qk21.c

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/* integration/qk21.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., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

#include <config.h>
#include <gsl/gsl_integration.h>

/* Gauss quadrature weights and kronrod quadrature abscissae and
   weights as evaluated with 80 decimal digit arithmetic by
   L. W. Fullerton, Bell Labs, Nov. 1981. */

static const double xgk[11] =   /* abscissae of the 21-point kronrod rule */
{
  0.995657163025808080735527280689003,
  0.973906528517171720077964012084452,
  0.930157491355708226001207180059508,
  0.865063366688984510732096688423493,
  0.780817726586416897063717578345042,
  0.679409568299024406234327365114874,
  0.562757134668604683339000099272694,
  0.433395394129247190799265943165784,
  0.294392862701460198131126603103866,
  0.148874338981631210884826001129720,
  0.000000000000000000000000000000000
};

/* xgk[1], xgk[3], ... abscissae of the 10-point gauss rule. 
   xgk[0], xgk[2], ... abscissae to optimally extend the 10-point gauss rule */

static const double wg[5] =     /* weights of the 10-point gauss rule */
{
  0.066671344308688137593568809893332,
  0.149451349150580593145776339657697,
  0.219086362515982043995534934228163,
  0.269266719309996355091226921569469,
  0.295524224714752870173892994651338
};

static const double wgk[11] =   /* weights of the 21-point kronrod rule */
{
  0.011694638867371874278064396062192,
  0.032558162307964727478818972459390,
  0.054755896574351996031381300244580,
  0.075039674810919952767043140916190,
  0.093125454583697605535065465083366,
  0.109387158802297641899210590325805,
  0.123491976262065851077958109831074,
  0.134709217311473325928054001771707,
  0.142775938577060080797094273138717,
  0.147739104901338491374841515972068,
  0.149445554002916905664936468389821
};


void
gsl_integration_qk21 (const gsl_function * f, double a, double b,
                      double *result, double *abserr,
                      double *resabs, double *resasc)
{
  double fv1[11], fv2[11];
  gsl_integration_qk (11, xgk, wg, wgk, fv1, fv2, f, a, b, result, abserr, resabs, resasc);
}