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 "lls.h"
32
33void av_init_lls(LLSModel *m, int indep_count){
34    memset(m, 0, sizeof(LLSModel));
35
36    m->indep_count= indep_count;
37}
38
39void 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
50void 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
97double 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
112int 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
138