/* multifit_nlinear/convergence.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
* Copyright (C) 2015 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.
*/
#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_multifit_nlinear.h>
#include <gsl/gsl_blas.h>
static int test_delta (const gsl_vector * dx, const gsl_vector * x,
double epsabs, double epsrel);
static double scaled_infnorm(const gsl_vector *x, const gsl_vector *g);
/*
gsl_multifit_nlinear_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: 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
w - workspace
*/
int
gsl_multifit_nlinear_test (const double xtol, const double gtol,
const double ftol, int *info,
const gsl_multifit_nlinear_workspace * w)
{
int status;
double gnorm, fnorm, phi;
*info = 0;
status = test_delta(w->dx, w->x, xtol*xtol, xtol);
if (status == GSL_SUCCESS)
{
*info = 1;
return GSL_SUCCESS;
}
/* compute gnorm = max_i( g_i * max(x_i, 1) ) */
gnorm = scaled_infnorm(w->x, w->g);
/* compute fnorm = ||f|| */
fnorm = gsl_blas_dnrm2(w->f);
phi = 0.5 * fnorm * fnorm;
if (gnorm <= gtol * GSL_MAX(phi, 1.0))
{
*info = 2;
return GSL_SUCCESS;
}
#if 0 /* XXX */
if (dfnorm <= ftol * GSL_MAX(fnorm, 1.0))
{
*info = 3;
return GSL_SUCCESS;
}
#else
(void)ftol;
#endif
return GSL_CONTINUE;
}
static int
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;
}
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;
}