/* 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;  /* in original fortran 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);

}