Variables
o2scl_inte_gk_coeffs Namespace Reference

A namespace for the GSL adaptive Gauss-Kronrod integration coefficients. More...

Variables

static const double qk15_xgk [8]
 Abscissae of the 15-point Kronrod rule. More...
 
static const double qk15_wg [4]
 Weights of the 7-point Gauss rule. More...
 
static const double qk15_wgk [8]
 Weights of the 15-point Kronrod rule. More...
 
static const double qk21_xgk [11]
 Abscissae of the 21-point Kronrod rule. More...
 
static const double qk21_wg [5]
 Weights of the 10-point Gauss rule. More...
 
static const double qk21_wgk [11]
 Weights of the 21-point Kronrod rule. More...
 
static const double qk31_xgk [16]
 Abscissae of the 31-point Kronrod rule. More...
 
static const double qk31_wg [8]
 Weights of the 15-point Gauss rule. More...
 
static const double qk31_wgk [16]
 Weights of the 31-point Kronrod rule. More...
 
static const double qk41_xgk [21]
 Abscissae of the 41-point Kronrod rule. More...
 
static const double qk41_wg [11]
 Weights of the 20-point Gauss rule. More...
 
static const double qk41_wgk [21]
 Weights of the 41-point Kronrod rule. More...
 
static const double qk51_xgk [26]
 Abscissae of the 51-point Kronrod rule. More...
 
static const double qk51_wg [13]
 Weights of the 25-point Gauss rule. More...
 
static const double qk51_wgk [26]
 Weights of the 51-point Kronrod rule. More...
 
static const double qk61_xgk [31]
 Abscissae of the 61-point Kronrod rule.
 
static const double qk61_wg [15]
 Weights of the 30-point Gauss rule. More...
 
static const double qk61_wgk [31]
 Weights of the 61-point Kronrod rule.
 

Detailed Description

The storage scheme follows that of QUADPACK: symmetry about the origin permits storing only those abscissae in the interval $ [0, 1). $ Similiarly for the weights. The odd-indexed abscissae xgk[1], xgk[3],... belong to the low-order Gauss rule. For the full Gauss-Kronrod rule, the array wgk[] holds the weights corresponding to the abscissae xgk[]. For the low-order rule, wg[i] is the weight correpsonding to xgk[2*i+1].

Documentation from GSL:
Gauss quadrature weights and kronrod quadrature abscissae and weights as evaluated with 80 decimal digit arithmetic by L. W. Fullerton, Bell Labs, Nov. 1981.

Variable Documentation

◆ qk15_wg

const double o2scl_inte_gk_coeffs::qk15_wg[4]
static
Initial value:
=
{
0.129484966168869693270611432679082,
0.279705391489276667901467771423780,
0.381830050505118944950369775488975,
0.417959183673469387755102040816327
}

Definition at line 70 of file inte_kronrod_gsl.h.

◆ qk15_wgk

const double o2scl_inte_gk_coeffs::qk15_wgk[8]
static
Initial value:
=
{
0.022935322010529224963732008058970,
0.063092092629978553290700663189204,
0.104790010322250183839876322541518,
0.140653259715525918745189590510238,
0.169004726639267902826583426598550,
0.190350578064785409913256402421014,
0.204432940075298892414161999234649,
0.209482141084727828012999174891714
}

Definition at line 79 of file inte_kronrod_gsl.h.

◆ qk15_xgk

const double o2scl_inte_gk_coeffs::qk15_xgk[8]
static
Initial value:
={
0.991455371120812639206854697526329,
0.949107912342758524526189684047851,
0.864864423359769072789712788640926,
0.741531185599394439863864773280788,
0.586087235467691130294144838258730,
0.405845151377397166906606412076961,
0.207784955007898467600689403773245,
0.000000000000000000000000000000000
}

Definition at line 58 of file inte_kronrod_gsl.h.

◆ qk21_wg

const double o2scl_inte_gk_coeffs::qk21_wg[5]
static
Initial value:
=
{
0.066671344308688137593568809893332,
0.149451349150580593145776339657697,
0.219086362515982043995534934228163,
0.269266719309996355091226921569469,
0.295524224714752870173892994651338
}

Definition at line 108 of file inte_kronrod_gsl.h.

◆ qk21_wgk

const double o2scl_inte_gk_coeffs::qk21_wgk[11]
static
Initial value:
=
{
0.011694638867371874278064396062192,
0.032558162307964727478818972459390,
0.054755896574351996031381300244580,
0.075039674810919952767043140916190,
0.093125454583697605535065465083366,
0.109387158802297641899210590325805,
0.123491976262065851077958109831074,
0.134709217311473325928054001771707,
0.142775938577060080797094273138717,
0.147739104901338491374841515972068,
0.149445554002916905664936468389821
}

Definition at line 118 of file inte_kronrod_gsl.h.

◆ qk21_xgk

const double o2scl_inte_gk_coeffs::qk21_xgk[11]
static
Initial value:
=
{
0.995657163025808080735527280689003,
0.973906528517171720077964012084452,
0.930157491355708226001207180059508,
0.865063366688984510732096688423493,
0.780817726586416897063717578345042,
0.679409568299024406234327365114874,
0.562757134668604683339000099272694,
0.433395394129247190799265943165784,
0.294392862701460198131126603103866,
0.148874338981631210884826001129720,
0.000000000000000000000000000000000
}

Definition at line 92 of file inte_kronrod_gsl.h.

◆ qk31_wg

const double o2scl_inte_gk_coeffs::qk31_wg[8]
static
Initial value:
=
{
0.030753241996117268354628393577204,
0.070366047488108124709267416450667,
0.107159220467171935011869546685869,
0.139570677926154314447804794511028,
0.166269205816993933553200860481209,
0.186161000015562211026800561866423,
0.198431485327111576456118326443839,
0.202578241925561272880620199967519
}

Definition at line 155 of file inte_kronrod_gsl.h.

◆ qk31_wgk

const double o2scl_inte_gk_coeffs::qk31_wgk[16]
static
Initial value:
=
{
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
}

Definition at line 168 of file inte_kronrod_gsl.h.

◆ qk31_xgk

const double o2scl_inte_gk_coeffs::qk31_xgk[16]
static
Initial value:
=
{
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
}

Definition at line 134 of file inte_kronrod_gsl.h.

◆ qk41_wg

const double o2scl_inte_gk_coeffs::qk41_wg[11]
static
Initial value:
=
{
0.017614007139152118311861962351853,
0.040601429800386941331039952274932,
0.062672048334109063569506535187042,
0.083276741576704748724758143222046,
0.101930119817240435036750135480350,
0.118194531961518417312377377711382,
0.131688638449176626898494499748163,
0.142096109318382051329298325067165,
0.149172986472603746787828737001969,
0.152753387130725850698084331955098
}

Definition at line 215 of file inte_kronrod_gsl.h.

◆ qk41_wgk

const double o2scl_inte_gk_coeffs::qk41_wgk[21]
static
Initial value:
=
{
0.003073583718520531501218293246031,
0.008600269855642942198661787950102,
0.014626169256971252983787960308868,
0.020388373461266523598010231432755,
0.025882133604951158834505067096153,
0.031287306777032798958543119323801,
0.036600169758200798030557240707211,
0.041668873327973686263788305936895,
0.046434821867497674720231880926108,
0.050944573923728691932707670050345,
0.055195105348285994744832372419777,
0.059111400880639572374967220648594,
0.062653237554781168025870122174255,
0.065834597133618422111563556969398,
0.068648672928521619345623411885368,
0.071054423553444068305790361723210,
0.073030690332786667495189417658913,
0.074582875400499188986581418362488,
0.075704497684556674659542775376617,
0.076377867672080736705502835038061,
0.076600711917999656445049901530102
}

Definition at line 230 of file inte_kronrod_gsl.h.

◆ qk41_xgk

const double o2scl_inte_gk_coeffs::qk41_xgk[21]
static
Initial value:
=
{
0.998859031588277663838315576545863,
0.993128599185094924786122388471320,
0.981507877450250259193342994720217,
0.963971927277913791267666131197277,
0.940822633831754753519982722212443,
0.912234428251325905867752441203298,
0.878276811252281976077442995113078,
0.839116971822218823394529061701521,
0.795041428837551198350638833272788,
0.746331906460150792614305070355642,
0.693237656334751384805490711845932,
0.636053680726515025452836696226286,
0.575140446819710315342946036586425,
0.510867001950827098004364050955251,
0.443593175238725103199992213492640,
0.373706088715419560672548177024927,
0.301627868114913004320555356858592,
0.227785851141645078080496195368575,
0.152605465240922675505220241022678,
0.076526521133497333754640409398838,
0.000000000000000000000000000000000
}

Definition at line 189 of file inte_kronrod_gsl.h.

◆ qk51_wg

const double o2scl_inte_gk_coeffs::qk51_wg[13]
static
Initial value:
=
{
0.011393798501026287947902964113235,
0.026354986615032137261901815295299,
0.040939156701306312655623487711646,
0.054904695975835191925936891540473,
0.068038333812356917207187185656708,
0.080140700335001018013234959669111,
0.091028261982963649811497220702892,
0.100535949067050644202206890392686,
0.108519624474263653116093957050117,
0.114858259145711648339325545869556,
0.119455763535784772228178126512901,
0.122242442990310041688959518945852,
0.123176053726715451203902873079050
}

Definition at line 287 of file inte_kronrod_gsl.h.

◆ qk51_wgk

const double o2scl_inte_gk_coeffs::qk51_wgk[26]
static
Initial value:
=
{
0.001987383892330315926507851882843,
0.005561932135356713758040236901066,
0.009473973386174151607207710523655,
0.013236229195571674813656405846976,
0.016847817709128298231516667536336,
0.020435371145882835456568292235939,
0.024009945606953216220092489164881,
0.027475317587851737802948455517811,
0.030792300167387488891109020215229,
0.034002130274329337836748795229551,
0.037116271483415543560330625367620,
0.040083825504032382074839284467076,
0.042872845020170049476895792439495,
0.045502913049921788909870584752660,
0.047982537138836713906392255756915,
0.050277679080715671963325259433440,
0.052362885806407475864366712137873,
0.054251129888545490144543370459876,
0.055950811220412317308240686382747,
0.057437116361567832853582693939506,
0.058689680022394207961974175856788,
0.059720340324174059979099291932562,
0.060539455376045862945360267517565,
0.061128509717053048305859030416293,
0.061471189871425316661544131965264,
0.061580818067832935078759824240066
}

Definition at line 305 of file inte_kronrod_gsl.h.

◆ qk51_xgk

const double o2scl_inte_gk_coeffs::qk51_xgk[26]
static
Initial value:
=
{
0.999262104992609834193457486540341,
0.995556969790498097908784946893902,
0.988035794534077247637331014577406,
0.976663921459517511498315386479594,
0.961614986425842512418130033660167,
0.942974571228974339414011169658471,
0.920747115281701561746346084546331,
0.894991997878275368851042006782805,
0.865847065293275595448996969588340,
0.833442628760834001421021108693570,
0.797873797998500059410410904994307,
0.759259263037357630577282865204361,
0.717766406813084388186654079773298,
0.673566368473468364485120633247622,
0.626810099010317412788122681624518,
0.577662930241222967723689841612654,
0.526325284334719182599623778158010,
0.473002731445714960522182115009192,
0.417885382193037748851814394594572,
0.361172305809387837735821730127641,
0.303089538931107830167478909980339,
0.243866883720988432045190362797452,
0.183718939421048892015969888759528,
0.122864692610710396387359818808037,
0.061544483005685078886546392366797,
0.000000000000000000000000000000000
}

Definition at line 256 of file inte_kronrod_gsl.h.

◆ qk61_wg

const double o2scl_inte_gk_coeffs::qk61_wg[15]
static
Initial value:
=
{
0.007968192496166605615465883474674,
0.018466468311090959142302131912047,
0.028784707883323369349719179611292,
0.038799192569627049596801936446348,
0.048402672830594052902938140422808,
0.057493156217619066481721689402056,
0.065974229882180495128128515115962,
0.073755974737705206268243850022191,
0.080755895229420215354694938460530,
0.086899787201082979802387530715126,
0.092122522237786128717632707087619,
0.096368737174644259639468626351810,
0.099593420586795267062780282103569,
0.101762389748405504596428952168554,
0.102852652893558840341285636705415
}

Definition at line 372 of file inte_kronrod_gsl.h.

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