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- /* integration/qk.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.
- */
- #include "gsl__config.h"
- #include <float.h>
- #include <math.h>
- #include "gsl_integration.h"
- #include "gsl_integration__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);
- }
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