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/* integration/exponential.c
*
* Copyright (C) 2017 Konrad Griessinger, 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.
*/
/*
* The code in this module is based on IQPACK, specifically the LGPL
* implementation found in HERMITE_RULE:
* https://people.sc.fsu.edu/~jburkardt/c_src/hermite_rule/hermite_rule.html
*/
#include <stdio.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_sf_gamma.h>
static int
exponential_check(const size_t n, const gsl_integration_fixed_params * params)
{
(void) n;
if (fabs(params->b - params->a) <= GSL_DBL_EPSILON)
{
GSL_ERROR("|b - a| too small", GSL_EDOM);
}
else if (params->a >= params->b)
{
GSL_ERROR("lower integration limit must be smaller than upper limit", GSL_EDOM);
}
else if (params->alpha <= -1.0)
{
GSL_ERROR("alpha must be > -1", GSL_EDOM);
}
else
{
return GSL_SUCCESS;
}
}
static int
exponential_init(const size_t n, double * diag, double * subdiag, gsl_integration_fixed_params * params)
{
size_t i;
double a2i = params->alpha;
/* construct the diagonal and subdiagonal elements of Jacobi matrix */
for (i = 1; i <= n; i++)
{
diag[i-1] = 0.0;
a2i += 2.0;
subdiag[i-1] = (i + params->alpha*(i%2))/sqrt( a2i*a2i - 1.0 );
}
params->zemu = 2.0/(params->alpha + 1.0);
params->shft = 0.5*(params->b + params->a);
params->slp = 0.5*(params->b - params->a);
params->al = params->alpha;
params->be = 0.0;
return GSL_SUCCESS;
}
static const gsl_integration_fixed_type exponential_type =
{
exponential_check,
exponential_init
};
const gsl_integration_fixed_type *gsl_integration_fixed_exponential = &exponential_type;
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