FFmpeg
 All Data Structures Files Functions Variables Typedefs Enumerations Enumerator Macros Groups Pages
lls.c
Go to the documentation of this file.
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 "lls.h"
32 
33 void av_init_lls(LLSModel *m, int indep_count)
34 {
35  memset(m, 0, sizeof(LLSModel));
36  m->indep_count = indep_count;
37 }
38 
39 void 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 
51 void 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 
108 double 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 
125 int 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