679738530d012d4728fbfe2591120817a4644f4e
[libav.git] / libavutil / lls.c
1 /*
2 * linear least squares model
3 *
4 * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
5 *
6 * This file is part of Libav.
7 *
8 * Libav 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 * Libav 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 Libav; 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 "lls.h"
32
33 void av_init_lls(LLSModel *m, int indep_count){
34 memset(m, 0, sizeof(LLSModel));
35
36 m->indep_count= indep_count;
37 }
38
39 void av_update_lls(LLSModel *m, double *var, double decay){
40 int i,j;
41
42 for(i=0; i<=m->indep_count; i++){
43 for(j=i; j<=m->indep_count; j++){
44 m->covariance[i][j] *= decay;
45 m->covariance[i][j] += var[i]*var[j];
46 }
47 }
48 }
49
50 void av_solve_lls(LLSModel *m, double threshold, int min_order){
51 int i,j,k;
52 double (*factor)[MAX_VARS+1]= (void*)&m->covariance[1][0];
53 double (*covar )[MAX_VARS+1]= (void*)&m->covariance[1][1];
54 double *covar_y = m->covariance[0];
55 int count= m->indep_count;
56
57 for(i=0; i<count; i++){
58 for(j=i; j<count; j++){
59 double sum= covar[i][j];
60
61 for(k=i-1; k>=0; k--)
62 sum -= factor[i][k]*factor[j][k];
63
64 if(i==j){
65 if(sum < threshold)
66 sum= 1.0;
67 factor[i][i]= sqrt(sum);
68 }else
69 factor[j][i]= sum / factor[i][i];
70 }
71 }
72 for(i=0; i<count; i++){
73 double sum= covar_y[i+1];
74 for(k=i-1; k>=0; k--)
75 sum -= factor[i][k]*m->coeff[0][k];
76 m->coeff[0][i]= sum / factor[i][i];
77 }
78
79 for(j=count-1; j>=min_order; j--){
80 for(i=j; i>=0; i--){
81 double sum= m->coeff[0][i];
82 for(k=i+1; k<=j; k++)
83 sum -= factor[k][i]*m->coeff[j][k];
84 m->coeff[j][i]= sum / factor[i][i];
85 }
86
87 m->variance[j]= covar_y[0];
88 for(i=0; i<=j; i++){
89 double sum= m->coeff[j][i]*covar[i][i] - 2*covar_y[i+1];
90 for(k=0; k<i; k++)
91 sum += 2*m->coeff[j][k]*covar[k][i];
92 m->variance[j] += m->coeff[j][i]*sum;
93 }
94 }
95 }
96
97 double av_evaluate_lls(LLSModel *m, double *param, int order){
98 int i;
99 double out= 0;
100
101 for(i=0; i<=order; i++)
102 out+= param[i]*m->coeff[order][i];
103
104 return out;
105 }
106
107 #ifdef TEST
108
109 #include <stdlib.h>
110 #include <stdio.h>
111
112 int main(void){
113 LLSModel m;
114 int i, order;
115
116 av_init_lls(&m, 3);
117
118 for(i=0; i<100; i++){
119 double var[4];
120 double eval;
121 var[0] = (rand() / (double)RAND_MAX - 0.5)*2;
122 var[1] = var[0] + rand() / (double)RAND_MAX - 0.5;
123 var[2] = var[1] + rand() / (double)RAND_MAX - 0.5;
124 var[3] = var[2] + rand() / (double)RAND_MAX - 0.5;
125 av_update_lls(&m, var, 0.99);
126 av_solve_lls(&m, 0.001, 0);
127 for(order=0; order<3; order++){
128 eval= av_evaluate_lls(&m, var+1, order);
129 printf("real:%9f order:%d pred:%9f var:%f coeffs:%f %9f %9f\n",
130 var[0], order, eval, sqrt(m.variance[order] / (i+1)),
131 m.coeff[order][0], m.coeff[order][1], m.coeff[order][2]);
132 }
133 }
134 return 0;
135 }
136
137 #endif