2 * linear least squares model
4 * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
6 * This library is free software; you can redistribute it and/or
7 * modify it under the terms of the GNU Lesser General Public
8 * License as published by the Free Software Foundation; either
9 * version 2 of the License, or (at your option) any later version.
11 * This library is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 * Lesser General Public License for more details.
16 * You should have received a copy of the GNU Lesser General Public
17 * License along with this library; if not, write to the Free Software
18 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
23 * linear least squares model
32 #define av_log(a,b,...) printf(__VA_ARGS__)
35 void av_init_lls(LLSModel *m, int indep_count){
36 memset(m, 0, sizeof(LLSModel));
38 m->indep_count= indep_count;
41 void av_update_lls(LLSModel *m, double *var, double decay){
44 for(i=0; i<=m->indep_count; i++){
45 for(j=i; j<=m->indep_count; j++){
46 m->covariance[i][j] *= decay;
47 m->covariance[i][j] += var[i]*var[j];
52 void av_solve_lls(LLSModel *m, double threshold, int min_order){
54 double (*factor)[MAX_VARS+1]= &m->covariance[1][0];
55 double (*covar )[MAX_VARS+1]= &m->covariance[1][1];
56 double *covar_y = m->covariance[0];
57 int count= m->indep_count;
59 for(i=0; i<count; i++){
60 for(j=i; j<count; j++){
61 double sum= covar[i][j];
64 sum -= factor[i][k]*factor[j][k];
69 factor[i][i]= sqrt(sum);
71 factor[j][i]= sum / factor[i][i];
74 for(i=0; i<count; i++){
75 double sum= covar_y[i+1];
77 sum -= factor[i][k]*m->coeff[0][k];
78 m->coeff[0][i]= sum / factor[i][i];
81 for(j=count-1; j>=min_order; j--){
83 double sum= m->coeff[0][i];
85 sum -= factor[k][i]*m->coeff[j][k];
86 m->coeff[j][i]= sum / factor[i][i];
89 m->variance[j]= covar_y[0];
91 double sum= m->coeff[j][i]*covar[i][i] - 2*covar_y[i+1];
93 sum += 2*m->coeff[j][k]*covar[k][i];
94 m->variance[j] += m->coeff[j][i]*sum;
99 double av_evaluate_lls(LLSModel *m, double *param, int order){
103 for(i=0; i<=order; i++)
104 out+= param[i]*m->coeff[order][i];
120 for(i=0; i<100; i++){
122 double eval, variance;
124 var[1] = rand() / (double)RAND_MAX;
125 var[2] = rand() / (double)RAND_MAX;
126 var[3] = rand() / (double)RAND_MAX;
128 var[2]= var[1] + var[3]/2;
130 var[0] = var[1] + var[2] + var[3] + var[1]*var[2]/100;
132 var[0] = (rand() / (double)RAND_MAX - 0.5)*2;
133 var[1] = var[0] + rand() / (double)RAND_MAX - 0.5;
134 var[2] = var[1] + rand() / (double)RAND_MAX - 0.5;
135 var[3] = var[2] + rand() / (double)RAND_MAX - 0.5;
137 av_update_lls(&m, var, 0.99);
138 av_solve_lls(&m, 0.001, 0);
139 for(order=0; order<3; order++){
140 eval= av_evaluate_lls(&m, var+1, order);
141 av_log(NULL, AV_LOG_DEBUG, "real:%f order:%d pred:%f var:%f coeffs:%f %f %f\n",
142 var[0], order, eval, sqrt(m.variance[order] / (i+1)),
143 m.coeff[order][0], m.coeff[order][1], m.coeff[order][2]);