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qk.c

/* 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 <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);

}

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