/* multifit_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.

 *

 * 5 routines are needed to implement the update procedure:

 *

 * 1. accept - update parameter after a step has been accepted

 * 2. reject - update parameter after a step has been rejected

 * 3. free   - free workspace state

 */

#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_multifit_nlinear.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_blas.h>

#define LM_ONE_THIRD         (0.333333333333333)

static int nielsen_init(const gsl_matrix * J, 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 * J, const gsl_vector * diag,

             double * mu, long * nu)

{

  const double mu0 = 1.0e-3;

  const size_t p = J->size2;

  size_t j;

  double max = -1.0;

  *nu = 2;

  /* set mu = mu0 * max(diag(J~^T J~)), with J~ = J D^{-1} */

  for (j = 0; j < p; ++j)

    {

      gsl_vector_const_view v = gsl_matrix_const_column(J, j);

      double dj = gsl_vector_get(diag, j);

      double norm = gsl_blas_dnrm2(&v.vector) / dj;

      max = GSL_MAX(max, norm);

    }

  *mu = mu0 * max * 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;

}