#
# gauss-kronrod.txt, 24 Mar 10

# Gauss quadrature weights and kronrod quadrature abscissae and
# weights as evaluated with 80 decimal digit arithmetic by
# L. W. Fullerton, Bell Labs, Nov. 1981. */

!fuzz 0.0000001

!msgpostfix Gauss-Kronrod quadrature weights for 7 points\n

!need all
# weights of the 7-point gauss rule */
0.129484966168869693270611432679082
0.279705391489276667901467771423780
0.381830050505118944950369775488975
0.417959183673469387755102040816327

!msgpostfix Gauss-Kronrod quadrature weights for 10 points\n

!need all
# weights of the 10-point gauss rule */
0.066671344308688137593568809893332
0.149451349150580593145776339657697
0.219086362515982043995534934228163
0.269266719309996355091226921569469
0.295524224714752870173892994651338

!msgpostfix Gauss-Kronrod quadrature coefficients for 15 points\n

!need all
# abscissae of the 15-point kronrod rule */
0.991455371120812639206854697526329
0.949107912342758524526189684047851
0.864864423359769072789712788640926
0.741531185599394439863864773280788
0.586087235467691130294144838258730
0.405845151377397166906606412076961
0.207784955007898467600689403773245
#0.000000000000000000000000000000000
# weights of the 15-point kronrod rule */
0.022935322010529224963732008058970
0.063092092629978553290700663189204
0.104790010322250183839876322541518
0.140653259715525918745189590510238
0.169004726639267902826583426598550
0.190350578064785409913256402421014
0.204432940075298892414161999234649
0.209482141084727828012999174891714

!msgpostfix Gauss-Kronrod quadrature coefficients for 21 points\n

!need all
# abscissae of the 21-point kronrod rule */
0.995657163025808080735527280689003
0.973906528517171720077964012084452
0.930157491355708226001207180059508
0.865063366688984510732096688423493
0.780817726586416897063717578345042
0.679409568299024406234327365114874
0.562757134668604683339000099272694
0.433395394129247190799265943165784
0.294392862701460198131126603103866
0.148874338981631210884826001129720
#0.000000000000000000000000000000000

# weights of the 21-point kronrod rule */
0.011694638867371874278064396062192
0.032558162307964727478818972459390
0.054755896574351996031381300244580
0.075039674810919952767043140916190
0.093125454583697605535065465083366
0.109387158802297641899210590325805
0.123491976262065851077958109831074
0.134709217311473325928054001771707
0.142775938577060080797094273138717
0.147739104901338491374841515972068
0.149445554002916905664936468389821

!msgpostfix Gauss-Kronrod quadrature coefficients for 31 points\n

!need all
# 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

# 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

!msgpostfix Gauss-Kronrod quadrature coefficients for 61 points\n

!need all
# abscissae of the 61-point kronrod rule */
0.999484410050490637571325895705811
0.996893484074649540271630050918695
0.991630996870404594858628366109486
0.983668123279747209970032581605663
0.973116322501126268374693868423707
0.960021864968307512216871025581798
0.944374444748559979415831324037439
0.926200047429274325879324277080474
0.905573307699907798546522558925958
0.882560535792052681543116462530226
0.857205233546061098958658510658944
0.829565762382768397442898119732502
0.799727835821839083013668942322683
0.767777432104826194917977340974503
0.733790062453226804726171131369528
0.697850494793315796932292388026640
0.660061064126626961370053668149271
0.620526182989242861140477556431189
0.579345235826361691756024932172540
0.536624148142019899264169793311073
0.492480467861778574993693061207709
0.447033769538089176780609900322854
0.400401254830394392535476211542661
0.352704725530878113471037207089374
0.304073202273625077372677107199257
0.254636926167889846439805129817805
0.204525116682309891438957671002025
0.153869913608583546963794672743256
0.102806937966737030147096751318001
0.051471842555317695833025213166723
#0.000000000000000000000000000000000

# weights of the 61-point kronrod rule */
0.001389013698677007624551591226760
0.003890461127099884051267201844516
0.006630703915931292173319826369750
0.009273279659517763428441146892024
0.011823015253496341742232898853251
0.014369729507045804812451432443580
0.016920889189053272627572289420322
0.019414141193942381173408951050128
0.021828035821609192297167485738339
0.024191162078080601365686370725232
0.026509954882333101610601709335075
0.028754048765041292843978785354334
0.030907257562387762472884252943092
0.032981447057483726031814191016854
0.034979338028060024137499670731468
0.036882364651821229223911065617136
0.038678945624727592950348651532281
0.040374538951535959111995279752468
0.041969810215164246147147541285970
0.043452539701356069316831728117073
0.044814800133162663192355551616723
0.046059238271006988116271735559374
0.047185546569299153945261478181099
0.048185861757087129140779492298305
0.049055434555029778887528165367238
0.049795683427074206357811569379942
0.050405921402782346840893085653585
0.050881795898749606492297473049805
0.051221547849258772170656282604944
0.051426128537459025933862879215781
0.051494729429451567558340433647099

# Gauss-Kronrod-Patterson quadrature coefficients
# These coefficients were calculated with 101 decimal digit
# arithmetic by L. W. Fullerton, Bell Labs, Nov # 1981.

!msgpostfix Gauss-Kronrod-Patterson quadrature coefficients for 10 points (Numerical recipes in C)\n

!need all
 
# x1, abscissae common to the 10-, 21-, 43- and 87-point rule */
0.973906528517171720077964012084452
0.865063366688984510732096688423493
0.679409568299024406234327365114874
0.433395394129247190799265943165784
0.148874338981631210884826001129720

# w10, weights of the 10-point formula */
0.066671344308688137593568809893332
0.149451349150580593145776339657697
0.219086362515982043995534934228163
0.269266719309996355091226921569469
0.295524224714752870173892994651338

!msgpostfix Gauss-Kronrod-Patterson quadrature coefficients for 21 points\n

!need all

# x1, abscissae common to the 10-, 21-, 43- and 87-point rule */
0.973906528517171720077964012084452
0.865063366688984510732096688423493
0.679409568299024406234327365114874
0.433395394129247190799265943165784
0.148874338981631210884826001129720

# x2, abscissae common to the 21-, 43- and 87-point rule */
0.995657163025808080735527280689003
0.930157491355708226001207180059508
0.780817726586416897063717578345042
0.562757134668604683339000099272694
0.294392862701460198131126603103866

# w21a, weights of the 21-point formula for abscissae x1 */
0.032558162307964727478818972459390
0.075039674810919952767043140916190
0.109387158802297641899210590325805
0.134709217311473325928054001771707
0.147739104901338491374841515972068

# w21b, weights of the 21-point formula for abscissae x2 */
0.011694638867371874278064396062192
0.054755896574351996031381300244580
0.093125454583697605535065465083366
0.123491976262065851077958109831074
0.142775938577060080797094273138717
0.149445554002916905664936468389821

!msgpostfix Gauss-Kronrod-Patterson quadrature coefficients for 43 points\n

!need all

# x1, abscissae common to the 10-, 21-, 43- and 87-point rule */
0.973906528517171720077964012084452
0.865063366688984510732096688423493
0.679409568299024406234327365114874
0.433395394129247190799265943165784
0.148874338981631210884826001129720

# x2, abscissae common to the 21-, 43- and 87-point rule */
0.995657163025808080735527280689003
0.930157491355708226001207180059508
0.780817726586416897063717578345042
0.562757134668604683339000099272694
0.294392862701460198131126603103866

# x3, abscissae common to the 43- and 87-point rule */
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 */
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 */
0.001844477640212414100389106552965
0.010798689585891651740465406741293
0.021895363867795428102523123075149
0.032597463975345689443882222526137
0.042163137935191811847627924327955
0.050741939600184577780189020092084
0.058379395542619248375475369330206
0.064746404951445885544689259517511
0.069566197912356484528633315038405
0.072824441471833208150939535192842
0.074507751014175118273571813842889
0.074722147517403005594425168280423

!msgpostfix Gauss-Kronrod-Patterson quadrature coefficients for 87 points\n

!need all

# x1, abscissae common to the 10-, 21-, 43- and 87-point rule */
0.973906528517171720077964012084452
0.865063366688984510732096688423493
0.679409568299024406234327365114874
0.433395394129247190799265943165784
0.148874338981631210884826001129720

# x2, abscissae common to the 21-, 43- and 87-point rule */
0.995657163025808080735527280689003
0.930157491355708226001207180059508
0.780817726586416897063717578345042
0.562757134668604683339000099272694
0.294392862701460198131126603103866

# x3, abscissae common to the 43- and 87-point rule */
0.999333360901932081394099323919911
0.987433402908088869795961478381209
0.954807934814266299257919200290473
0.900148695748328293625099494069092
0.825198314983114150847066732588520
0.732148388989304982612354848755461
0.622847970537725238641159120344323
0.499479574071056499952214885499755
0.364901661346580768043989548502644
0.222254919776601296498260928066212
0.074650617461383322043914435796506

# x4, abscissae of the 87-point rule */
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 */
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    */
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

