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- /* integration/qng.h
- *
- * 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.
- */
- /* 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
- } ;
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