qng.h

开放gsl矩阵运算

/* 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., 675 Mass Ave, Cambridge, MA 02139, 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
} ;