/**
* \file GaussKronrodNodesWeights.h
* \sa R Piessens, E de Doncker-Kapenger, C Ueberhuber, D Kahaner, QUADPACK, A Subroutine Package
* for Automatic Integration, Springer Verlag, 1983.
*/
#ifndef EIGEN_QUADRATURE_KRONROD_H
#define EIGEN_QUADRATURE_KRONROD_H
namespace Eigen
{
/**
* \brief The abscissae and weights are given for the interval (-1,1).
* Because of symmetry, only the positive abscissae and their
* corresponding weights are given.
*
* \param abscissaeGaussKronrod15 The abscissae of the 15 point kronrod rule.
* \param abscissaeGaussKronrod21 The abscissae of the 21 point kronrod rule.
* \param abscissaeGaussKronrod31 The abscissae of the 31 point kronrod rule.
* \param abscissaeGaussKronrod41 The abscissae of the 41 point kronrod rule.
* \param abscissaeGaussKronrod51 The abscissae of the 51 point kronrod rule.
* \param abscissaeGaussKronrod61 The abscissae of the 61 point kronrod rule.
* \param abscissaeGaussKronrod71 The abscissae of the 71 point kronrod rule.
* \param abscissaeGaussKronrod81 The abscissae of the 81 point kronrod rule.
* \param abscissaeGaussKronrod91 The abscissae of the 91 point kronrod rule.
* \param abscissaeGaussKronrod101 The abscissae of the 101 point kronrod rule.
* \param abscissaeGaussKronrod121 The abscissae of the 121 point kronrod rule.
* \param abscissaeGaussKronrod201 The abscissae of the 201 point kronrod rule.
*
* \param weightsGaussKronrod15 The weights of the 15 point kronrod rule.
* \param weightsGaussKronrod21 The weights of the 21 point kronrod rule.
* \param weightsGaussKronrod31 The weights of the 31 point kronrod rule.
* \param weightsGaussKronrod41 The weights of the 41 point kronrod rule.
* \param weightsGaussKronrod51 The weights of the 51 point kronrod rule.
* \param weightsGaussKronrod61 The weights of the 61 point kronrod rule.
* \param weightsGaussKronrod71 The weights of the 71 point kronrod rule.
* \param weightsGaussKronrod81 The weights of the 81 point kronrod rule.
* \param weightsGaussKronrod91 The weights of the 91 point kronrod rule.
* \param weightsGaussKronrod101 The weights of the 101 point kronrod rule.
* \param weightsGaussKronrod121 The weights of the 121 point kronrod rule.
* \param weightsGaussKronrod201 The weights of the 201 point kronrod rule.
*
* \param abscissaeGauss15 The abscissae of the 7 point gauss rule.
* \param abscissaeGauss21 The abscissae of the 10 point gauss rule.
* \param abscissaeGauss31 The abscissae of the 15 point gauss rule.
* \param abscissaeGauss41 The abscissae of the 20 point gauss rule.
* \param abscissaeGauss51 The abscissae of the 25 point gauss rule.
* \param abscissaeGauss61 The abscissae of the 30 point gauss rule.
* \param abscissaeGauss71 The abscissae of the 35 point gauss rule.
* \param abscissaeGauss81 The abscissae of the 40 point gauss rule.
* \param abscissaeGauss91 The abscissae of the 45 point gauss rule.
* \param abscissaeGauss101 The abscissae of the 50 point gauss rule.
* \param abscissaeGauss121 The abscissae of the 60 point gauss rule.
* \param abscissaeGauss201 The abscissae of the 100 point gauss rule.
*
* \param weightsGauss15 The weights of the 7 point gauss rule.
* \param weightsGauss21 The weights of the 10 point gauss rule.
* \param weightsGauss31 The weights of the 15 point gauss rule.
* \param weightsGauss41 The weights of the 20 point gauss rule.
* \param weightsGauss51 The weights of the 25 point gauss rule.
* \param weightsGauss61 The weights of the 30 point gauss rule.
* \param weightsGauss71 The weights of the 35 point gauss rule.
* \param weightsGauss81 The weights of the 40 point gauss rule.
* \param weightsGauss91 The weights of the 45 point gauss rule.
* \param weightsGauss101 The weights of the 50 point gauss rule.
* \param weightsGauss121 The weights of the 60 point gauss rule.
* \param weightsGauss201 The weights of the 100 point gauss rule.
*/
template <typename Scalar>
class QuadratureKronrod
{
public:
static Array<Scalar, 8, 1> abscissaeGaussKronrod15;
static Array<Scalar, 8, 1> weightsGaussKronrod15;
static Array<Scalar, 4, 1> abscissaeGauss15;
static Array<Scalar, 4, 1> weightsGauss15;
static Array<Scalar, 11, 1> abscissaeGaussKronrod21;
static Array<Scalar, 11, 1> weightsGaussKronrod21;
static Array<Scalar, 5, 1> abscissaeGauss21;
static Array<Scalar, 5, 1> weightsGauss21;
static Array<Scalar, 16, 1> abscissaeGaussKronrod31;
static Array<Scalar, 16, 1> weightsGaussKronrod31;
static Array<Scalar, 8, 1> abscissaeGauss31;
static Array<Scalar, 8, 1> weightsGauss31;
static Array<Scalar, 21, 1> abscissaeGaussKronrod41;
static Array<Scalar, 21, 1> weightsGaussKronrod41;
static Array<Scalar, 10, 1> abscissaeGauss41;
static Array<Scalar, 10, 1> weightsGauss41;
static Array<Scalar, 26, 1> abscissaeGaussKronrod51;
static Array<Scalar, 26, 1> weightsGaussKronrod51;
static Array<Scalar, 13, 1> abscissaeGauss51;
static Array<Scalar, 13, 1> weightsGauss51;
static Array<Scalar, 31, 1> abscissaeGaussKronrod61;
static Array<Scalar, 31, 1> weightsGaussKronrod61;
static Array<Scalar, 15, 1> abscissaeGauss61;
static Array<Scalar, 15, 1> weightsGauss61;
static Array<Scalar, 36, 1> abscissaeGaussKronrod71;
static Array<Scalar, 36, 1> weightsGaussKronrod71;
static Array<Scalar, 18, 1> abscissaeGauss71;
static Array<Scalar, 18, 1> weightsGauss71;
static Array<Scalar, 41, 1> abscissaeGaussKronrod81;
static Array<Scalar, 41, 1> weightsGaussKronrod81;
static Array<Scalar, 20, 1> abscissaeGauss81;
static Array<Scalar, 20, 1> weightsGauss81;
static Array<Scalar, 46, 1> abscissaeGaussKronrod91;
static Array<Scalar, 46, 1> weightsGaussKronrod91;
static Array<Scalar, 23, 1> abscissaeGauss91;
static Array<Scalar, 23, 1> weightsGauss91;
static Array<Scalar, 51, 1> abscissaeGaussKronrod101;
static Array<Scalar, 51, 1> weightsGaussKronrod101;
static Array<Scalar, 25, 1> abscissaeGauss101;
static Array<Scalar, 25, 1> weightsGauss101;
static Array<Scalar, 61, 1> abscissaeGaussKronrod121;
static Array<Scalar, 61, 1> weightsGaussKronrod121;
static Array<Scalar, 30, 1> abscissaeGauss121;
static Array<Scalar, 30, 1> weightsGauss121;
static Array<Scalar, 101, 1> abscissaeGaussKronrod201;
static Array<Scalar, 101, 1> weightsGaussKronrod201;
static Array<Scalar, 50, 1> abscissaeGauss201;
static Array<Scalar, 50, 1> weightsGauss201;
static void computeNodesAndWeights()
{
QuadratureKronrod::computeForRule<7>(abscissaeGaussKronrod15, weightsGaussKronrod15, abscissaeGauss15, weightsGauss15);
QuadratureKronrod::computeForRule<10>(abscissaeGaussKronrod21, weightsGaussKronrod21, abscissaeGauss21, weightsGauss21);
QuadratureKronrod::computeForRule<15>(abscissaeGaussKronrod31, weightsGaussKronrod31, abscissaeGauss31, weightsGauss31);
QuadratureKronrod::computeForRule<20>(abscissaeGaussKronrod41, weightsGaussKronrod41, abscissaeGauss41, weightsGauss41);
QuadratureKronrod::computeForRule<25>(abscissaeGaussKronrod51, weightsGaussKronrod51, abscissaeGauss51, weightsGauss51);
QuadratureKronrod::computeForRule<30>(abscissaeGaussKronrod61, weightsGaussKronrod61, abscissaeGauss61, weightsGauss61);
QuadratureKronrod::computeForRule<35>(abscissaeGaussKronrod71, weightsGaussKronrod71, abscissaeGauss71, weightsGauss71);
QuadratureKronrod::computeForRule<40>(abscissaeGaussKronrod81, weightsGaussKronrod81, abscissaeGauss81, weightsGauss81);
QuadratureKronrod::computeForRule<45>(abscissaeGaussKronrod91, weightsGaussKronrod91, abscissaeGauss91, weightsGauss91);
QuadratureKronrod::computeForRule<50>(abscissaeGaussKronrod101, weightsGaussKronrod101, abscissaeGauss101, weightsGauss101);
QuadratureKronrod::computeForRule<60>(abscissaeGaussKronrod121, weightsGaussKronrod121, abscissaeGauss121, weightsGauss121);
QuadratureKronrod::computeForRule<100>(abscissaeGaussKronrod201, weightsGaussKronrod201, abscissaeGauss201, weightsGauss201);
}
template <Index N>
static void computeForRule(Array<Scalar, N+1, 1>& kronrodAbscissae, Array<Scalar, N+1, 1>& kronrodWeights,
Array<Scalar, (N+1)/2, 1>& gaussAbscissae, Array<Scalar, (N+1)/2, 1>& gaussWeights)
{
Eigen::Array<Scalar, Eigen::Dynamic, 1> xGK;
Eigen::Array<Scalar, Eigen::Dynamic, 1> wGK;
Eigen::Array<Scalar, Eigen::Dynamic, 1> xG;
Eigen::Array<Scalar, Eigen::Dynamic, 1> wG;
Eigen::LaurieGautschi<Scalar>::computeAbscissaeAndWeights(N,xGK,wGK,xG,wG);
//Eigen::Piessens<Scalar>::computeAbscissaeAndWeights(N,xGK,wGK,xG,wG);
//Eigen::Monegato<Scalar>::computeAbscissaeAndWeights(N,xGK,wGK,xG,wG);
for(size_t i=0; i<N+1; ++i)
{
kronrodAbscissae(i) = xGK(i);
kronrodWeights(i) = wGK(i);
}
for(size_t i=0; i<(N+1)/2; ++i)
{
gaussAbscissae(i) = xG(i);
gaussWeights(i) = wG(i);
}
}
};
// Nodes and Weights - Rule 15
template <typename Scalar>
Array<Scalar, 8, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod15 =
(Array<Scalar, 8, 1>() <<
0.99145537112081263920685469752632851664204433837033,
0.94910791234275852452618968404785126240077093767062,
0.86486442335976907278971278864092620121097230707409,
0.74153118559939443986386477328078840707414764714139,
0.58608723546769113029414483825872959843678075060436,
0.40584515137739716690660641207696146334738201409937,
0.20778495500789846760068940377324491347978440714517,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 8, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod15 =
(Array<Scalar, 8, 1>() <<
0.02293532201052922496373200805896959199356081127575,
0.06309209262997855329070066318920428666507115721155,
0.10479001032225018383987632254151801744375665421383,
0.14065325971552591874518959051023792039988975724800,
0.16900472663926790282658342659855028410624490030294,
0.19035057806478540991325640242101368282607807545536,
0.20443294007529889241416199923464908471651760418072,
0.20948214108472782801299917489171426369776208022370
).finished();
template <typename Scalar>
Array<Scalar, 4, 1> QuadratureKronrod<Scalar>::abscissaeGauss15 =
(Array<Scalar, 4, 1>() <<
0.94910791234275852452618968404785126240077093767062,
0.74153118559939443986386477328078840707414764714139,
0.40584515137739716690660641207696146334738201409937,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 4, 1> QuadratureKronrod<Scalar>::weightsGauss15 =
(Array<Scalar, 4, 1>() <<
0.12948496616886969327061143267908201832858740225995,
0.27970539148927666790146777142377958248692506522660,
0.38183005050511894495036977548897513387836508353386,
0.41795918367346938775510204081632653061224489795918
).finished();
// Nodes and Weights - Rule 21
template <typename Scalar>
Array<Scalar, 11, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod21 =
(Array<Scalar, 11, 1>() <<
0.99565716302580808073552728068900284792126058721948,
0.97390652851717172007796401208445205342826994669238,
0.93015749135570822600120718005950834622516790998194,
0.86506336668898451073209668842349304852754301496533,
0.78081772658641689706371757834504237716340752029816,
0.67940956829902440623432736511487357576929471183481,
0.56275713466860468333900009927269414084301388194197,
0.43339539412924719079926594316578416220007183765625,
0.29439286270146019813112660310386556616268662515696,
0.14887433898163121088482600112971998461756485942069,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 11, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod21 =
(Array<Scalar, 11, 1>() <<
0.01169463886737187427806439606219204839621733248193,
0.03255816230796472747881897245938976061738893984566,
0.05475589657435199603138130024458017637372111405833,
0.07503967481091995276704314091619000939521938200091,
0.09312545458369760553506546508336634439001882888076,
0.10938715880229764189921059032580496027181329983435,
0.12349197626206585107795810983107415951230034952865,
0.13470921731147332592805400177170683276099191300856,
0.14277593857706008079709427313871706088597905653191,
0.14773910490133849137484151597206804552373162548521,
0.14944555400291690566493646838982120374523631668747
).finished();
template <typename Scalar>
Array<Scalar, 5, 1> QuadratureKronrod<Scalar>::abscissaeGauss21 =
(Array<Scalar, 5, 1>() <<
0.97390652851717172007796401208445205342826994669238,
0.86506336668898451073209668842349304852754301496533,
0.67940956829902440623432736511487357576929471183481,
0.43339539412924719079926594316578416220007183765625,
0.14887433898163121088482600112971998461756485942069
).finished();
template <typename Scalar>
Array<Scalar, 5, 1> QuadratureKronrod<Scalar>::weightsGauss21 =
(Array<Scalar, 5, 1>() <<
0.06667134430868813759356880989333179285786483432016,
0.14945134915058059314577633965769733240255663966943,
0.21908636251598204399553493422816319245877187052268,
0.26926671930999635509122692156946935285975993846088,
0.29552422471475287017389299465133832942104671702685
).finished();
// Nodes and Weights - Rule 31
template <typename Scalar>
Array<Scalar, 16, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod31 =
(Array<Scalar, 16, 1>() <<
0.99800229869339706028517284015227120907340644231556,
0.98799251802048542848956571858661258114697281712376,
0.96773907567913913425734797878433722528335733730013,
0.93727339240070590430775894771020947124399627351530,
0.89726453234408190088250965645449588283177871149443,
0.84820658341042721620064832077421685136625617473699,
0.79041850144246593296764929481794734686214051995698,
0.72441773136017004741618605461393800963089929458410,
0.65099674129741697053373589531327469254694822609260,
0.57097217260853884753722673725391064123838639628275,
0.48508186364023968069365574023235061286633893089407,
0.39415134707756336989720737098104546836275277615870,
0.29918000715316881216678002426638896266160338274382,
0.20119409399743452230062830339459620781283645446264,
0.10114206691871749902707423144739233878745105740164,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 16, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod31 =
(Array<Scalar, 16, 1>() <<
0.00537747987292334898779205143012764981830804024313,
0.01500794732931612253837476307580726809463943643739,
0.02546084732671532018687400101965335939727174504686,
0.03534636079137584622203794847836004812263067899242,
0.04458975132476487660822729937327969022325664966792,
0.05348152469092808726534314723943029677155476094712,
0.06200956780067064028513923096080293219040000421033,
0.06985412131872825870952007709914747578604543514067,
0.07684968075772037889443277748265900672210910116795,
0.08308050282313302103828924728610378960155418825337,
0.08856444305621177064727544369377430321226673269066,
0.09312659817082532122548687274734571856192788132132,
0.09664272698362367850517990762758933513665656863050,
0.09917359872179195933239317348460313105956726081671,
0.10076984552387559504494666261756972191634838013536,
0.10133000701479154901737479276749254677092627259660
).finished();
template <typename Scalar>
Array<Scalar, 8, 1> QuadratureKronrod<Scalar>::abscissaeGauss31 =
(Array<Scalar, 8, 1>() <<
0.98799251802048542848956571858661258114697281712376,
0.93727339240070590430775894771020947124399627351530,
0.84820658341042721620064832077421685136625617473699,
0.72441773136017004741618605461393800963089929458410,
0.57097217260853884753722673725391064123838639628275,
0.39415134707756336989720737098104546836275277615870,
0.20119409399743452230062830339459620781283645446264,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 8, 1> QuadratureKronrod<Scalar>::weightsGauss31 =
(Array<Scalar, 8, 1>() <<
0.03075324199611726835462839357720441772174814483343,
0.07036604748810812470926741645066733846670803275433,
0.10715922046717193501186954668586930341554371575810,
0.13957067792615431444780479451102832252085027531551,
0.16626920581699393355320086048120881113090018009841,
0.18616100001556221102680056186642282450622601227793,
0.19843148532711157645611832644383932481869255995754,
0.20257824192556127288062019996751931483866215800948
).finished();
// Nodes and Weights - Rule 41
template <typename Scalar>
Array<Scalar, 21, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod41 =
(Array<Scalar, 21, 1>() <<
0.99885903158827766383831557654586300999957020432630,
0.99312859918509492478612238847132027822264713090166,
0.98150787745025025919334299472021694456725093981024,
0.96397192727791379126766613119727722191206032780619,
0.94082263383175475351998272221244338027429557377965,
0.91223442825132590586775244120329811304918479742369,
0.87827681125228197607744299511307846671124526828251,
0.83911697182221882339452906170152068532962936506564,
0.79504142883755119835063883327278794295938959911578,
0.74633190646015079261430507035564159031073067956918,
0.69323765633475138480549071184593153338642585141021,
0.63605368072651502545283669622628593674338911679937,
0.57514044681971031534294603658642513281381264014772,
0.51086700195082709800436405095525099842549132920243,
0.44359317523872510319999221349264010784010101082300,
0.37370608871541956067254817702492723739574632170568,
0.30162786811491300432055535685859226061539650501373,
0.22778585114164507808049619536857462474308893768293,
0.15260546524092267550522024102267752791167622481842,
0.07652652113349733375464040939883821100479626681350,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 21, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod41 =
(Array<Scalar, 21, 1>() <<
0.00307358371852053150121829324603098748803350468825,
0.00860026985564294219866178795010234725212892276671,
0.01462616925697125298378796030886835616388105016225,
0.02038837346126652359801023143275470512283862794019,
0.02588213360495115883450506709615314299947911804867,
0.03128730677703279895854311932380073788776928036281,
0.03660016975820079803055724070721100848745349674750,
0.04166887332797368626378830593689473804396084315301,
0.04643482186749767472023188092610751684212707100708,
0.05094457392372869193270767005034494866483636580926,
0.05519510534828599474483237241977732919475345622815,
0.05911140088063957237496722064859421713641936597704,
0.06265323755478116802587012217425498058581974469890,
0.06583459713361842211156355696939794314722350634338,
0.06864867292852161934562341188536780171548970495824,
0.07105442355344406830579036172321016741291215932221,
0.07303069033278666749518941765891311276062684523455,
0.07458287540049918898658141836248752861611649357209,
0.07570449768455667465954277537661655826336315590041,
0.07637786767208073670550283503806100180080103676495,
0.07660071191799965644504990153010174082793250062867
).finished();
template <typename Scalar>
Array<Scalar, 10, 1> QuadratureKronrod<Scalar>::abscissaeGauss41 =
(Array<Scalar, 10, 1>() <<
0.99312859918509492478612238847132027822264713090166,
0.96397192727791379126766613119727722191206032780619,
0.91223442825132590586775244120329811304918479742369,
0.83911697182221882339452906170152068532962936506564,
0.74633190646015079261430507035564159031073067956918,
0.63605368072651502545283669622628593674338911679937,
0.51086700195082709800436405095525099842549132920243,
0.37370608871541956067254817702492723739574632170568,
0.22778585114164507808049619536857462474308893768293,
0.07652652113349733375464040939883821100479626681350
).finished();
template <typename Scalar>
Array<Scalar, 10, 1> QuadratureKronrod<Scalar>::weightsGauss41 =
(Array<Scalar, 10, 1>() <<
0.01761400713915211831186196235185281636214310554334,
0.04060142980038694133103995227493210987909063998995,
0.06267204833410906356950653518704160635160107657844,
0.08327674157670474872475814322204620610017782858316,
0.10193011981724043503675013548034987616669165602339,
0.11819453196151841731237737771138228700504121954897,
0.13168863844917662689849449974816313491611051114698,
0.14209610931838205132929832506716493303451541339202,
0.14917298647260374678782873700196943669267990408137,
0.15275338713072585069808433195509759349194864511238
).finished();
// Nodes and Weights - Rule 51
template <typename Scalar>
Array<Scalar, 26, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod51 =
(Array<Scalar, 26, 1>() <<
0.99926210499260983419345748654034059370452496042280,
0.99555696979049809790878494689390161725756264940481,
0.98803579453407724763733101457740622707248415209161,
0.97666392145951751149831538647959406774537055531441,
0.96161498642584251241813003366016724169212642963710,
0.94297457122897433941401116965847053190520157060899,
0.92074711528170156174634608454633063157457035996277,
0.89499199787827536885104200678280495417455484975358,
0.86584706529327559544899696958834008820284409402824,
0.83344262876083400142102110869356956946096411382352,
0.79787379799850005941041090499430656940863230009338,
0.75925926303735763057728286520436097638752201889833,
0.71776640681308438818665407977329778059771167555516,
0.67356636847346836448512063324762217588341672807275,
0.62681009901031741278812268162451788101954628995069,
0.57766293024122296772368984161265406739573503929152,
0.52632528433471918259962377815801017803683252320191,
0.47300273144571496052218211500919204133181773846163,
0.41788538219303774885181439459457248709336998140070,
0.36117230580938783773582173012764066742207834704338,
0.30308953893110783016747890998033932920041937876655,
0.24386688372098843204519036279745158640563315632598,
0.18371893942104889201596988875952841578528447834991,
0.12286469261071039638735981880803680553220534604978,
0.06154448300568507888654639236679663128172434803982,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 26, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod51 =
(Array<Scalar, 26, 1>() <<
0.00198738389233031592650785188284340988942998042825,
0.00556193213535671375804023690106552207017692954963,
0.00947397338617415160720771052365532387164532684837,
0.01323622919557167481365640584697623807757808499786,
0.01684781770912829823151666753633631584040265462471,
0.02043537114588283545656829223593897367875800609767,
0.02400994560695321622009248916488108139293152820966,
0.02747531758785173780294845551781107861479601328871,
0.03079230016738748889110902021522858560087716239329,
0.03400213027432933783674879522955120322567052825005,
0.03711627148341554356033062536761987599599780268805,
0.04008382550403238207483928446707564640141054926659,
0.04287284502017004947689579243949516110199950419988,
0.04550291304992178890987058475266039304370776893570,
0.04798253713883671390639225575691475498359220742327,
0.05027767908071567196332525943344008444058763060478,
0.05236288580640747586436671213787271488735155072371,
0.05425112988854549014454337045987560682607683844126,
0.05595081122041231730824068638274734682027103511277,
0.05743711636156783285358269393950647199483285682390,
0.05868968002239420796197417585678776413979564625483,
0.05972034032417405997909929193256185383536304547619,
0.06053945537604586294536026751756542716231236571046,
0.06112850971705304830585903041629271192267855232196,
0.06147118987142531666154413196526417758653796287689,
0.06158081806783293507875982424006455319043693690314
).finished();
template <typename Scalar>
Array<Scalar, 13, 1> QuadratureKronrod<Scalar>::abscissaeGauss51 =
(Array<Scalar, 13, 1>() <<
0.99555696979049809790878494689390161725756264940481,
0.97666392145951751149831538647959406774537055531441,
0.94297457122897433941401116965847053190520157060899,
0.89499199787827536885104200678280495417455484975358,
0.83344262876083400142102110869356956946096411382352,
0.75925926303735763057728286520436097638752201889833,
0.67356636847346836448512063324762217588341672807275,
0.57766293024122296772368984161265406739573503929152,
0.47300273144571496052218211500919204133181773846163,
0.36117230580938783773582173012764066742207834704338,
0.24386688372098843204519036279745158640563315632598,
0.12286469261071039638735981880803680553220534604978,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 13, 1> QuadratureKronrod<Scalar>::weightsGauss51 =
(Array<Scalar, 13, 1>() <<
0.01139379850102628794790296411323477360332052629291,
0.02635498661503213726190181529529914493596328170332,
0.04093915670130631265562348771164595366084578336410,
0.05490469597583519192593689154047332416010998555311,
0.06803833381235691720718718565670796855470949435464,
0.08014070033500101801323495966911130229022573285368,
0.09102826198296364981149722070289165338099255895933,
0.10053594906705064420220689039268582698846609452814,
0.10851962447426365311609395705011661934007758798672,
0.11485825914571164833932554586955580864093619166818,
0.11945576353578477222817812651290104739017670141373,
0.12224244299031004168895951894585150583505924756306,
0.12317605372671545120390287307905014243823362751815
).finished();
// Nodes and Weights - Rule 61
template <typename Scalar>
Array<Scalar, 31, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod61 =
(Array<Scalar, 31, 1>() <<
0.99948441005049063757132589570581081946887394701851,
0.99689348407464954027163005091869528334088203811775,
0.99163099687040459485862836610948572485050033374616,
0.98366812327974720997003258160566280194031785470971,
0.97311632250112626837469386842370688488763796428344,
0.96002186496830751221687102558179766293035921740392,
0.94437444474855997941583132403743912158564371496498,
0.92620004742927432587932427708047400408647453682533,
0.90557330769990779854652255892595831956897536366223,
0.88256053579205268154311646253022559005668914714648,
0.85720523354606109895865851065894385682080017062360,
0.82956576238276839744289811973250191643906869617034,
0.79972783582183908301366894232268324073569842937778,
0.76777743210482619491797734097450313169488361723291,
0.73379006245322680472617113136952764566938172775469,
0.69785049479331579693229238802664006838235380065395,
0.66006106412662696137005366814927075303835037480883,
0.62052618298924286114047755643118929920736469282953,
0.57934523582636169175602493217254049590705158881215,
0.53662414814201989926416979331107279416417800693030,
0.49248046786177857499369306120770879564426564096319,
0.44703376953808917678060990032285400016240759386142,
0.40040125483039439253547621154266063361104593297078,
0.35270472553087811347103720708937386065363100802143,
0.30407320227362507737267710719925655353115778980946,
0.25463692616788984643980512981780510788278930330252,
0.20452511668230989143895767100202470952410426459556,
0.15386991360858354696379467274325592041855197124434,
0.10280693796673703014709675131800059247190133296516,
0.05147184255531769583302521316672257374914145366657,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 31, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod61 =
(Array<Scalar, 31, 1>() <<
0.00138901369867700762455159122675969968104884129196,
0.00389046112709988405126720184451550327851514298489,
0.00663070391593129217331982636975016813362838821778,
0.00927327965951776342844114689202436042127002493819,
0.01182301525349634174223289885325059289626440625061,
0.01436972950704580481245143244358001019584189989500,
0.01692088918905327262757228942032209236856670378384,
0.01941414119394238117340895105012845585142101419143,
0.02182803582160919229716748573833899340150729605683,
0.02419116207808060136568637072523202676039137782818,
0.02650995488233310161060170933507541436651757952275,
0.02875404876504129284397878535433421114467916054207,
0.03090725756238776247288425294309227263527045852381,
0.03298144705748372603181419101685392751059929121386,
0.03497933802806002413749967073146787509722691279482,
0.03688236465182122922391106561713596773695516478103,
0.03867894562472759295034865153228105025092362982155,
0.04037453895153595911199527975246811421612606212603,
0.04196981021516424614714754128596975779008865671899,
0.04345253970135606931683172811707325807460330863170,
0.04481480013316266319235555161672324375743139279637,
0.04605923827100698811627173555937358059469287557182,
0.04718554656929915394526147818109948648288480730063,
0.04818586175708712914077949229830459260579923610843,
0.04905543455502977888752816536723817360588740529530,
0.04979568342707420635781156937994232853920960281370,
0.05040592140278234684089308565358502890219701825162,
0.05088179589874960649229747304980469185338491426092,
0.05122154784925877217065628260494420825114695242525,
0.05142612853745902593386287921578125982955203486240,
0.05149472942945156755834043364709930753273688039646
).finished();
template <typename Scalar>
Array<Scalar, 15, 1> QuadratureKronrod<Scalar>::abscissaeGauss61 =
(Array<Scalar, 15, 1>() <<
0.99689348407464954027163005091869528334088203811775,
0.98366812327974720997003258160566280194031785470971,
0.96002186496830751221687102558179766293035921740392,
0.92620004742927432587932427708047400408647453682533,
0.88256053579205268154311646253022559005668914714648,
0.82956576238276839744289811973250191643906869617034,
0.76777743210482619491797734097450313169488361723291,
0.69785049479331579693229238802664006838235380065395,
0.62052618298924286114047755643118929920736469282953,
0.53662414814201989926416979331107279416417800693030,
0.44703376953808917678060990032285400016240759386142,
0.35270472553087811347103720708937386065363100802143,
0.25463692616788984643980512981780510788278930330252,
0.15386991360858354696379467274325592041855197124434,
0.05147184255531769583302521316672257374914145366657
).finished();
template <typename Scalar>
Array<Scalar, 15, 1> QuadratureKronrod<Scalar>::weightsGauss61 =
(Array<Scalar, 15, 1>() <<
0.00796819249616660561546588347467362245048069658715,
0.01846646831109095914230213191204726909620653396818,
0.02878470788332336934971917961129204363958889454629,
0.03879919256962704959680193644634769203320097676640,
0.04840267283059405290293814042280751781527180919737,
0.05749315621761906648172168940205612879712067072176,
0.06597422988218049512812851511596236123744295365666,
0.07375597473770520626824385002219073415377052603705,
0.08075589522942021535469493846052973087589280370844,
0.08689978720108297980238753071512570257675332874355,
0.09212252223778612871763270708761876719691323441823,
0.09636873717464425963946862635180986509640646143016,
0.09959342058679526706278028210356947652986926366670,
0.10176238974840550459642895216855404463270628948713,
0.10285265289355884034128563670541504386837555706493
).finished();
// Nodes and Weights - Rule 71
template <typename Scalar>
Array<Scalar, 36, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod71 =
(Array<Scalar, 36, 1>() <<
0.99961929856058782041953501908431046312122344098794,
0.99770656909960029726016313931209472519327463717101,
0.99382029303890921225840752201784028500756549314159,
0.98793576444385149803511708918548598531300829571417,
0.98013165785134098801985990365260988816688816643335,
0.97043761603922983321507048258477014252488123931238,
0.95883869699584307892126219427392217538678025386427,
0.94534514820782732953872598552997464486281125124787,
0.93000375305070609922503535864064081717372299765533,
0.91285426135931761446493706355576423048806101362556,
0.89391630583904940482411214013268317995163371208619,
0.87321912502522233152328234914138526664433890227937,
0.85081354468109158704203280179571293221562523873360,
0.82674989909222540683405061274855757904689061798231,
0.80106721312570571470358184335837821672915468266178,
0.77381025228691255526742300920988748101181007297155,
0.74503897566640677164430817613858088537216200738750,
0.71481450155662878326440863122444674696204396852173,
0.68319041848815657677750427209465627245583162169621,
0.65022436466589038867579280898455926336976232592837,
0.61598571048722183053960576573763958060437543282625,
0.58054534474976450993450200818969007093207020356433,
0.54396835169625813820629328275772195267411067648783,
0.50632277324148861502429755583732737658608793863637,
0.46768618346152964902238333071075817099648473017136,
0.42813754151781425418762061300147985878471844648853,
0.38775069602784231260916836932812549811185119580936,
0.34660155443081394587697983493023823180840876937729,
0.30477400147105037961997631656077667943504232291863,
0.26235294120929605797089520045558051348630439864578,
0.21941825841501800318906027538425963000063532656757,
0.17605106116598956997430365644505992967542971232976,
0.13233927061341662561114208274719221355992727169910,
0.08837134327565926360092943349754880342411743476510,
0.04423040796047631902497910724648175796711437032383,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 36, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod71 =
(Array<Scalar, 36, 1>() <<
0.00102550911074666801006956437298132913634921030706,
0.00287226001447070188175126346596935559720130883926,
0.00489809089031614709134489995355345719632799389497,
0.00685548721878420013489017671059314269258714775681,
0.00874803476789701226762937017103524588617649633070,
0.01064412676080364548520974626298521833239102927401,
0.01255213863161942856328562549320926369826006957553,
0.01442614862529363429700928603045290106973954647845,
0.01624977199984979251411432365271640468771985708338,
0.01804665112955870366183510500927265777645403257829,
0.01982463073192568430864633416826825982695039151445,
0.02156072900282074084433582290901980023837200422120,
0.02324181089546663502483166236397397407862232471778,
0.02487938986497896142316498112220908754540096768188,
0.02647872983924452154290308599311750111721575798899,
0.02802485927048032502869308406000651692913135080711,
0.02950731294048380503159847508360512949719541602423,
0.03093298569089254124584577413599566869200123205647,
0.03230574967486032561801474409387789273907226946487,
0.03361454962779494244108331458137284946324198895395,
0.03485077628981657862883631795167583760136994493590,
0.03601932106443251160286472895539991131861935891999,
0.03712347803674947651991054179868437562892996972235,
0.03815455393845179802844670519848738586957355006794,
0.03910531516466664309273221987791124541581708553489,
0.03997983486093488779275160637760618088208667334682,
0.04078134475859293797125394533241037525076355046502,
0.04150279114110496636106397836894150439113925391415,
0.04213802289742381614517983543503522074367479896450,
0.04269093484449388936791278778195848585871259590150,
0.04316504612011059575016094844755100917095935153618,
0.04355454541697310298508166546078403157623950944932,
0.04385415492459730857308029613026789252900261518504,
0.04406798346693598707683395305061859923249071421063,
0.04420009752589896947154443219235054970162309288894,
0.04424566572105622843217879601220347725717507881493
).finished();
template <typename Scalar>
Array<Scalar, 18, 1> QuadratureKronrod<Scalar>::abscissaeGauss71 =
(Array<Scalar, 18, 1>() <<
0.99770656909960029726016313931209472519327463717101,
0.98793576444385149803511708918548598531300829571417,
0.97043761603922983321507048258477014252488123931238,
0.94534514820782732953872598552997464486281125124787,
0.91285426135931761446493706355576423048806101362556,
0.87321912502522233152328234914138526664433890227937,
0.82674989909222540683405061274855757904689061798231,
0.77381025228691255526742300920988748101181007297155,
0.71481450155662878326440863122444674696204396852173,
0.65022436466589038867579280898455926336976232592837,
0.58054534474976450993450200818969007093207020356433,
0.50632277324148861502429755583732737658608793863637,
0.42813754151781425418762061300147985878471844648853,
0.34660155443081394587697983493023823180840876937729,
0.26235294120929605797089520045558051348630439864578,
0.17605106116598956997430365644505992967542971232976,
0.08837134327565926360092943349754880342411743476510,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 18, 1> QuadratureKronrod<Scalar>::weightsGauss71 =
(Array<Scalar, 18, 1>() <<
0.00588343342044308497575389624011262403075431779823,
0.01365082834836149226640400292051638397399403784142,
0.02132297991148358088343798396620507832380964471994,
0.02882926010889425404871603971448491626152772662959,
0.03611011586346338053271696964754993830853577896999,
0.04310842232617021878230645937490820342280658716399,
0.04976937040135352980519967608499495859449495319457,
0.05604081621237012857832774716510096444034853490456,
0.06187367196608018888701413878868865226537122580410,
0.06722228526908690396430550874814855854709311914960,
0.07204479477256006466546190978527775614726739302743,
0.07630345715544205353865853788422622552708008189564,
0.07996494224232426293266208098504575632883549943009,
0.08300059372885658837992652821617700348517450381345,
0.08538665339209912522594398739111756764119098828375,
0.08710444699718353424332203160554093668505671509385,
0.08814053043027546297073880759309664142545431727449,
0.08848679490710429063820738777761566918240915001061
).finished();
// Nodes and Weights - Rule 81
template <typename Scalar>
Array<Scalar, 41, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod81 =
(Array<Scalar, 41, 1>() <<
0.99970755925870001652122454213597471358259546611434,
0.99823770971055920034962270242058649233577038159505,
0.99525057344607275036560954016723640396135078520144,
0.99072623869945700645305435222137215496222208135109,
0.98472283986425006102933341488331281956810416420996,
0.97725994998377426266337028371290380697866793203799,
0.96832312685414990090376748802208053929226225295460,
0.95791681921379165580454099945275928509488349060275,
0.94607183716250003820183480835310183364449049027233,
0.93281280827867653336085216684520571643475357528269,
0.91814954307289887682909109264899900900889565336112,
0.90209880696887429672825333086849310358448808105767,
0.88469200870108974596916731568481615247744988567172,
0.86595950321225950382078180835461996357054655301110,
0.84592398558731071742075270176063153327242355905011,
0.82461223083331166319632023066609877390724038424299,
0.80206056614025212716548248052306700513426840614442,
0.77830565142651938769497154550649484802069131612689,
0.75337980343894219817195210861389792731211452767941,
0.72731825518992710328099645175493054855737867353333,
0.70016297748732993103067821243443810794745752806774,
0.67195668461417954837935451496149410997032598138385,
0.64273952430557996253724399164382458078430653187326,
0.61255388966798023795261245023069487738012378168315,
0.58144706582913000652989501202985449166039158983665,
0.54946712509512820207593130552951797023397510159565,
0.51666060738638370597736752352686730669850255178962,
0.48307580168617871290856657424482300459902239553311,
0.44876451363816376391523113354600061846497447744503,
0.41377920437160500152487974580371368297409962405292,
0.37817143547358892456847074204267036554749984414768,
0.34199409082575847300749248117919431006695362002733,
0.30530244173524671953945499726037915149778023393627,
0.26815218500725368114118434480859618342480437323625,
0.23059852188071949700436103627672748185567094334317,
0.19269758070137109971551685206514989481409202110521,
0.15450687937939447709272996582455060888266557312076,
0.11608407067525520848345128440802411376872853085422,
0.07748658833128284169115486612617194705087430189926,
0.03877241750605082193319344402462329467936463438314,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 41, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod81 =
(Array<Scalar, 41, 1>() <<
0.00078786332389437149872027155489686731646438112543,
0.00220748573572677796216880922531121147539447921678,
0.00376522867934192207419437277688852248174719104712,
0.00527194271488547391100911400749610401795296325231,
0.00673181348520739996342079325197287731781780936164,
0.00819757638675148244956105325366150439252190701325,
0.00967540148401718791503549171298574769106769313863,
0.01113132166402750374938616623733449344824035103306,
0.01255438476851726603177494941601931549647320859678,
0.01396255986698061404257329276730788872218488725171,
0.01536132635910245297306719365346221049653776351247,
0.01673453247500258319616665389692844862618082103791,
0.01807386840881819058019116416727673799123477315931,
0.01938764589431774100483071215654747790839959650200,
0.02067904327352817531538698511576519576908963214656,
0.02193818733583309346140081267327422472167322967377,
0.02315893101337702414441542631657291426916138363685,
0.02434569018227335927008045325065084644250141492898,
0.02550021760313012760411536558132073210208609486171,
0.02661573749902468675858406158693142228991791577345,
0.02768762611106109151543416219022982991880587861249,
0.02871838684109212328774430242495038364855427947406,
0.02970892727777659464157767791486382641598503632608,
0.03065436089141152537823603492997426208913617114202,
0.03155122361911536248171493595674374505113742718348,
0.03240098250760594428516927456513374062015435029682,
0.03320404434125756040053598377665629314697494328677,
0.03395686283420980625135217300229063782965844230293,
0.03465693584349753394613505048683965340397811449698,
0.03530514470862184103888891975079794872037448391518,
0.03590160278362810442749426164234802328728310552020,
0.03644382653034092475806451684526800902468673825359,
0.03693016953404855460457701491128601575795938601292,
0.03736118002546921808817250104671655660126038378354,
0.03773680126309354415257237969171128676159927920230,
0.03805546377885242099072980354540709765269970008461,
0.03831632400517485967847680297981699802520907959292,
0.03851974174995072693620904485019618182205811434106,
0.03866555543914104039741924425967757530593426930461,
0.03875302937875238614021147436365714157701740560300,
0.03878210476428280538640259652566010072577182998938
).finished();
template <typename Scalar>
Array<Scalar, 20, 1> QuadratureKronrod<Scalar>::abscissaeGauss81 =
(Array<Scalar, 20, 1>() <<
0.99823770971055920034962270242058649233577038159505,
0.99072623869945700645305435222137215496222208135109,
0.97725994998377426266337028371290380697866793203799,
0.95791681921379165580454099945275928509488349060275,
0.93281280827867653336085216684520571643475357528269,
0.90209880696887429672825333086849310358448808105767,
0.86595950321225950382078180835461996357054655301110,
0.82461223083331166319632023066609877390724038424299,
0.77830565142651938769497154550649484802069131612689,
0.72731825518992710328099645175493054855737867353333,
0.67195668461417954837935451496149410997032598138385,
0.61255388966798023795261245023069487738012378168315,
0.54946712509512820207593130552951797023397510159565,
0.48307580168617871290856657424482300459902239553311,
0.41377920437160500152487974580371368297409962405292,
0.34199409082575847300749248117919431006695362002733,
0.26815218500725368114118434480859618342480437323625,
0.19269758070137109971551685206514989481409202110521,
0.11608407067525520848345128440802411376872853085422,
0.03877241750605082193319344402462329467936463438314
).finished();
template <typename Scalar>
Array<Scalar, 20, 1> QuadratureKronrod<Scalar>::weightsGauss81 =
(Array<Scalar, 20, 1>() <<
0.00452127709853319125847173287818533272783111019971,
0.01049828453115281361474217106727965237679262131580,
0.01642105838190788871286348488236392729234229334696,
0.02224584919416695726150432418420857320703319667935,
0.02793700698002340109848915750772107730255086205077,
0.03346019528254784739267818308641084897724178665376,
0.03878216797447201763997203129044616225345921123203,
0.04387090818567327199167468604171549581100683717024,
0.04869580763507223206143416044814638806784302737712,
0.05322784698393682435499647977226050455532117182201,
0.05743976909939155136661773091042598560010483585445,
0.06130624249292893916653799640839859590259376351117,
0.06480401345660103807455452956675273003269296420849,
0.06791204581523390382569010823192398598419723837929,
0.07061164739128677969548363085528683235955910399559,
0.07288658239580405906051068344251783585755908098580,
0.07472316905796826420018933626132467319120293442036,
0.07611036190062624237155807592249482301255955384507,
0.07703981816424796558830753428381024852443975416394,
0.07750594797842481126372396295832632696366865278811
).finished();
// Nodes and Weights - Rule 91
template <typename Scalar>
Array<Scalar, 46, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod91 =
(Array<Scalar, 46, 1>() <<
0.99976825819812844184050501808521584761778222189509,
0.99860364518193663815654767690082054809228852721448,
0.99623648400262042934511873220069067464977892521152,
0.99264999844720374174861712059773534497500164330364,
0.98788929755834198035845135712826787436469148879696,
0.98196871503454056823931847363434148153836524922046,
0.97487472859984626283011247237626660754074730116341,
0.96660831039689460473642516089247809711667903060942,
0.95719162401328142632709071186085980254412868260598,
0.94664169099562906178472059695383707845046834416714,
0.93496270170823072849720985525389099772434749839611,
0.92216393671900038809746736096052731926536287725066,
0.90826680768346396973605068382241808590437868337987,
0.89329167175324173846464905149305734636540124041379,
0.87725158719302201212972841148989357243612789849954,
0.86016247596066422533907887056713438778341442357702,
0.84204857691040695822975484057647336894431244265745,
0.82293422050208633703577526002650202999341525805627,
0.80283895116683677464879103408690607617541369942643,
0.78178431259390629131236318809860281766027351683906,
0.75979816452041089331911717455595240315934812011636,
0.73690884894549035262373884859489201987960568083762,
0.71314122427549174186073675931964340779561425372465,
0.68852168077120052523201982588043823595523300561853,
0.66308170860223379808352326376326032948162534249687,
0.63685339445322335927122384590338315069203124346568,
0.60986605449389570894381986808230584011038649491498,
0.58215021256935318668096733444417713100008882598323,
0.55374067215934876332312890149007883417942668039810,
0.52467282046291606709113410046016240260710827080028,
0.49497965749810183702993192041027660372919586028089,
0.46469512391963509857960150230974851083981266723719,
0.43385684374178294432166447428181289994755173351281,
0.40250294385854191407797450854834645597029935756940,
0.37066934235973061895322964085585254593836191642981,
0.33839265425060216164340410003187298953234144313742,
0.30571272186623304325858534427814131940857839940069,
0.27266976975237756060876539161564518189821175427664,
0.23930185320471224179064130404859896962578658675486,
0.20564748978326374571978722547154393070323638569943,
0.17174806594978090965313436541849815218083385269234,
0.13764520598325302875659004142306555310676555654153,
0.10337830283214540467276673615057417548074590315259,
0.06898698016314417249041461410381172969392066693097,
0.03451344875177766949491534277959965665394030693585,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 46, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod91 =
(Array<Scalar, 46, 1>() <<
0.00062429185718321579857663066059662918012169021712,
0.00174909651748535281285516187173085451060602294185,
0.00298417191546646641998503281623961554312494201463,
0.00417984253266509402229000496101711163585669889060,
0.00533932741808091123159062611497603209976404263396,
0.00650505471381696245904611633672298845714802006140,
0.00768283318432149209385511436140106223666562795019,
0.00884569677730051624106815234208503432536098150154,
0.00998469672095943272307954145417903769666978042970,
0.01111490008447190508121416984333781971203603824680,
0.01224167381140228811054606558412293322915204182020,
0.01335197006885853998622059924442501930963026478306,
0.01443876216592827376541528869012420064884302430462,
0.01550957989105782085098413853805035872321392001603,
0.01656805497063899757282455227144833435996323736845,
0.01760592823349179892606175575954299643495333036010,
0.01861770602562484479718322571024115120208025395210,
0.01960791451368152118747566973260204511490037731486,
0.02057913131743379223158230090375461301131538208475,
0.02152536104976848200630137341864843337072862418308,
0.02244212099311634372269863847029007990818455855580,
0.02333248915075203001289733158912301176791164139547,
0.02419844417232129113332510712740896880597195801619,
0.02503528547727422745626205933879306013580656266019,
0.02583923328997513115912223308380120472230411615960,
0.02661260570454035168063547182183051788811540169958,
0.02735705869931106756998238581749345123775004557503,
0.02806873537773934426971004212203570044889225018607,
0.02874437835191346477732940766106574336017984206002,
0.02938590583816742107250843684941804435493284536361,
0.02999482799045285292199349638404121450838986974628,
0.03056789199447173972249252053845442669853092956157,
0.03110225031086367084980881406978430961362268833061,
0.03159963354172971455344564253125185922453333794127,
0.03206152703486851892940119666539450559009394304134,
0.03248514058861336432416886222383084559924471982830,
0.03286795999547159469562119073429122583191588601916,
0.03321166534480586792126042755694344444575877149100,
0.03351780561085007806314526562438369890686100054127,
0.03378396062701886695872739048248957350422138863593,
0.03400789127506731448126888746030257764555957519386,
0.03419132258692411201484025624573949944920924709690,
0.03433593627332217900296412964336557875142219514127,
0.03443961425268577159747120385314938034943289238764,
0.03450034175251302542891776315122965078611807559511,
0.03451995999118589472369263667768431132580391340384
).finished();
template <typename Scalar>
Array<Scalar, 23, 1> QuadratureKronrod<Scalar>::abscissaeGauss91 =
(Array<Scalar, 23, 1>() <<
0.99860364518193663815654767690082054809228852721448,
0.99264999844720374174861712059773534497500164330364,
0.98196871503454056823931847363434148153836524922046,
0.96660831039689460473642516089247809711667903060942,
0.94664169099562906178472059695383707845046834416714,
0.92216393671900038809746736096052731926536287725066,
0.89329167175324173846464905149305734636540124041379,
0.86016247596066422533907887056713438778341442357702,
0.82293422050208633703577526002650202999341525805627,
0.78178431259390629131236318809860281766027351683906,
0.73690884894549035262373884859489201987960568083762,
0.68852168077120052523201982588043823595523300561853,
0.63685339445322335927122384590338315069203124346568,
0.58215021256935318668096733444417713100008882598323,
0.52467282046291606709113410046016240260710827080028,
0.46469512391963509857960150230974851083981266723719,
0.40250294385854191407797450854834645597029935756940,
0.33839265425060216164340410003187298953234144313742,
0.27266976975237756060876539161564518189821175427664,
0.20564748978326374571978722547154393070323638569943,
0.13764520598325302875659004142306555310676555654153,
0.06898698016314417249041461410381172969392066693097,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 23, 1> QuadratureKronrod<Scalar>::weightsGauss91 =
(Array<Scalar, 23, 1>() <<
0.00358266315528355893114302865935139257058563635818,
0.00832318929621824164573585312223385375615793129295,
0.01303110499158278432063108246968692602714117158264,
0.01767753525793759061709254666957708852065127812647,
0.02223984755057873239395075855216899334487570870130,
0.02669621396757766480567477879310752778782491056589,
0.03102537493451546716250793889376806388592115212397,
0.03520669220160901624769979826157509081008807471271,
0.03922023672930244756418718534392933821813012459631,
0.04304688070916497115169111308116694178831923616319,
0.04666838771837336526776847574165410120498614148785,
0.05006749923795202979913210247487431739149869293515,
0.05322801673126895194590404401931040379848221694018,
0.05613487875978647664392394037486976324148018494616,
0.05877423271884173857436151763183142253126572546098,
0.06113350083106652250188637053632557326012423426524,
0.06320144007381993774996373029066688186630023727582,
0.06496819575072343085382657035907569508384972548758,
0.06642534844984252808291471563910373761317454675067,
0.06756595416360753627091022387364863097947258092395,
0.06838457737866967453169209933431609707348491305464,
0.06887731697766132288200284829805578888452413011065,
0.06904182482923202011079855515940474072332289227500
).finished();
// Nodes and Weights - Rule 101
template <typename Scalar>
Array<Scalar, 51, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod101 =
(Array<Scalar, 51, 1>() <<
0.99981190136436471898752764191979778490900714786428,
0.99886640442007105018545944497421850599624351290408,
0.99694438701887617830552521284551574074542656874602,
0.99403196943209071258510820042069472815747797106832,
0.99016501066968000942392663658159575132877674133477,
0.98535408404800588230900962563248940401559263094541,
0.97958729676076942938993428547746899117341045817570,
0.97286438510669207371334410460625205366917340704995,
0.96520165106614520049209141719129593627549507978394,
0.95661095524280794299774564415662209405143412462605,
0.94709403424493944376335887833533441316436721753676,
0.93665661894487793378087494727249660215373159809520,
0.92531354647480188621729501218597896170837009890339,
0.91307855665579189308973564277165709478418819169778,
0.89995988756429461789335121594253760342125497503872,
0.88596797952361304863754098246675363419429031075581,
0.87111919820410031041116631276794734769410099155684,
0.85542976942994608461136264393475746765483303948691,
0.83891258696722439582669453115982171629679423354273,
0.82158207085933594835625411087393953776074138334349,
0.80345686805045941104583132344339868468195642520966,
0.78455583290039926390530519634099120084731627255644,
0.76489567937235152255213391009405332066417203426695,
0.74449430222606853826053625268219424287018793132958,
0.72337276602259251579221941156517307053014928418822,
0.70155246870682225108954625788365572814971922848470,
0.67905338940674727147750574623528945542568600842673,
0.65589646568543936078162486400367981904141052838233,
0.63210506844506487645226444165317494562655419021859,
0.60770292718495023918038179639183289360420502067599,
0.58271281781783653230059341928604868801078591807290,
0.55715830451465005431552290962580160781589838223775,
0.53106482452270813956871444365352729284157032257425,
0.50445814490746420165145913184914119263537867827068,
0.47736339223304303620238841113348793007606445039659,
0.44980633497403878914713146777837581731506451346517,
0.42181415731061309702869639767299001110343390879166,
0.39341431189756512739422925382381727024613946867266,
0.36463382886161427721485091875517338779531125640738,
0.33550024541943735683698825729107169784121859303680,
0.30604211922918460908352322458238267491364761240808,
0.27628819377953199032764527852113018571480158713200,
0.24626694739814402597841233060681906225445876784272,
0.21600723687604175684728453261710133370575597251013,
0.18553858172277277270028588015893298081440861045060,
0.15489058999814590207162862094110950120185022005494,
0.12409272435916037178300113567216009078143172259769,
0.09317470156008614085445037763960034788567138392214,
0.06216656481941616908016236906249366229724267742777,
0.03109833832718887611232898966594919424729622296000,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 51, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod101 =
(Array<Scalar, 51, 1>() <<
0.00050676166803489136800323005679418875182879376563,
0.00142011023816635705848924160910481934652645245411,
0.00242310374582057327186801995970143275616529077528,
0.00339459089289723743085662727982835774647902739813,
0.00433770360526373578354342360625291962127768748888,
0.00528690708431070081496631090522651841927406286998,
0.00624676165289346880527846119294362879366575110822,
0.00719585591375833177104770901157397246654579768609,
0.00812753366255938737868037294245956987246699844772,
0.00905390685313200073482984638318670974026478257534,
0.00997908051277197271520006896555491352835623156784,
0.01089303114914542139185373632048379056944269951885,
0.01179073210054285467626745948807510643296154432320,
0.01267806183701224440357173722638836784313869359541,
0.01355761601155914093045815780333977992202586708240,
0.01442332487228954690873605873699027758803460839370,
0.01527146381217306258703163983580949905342101469485,
0.01610536347829330632879586448333389813140260935888,
0.01692665787573854108211355546392361200532841207090,
0.01773116846670068736945143328713021401556189039555,
0.01851604246177747374224081714934718333316987698583,
0.01928332352180814825301889801162132421117243231650,
0.02003404583071943486093518979257578870512514064793,
0.02076512847171916224208023972166701446741771437993,
0.02147433820180993345171927343976448497995531229818,
0.02216298492660156610684349832667521094279850151824,
0.02283171756887400699163339995992033749214277945418,
0.02347818407891019300458609050334622304513636748516,
0.02410062587721830597666576014469811068703941778003,
0.02469990353732573949476020971483749324030400159067,
0.02527641257483270914647897860737446154499106952106,
0.02582833680912179520884486377406142381526019962380,
0.02635430681869013845472576260957721404783898088646,
0.02685489636290659736893714711520551156209704917336,
0.02733033189010964383305404350544173245562448595110,
0.02777922389243983336140685575895975209594524979909,
0.02820054057947867914629860187746193364776090154299,
0.02859466838340605773904731791010499100505911124158,
0.02896171979050103356757141731956685768195060652065,
0.02930066703511978233684077865154509911023252219986,
0.02961078494045995503025213539965659277620209307433,
0.02989233581703979245880464830873980542938987086275,
0.03014535377457083519407513020913017271701705074418,
0.03036913320016487318137849566585392442983158643626,
0.03056323770631003720546053583408408633745212487948,
0.03072784566941669020593437016581195240625267413048,
0.03086293412170997376026432332960616247053522064300,
0.03096809562366843795854210956298413399486076114109,
0.03104317399694570106876064569864783540375985841535,
0.03108828778240521910421818490634306613818955150864,
0.03110336664174957546715464493457708644263854335374
).finished();
template <typename Scalar>
Array<Scalar, 25, 1> QuadratureKronrod<Scalar>::abscissaeGauss101 =
(Array<Scalar, 25, 1>() <<
0.99886640442007105018545944497421850599624351290408,
0.99403196943209071258510820042069472815747797106832,
0.98535408404800588230900962563248940401559263094541,
0.97286438510669207371334410460625205366917340704995,
0.95661095524280794299774564415662209405143412462605,
0.93665661894487793378087494727249660215373159809520,
0.91307855665579189308973564277165709478418819169778,
0.88596797952361304863754098246675363419429031075581,
0.85542976942994608461136264393475746765483303948691,
0.82158207085933594835625411087393953776074138334349,
0.78455583290039926390530519634099120084731627255644,
0.74449430222606853826053625268219424287018793132958,
0.70155246870682225108954625788365572814971922848470,
0.65589646568543936078162486400367981904141052838233,
0.60770292718495023918038179639183289360420502067599,
0.55715830451465005431552290962580160781589838223775,
0.50445814490746420165145913184914119263537867827068,
0.44980633497403878914713146777837581731506451346517,
0.39341431189756512739422925382381727024613946867266,
0.33550024541943735683698825729107169784121859303680,
0.27628819377953199032764527852113018571480158713200,
0.21600723687604175684728453261710133370575597251013,
0.15489058999814590207162862094110950120185022005494,
0.09317470156008614085445037763960034788567138392214,
0.03109833832718887611232898966594919424729622296000
).finished();
template <typename Scalar>
Array<Scalar, 25, 1> QuadratureKronrod<Scalar>::weightsGauss101 =
(Array<Scalar, 25, 1>() <<
0.00290862255315514095840072434285548080667299645995,
0.00675979919574540150277887817798503180187383240647,
0.01059054838365096926356968149924102233940181908646,
0.01438082276148557441937890892732434993703178617059,
0.01811556071348939035125994342235461984466731704973,
0.02178024317012479298159206906269034122731346235793,
0.02536067357001239044019487838544272346016125997571,
0.02884299358053519802990637311323243251784686559354,
0.03221372822357801664816582732300395344858905883343,
0.03545983561514615416073461100097579709696000049698,
0.03856875661258767524477015023638593486477170500052,
0.04152846309014769742241197896406701780897797548584,
0.04432750433880327549202228683039419746076129835545,
0.04695505130394843296563301363498768251406430618605,
0.04940093844946631492124358075143272869228705096661,
0.05165570306958113848990529584009527964982544939544,
0.05371062188899624652345879725566455276802321352992,
0.05555774480621251762356742561226949759513529998390,
0.05718992564772838372302931506599316301157537225709,
0.05860084981322244583512243663084846620976751344403,
0.05978505870426545750957640531258523079666604207267,
0.06073797084177021603175001538481100160979927323540,
0.06145589959031666375640678608391537509726757576401,
0.06193606742068324338408750978083068857287705669124,
0.06217661665534726232103310736061343086768246920103
).finished();
// Nodes and Weights - Rule 121
template <typename Scalar>
Array<Scalar, 61, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod121 =
(Array<Scalar, 61, 1>() <<
0.99986894039735508603454696805483048308252339364253,
0.99921012322743602203422958579764926639879897871133,
0.99787067797281103000055449680255041109802834093833,
0.99584052511883817387674671337744065277489029497714,
0.99314406509020969852781424310993230666589953769707,
0.98978789522222171736727898701609604257739315378694,
0.98576273403417081406883799910761849326959871083386,
0.98106720175259818561857679982677003388053857922189,
0.97571130869063093805424022397979537946475594414538,
0.96970178876505273372154409891379427254093434486825,
0.96303809044100194217445769061433368420308650851500,
0.95572225583999610739723184582969950248009374476661,
0.94776254337082142416238277974195989092969410130796,
0.93916627611642324949541901160970509641940342040120,
0.92993671378354345915802464683245381420494070890654,
0.92007847617762755285665686251989682878376887601371,
0.90960021010202694746557389315600630364455686348403,
0.89851031081004594193778932957262833016445844274707,
0.88681462876695505446866905561876851436297727385471,
0.87451992264689831512930809991243580515918229443578,
0.86163582612712916884010876561015688672720821191562,
0.84817198478592963249051549499437560129752871650678,
0.83413634063502318823513056433153895616632797500262,
0.81953752616214575936851810851972357189949051896959,
0.80438634842167500661914227180660775048846373673656,
0.78869373993226405456994479977721573524633292787923,
0.77246944634325712130468945617575041059983850332073,
0.75572377530658568686884206660237310592890019956471,
0.73846873678927334614831784537093050545190770229944,
0.72071651335573039943602106101352107776477399473324,
0.70247844071277491341354556676393514423069049151760,
0.68376632738135543722293023922429715908759460433887,
0.66459333948891834538628881414033517814480799774455,
0.64497282848947706781344789642044471716519001934666,
0.62491753372827970746014412059280947928268675981204,
0.60444059704851036344420877631120172065042105359106,
0.58355624965567953080935429206168664732529695996909,
0.56227890075394453917827258748599872906318823765940,
0.54062251531844021045684191707599245063719726744878,
0.51860140005856974741788934848472130132984667628869,
0.49623073093171768406858727593889830377761134305524,
0.47352584176170711110816305375279463800786800509984,
0.45050174562863861734206716711875032408754056360999,
0.42717374158307838930745285353031192335344213618423,
0.40355780908279404695333333368401568081423124589053,
0.37967005657679797715495267052188770405637443316239,
0.35552636501293175588409210698088763021622142976651,
0.33114284826844819425235296535055270480012149637631,
0.30653613242384558698842567017265989136532053439467,
0.28172293742326169169069486033944159830826306079538,
0.25671982824253729939215528961771483496009022967204,
0.23154355137602933801034463134675544074353905193959,
0.20621121086087678024608930136722267382406551852335,
0.18073996487342541724087694126185263123177216863905,
0.15514687531461929153617689855444662362933578843402,
0.12944913539694500314644416464957577475987352436647,
0.10366414973805567097692423407501883537630426619863,
0.07780933394953656941928550708222528757759478289772,
0.05190205753879922246314126084963723796593693305509,
0.02595977230124779858917038540034482566031476071728,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 61, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod121 =
(Array<Scalar, 61, 1>() <<
0.00035309352008476328873302150506396067820554489853,
0.00098957111594993012002795471522501001707498606076,
0.00168881658669538272849089285105177845280274177469,
0.00236661114697454617075475538520317633315532160502,
0.00302530527821396938049320055216641290240634905666,
0.00368912213435713356782149157136472153921088296969,
0.00436146638924688454590356599869214359782276998026,
0.00502758855697275303082752008261190854561998819561,
0.00568300310799120346648467571699154030415431078060,
0.00633636534216254504799580887837090652934518564671,
0.00699076245664291472692253153841534937056702016655,
0.00763935787810120919989669059239195349160759882912,
0.00827878115796801323966142828447078823241218583717,
0.00891334185215251454610013327637323498094064454821,
0.00954507013554903770056092516381352299744866414013,
0.01016985984860481299714318208572482794015404599887,
0.01078522284204381631750127741952879057916973310398,
0.01139368492941710872440593756091481437036855202376,
0.01199659638647986661732163593813166954215294680801,
0.01259114041876269638053880248826790662577710230923,
0.01317540660371342750620081979004402932037003022067,
0.01375101092307560054089755109416989805354339164989,
0.01431887215442789937035515803915600785470840146381,
0.01487690562344235570814655024966329586556913856472,
0.01542359803641373989397778363148163169047625524956,
0.01596003744934033355994981103588918423169316792324,
0.01648685780200353115743507689306805446791494560564,
0.01700244529575939575670279579554073187580588123302,
0.01750557806830523681292548656619025120665578599915,
0.01799701182836498525925640182815936357315182357777,
0.01847718567886398682948269679412403693476107997848,
0.01894481804101016688214698965950324848350668749227,
0.01939891427004672519965813885528064708101401901242,
0.01984000938527257124526765005244593165383386796636,
0.02026840565003063810461444077298412851468322177833,
0.02068307361792965307984840163452720256611289248871,
0.02108320540912487808345587005640913822849056383719,
0.02146918421657572995510375908055968070647062620577,
0.02184121436913142190366087107926959818357547855685,
0.02219846947126649229671310378395216714738953151697,
0.02254030223805028212731124333425081265066909380287,
0.02286698888783978160371241817159477370209744385441,
0.02317866262411930143640919197308030421619718533173,
0.02347466875931088521516214970827055070559381432420,
0.02375450343651776669480062293094101720463883872448,
0.02401836617317175928431662138798116606010655200640,
0.02426633771149105650424641365034412183131195279715,
0.02449791452590019789919446326522050049632493665594,
0.02471272496709623460174523761205724250739759370788,
0.02491091263261197247357887006487721264874660274884,
0.02509251862664474061093109702616181054149913651710,
0.02525717697351328657763893489291540401679249790887,
0.02540464114326442690732349325450960796495815128648,
0.02553501298607099536450151815998273053431323202531,
0.02564830231130669156727699936154427063030445683730,
0.02574427177483327835345017378864237099131910116066,
0.02582279593614917829003082527854324007813305881338,
0.02588394414600359533197858687343537654901210069360,
0.02592769956371017513985574241157347171723158109308,
0.02595394793410606119738320085065067300844960043221,
0.02596268333963692375153481541246139454955940844745
).finished();
template <typename Scalar>
Array<Scalar, 30, 1> QuadratureKronrod<Scalar>::abscissaeGauss121 =
(Array<Scalar, 30, 1>() <<
0.99921012322743602203422958579764926639879897871133,
0.99584052511883817387674671337744065277489029497714,
0.98978789522222171736727898701609604257739315378694,
0.98106720175259818561857679982677003388053857922189,
0.96970178876505273372154409891379427254093434486825,
0.95572225583999610739723184582969950248009374476661,
0.93916627611642324949541901160970509641940342040120,
0.92007847617762755285665686251989682878376887601371,
0.89851031081004594193778932957262833016445844274707,
0.87451992264689831512930809991243580515918229443578,
0.84817198478592963249051549499437560129752871650678,
0.81953752616214575936851810851972357189949051896959,
0.78869373993226405456994479977721573524633292787923,
0.75572377530658568686884206660237310592890019956471,
0.72071651335573039943602106101352107776477399473324,
0.68376632738135543722293023922429715908759460433887,
0.64497282848947706781344789642044471716519001934666,
0.60444059704851036344420877631120172065042105359106,
0.56227890075394453917827258748599872906318823765940,
0.51860140005856974741788934848472130132984667628869,
0.47352584176170711110816305375279463800786800509984,
0.42717374158307838930745285353031192335344213618423,
0.37967005657679797715495267052188770405637443316239,
0.33114284826844819425235296535055270480012149637631,
0.28172293742326169169069486033944159830826306079538,
0.23154355137602933801034463134675544074353905193959,
0.18073996487342541724087694126185263123177216863905,
0.12944913539694500314644416464957577475987352436647,
0.07780933394953656941928550708222528757759478289772,
0.02595977230124779858917038540034482566031476071728
).finished();
template <typename Scalar>
Array<Scalar, 30, 1> QuadratureKronrod<Scalar>::weightsGauss121 =
(Array<Scalar, 30, 1>() <<
0.00202681196887375849643171020989232469531166822556,
0.00471272992695356864089482171407723594808497019372,
0.00738993116334545553151695602208606088222818020623,
0.01004755718228798435788576437705725649965174748768,
0.01267816647681596013149537926951423498833836430263,
0.01527461859678479930672603809882533517790938411507,
0.01782990101420772026039626124834856763385921958339,
0.02033712072945728677503214741710630146201711250534,
0.02278951694399781986378345819290020781016738421521,
0.02518047762152124837957096597236127913178083294419,
0.02750355674992479163522319763862224764840347075416,
0.02975249150078894524083648467348771033247515812411,
0.03192121901929632894945889953676047676669729228299,
0.03400389272494642283491440155525874118727622355286,
0.03599489805108450306657864628806233859424242002100,
0.03788886756924344403094079420927603181008428106381,
0.03968069545238079947012283481171000876280351129417,
0.04136555123558475561316383680665889688018700852151,
0.04293889283593564195423122065638280694921177196492,
0.04439647879578711332778416409137736966388498573401,
0.04573437971611448664719645529090933300793497425868,
0.04694898884891220484701315639470156627557490258344,
0.04803703181997118096366665272873365360250002924692,
0.04899557545575683538947568685789429835758389599909,
0.04982203569055018101115923089370331247921559724378,
0.05051418453250937459823873574165364323995616273742,
0.05107015606985562740454912073449103536619708311367,
0.05148845150098093399504439717705431173392382665958,
0.05176794317491018754380364302882373293234694549920,
0.05190787763122063973286493836226968018015159556564
).finished();
// Nodes and Weights - Rule 201
template <typename Scalar>
Array<Scalar, 101, 1> QuadratureKronrod<Scalar>::abscissaeGaussKronrod201 =
(Array<Scalar, 101, 1>() <<
0.99995250325234874194558759586872675230201032186296,
0.99971372677344123367822846934230067671834952730840,
0.99922816588380125603468689462902570985161537549449,
0.99849195063959581840016335918634916230485485042057,
0.99751361312272973925231594907328863008404380861059,
0.99629513473312514918613173224113103543643128814043,
0.99483262193692678214229984365392976193623306275107,
0.99312493703744345965200989284878347073177145886652,
0.99117498765102584468434111430887815181054026590303,
0.98898439524299174800441874580773663183933363710695,
0.98655201560314858543214329463373901430393735434646,
0.98387754070605701549610015551100816734436701685080,
0.98096284258061262094794383303858458336270892150820,
0.97780935848691828855378108842920192863523449426625,
0.97441692579132830191156952676419699735650628441883,
0.97078577576370633193089785789750538855055719947821,
0.96691753657125109640782216846696070235549924264129,
0.96281365425581552729365932603016638643733150673041,
0.95847452546444300989234207911968140986589441225372,
0.95390078292549174284933693089435764464522145101467,
0.94909405007764308807002661063238399920305087971147,
0.94405587013625597796277470641521874673972037338210,
0.93878704353080861159581415143454540129149440268213,
0.93328853504307954592433366813086250408354607429702,
0.92756205890488017513109041315467906526813611874056,
0.92160929814533395266695132848198745912458279773220,
0.91543138327874017569217880264508697295963148874566,
0.90902957098252969046712633778914606444327728958459,
0.90240571020837873902681113376935748186170440444374,
0.89556164497072698669852102243022776984818176899772,
0.88849879400991357098633030987871529168085698938796,
0.88121867938501841557331682542780558244549441102126,
0.87372330591888454232901721359869700713999812944025,
0.86601468849716462341073996967624296638031483930559,
0.85809450656528158256769359279995027785553637603413,
0.84996452787959128429336259142010465407379077950067,
0.84162692263159422803428490828685310746728377281023,
0.83308387988840082354291583384475567990749483030996,
0.82433731934785511555382066394577351308957189674952,
0.81538923833917625439398875864925800538255037651370,
0.80624197522998149898858119947772518581699983645897,
0.79689789239031447638957288218324598288952685596429,
0.78735913298215327121915096807989317961453460725592,
0.77762790964949547562755138683449010653853979993608,
0.76770672752390789522106835290910988619423163187483,
0.75759811851970717603566796443840077231310897190004,
0.74730443440010216722543283418354970398268442664090,
0.73682808980202070551242771482010100284327844624712,
0.72617175233016540458785543702154726618162507726741,
0.71533811757305644645996712270436596408439783859563,
0.70432973201100171130158275065992755531836865624424,
0.69314919935580196594864794167543726558700001793073,
0.68179934329913790750199866457132454892446683289894,
0.67028301560314101580258701432322661366980568402882,
0.65860294402143308554822559819231646499591256882672,
0.64676190851412927983263030445863043501973378424853,
0.63476288086691287961700686682300223062843045115192,
0.62260886020370777160419084517231224465381773228982,
0.61030274223394973052304014680666051705840336769498,
0.59784747024717872126480654514934063639489919232049,
0.58524615484722223751330407348246631581348705331813,
0.57250193262138119131687044352572544896003394967556,
0.55961785385987287004483883274572350988535188007656,
0.54659701206509416746799425718174990395624177593753,
0.53344264632810924391925934260941164781644110851200,
0.52015801988176305664681574945520853076893769042009,
0.50674632405992146013910672747973470564589036548717,
0.49321078920819093356930879344933399099072332535856,
0.47955477168853305490480433055889014820419073581020,
0.46578164977335804224921662339575458161165111021221,
0.45189474208663614330483287246151294430151576448075,
0.43789740217203151310897804362219596212570176348410,
0.42379309169388210181506692715279269905002159373794,
0.40958529167830154252886840005715770149536438916475,
0.39527743404816671610367673557861642687518028284140,
0.38087298162462995676336254886958740374970726512371,
0.36637548876362800231863519558827019975726941799314,
0.35178852637242172097234382954897056524931809638907,
0.33711562544519365010380511464074285765053795714571,
0.32236034390052915172247658239832542740219162302309,
0.30752631562753657120752788303988100046876429120433,
0.29261718803847196473755588823549438456153898917258,
0.27763657675183495616346814290881136285663496860995,
0.26258812037150347916892933625498214113202269453552,
0.24747551869798892096614882491742687591540876456389,
0.23230248184497396964950996320796411069750977150714,
0.21707269541726899854706722200296707797219389992710,
0.20178986409573599723604885953039646294369200355905,
0.18645773958437819065168393518669992652130113816299,
0.17108008053860327488753237470708980746585972511807,
0.15566062775725995230028233532247535151338751890639,
0.14020313723611397320751460468240551661687300626336,
0.12471139826072812045287156735452075155899823333651,
0.10918920358006111500342600657938488688489962996916,
0.09364033428354398098988456682945235155973991630929,
0.07806858281343663669481737120155257397635002744853,
0.06247776146923010010357548046587278110387007259524,
0.04687168242159163161492391293384830953706539908602,
0.03125415208386678081857435045254965009647374420346,
0.01562898442154308287221669999742934014775618285556,
0.00000000000000000000000000000000000000000000000000
).finished();
template <typename Scalar>
Array<Scalar, 101, 1> QuadratureKronrod<Scalar>::weightsGaussKronrod201 =
(Array<Scalar, 101, 1>() <<
0.00012796430957024721771296604719777847195024888314,
0.00035867672428027546451819698699002695000334366552,
0.00061229953852751686968468056548070834614262353518,
0.00085841483623935311664167374912297679663629462243,
0.00109796416132059890255397465155433695320668680377,
0.00133983780660382341754863019304498885110952126241,
0.00158539114055099209687612715239439499710635284278,
0.00182937001345660807993702363601705354484262856545,
0.00207023170435975873786445531287183441533108495909,
0.00231123008487149478622574422551013428738043877307,
0.00255360720035108161107860930247813105889546630505,
0.00279496754149865554132924610296587377583807221606,
0.00303416468796449379917327454133990046860593313429,
0.00327287902049999951685865323103972155152040933937,
0.00351196946843139471347132584863839017075918804593,
0.00375002082356796252973315848571211234815922368507,
0.00398619744931235184550297813723407560532468657842,
0.00422153240339578242265345682700445192052466529462,
0.00445663655824494510224150713533978978713271961637,
0.00469055184548748439481506164708745018600910075929,
0.00492264171642177778021256522028596859149482883314,
0.00515360688570317554082069990644640034295769630886,
0.00538389880957824664615043517317289909958011793608,
0.00561281343110871597561315793834039501636153255547,
0.00583984643867452187979812998241983823823136309861,
0.00606550320973303863921033440183559298376742116472,
0.00629012776973767504951202123451843743076930245062,
0.00651317411315535135623979587712921532296014614460,
0.00673423042383435906546110501890771393375794286618,
0.00695367647707533778618333444634079607272882365501,
0.00717178053315253341524750684836420331388733863189,
0.00738810306985931173687401288774170241141466081296,
0.00760230005117430829817610049263739864681050864527,
0.00781466520662034505085711719016354399072460775306,
0.00802541132258648471308962366547616916200657491446,
0.00823417501731623690079536275494453055496288986340,
0.00844066393687280440093304148919420862913744658522,
0.00864511004867877912656139959329107529390995475094,
0.00884768427998831020007201725385439489287388704377,
0.00904808029993671228835071165243690477400271230057,
0.00924604652391111724687570119177700799209325218608,
0.00944176898875185552314903500699258800726938238310,
0.00963538626179462391106485411435148851979409901308,
0.00982663642373088065571326334283803573470396510601,
0.01001530101161305053268537450183723383477657205865,
0.01020153095088495986015919422291444604170764482781,
0.01038543929706851271926198711586114579021961800284,
0.01056679983247565098373215943168121363502057278619,
0.01074542170778693080646692567379385062368419611030,
0.01092142841500597232724852424011180927323636614697,
0.01109491257094606883971232155924910988765741030054,
0.01126567746332956237923986454364445975020263538030,
0.01143355579967040516909625306002457417492109489982,
0.01159864925643444521982733110763019057800050447511,
0.01176103385541580107532667409174481684699820604850,
0.01192053786750440393445381605750602287206317500254,
0.01207701451438569994891221026442585729555689105328,
0.01223054787113266210109559371404225931637605012182,
0.01238120033058132478094426900828573870330496911285,
0.01252882177740552594442502987847792106610336206449,
0.01267328363219971069040254068582595376734875571756,
0.01281465559402401820734387481377863160543256944343,
0.01295298874891947508181321347643329979562489424432,
0.01308815204304083947131249628348670851036112224233,
0.01322003331459425763799456688719462334189620391816,
0.01334869039477997219532795119897057181197377482865,
0.01347416490042760653129384849738331885547322480541,
0.01359634288062617797837336787649308030170304524353,
0.01371512721021576932690771893822620264523809273465,
0.01383056582631592119521912896609004389004651368400,
0.01394269234050930765052410813271065280007760112975,
0.01405140838748433908894290183169630886722307263276,
0.01415663080386553141797847993528261640630526208010,
0.01425839919822706151742984801432832105691149679315,
0.01435674034589556885653893978408636354274396518129,
0.01445157028450311174994356610608770124062851800510,
0.01454281897629966555537908242478331367093974940807,
0.01463051894733967823881185958389904589719486669315,
0.01471469106719224107616070689745858786072765279902,
0.01479526485272091523273713296861772987622838214603,
0.01487218274551550851114896175149252660492892913239,
0.01494547117901571779314143269144247770437604078025,
0.01501514584992601775929409587145443755032002323588,
0.01508114903502136704084960300677971411706204873991,
0.01514343516330660012211995270464269800292539698574,
0.01520202535514477439125881646888569025211919463334,
0.01525693069928626681152511683204470629971399732269,
0.01530810567790395821753937559915116616801682403691,
0.01535551634411844871530936744265760333339456402763,
0.01539917910754267008730746329865897219178834017417,
0.01543910086714820098073247575245749712612887092387,
0.01547524789208464777691069202608380676296793168412,
0.01550759760659890369589537474066318545807510752952,
0.01553616215856523293822391298200717744826237954682,
0.01556094454341676462938645995315419106586887459681,
0.01558192251438053678351080364024221646030414904878,
0.01559908471168710670698089639871094604147763682664,
0.01561243933403481989468460959619688421126306083370,
0.01562198563724487346851127872839698584387203112330,
0.01562771265700169003321136142695117550866696845783,
0.01562962018460484993210603370275515394376090869371
).finished();
template <typename Scalar>
Array<Scalar, 50, 1> QuadratureKronrod<Scalar>::abscissaeGauss201 =
(Array<Scalar, 50, 1>() <<
0.99971372677344123367822846934230067671834952730840,
0.99849195063959581840016335918634916230485485042057,
0.99629513473312514918613173224113103543643128814043,
0.99312493703744345965200989284878347073177145886652,
0.98898439524299174800441874580773663183933363710695,
0.98387754070605701549610015551100816734436701685080,
0.97780935848691828855378108842920192863523449426625,
0.97078577576370633193089785789750538855055719947821,
0.96281365425581552729365932603016638643733150673041,
0.95390078292549174284933693089435764464522145101467,
0.94405587013625597796277470641521874673972037338210,
0.93328853504307954592433366813086250408354607429702,
0.92160929814533395266695132848198745912458279773220,
0.90902957098252969046712633778914606444327728958459,
0.89556164497072698669852102243022776984818176899772,
0.88121867938501841557331682542780558244549441102126,
0.86601468849716462341073996967624296638031483930559,
0.84996452787959128429336259142010465407379077950067,
0.83308387988840082354291583384475567990749483030996,
0.81538923833917625439398875864925800538255037651370,
0.79689789239031447638957288218324598288952685596429,
0.77762790964949547562755138683449010653853979993608,
0.75759811851970717603566796443840077231310897190004,
0.73682808980202070551242771482010100284327844624712,
0.71533811757305644645996712270436596408439783859563,
0.69314919935580196594864794167543726558700001793073,
0.67028301560314101580258701432322661366980568402882,
0.64676190851412927983263030445863043501973378424853,
0.62260886020370777160419084517231224465381773228982,
0.59784747024717872126480654514934063639489919232049,
0.57250193262138119131687044352572544896003394967556,
0.54659701206509416746799425718174990395624177593753,
0.52015801988176305664681574945520853076893769042009,
0.49321078920819093356930879344933399099072332535856,
0.46578164977335804224921662339575458161165111021221,
0.43789740217203151310897804362219596212570176348410,
0.40958529167830154252886840005715770149536438916475,
0.38087298162462995676336254886958740374970726512371,
0.35178852637242172097234382954897056524931809638907,
0.32236034390052915172247658239832542740219162302309,
0.29261718803847196473755588823549438456153898917258,
0.26258812037150347916892933625498214113202269453552,
0.23230248184497396964950996320796411069750977150714,
0.20178986409573599723604885953039646294369200355905,
0.17108008053860327488753237470708980746585972511807,
0.14020313723611397320751460468240551661687300626336,
0.10918920358006111500342600657938488688489962996916,
0.07806858281343663669481737120155257397635002744853,
0.04687168242159163161492391293384830953706539908602,
0.01562898442154308287221669999742934014775618285556
).finished();
template <typename Scalar>
Array<Scalar, 50, 1> QuadratureKronrod<Scalar>::weightsGauss201 =
(Array<Scalar, 50, 1>() <<
0.00073463449050567173040632065833033639067047356248,
0.00170939265351810523952935837149119524373138549146,
0.00268392537155348241943959042900112008193111495100,
0.00365596120132637518234245872752519569920656740515,
0.00462445006342211935109578908297847665035249529489,
0.00558842800386551515721194634843921073131869400808,
0.00654694845084532276415210333149526369993836336648,
0.00749907325546471157882874401639778316358347894815,
0.00844387146966897140262083490230100193464445988410,
0.00938041965369445795141823766081211873078704323867,
0.01030780257486896958578210172783537797605834384143,
0.01122511402318597711722157336633358477722641956438,
0.01213145766297949740774479244874817073696312331126,
0.01302594789297154228555858375890179013496473584175,
0.01390771070371877268795414910800463779518081214312,
0.01477588452744130176887998752035425716938874311460,
0.01562962107754600272393686595379192555246997980994,
0.01646808617614521264310498008821078082116766160380,
0.01729046056832358243934419836674167481162350856517,
0.01809594072212811666439075142049303134757874495839,
0.01888373961337490455294116588154323429711127634742,
0.01965308749443530586538147024544406555526959949125,
0.02040323264620943276683885165758377060570969930262,
0.02113344211252764154267230044096968163532972887451,
0.02184300241624738631395374130439802476534899982325,
0.02253122025633627270179697093167396234015893534871,
0.02319742318525412162248885418272728845115448573609,
0.02384096026596820596256041190228343214470744909262,
0.02446120270795705271997502334977289064629573239780,
0.02505754448157958970376422562092326422383855852793,
0.02562940291020811607564200986215087092697767002027,
0.02617621923954567634230874175730188501127513119069,
0.02669745918357096266038466418633635063465575039001,
0.02719261344657688013649156780217069226698789601200,
0.02766119822079238829420415587042645529240035866422,
0.02810275565910117331764833018699455045141809940021,
0.02851685432239509799093676286445787325984272548397,
0.02890308960112520313487622813451526531560786805526,
0.02926108411063827662011902349564095444308419504535,
0.02959048805991264251175451067883658517280628507137,
0.02989097959333283091683680666859582765809141426080,
0.03016226510516914491906868161047923265710232578271,
0.03040407952645482001650785981882517660560724831012,
0.03061618658398044849645944326205319285308602378906,
0.03079837903115259042771390303055976009497083447037,
0.03095047885049098823406346347074792738298717776694,
0.03107233742756651658781017024291803484591543634796,
0.03116383569620990678381832121718665334383636868393,
0.03122488425484935773237649864809813488180274068218,
0.03125542345386335694764247438619802878783383672609
).finished();
}
#endif // EIGEN_QUADRATURE_KRONROD_H