| /* integration/qk31.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., 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[16] = /* abscissae of the 31-point kronrod rule */ |
| { |
| 0.998002298693397060285172840152271, |
| 0.987992518020485428489565718586613, |
| 0.967739075679139134257347978784337, |
| 0.937273392400705904307758947710209, |
| 0.897264532344081900882509656454496, |
| 0.848206583410427216200648320774217, |
| 0.790418501442465932967649294817947, |
| 0.724417731360170047416186054613938, |
| 0.650996741297416970533735895313275, |
| 0.570972172608538847537226737253911, |
| 0.485081863640239680693655740232351, |
| 0.394151347077563369897207370981045, |
| 0.299180007153168812166780024266389, |
| 0.201194093997434522300628303394596, |
| 0.101142066918717499027074231447392, |
| 0.000000000000000000000000000000000 |
| }; |
| |
| /* xgk[1], xgk[3], ... abscissae of the 15-point gauss rule. |
| xgk[0], xgk[2], ... abscissae to optimally extend the 15-point gauss rule */ |
| |
| static const double wg[8] = /* weights of the 15-point gauss rule */ |
| { |
| 0.030753241996117268354628393577204, |
| 0.070366047488108124709267416450667, |
| 0.107159220467171935011869546685869, |
| 0.139570677926154314447804794511028, |
| 0.166269205816993933553200860481209, |
| 0.186161000015562211026800561866423, |
| 0.198431485327111576456118326443839, |
| 0.202578241925561272880620199967519 |
| }; |
| |
| static const double wgk[16] = /* weights of the 31-point kronrod rule */ |
| { |
| 0.005377479872923348987792051430128, |
| 0.015007947329316122538374763075807, |
| 0.025460847326715320186874001019653, |
| 0.035346360791375846222037948478360, |
| 0.044589751324764876608227299373280, |
| 0.053481524690928087265343147239430, |
| 0.062009567800670640285139230960803, |
| 0.069854121318728258709520077099147, |
| 0.076849680757720378894432777482659, |
| 0.083080502823133021038289247286104, |
| 0.088564443056211770647275443693774, |
| 0.093126598170825321225486872747346, |
| 0.096642726983623678505179907627589, |
| 0.099173598721791959332393173484603, |
| 0.100769845523875595044946662617570, |
| 0.101330007014791549017374792767493 |
| }; |
| |
| void |
| gsl_integration_qk31 (const gsl_function * f, double a, double b, |
| double *result, double *abserr, |
| double *resabs, double *resasc) |
| { |
| double fv1[16], fv2[16]; |
| gsl_integration_qk (16, xgk, wg, wgk, fv1, fv2, f, a, b, result, abserr, resabs, resasc); |
| } |