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- /* integration/qk61.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 "gsl__config.h"
- #include "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);
- }
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