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/* multifit_nlinear/nielsen.c
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*
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* Copyright (C) 2016 Patrick Alken
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/*
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* This module contains routines for updating the Levenberg-Marquardt
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* damping parameter on each iteration using Nielsen's method:
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*
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* [1] H. B. Nielsen, K. Madsen, Introduction to Optimization and
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* Data Fitting, Informatics and Mathematical Modeling,
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* Technical University of Denmark (DTU), 2010.
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*
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* 5 routines are needed to implement the update procedure:
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*
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* 1. accept - update parameter after a step has been accepted
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* 2. reject - update parameter after a step has been rejected
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* 3. free - free workspace state
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*/
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#include <config.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_vector.h>
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#include <gsl/gsl_matrix.h>
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#include <gsl/gsl_linalg.h>
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#include <gsl/gsl_multifit_nlinear.h>
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#include <gsl/gsl_errno.h>
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#include <gsl/gsl_blas.h>
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#define LM_ONE_THIRD (0.333333333333333)
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static int nielsen_init(const gsl_matrix * J, const gsl_vector * diag,
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double * mu, long * nu);
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static int nielsen_accept(const double rho, double * mu, long * nu);
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static int nielsen_reject(double * mu, long * nu);
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static int
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nielsen_init(const gsl_matrix * J, const gsl_vector * diag,
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double * mu, long * nu)
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{
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const double mu0 = 1.0e-3;
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const size_t p = J->size2;
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size_t j;
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double max = -1.0;
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*nu = 2;
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/* set mu = mu0 * max(diag(J~^T J~)), with J~ = J D^{-1} */
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for (j = 0; j < p; ++j)
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{
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gsl_vector_const_view v = gsl_matrix_const_column(J, j);
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double dj = gsl_vector_get(diag, j);
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double norm = gsl_blas_dnrm2(&v.vector) / dj;
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max = GSL_MAX(max, norm);
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}
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*mu = mu0 * max * max;
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return GSL_SUCCESS;
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}
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static int
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nielsen_accept(const double rho, double * mu, long * nu)
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{
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double b;
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/* reset nu */
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*nu = 2;
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b = 2.0 * rho - 1.0;
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b = 1.0 - b*b*b;
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*mu *= GSL_MAX(LM_ONE_THIRD, b);
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return GSL_SUCCESS;
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}
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static int
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nielsen_reject(double * mu, long * nu)
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{
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*mu *= (double) *nu;
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/* nu := 2*nu */
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*nu <<= 1;
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return GSL_SUCCESS;
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}
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