/* multilarge_nlinear/nielsen.c
*
* Copyright (C) 2016 Patrick Alken
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/*
* This module contains routines for updating the Levenberg-Marquardt
* damping parameter on each iteration using Nielsen's method:
*
* [1] H. B. Nielsen, K. Madsen, Introduction to Optimization and
* Data Fitting, Informatics and Mathematical Modeling,
* Technical University of Denmark (DTU), 2010.
*
* 3 routines are needed to implement the update procedure:
*
* 1. init - initialize parameter prior to iteration
* 2. accept - update parameter after a step has been accepted
* 3. reject - update parameter after a step has been rejected
*/
#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_blas.h>
#define LM_ONE_THIRD (0.333333333333333)
static int nielsen_init(const gsl_matrix * JTJ, const gsl_vector * diag,
double * mu, long * nu);
static int nielsen_accept(const double rho, double * mu, long * nu);
static int nielsen_reject(double * mu, long * nu);
static int
nielsen_init(const gsl_matrix * JTJ, const gsl_vector * diag,
double * mu, long * nu)
{
const double mu0 = 1.0e-3;
size_t i;
double max = -1.0;
*nu = 2;
if (JTJ == NULL)
{
/* not using cholesky solver */
*mu = mu0;
return GSL_SUCCESS;
}
/* set mu = mu0 * max(diag(J~^T J~)), with J~ = J D^{-1} */
for (i = 0; i < JTJ->size1; ++i)
{
double JTJi = gsl_matrix_get(JTJ, i, i);
double di = gsl_vector_get(diag, i);
double val = JTJi / (di * di);
max = GSL_MAX(max, val);
}
*mu = mu0 * max;
return GSL_SUCCESS;
}
static int
nielsen_accept(const double rho, double * mu, long * nu)
{
double b;
/* reset nu */
*nu = 2;
b = 2.0 * rho - 1.0;
b = 1.0 - b*b*b;
*mu *= GSL_MAX(LM_ONE_THIRD, b);
return GSL_SUCCESS;
}
static int
nielsen_reject(double * mu, long * nu)
{
*mu *= (double) *nu;
/* nu := 2*nu */
*nu <<= 1;
return GSL_SUCCESS;
}