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
update_lls(LLSModel * m,const double * var)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
avpriv_solve_lls(LLSModel * m,double threshold,unsigned short min_order)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
evaluate_lls(LLSModel * m,const double * param,int order)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
avpriv_init_lls(LLSModel * m,int indep_count)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;
120 m->evaluate_lls = evaluate_lls;
121 if (ARCH_X86)
122 ff_init_lls_x86(m);
123 }
124