qk61.c

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/* integration/qk61.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[31] =   /* abscissae of the 61-point kronrod rule */
{
  0.999484410050490637571325895705811,
  0.996893484074649540271630050918695,
  0.991630996870404594858628366109486,
  0.983668123279747209970032581605663,
  0.973116322501126268374693868423707,
  0.960021864968307512216871025581798,
  0.944374444748559979415831324037439,
  0.926200047429274325879324277080474,
  0.905573307699907798546522558925958,
  0.882560535792052681543116462530226,
  0.857205233546061098958658510658944,
  0.829565762382768397442898119732502,
  0.799727835821839083013668942322683,
  0.767777432104826194917977340974503,
  0.733790062453226804726171131369528,
  0.697850494793315796932292388026640,
  0.660061064126626961370053668149271,
  0.620526182989242861140477556431189,
  0.579345235826361691756024932172540,
  0.536624148142019899264169793311073,
  0.492480467861778574993693061207709,
  0.447033769538089176780609900322854,
  0.400401254830394392535476211542661,
  0.352704725530878113471037207089374,
  0.304073202273625077372677107199257,
  0.254636926167889846439805129817805,
  0.204525116682309891438957671002025,
  0.153869913608583546963794672743256,
  0.102806937966737030147096751318001,
  0.051471842555317695833025213166723,
  0.000000000000000000000000000000000
};

/* xgk[1], xgk[3], ... abscissae of the 30-point gauss rule. 
   xgk[0], xgk[2], ... abscissae to optimally extend the 30-point gauss rule */

static const double wg[15] =    /* weights of the 30-point gauss rule */
{
  0.007968192496166605615465883474674,
  0.018466468311090959142302131912047,
  0.028784707883323369349719179611292,
  0.038799192569627049596801936446348,
  0.048402672830594052902938140422808,
  0.057493156217619066481721689402056,
  0.065974229882180495128128515115962,
  0.073755974737705206268243850022191,
  0.080755895229420215354694938460530,
  0.086899787201082979802387530715126,
  0.092122522237786128717632707087619,
  0.096368737174644259639468626351810,
  0.099593420586795267062780282103569,
  0.101762389748405504596428952168554,
  0.102852652893558840341285636705415
};

static const double wgk[31] =   /* weights of the 61-point kronrod rule */
{
  0.001389013698677007624551591226760,
  0.003890461127099884051267201844516,
  0.006630703915931292173319826369750,
  0.009273279659517763428441146892024,
  0.011823015253496341742232898853251,
  0.014369729507045804812451432443580,
  0.016920889189053272627572289420322,
  0.019414141193942381173408951050128,
  0.021828035821609192297167485738339,
  0.024191162078080601365686370725232,
  0.026509954882333101610601709335075,
  0.028754048765041292843978785354334,
  0.030907257562387762472884252943092,
  0.032981447057483726031814191016854,
  0.034979338028060024137499670731468,
  0.036882364651821229223911065617136,
  0.038678945624727592950348651532281,
  0.040374538951535959111995279752468,
  0.041969810215164246147147541285970,
  0.043452539701356069316831728117073,
  0.044814800133162663192355551616723,
  0.046059238271006988116271735559374,
  0.047185546569299153945261478181099,
  0.048185861757087129140779492298305,
  0.049055434555029778887528165367238,
  0.049795683427074206357811569379942,
  0.050405921402782346840893085653585,
  0.050881795898749606492297473049805,
  0.051221547849258772170656282604944,
  0.051426128537459025933862879215781,
  0.051494729429451567558340433647099
};

void
gsl_integration_qk61 (const gsl_function * f, double a, double b,
                      double *result, double *abserr,
                      double *resabs, double *resasc)
{
  double fv1[31], fv2[31];
  gsl_integration_qk (31, xgk, wg, wgk, fv1, fv2, f, a, b, result, abserr, resabs, resasc);
}