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lls1.c
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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 
37 av_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 
43 void 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 
55 void 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 
112 double 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
124 av_cold void av_init_lls(LLSModel *m, int indep_count)
125 {
126  avpriv_init_lls(m, indep_count);
127 }
128 void av_update_lls(LLSModel *m, double *param, double decay)
129 {
130  avpriv_update_lls(m, param, decay);
131 }
132 void av_solve_lls(LLSModel *m, double threshold, int min_order)
133 {
134  avpriv_solve_lls(m, threshold, min_order);
135 }
136 double 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 
150 int 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