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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 "internal.h"
33 #include "version.h"
34 #include "lls.h"
35 
36 static void update_lls(LLSModel *m, const double *var)
37 {
38  int i, j;
39 
40  for (i = 0; i <= m->indep_count; i++) {
41  for (j = i; j <= m->indep_count; j++) {
42  m->covariance[i][j] += var[i] * var[j];
43  }
44  }
45 }
46 
47 void avpriv_solve_lls(LLSModel *m, double threshold, unsigned short min_order)
48 {
49  int i, j, k;
50  double (*factor)[MAX_VARS_ALIGN] = (void *) &m->covariance[1][0];
51  double (*covar) [MAX_VARS_ALIGN] = (void *) &m->covariance[1][1];
52  double *covar_y = m->covariance[0];
53  int count = m->indep_count;
54 
55  for (i = 0; i < count; i++) {
56  for (j = i; j < count; j++) {
57  double sum = covar[i][j];
58 
59  for (k = 0; k <= i-1; k++)
60  sum -= factor[i][k] * factor[j][k];
61 
62  if (i == j) {
63  if (sum < threshold)
64  sum = 1.0;
65  factor[i][i] = sqrt(sum);
66  } else {
67  factor[j][i] = sum / factor[i][i];
68  }
69  }
70  }
71 
72  for (i = 0; i < count; i++) {
73  double sum = covar_y[i + 1];
74 
75  for (k = 0; k <= i-1; k++)
76  sum -= factor[i][k] * m->coeff[0][k];
77 
78  m->coeff[0][i] = sum / factor[i][i];
79  }
80 
81  for (j = count - 1; j >= min_order; j--) {
82  for (i = j; i >= 0; i--) {
83  double sum = m->coeff[0][i];
84 
85  for (k = i + 1; k <= j; k++)
86  sum -= factor[k][i] * m->coeff[j][k];
87 
88  m->coeff[j][i] = sum / factor[i][i];
89  }
90 
91  m->variance[j] = covar_y[0];
92 
93  for (i = 0; i <= j; i++) {
94  double sum = m->coeff[j][i] * covar[i][i] - 2 * covar_y[i + 1];
95 
96  for (k = 0; k < i; k++)
97  sum += 2 * m->coeff[j][k] * covar[k][i];
98 
99  m->variance[j] += m->coeff[j][i] * sum;
100  }
101  }
102 }
103 
104 static double evaluate_lls(LLSModel *m, const double *param, int order)
105 {
106  int i;
107  double out = 0;
108 
109  for (i = 0; i <= order; i++)
110  out += param[i] * m->coeff[order][i];
111 
112  return out;
113 }
114 
115 av_cold void avpriv_init_lls(LLSModel *m, int indep_count)
116 {
117  memset(m, 0, sizeof(LLSModel));
118  m->indep_count = indep_count;
119  m->update_lls = update_lls;
121  if (ARCH_X86)
122  ff_init_lls_x86(m);
123 }
124 
125 #ifdef TEST
126 
127 #include <stdio.h>
128 #include <limits.h>
129 #include "lfg.h"
130 
131 int main(void)
132 {
133  LLSModel m;
134  int i, order;
135  AVLFG lfg;
136 
137  av_lfg_init(&lfg, 1);
138  avpriv_init_lls(&m, 3);
139 
140  for (i = 0; i < 100; i++) {
141  LOCAL_ALIGNED(32, double, var, [4]);
142  double eval;
143 
144  var[0] = (av_lfg_get(&lfg) / (double) UINT_MAX - 0.5) * 2;
145  var[1] = var[0] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
146  var[2] = var[1] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
147  var[3] = var[2] + av_lfg_get(&lfg) / (double) UINT_MAX - 0.5;
148  m.update_lls(&m, var);
149  avpriv_solve_lls(&m, 0.001, 0);
150  for (order = 0; order < 3; order++) {
151  eval = m.evaluate_lls(&m, var + 1, order);
152  printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n",
153  var[0], order, eval, sqrt(m.variance[order] / (i + 1)),
154  m.coeff[order][0], m.coeff[order][1],
155  m.coeff[order][2]);
156  }
157  }
158  return 0;
159 }
160 
161 #endif
Definition: lfg.h:25
double covariance[(((32+1)+(4)-1)&~((4)-1))][(((32+1)+(4)-1)&~((4)-1))]
Definition: lls.h:39
Linear least squares model.
Definition: lls.h:38
static double evaluate_lls(LLSModel *m, const double *param, int order)
Definition: lls.c:104
double variance[MAX_VARS]
Definition: lls.h:41
Macro definitions for various function/variable attributes.
#define av_cold
Definition: attributes.h:82
unsigned m
Definition: audioconvert.c:187
#define MAX_VARS_ALIGN
Definition: lls.h:31
Libavutil version macros.
av_cold void avpriv_init_lls(LLSModel *m, int indep_count)
Definition: lls.c:115
GLsizei count
Definition: opengl_enc.c:109
common internal API header
FILE * out
Definition: movenc-test.c:54
void avpriv_solve_lls(LLSModel *m, double threshold, unsigned short min_order)
Definition: lls.c:47
double(* evaluate_lls)(struct LLSModel *m, const double *var, int order)
Inner product of var[] and the LPC coefs.
Definition: lls.h:57
static unsigned int av_lfg_get(AVLFG *c)
Get the next random unsigned 32-bit number using an ALFG.
Definition: lfg.h:38
static const int factor[16]
Definition: vf_pp7.c:75
av_cold void av_lfg_init(AVLFG *c, unsigned int seed)
Definition: lfg.c:30
double coeff[32][32]
Definition: lls.h:40
#define LOCAL_ALIGNED(a, t, v,...)
Definition: internal.h:110
void(* update_lls)(struct LLSModel *m, const double *var)
Take the outer-product of var[] with itself, and add to the covariance matrix.
Definition: lls.h:50
static void update_lls(LLSModel *m, const double *var)
Definition: lls.c:36
int indep_count
Definition: lls.h:42
int main(int argc, char **argv)
Definition: main.c:22
void ff_init_lls_x86(LLSModel *m)
Definition: lls_init.c:31
for(j=16;j >0;--j)