/* 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

} ;