| /* integration/qng.h |
| * |
| * 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. |
| */ |
| |
| /* Gauss-Kronrod-Patterson quadrature coefficients for use in |
| quadpack routine qng. These coefficients were calculated with |
| 101 decimal digit arithmetic by L. W. Fullerton, Bell Labs, Nov |
| 1981. */ |
| |
| /* x1, abscissae common to the 10-, 21-, 43- and 87-point rule */ |
| static const double x1[5] = { |
| 0.973906528517171720077964012084452, |
| 0.865063366688984510732096688423493, |
| 0.679409568299024406234327365114874, |
| 0.433395394129247190799265943165784, |
| 0.148874338981631210884826001129720 |
| } ; |
| |
| /* w10, weights of the 10-point formula */ |
| static const double w10[5] = { |
| 0.066671344308688137593568809893332, |
| 0.149451349150580593145776339657697, |
| 0.219086362515982043995534934228163, |
| 0.269266719309996355091226921569469, |
| 0.295524224714752870173892994651338 |
| } ; |
| |
| /* x2, abscissae common to the 21-, 43- and 87-point rule */ |
| static const double x2[5] = { |
| 0.995657163025808080735527280689003, |
| 0.930157491355708226001207180059508, |
| 0.780817726586416897063717578345042, |
| 0.562757134668604683339000099272694, |
| 0.294392862701460198131126603103866 |
| } ; |
| |
| /* w21a, weights of the 21-point formula for abscissae x1 */ |
| static const double w21a[5] = { |
| 0.032558162307964727478818972459390, |
| 0.075039674810919952767043140916190, |
| 0.109387158802297641899210590325805, |
| 0.134709217311473325928054001771707, |
| 0.147739104901338491374841515972068 |
| } ; |
| |
| /* w21b, weights of the 21-point formula for abscissae x2 */ |
| static const double w21b[6] = { |
| 0.011694638867371874278064396062192, |
| 0.054755896574351996031381300244580, |
| 0.093125454583697605535065465083366, |
| 0.123491976262065851077958109831074, |
| 0.142775938577060080797094273138717, |
| 0.149445554002916905664936468389821 |
| } ; |
| |
| /* x3, abscissae common to the 43- and 87-point rule */ |
| static const double x3[11] = { |
| 0.999333360901932081394099323919911, |
| 0.987433402908088869795961478381209, |
| 0.954807934814266299257919200290473, |
| 0.900148695748328293625099494069092, |
| 0.825198314983114150847066732588520, |
| 0.732148388989304982612354848755461, |
| 0.622847970537725238641159120344323, |
| 0.499479574071056499952214885499755, |
| 0.364901661346580768043989548502644, |
| 0.222254919776601296498260928066212, |
| 0.074650617461383322043914435796506 |
| } ; |
| |
| /* w43a, weights of the 43-point formula for abscissae x1, x3 */ |
| static const double w43a[10] = { |
| 0.016296734289666564924281974617663, |
| 0.037522876120869501461613795898115, |
| 0.054694902058255442147212685465005, |
| 0.067355414609478086075553166302174, |
| 0.073870199632393953432140695251367, |
| 0.005768556059769796184184327908655, |
| 0.027371890593248842081276069289151, |
| 0.046560826910428830743339154433824, |
| 0.061744995201442564496240336030883, |
| 0.071387267268693397768559114425516 |
| } ; |
| |
| /* w43b, weights of the 43-point formula for abscissae x3 */ |
| static const double w43b[12] = { |
| 0.001844477640212414100389106552965, |
| 0.010798689585891651740465406741293, |
| 0.021895363867795428102523123075149, |
| 0.032597463975345689443882222526137, |
| 0.042163137935191811847627924327955, |
| 0.050741939600184577780189020092084, |
| 0.058379395542619248375475369330206, |
| 0.064746404951445885544689259517511, |
| 0.069566197912356484528633315038405, |
| 0.072824441471833208150939535192842, |
| 0.074507751014175118273571813842889, |
| 0.074722147517403005594425168280423 |
| } ; |
| |
| /* x4, abscissae of the 87-point rule */ |
| static const double x4[22] = { |
| 0.999902977262729234490529830591582, |
| 0.997989895986678745427496322365960, |
| 0.992175497860687222808523352251425, |
| 0.981358163572712773571916941623894, |
| 0.965057623858384619128284110607926, |
| 0.943167613133670596816416634507426, |
| 0.915806414685507209591826430720050, |
| 0.883221657771316501372117548744163, |
| 0.845710748462415666605902011504855, |
| 0.803557658035230982788739474980964, |
| 0.757005730685495558328942793432020, |
| 0.706273209787321819824094274740840, |
| 0.651589466501177922534422205016736, |
| 0.593223374057961088875273770349144, |
| 0.531493605970831932285268948562671, |
| 0.466763623042022844871966781659270, |
| 0.399424847859218804732101665817923, |
| 0.329874877106188288265053371824597, |
| 0.258503559202161551802280975429025, |
| 0.185695396568346652015917141167606, |
| 0.111842213179907468172398359241362, |
| 0.037352123394619870814998165437704 |
| } ; |
| |
| /* w87a, weights of the 87-point formula for abscissae x1, x2, x3 */ |
| static const double w87a[21] = { |
| 0.008148377384149172900002878448190, |
| 0.018761438201562822243935059003794, |
| 0.027347451050052286161582829741283, |
| 0.033677707311637930046581056957588, |
| 0.036935099820427907614589586742499, |
| 0.002884872430211530501334156248695, |
| 0.013685946022712701888950035273128, |
| 0.023280413502888311123409291030404, |
| 0.030872497611713358675466394126442, |
| 0.035693633639418770719351355457044, |
| 0.000915283345202241360843392549948, |
| 0.005399280219300471367738743391053, |
| 0.010947679601118931134327826856808, |
| 0.016298731696787335262665703223280, |
| 0.021081568889203835112433060188190, |
| 0.025370969769253827243467999831710, |
| 0.029189697756475752501446154084920, |
| 0.032373202467202789685788194889595, |
| 0.034783098950365142750781997949596, |
| 0.036412220731351787562801163687577, |
| 0.037253875503047708539592001191226 |
| } ; |
| |
| /* w87b, weights of the 87-point formula for abscissae x4 */ |
| static const double w87b[23] = { |
| 0.000274145563762072350016527092881, |
| 0.001807124155057942948341311753254, |
| 0.004096869282759164864458070683480, |
| 0.006758290051847378699816577897424, |
| 0.009549957672201646536053581325377, |
| 0.012329447652244853694626639963780, |
| 0.015010447346388952376697286041943, |
| 0.017548967986243191099665352925900, |
| 0.019938037786440888202278192730714, |
| 0.022194935961012286796332102959499, |
| 0.024339147126000805470360647041454, |
| 0.026374505414839207241503786552615, |
| 0.028286910788771200659968002987960, |
| 0.030052581128092695322521110347341, |
| 0.031646751371439929404586051078883, |
| 0.033050413419978503290785944862689, |
| 0.034255099704226061787082821046821, |
| 0.035262412660156681033782717998428, |
| 0.036076989622888701185500318003895, |
| 0.036698604498456094498018047441094, |
| 0.037120549269832576114119958413599, |
| 0.037334228751935040321235449094698, |
| 0.037361073762679023410321241766599 |
| } ; |
| |