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 "config.h"
32 #include "attributes.h"
33 #include "lls.h"
34
update_lls(LLSModel * m,const double * var)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
avpriv_solve_lls(LLSModel * m,double threshold,unsigned short min_order)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 = 0; k <= i-1; 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 = 0; k <= i-1; 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
evaluate_lls(LLSModel * m,const double * param,int order)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
avpriv_init_lls(LLSModel * m,int indep_count)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;
119 m->evaluate_lls = evaluate_lls;
120 #if ARCH_X86
121 ff_init_lls_x86(m);
122 #endif
123 }
124