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/* integration/qc25s.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_qaws_params
{
gsl_function *function;
double a;
double b;
gsl_integration_qaws_table *table;
};
static double fn_qaws (double t, void *params);
static double fn_qaws_L (double x, void *params);
static double fn_qaws_R (double x, void *params);
static void
compute_result (const double * r, const double * cheb12, const double * cheb24,
double * result12, double * result24);
static void
qc25s (gsl_function * f, double a, double b, double a1, double b1,
gsl_integration_qaws_table * t,
double *result, double *abserr, int *err_reliable);
static void
qc25s (gsl_function * f, double a, double b, double a1, double b1,
gsl_integration_qaws_table * t,
double *result, double *abserr, int *err_reliable)
{
gsl_function weighted_function;
struct fn_qaws_params fn_params;
fn_params.function = f;
fn_params.a = a;
fn_params.b = b;
fn_params.table = t;
weighted_function.params = &fn_params;
if (a1 == a && (t->alpha != 0.0 || t->mu != 0))
{
double cheb12[13], cheb24[25];
double factor = pow(0.5 * (b1 - a1), t->alpha + 1.0);
weighted_function.function = &fn_qaws_R;
gsl_integration_qcheb (&weighted_function, a1, b1, cheb12, cheb24);
if (t->mu == 0)
{
double res12 = 0, res24 = 0;
double u = factor;
compute_result (t->ri, cheb12, cheb24, &res12, &res24);
*result = u * res24;
*abserr = fabs(u * (res24 - res12));
}
else
{
double res12a = 0, res24a = 0;
double res12b = 0, res24b = 0;
double u = factor * log(b1 - a1);
double v = factor;
compute_result (t->ri, cheb12, cheb24, &res12a, &res24a);
compute_result (t->rg, cheb12, cheb24, &res12b, &res24b);
*result = u * res24a + v * res24b;
*abserr = fabs(u * (res24a - res12a)) + fabs(v * (res24b - res12b));
}
*err_reliable = 0;
return;
}
else if (b1 == b && (t->beta != 0.0 || t->nu != 0))
{
double cheb12[13], cheb24[25];
double factor = pow(0.5 * (b1 - a1), t->beta + 1.0);
weighted_function.function = &fn_qaws_L;
gsl_integration_qcheb (&weighted_function, a1, b1, cheb12, cheb24);
if (t->nu == 0)
{
double res12 = 0, res24 = 0;
double u = factor;
compute_result (t->rj, cheb12, cheb24, &res12, &res24);
*result = u * res24;
*abserr = fabs(u * (res24 - res12));
}
else
{
double res12a = 0, res24a = 0;
double res12b = 0, res24b = 0;
double u = factor * log(b1 - a1);
double v = factor;
compute_result (t->rj, cheb12, cheb24, &res12a, &res24a);
compute_result (t->rh, cheb12, cheb24, &res12b, &res24b);
*result = u * res24a + v * res24b;
*abserr = fabs(u * (res24a - res12a)) + fabs(v * (res24b - res12b));
}
*err_reliable = 0;
return;
}
else
{
double resabs, resasc;
weighted_function.function = &fn_qaws;
gsl_integration_qk15 (&weighted_function, a1, b1, result, abserr,
&resabs, &resasc);
if (*abserr == resasc)
{
*err_reliable = 0;
}
else
{
*err_reliable = 1;
}
return;
}
}
static double
fn_qaws (double x, void *params)
{
struct fn_qaws_params *p = (struct fn_qaws_params *) params;
gsl_function *f = p->function;
gsl_integration_qaws_table *t = p->table;
double factor = 1.0;
if (t->alpha != 0.0)
factor *= pow(x - p->a, t->alpha);
if (t->beta != 0.0)
factor *= pow(p->b - x, t->beta);
if (t->mu == 1)
factor *= log(x - p->a);
if (t->nu == 1)
factor *= log(p->b - x);
return factor * GSL_FN_EVAL (f, x);
}
static double
fn_qaws_L (double x, void *params)
{
struct fn_qaws_params *p = (struct fn_qaws_params *) params;
gsl_function *f = p->function;
gsl_integration_qaws_table *t = p->table;
double factor = 1.0;
if (t->alpha != 0.0)
factor *= pow(x - p->a, t->alpha);
if (t->mu == 1)
factor *= log(x - p->a);
return factor * GSL_FN_EVAL (f, x);
}
static double
fn_qaws_R (double x, void *params)
{
struct fn_qaws_params *p = (struct fn_qaws_params *) params;
gsl_function *f = p->function;
gsl_integration_qaws_table *t = p->table;
double factor = 1.0;
if (t->beta != 0.0)
factor *= pow(p->b - x, t->beta);
if (t->nu == 1)
factor *= log(p->b - x);
return factor * GSL_FN_EVAL (f, x);
}
static void
compute_result (const double * r, const double * cheb12, const double * cheb24,
double * result12, double * result24)
{
size_t i;
double res12 = 0;
double res24 = 0;
for (i = 0; i < 13; i++)
{
res12 += r[i] * cheb12[i];
}
for (i = 0; i < 25; i++)
{
res24 += r[i] * cheb24[i];
}
*result12 = res12;
*result24 = res24;
}
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