModel *m, int indep_count)
{
avpriv_init_lls(m, indep_count);
}
void av_update_lls(LLSModel *m, double *param, double decay)
{
avpriv_update_lls(m, param, decay);
}
void av_solve_lls(LLSModel *m, double threshold, int min_order)
{
avpriv_solve_lls(m, threshold, min_order);
}
double av_evaluate_lls(LLSModel *m, double *param, int order)
{
return avpriv_evaluate_lls(m, param, order);
}
#endif /* FF_API_LLS_PRIVATE */
#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);
avpriv_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;
avpriv_update_lls(&m, var, 0.99);
avpriv_solve_lls(&m, 0.001, 0);
for (order = 0; order < 3; order++) {
eval = avpriv_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
|
