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- /* integration/qc25f.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.
- */
- struct fn_fourier_params
- {
- gsl_function *function;
- double omega;
- };
- static double fn_sin (double t, void *params);
- static double fn_cos (double t, void *params);
- static void
- qc25f (gsl_function * f, double a, double b,
- gsl_integration_qawo_table * wf, size_t level,
- double *result, double *abserr, double *resabs, double *resasc);
- static void
- qc25f (gsl_function * f, double a, double b,
- gsl_integration_qawo_table * wf, size_t level,
- double *result, double *abserr, double *resabs, double *resasc)
- {
- const double center = 0.5 * (a + b);
- const double half_length = 0.5 * (b - a);
- const double omega = wf->omega ;
-
- const double par = omega * half_length;
- if (fabs (par) < 2)
- {
- gsl_function weighted_function;
- struct fn_fourier_params fn_params;
- fn_params.function = f;
- fn_params.omega = omega;
- if (wf->sine == GSL_INTEG_SINE)
- {
- weighted_function.function = &fn_sin;
- }
- else
- {
- weighted_function.function = &fn_cos;
- }
- weighted_function.params = &fn_params;
- gsl_integration_qk15 (&weighted_function, a, b, result, abserr,
- resabs, resasc);
-
- return;
- }
- else
- {
- double *moment;
- double cheb12[13], cheb24[25];
- double result_abs, res12_cos, res12_sin, res24_cos, res24_sin;
- double est_cos, est_sin;
- double c, s;
- size_t i;
- gsl_integration_qcheb (f, a, b, cheb12, cheb24);
- if (level >= wf->n)
- {
- /* table overflow should not happen, check before calling */
- GSL_ERROR_VOID("table overflow in internal function", GSL_ESANITY);
- }
- /* obtain moments from the table */
- moment = wf->chebmo + 25 * level;
- res12_cos = cheb12[12] * moment[12];
- res12_sin = 0 ;
- for (i = 0; i < 6; i++)
- {
- size_t k = 10 - 2 * i;
- res12_cos += cheb12[k] * moment[k];
- res12_sin += cheb12[k + 1] * moment[k + 1];
- }
- res24_cos = cheb24[24] * moment[24];
- res24_sin = 0 ;
- result_abs = fabs(cheb24[24]) ;
- for (i = 0; i < 12; i++)
- {
- size_t k = 22 - 2 * i;
- res24_cos += cheb24[k] * moment[k];
- res24_sin += cheb24[k + 1] * moment[k + 1];
- result_abs += fabs(cheb24[k]) + fabs(cheb24[k+1]);
- }
- est_cos = fabs(res24_cos - res12_cos);
- est_sin = fabs(res24_sin - res12_sin);
- c = half_length * cos(center * omega);
- s = half_length * sin(center * omega);
- if (wf->sine == GSL_INTEG_SINE)
- {
- *result = c * res24_sin + s * res24_cos;
- *abserr = fabs(c * est_sin) + fabs(s * est_cos);
- }
- else
- {
- *result = c * res24_cos - s * res24_sin;
- *abserr = fabs(c * est_cos) + fabs(s * est_sin);
- }
-
- *resabs = result_abs * half_length;
- *resasc = GSL_DBL_MAX;
- return;
- }
- }
- static double
- fn_sin (double x, void *params)
- {
- struct fn_fourier_params *p = (struct fn_fourier_params *) params;
- gsl_function *f = p->function;
- double w = p->omega;
- double wx = w * x;
- double sinwx = sin(wx) ;
- return GSL_FN_EVAL (f, x) * sinwx;
- }
- static double
- fn_cos (double x, void *params)
- {
- struct fn_fourier_params *p = (struct fn_fourier_params *) params;
- gsl_function *f = p->function;
- double w = p->omega;
- double wx = w * x;
- double coswx = cos(wx) ;
- return GSL_FN_EVAL (f, x) * coswx ;
- }
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