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