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/* integration/qc25c.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 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 2 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.
*/
struct fn_cauchy_params
{
gsl_function *function;
double singularity;
};
static double fn_cauchy (double t, void *params);
static void compute_moments (double cc, double *moment);
static void
qc25c (gsl_function * f, double a, double b, double c,
double *result, double *abserr, int *err_reliable);
static void
qc25c (gsl_function * f, double a, double b, double c,
double *result, double *abserr, int *err_reliable)
{
double cc = (2 * c - b - a) / (b - a);
if (fabs (cc) > 1.1)
{
double resabs, resasc;
gsl_function weighted_function;
struct fn_cauchy_params fn_params;
fn_params.function = f;
fn_params.singularity = c;
weighted_function.function = &fn_cauchy;
weighted_function.params = &fn_params;
gsl_integration_qk15 (&weighted_function, a, b, result, abserr,
&resabs, &resasc);
if (*abserr == resasc)
{
*err_reliable = 0;
}
else
{
*err_reliable = 1;
}
return;
}
else
{
double cheb12[13], cheb24[25], moment[25];
double res12 = 0, res24 = 0;
size_t i;
gsl_integration_qcheb (f, a, b, cheb12, cheb24);
compute_moments (cc, moment);
for (i = 0; i < 13; i++)
{
res12 += cheb12[i] * moment[i];
}
for (i = 0; i < 25; i++)
{
res24 += cheb24[i] * moment[i];
}
*result = res24;
*abserr = fabs(res24 - res12) ;
*err_reliable = 0;
return;
}
}
static double
fn_cauchy (double x, void *params)
{
struct fn_cauchy_params *p = (struct fn_cauchy_params *) params;
gsl_function *f = p->function;
double c = p->singularity;
return GSL_FN_EVAL (f, x) / (x - c);
}
static void
compute_moments (double cc, double *moment)
{
size_t k;
double a0 = log (fabs ((1.0 - cc) / (1.0 + cc)));
double a1 = 2 + a0 * cc;
moment[0] = a0;
moment[1] = a1;
for (k = 2; k < 25; k++)
{
double a2;
if ((k % 2) == 0)
{
a2 = 2.0 * cc * a1 - a0;
}
else
{
const double km1 = k - 1.0;
a2 = 2.0 * cc * a1 - a0 - 4.0 / (km1 * km1 - 1.0);
}
moment[k] = a2;
a0 = a1;
a1 = a2;
}
}
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