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lls.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 "lls.h"
34 
35 static void update_lls(LLSModel *m, double *var)
36 {
37  int i, j;
38 
39  for (i = 0; i <= m->indep_count; i++) {
40  for (j = i; j <= m->indep_count; j++) {
41  m->covariance[i][j] += var[i] * var[j];
42  }
43  }
44 }
45 
46 void avpriv_solve_lls(LLSModel *m, double threshold, unsigned short min_order)
47 {
48  int i, j, k;
49  double (*factor)[MAX_VARS_ALIGN] = (void *) &m->covariance[1][0];
50  double (*covar) [MAX_VARS_ALIGN] = (void *) &m->covariance[1][1];
51  double *covar_y = m->covariance[0];
52  int count = m->indep_count;
53 
54  for (i = 0; i < count; i++) {
55  for (j = i; j < count; j++) {
56  double sum = covar[i][j];
57 
58  for (k = i - 1; k >= 0; k--)
59  sum -= factor[i][k] * factor[j][k];
60 
61  if (i == j) {
62  if (sum < threshold)
63  sum = 1.0;
64  factor[i][i] = sqrt(sum);
65  } else {
66  factor[j][i] = sum / factor[i][i];
67  }
68  }
69  }
70 
71  for (i = 0; i < count; i++) {
72  double sum = covar_y[i + 1];
73 
74  for (k = i - 1; k >= 0; k--)
75  sum -= factor[i][k] * m->coeff[0][k];
76 
77  m->coeff[0][i] = sum / factor[i][i];
78  }
79 
80  for (j = count - 1; j >= min_order; j--) {
81  for (i = j; i >= 0; i--) {
82  double sum = m->coeff[0][i];
83 
84  for (k = i + 1; k <= j; k++)
85  sum -= factor[k][i] * m->coeff[j][k];
86 
87  m->coeff[j][i] = sum / factor[i][i];
88  }
89 
90  m->variance[j] = covar_y[0];
91 
92  for (i = 0; i <= j; i++) {
93  double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1];
94 
95  for (k = 0; k < i; k++)
96  sum += 2 * m->coeff[j][k] * covar[k][i];
97 
98  m->variance[j] += m->coeff[j][i] * sum;
99  }
100  }
101 }
102 
103 static double evaluate_lls(LLSModel *m, double *param, int order)
104 {
105  int i;
106  double out = 0;
107 
108  for (i = 0; i <= order; i++)
109  out += param[i] * m->coeff[order][i];
110 
111  return out;
112 }
113 
114 av_cold void avpriv_init_lls(LLSModel *m, int indep_count)
115 {
116  memset(m, 0, sizeof(LLSModel));
117  m->indep_count = indep_count;
118  m->update_lls = update_lls;
120  if (ARCH_X86)
121  ff_init_lls_x86(m);
122 }
123 
124 #if FF_API_LLS_PRIVATE
125 av_cold void av_init_lls(LLSModel *m, int indep_count)
126 {
127  avpriv_init_lls(m, indep_count);
128 }
129 void av_update_lls(LLSModel *m, double *param, double decay)
130 {
131  m->update_lls(m, param);
132 }
133 void av_solve_lls(LLSModel *m, double threshold, int min_order)
134 {
135  avpriv_solve_lls(m, threshold, min_order);
136 }
137 double av_evaluate_lls(LLSModel *m, double *param, int order)
138 {
139  return m->evaluate_lls(m, param, order);
140 }
141 #endif /* FF_API_LLS_PRIVATE */
142 
143 #ifdef TEST
144 
145 #include <stdio.h>
146 #include <limits.h>
147 #include "lfg.h"
148 
149 int main(void)
150 {
151  LLSModel m;
152  int i, order;
153  AVLFG lfg;
154 
155  av_lfg_init(&lfg, 1);
156  avpriv_init_lls(&m, 3);
157 
158  for (i = 0; i < 100; i++) {
159  LOCAL_ALIGNED(32, double, var, [4]);
160  double eval;
161 
162  var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2;
163  var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
164  var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
165  var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
166  m.update_lls(&m, var);
167  avpriv_solve_lls(&m, 0.001, 0);
168  for (order = 0; order < 3; order++) {
169  eval = m.evaluate_lls(&m, var + 1, order);
170  printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n",
171  var[0], order, eval, sqrt(m.variance[order] / (i + 1)),
172  m.coeff[order][0], m.coeff[order][1],
173  m.coeff[order][2]);
174  }
175  }
176  return 0;
177 }
178 
179 #endif