/* integration/qk41.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 <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[21] =   /* abscissae of the 41-point kronrod rule */

{

  0.998859031588277663838315576545863,

  0.993128599185094924786122388471320,

  0.981507877450250259193342994720217,

  0.963971927277913791267666131197277,

  0.940822633831754753519982722212443,

  0.912234428251325905867752441203298,

  0.878276811252281976077442995113078,

  0.839116971822218823394529061701521,

  0.795041428837551198350638833272788,

  0.746331906460150792614305070355642,

  0.693237656334751384805490711845932,

  0.636053680726515025452836696226286,

  0.575140446819710315342946036586425,

  0.510867001950827098004364050955251,

  0.443593175238725103199992213492640,

  0.373706088715419560672548177024927,

  0.301627868114913004320555356858592,

  0.227785851141645078080496195368575,

  0.152605465240922675505220241022678,

  0.076526521133497333754640409398838,

  0.000000000000000000000000000000000

};

/* xgk[1], xgk[3], ... abscissae of the 20-point gauss rule. 

   xgk[0], xgk[2], ... abscissae to optimally extend the 20-point gauss rule */

static const double wg[10] =    /* weights of the 20-point gauss rule */

{

  0.017614007139152118311861962351853,

  0.040601429800386941331039952274932,

  0.062672048334109063569506535187042,

  0.083276741576704748724758143222046,

  0.101930119817240435036750135480350,

  0.118194531961518417312377377711382,

  0.131688638449176626898494499748163,

  0.142096109318382051329298325067165,

  0.149172986472603746787828737001969,

  0.152753387130725850698084331955098

};

static const double wgk[21] =   /* weights of the 41-point kronrod rule */

{

  0.003073583718520531501218293246031,

  0.008600269855642942198661787950102,

  0.014626169256971252983787960308868,

  0.020388373461266523598010231432755,

  0.025882133604951158834505067096153,

  0.031287306777032798958543119323801,

  0.036600169758200798030557240707211,

  0.041668873327973686263788305936895,

  0.046434821867497674720231880926108,

  0.050944573923728691932707670050345,

  0.055195105348285994744832372419777,

  0.059111400880639572374967220648594,

  0.062653237554781168025870122174255,

  0.065834597133618422111563556969398,

  0.068648672928521619345623411885368,

  0.071054423553444068305790361723210,

  0.073030690332786667495189417658913,

  0.074582875400499188986581418362488,

  0.075704497684556674659542775376617,

  0.076377867672080736705502835038061,

  0.076600711917999656445049901530102

};

void

gsl_integration_qk41 (const gsl_function * f, double a, double b,

                      double *result, double *abserr,

                      double *resabs, double *resasc)

{

  double fv1[21], fv2[21];

  gsl_integration_qk (21, xgk, wg, wgk, fv1, fv2, f, a, b, result, abserr, resabs, resasc);

}