![]() |
Object-oriented Scientific Computing Library: Version 0.910
|
A namespace for the GSL adaptive Gauss-Kronrod integration coefficients. More...
The storage scheme follows that of QUADPACK: symmetry about the origin permits storing only those abscissae in the interval 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.
Variables | |
static const double | qk15_xgk [8] |
Abscissae of the 15-point Kronrod rule. | |
static const double | qk15_wg [4] |
Weights of the 7-point Gauss rule. | |
static const double | qk15_wgk [8] |
Weights of the 15-point Kronrod rule. | |
static const double | qk21_xgk [11] |
Abscissae of the 21-point Kronrod rule. | |
static const double | qk21_wg [5] |
Weights of the 10-point Gauss rule. | |
static const double | qk21_wgk [11] |
Weights of the 21-point Kronrod rule. | |
static const double | qk31_xgk [16] |
Abscissae of the 31-point Kronrod rule. | |
static const double | qk31_wg [8] |
Weights of the 15-point Gauss rule. | |
static const double | qk31_wgk [16] |
Weights of the 31-point Kronrod rule. | |
static const double | qk41_xgk [21] |
Abscissae of the 41-point Kronrod rule. | |
static const double | qk41_wg [11] |
Weights of the 20-point Gauss rule. | |
static const double | qk41_wgk [21] |
Weights of the 41-point Kronrod rule. | |
static const double | qk51_xgk [26] |
Abscissae of the 51-point Kronrod rule. | |
static const double | qk51_wg [13] |
Weights of the 25-point Gauss rule. | |
static const double | qk51_wgk [26] |
Weights of the 51-point Kronrod rule. | |
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. | |
static const double | qk61_wgk [31] |
Weights of the 61-point Kronrod rule. |
const double o2scl_inte_gk_coeffs::qk15_xgk[8] [static] |
{ 0.991455371120812639206854697526329, 0.949107912342758524526189684047851, 0.864864423359769072789712788640926, 0.741531185599394439863864773280788, 0.586087235467691130294144838258730, 0.405845151377397166906606412076961, 0.207784955007898467600689403773245, 0.000000000000000000000000000000000 }
Definition at line 53 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk15_wg[4] [static] |
{ 0.129484966168869693270611432679082, 0.279705391489276667901467771423780, 0.381830050505118944950369775488975, 0.417959183673469387755102040816327 }
Definition at line 65 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk15_wgk[8] [static] |
{ 0.022935322010529224963732008058970, 0.063092092629978553290700663189204, 0.104790010322250183839876322541518, 0.140653259715525918745189590510238, 0.169004726639267902826583426598550, 0.190350578064785409913256402421014, 0.204432940075298892414161999234649, 0.209482141084727828012999174891714 }
Definition at line 74 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk21_xgk[11] [static] |
{ 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 87 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk21_wg[5] [static] |
{ 0.066671344308688137593568809893332, 0.149451349150580593145776339657697, 0.219086362515982043995534934228163, 0.269266719309996355091226921569469, 0.295524224714752870173892994651338 }
Definition at line 103 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk21_wgk[11] [static] |
{ 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 113 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk31_xgk[16] [static] |
{ 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 129 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk31_wg[8] [static] |
{ 0.030753241996117268354628393577204, 0.070366047488108124709267416450667, 0.107159220467171935011869546685869, 0.139570677926154314447804794511028, 0.166269205816993933553200860481209, 0.186161000015562211026800561866423, 0.198431485327111576456118326443839, 0.202578241925561272880620199967519 }
Definition at line 150 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk31_wgk[16] [static] |
{ 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 163 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk41_xgk[21] [static] |
{ 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 184 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk41_wg[11] [static] |
{ 0.017614007139152118311861962351853, 0.040601429800386941331039952274932, 0.062672048334109063569506535187042, 0.083276741576704748724758143222046, 0.101930119817240435036750135480350, 0.118194531961518417312377377711382, 0.131688638449176626898494499748163, 0.142096109318382051329298325067165, 0.149172986472603746787828737001969, 0.152753387130725850698084331955098 }
Definition at line 210 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk41_wgk[21] [static] |
{ 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 225 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk51_xgk[26] [static] |
{ 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 251 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk51_wg[13] [static] |
{ 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 282 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk51_wgk[26] [static] |
{ 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 300 of file gsl_inte_kronrod.h.
const double o2scl_inte_gk_coeffs::qk61_wg[15] [static] |
{ 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 367 of file gsl_inte_kronrod.h.
Documentation generated with Doxygen. Provided under the GNU Free Documentation License (see License Information).