/* multifit/convergence.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough

 * 

 * 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.

 */

#include <config.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_multifit_nlin.h>

#include <gsl/gsl_blas.h>

static double scaled_infnorm(const gsl_vector *x, const gsl_vector *g);

/*

gsl_multifit_fdfsolver_test()

  Convergence tests for nonlinear minimization

(1) |dx_i| <= xtol * (1 + |x_i|) for all i

(2) || g .* x ||_inf <= gtol ||f||^2

(3) ||f(x+dx) - f(x)|| <= ftol * max(||f(x)||, 1)

Inputs: s - fdfsolver

        xtol - tolerance for step size

        gtol - tolerance for gradient vector

        ftol - tolerance for residual vector

        info - (output)

          1 - stopped by small x step

          2 - stopped by small gradient

          3 - stopped by small residual vector change

*/

int

gsl_multifit_fdfsolver_test (const gsl_multifit_fdfsolver * s,

                             const double xtol, const double gtol,

                             const double ftol, int *info)

{

  int status;

  double gnorm, fnorm, phi;

  *info = 0;

  status = gsl_multifit_test_delta(s->dx, s->x, xtol*xtol, xtol);

  if (status == GSL_SUCCESS)

    {

      *info = 1;

      return GSL_SUCCESS;

    }

  /* compute gradient g = J^T f */

  (s->type->gradient) (s->state, s->g);

  /* compute gnorm = max_i( g_i * max(x_i, 1) ) */

  gnorm = scaled_infnorm(s->x, s->g);

  /* compute fnorm = ||f|| */

  fnorm = gsl_blas_dnrm2(s->f);

  phi = 0.5 * fnorm * fnorm;

  if (gnorm <= gtol * GSL_MAX(phi, 1.0))

    {

      *info = 2;

      return GSL_SUCCESS;

    }

#if 0

  if (dfnorm <= ftol * GSL_MAX(fnorm, 1.0))

    {

      *info = 3;

      return GSL_SUCCESS;

    }

#endif

  return GSL_CONTINUE;

} /* gsl_multifit_fdfsolver_test() */

int

gsl_multifit_test_delta (const gsl_vector * dx, const gsl_vector * x, 

                         double epsabs, double epsrel)

{

  size_t i;

  int ok = 1;

  const size_t n = x->size ;

  if (epsrel < 0.0)

    {

      GSL_ERROR ("relative tolerance is negative", GSL_EBADTOL);

    }

  for (i = 0 ; i < n ; i++)

    {

      double xi = gsl_vector_get(x,i);

      double dxi = gsl_vector_get(dx,i);

      double tolerance = epsabs + epsrel * fabs(xi)  ;

      if (fabs(dxi) < tolerance)

        {

          ok = 1;

        }

      else

        {

          ok = 0;

          break;

        }

    }

  if (ok)

    return GSL_SUCCESS ;

  return GSL_CONTINUE;

}

int

gsl_multifit_test_gradient (const gsl_vector * g, double epsabs)

{

  size_t i;

  double residual = 0;

  const size_t n = g->size;

  if (epsabs < 0.0)

    {

      GSL_ERROR ("absolute tolerance is negative", GSL_EBADTOL);

    }

  for (i = 0 ; i < n ; i++)

    {

      double gi = gsl_vector_get(g, i);

      residual += fabs(gi);

    }

  if (residual < epsabs)

    {

      return GSL_SUCCESS;

    }

  return GSL_CONTINUE ;

}

static double

scaled_infnorm(const gsl_vector *x, const gsl_vector *g)

{

  const size_t n = x->size;

  size_t i;

  double norm = 0.0;

  for (i = 0; i < n; ++i)

    {

      double xi = GSL_MAX(gsl_vector_get(x, i), 1.0);

      double gi = gsl_vector_get(g, i);

      double tmp = fabs(xi * gi);

      if (tmp > norm)

        norm = tmp;

    }

  return norm;

}