| /* integration/qk.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. |
| */ |
| |
| #include <config.h> |
| #include <float.h> |
| #include <math.h> |
| #include <gsl/gsl_integration.h> |
| #include "err.c" |
| |
| void |
| gsl_integration_qk (const int n, |
| const double xgk[], const double wg[], const double wgk[], |
| double fv1[], double fv2[], |
| const gsl_function * f, double a, double b, |
| 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 abs_half_length = fabs (half_length); |
| const double f_center = GSL_FN_EVAL (f, center); |
| |
| double result_gauss = 0; |
| double result_kronrod = f_center * wgk[n - 1]; |
| |
| double result_abs = fabs (result_kronrod); |
| double result_asc = 0; |
| double mean = 0, err = 0; |
| |
| int j; |
| |
| if (n % 2 == 0) |
| { |
| result_gauss = f_center * wg[n / 2 - 1]; |
| } |
| |
| for (j = 0; j < (n - 1) / 2; j++) |
| { |
| const int jtw = j * 2 + 1; /* j=1,2,3 jtw=2,4,6 */ |
| const double abscissa = half_length * xgk[jtw]; |
| const double fval1 = GSL_FN_EVAL (f, center - abscissa); |
| const double fval2 = GSL_FN_EVAL (f, center + abscissa); |
| const double fsum = fval1 + fval2; |
| fv1[jtw] = fval1; |
| fv2[jtw] = fval2; |
| result_gauss += wg[j] * fsum; |
| result_kronrod += wgk[jtw] * fsum; |
| result_abs += wgk[jtw] * (fabs (fval1) + fabs (fval2)); |
| } |
| |
| for (j = 0; j < n / 2; j++) |
| { |
| int jtwm1 = j * 2; |
| const double abscissa = half_length * xgk[jtwm1]; |
| const double fval1 = GSL_FN_EVAL (f, center - abscissa); |
| const double fval2 = GSL_FN_EVAL (f, center + abscissa); |
| fv1[jtwm1] = fval1; |
| fv2[jtwm1] = fval2; |
| result_kronrod += wgk[jtwm1] * (fval1 + fval2); |
| result_abs += wgk[jtwm1] * (fabs (fval1) + fabs (fval2)); |
| }; |
| |
| mean = result_kronrod * 0.5; |
| |
| result_asc = wgk[n - 1] * fabs (f_center - mean); |
| |
| for (j = 0; j < n - 1; j++) |
| { |
| result_asc += wgk[j] * (fabs (fv1[j] - mean) + fabs (fv2[j] - mean)); |
| } |
| |
| /* scale by the width of the integration region */ |
| |
| err = (result_kronrod - result_gauss) * half_length; |
| |
| result_kronrod *= half_length; |
| result_abs *= abs_half_length; |
| result_asc *= abs_half_length; |
| |
| *result = result_kronrod; |
| *resabs = result_abs; |
| *resasc = result_asc; |
| *abserr = rescale_error (err, result_abs, result_asc); |
| |
| } |