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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, const 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, const 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 #ifdef TEST
125 
126 #include <stdio.h>
127 #include <limits.h>
128 #include "lfg.h"
129 
130 int main(void)
131 {
132  LLSModel m;
133  int i, order;
134  AVLFG lfg;
135 
136  av_lfg_init(&lfg, 1);
137  avpriv_init_lls(&m, 3);
138 
139  for (i = 0; i < 100; i++) {
140  LOCAL_ALIGNED(32, double, var, [4]);
141  double eval;
142 
143  var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2;
144  var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
145  var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
146  var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
147  m.update_lls(&m, var);
148  avpriv_solve_lls(&m, 0.001, 0);
149  for (order = 0; order < 3; order++) {
150  eval = m.evaluate_lls(&m, var + 1, order);
151  printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n",
152  var[0], order, eval, sqrt(m.variance[order] / (i + 1)),
153  m.coeff[order][0], m.coeff[order][1],
154  m.coeff[order][2]);
155  }
156  }
157  return 0;
158 }
159 
160 #endif