ROOT  6.06/09
Reference Guide
Functions | Variables
ROOT::Math::Cephes Namespace Reference

Functions

double igamc (double a, double x)
 incomplete complementary gamma function igamc(a, x) = 1 - igam(a, x) More...
 
double igam (double a, double x)
 
double lgam (double x)
 
static double stirf (double x)
 
double gamma (double x)
 
double beta (double z, double w)
 
double incbet (double aa, double bb, double xx)
 DESCRIPTION: More...
 
double incbcf (double a, double b, double x)
 
double incbd (double a, double b, double x)
 
double pseries (double a, double b, double x)
 
double erfc (double a)
 
double erf (double x)
 
double ndtri (double y)
 
double igami (double a, double y)
 
double incbi (double a, double b, double y)
 

Variables

static double kBig = 4.503599627370496e15
 
static double kBiginv = 2.22044604925031308085e-16
 
static double LS2PI = 0.91893853320467274178
 
static double A []
 
static double B []
 
static double C []
 
static double P []
 
static double Q []
 
static double STIR [5]
 
static double erfP []
 
static double erfQ []
 
static double erfR []
 
static double erfS []
 
static double erfT []
 
static double erfU []
 
static double s2pi = 2.50662827463100050242E0
 
static double P0 [5]
 
static double Q0 [8]
 
static double P1 [9]
 
static double Q1 [8]
 
static double P2 [9]
 
static double Q2 [8]
 

Function Documentation

double ROOT::Math::Cephes::beta ( double  z,
double  w 
)

Definition at line 428 of file SpecFuncCephes.cxx.

double ROOT::Math::Cephes::erf ( double  x)

Definition at line 926 of file SpecFuncCephes.cxx.

Referenced by ROOT::Math::erf(), and erfc().

double ROOT::Math::Cephes::erfc ( double  a)

Definition at line 874 of file SpecFuncCephes.cxx.

Referenced by erf(), and ROOT::Math::erfc().

double ROOT::Math::Cephes::gamma ( double  x)

Definition at line 339 of file SpecFuncCephes.cxx.

Referenced by TLorentzVector::Boost(), ROOT::Math::VectorUtil::boost(), ROOT::Math::VectorUtil::boostX(), ROOT::Math::VectorUtil::boostY(), ROOT::Math::VectorUtil::boostZ(), ROOT::Math::RandomFunctions< EngineType, ROOT::Math::GSLRandomEngine >::BreitWigner(), ROOT::Math::Random< Engine >::BreitWigner(), ClassImp(), ParamHistFunc::createParamSet(), RooStats::HistFactory::RooBarlowBeestonLL::evaluate(), TF1::GetQuantiles(), incbet(), ROOT::Minuit2::SimplexBuilder::Minimum(), TMinuit::mnsimp(), pseries(), TMath::Quantiles(), TLorentzRotation::SetBoost(), ROOT::Math::Boost::SetComponents(), TMVA::SVWorkingSet::TakeStep(), TMVA::SVWorkingSet::TakeStepReg(), testStatFunc(), ROOT::Math::tgamma(), TMultiLayerPerceptron::Train(), and TMVA::MethodMLP::UpdateRegulators().

double ROOT::Math::Cephes::igam ( double  a,
double  x 
)

Definition at line 127 of file SpecFuncCephes.cxx.

Referenced by igamc(), and ROOT::Math::inc_gamma().

double ROOT::Math::Cephes::igamc ( double  a,
double  x 
)

incomplete complementary gamma function igamc(a, x) = 1 - igam(a, x)

Definition at line 51 of file SpecFuncCephes.cxx.

Referenced by igam(), igami(), and ROOT::Math::inc_gamma_c().

double ROOT::Math::Cephes::igami ( double  a,
double  y 
)

Definition at line 225 of file SpecFuncCephesInv.cxx.

Referenced by ROOT::Math::chisquared_quantile(), ROOT::Math::chisquared_quantile_c(), ROOT::Math::gamma_quantile(), and ROOT::Math::gamma_quantile_c().

double ROOT::Math::Cephes::incbcf ( double  a,
double  b,
double  x 
)

Definition at line 581 of file SpecFuncCephes.cxx.

Referenced by incbet().

double ROOT::Math::Cephes::incbd ( double  a,
double  b,
double  x 
)

Definition at line 674 of file SpecFuncCephes.cxx.

Referenced by incbet().

double ROOT::Math::Cephes::incbet ( double  aa,
double  bb,
double  xx 
)

DESCRIPTION:

Returns incomplete beta integral of the arguments, evaluated from zero to x. The function is defined as 

             x
-            -

| (a+b) | | a-1 b-1

--------— t (1-t) dt.
(a) (b) -

0

The domain of definition is 0 <= x <= 1. In this implementation a and b are restricted to positive values. The integral from x to 1 may be obtained by the symmetry relation

1 - incbet( a, b, x ) = incbet( b, a, 1-x ).

The integral is evaluated by a continued fraction expansion or, when b*x is small, by a power series.

ACCURACY:

Tested at uniformly distributed random points (a,b,x) with a and b in "domain" and x between 0 and 1. Relative error arithmetic domain # trials peak rms IEEE 0,5 10000 6.9e-15 4.5e-16 IEEE 0,85 250000 2.2e-13 1.7e-14 IEEE 0,1000 30000 5.3e-12 6.3e-13 IEEE 0,10000 250000 9.3e-11 7.1e-12 IEEE 0,100000 10000 8.7e-10 4.8e-11 Outputs smaller than the IEEE gradual underflow threshold were excluded from these statistics.

ERROR MESSAGES: message condition value returned incbet domain x<0, x>1 0.0 incbet underflow 0.0

Cephes Math Library, Release 2.8: June, 2000 Copyright 1984, 1995, 2000 by Stephen L. Moshier

Definition at line 484 of file SpecFuncCephes.cxx.

Referenced by ROOT::Math::inc_beta(), and incbi().

double ROOT::Math::Cephes::incbi ( double  a,
double  b,
double  y 
)

Definition at line 411 of file SpecFuncCephesInv.cxx.

Referenced by ROOT::Math::beta_quantile(), ROOT::Math::beta_quantile_c(), ROOT::Math::fdistribution_quantile(), and ROOT::Math::fdistribution_quantile_c().

double ROOT::Math::Cephes::lgam ( double  x)

Definition at line 197 of file SpecFuncCephes.cxx.

Referenced by beta(), igam(), igamc(), igami(), incbet(), incbi(), ROOT::Math::lgamma(), and pseries().

double ROOT::Math::Cephes::ndtri ( double  y)

Definition at line 137 of file SpecFuncCephesInv.cxx.

Referenced by igami(), incbi(), ROOT::Math::lognormal_quantile(), ROOT::Math::lognormal_quantile_c(), ROOT::Math::normal_quantile(), and ROOT::Math::normal_quantile_c().

double ROOT::Math::Cephes::pseries ( double  a,
double  b,
double  x 
)

Definition at line 766 of file SpecFuncCephes.cxx.

Referenced by incbet().

static double ROOT::Math::Cephes::stirf ( double  x)
static

Definition at line 316 of file SpecFuncCephes.cxx.

Referenced by gamma().

Variable Documentation

double ROOT::Math::Cephes::A[]
static
Initial value:
= {
8.11614167470508450300E-4,
-5.95061904284301438324E-4,
7.93650340457716943945E-4,
-2.77777777730099687205E-3,
8.33333333333331927722E-2
}

Definition at line 170 of file SpecFuncCephes.cxx.

Referenced by RooNovosibirsk::analyticalIntegral(), TUnfold::CreateSparseMatrix(), ROOT::Math::crystalball_integral(), ROOT::TMetaUtils::DataMemberInfo__ValidArrayIndex(), TPad::DrawDist(), ROOT::Math::SDeterminant< n, idim >::Dsfact(), PiecewiseInterpolation::evaluate(), RooStats::HistFactory::RooBarlowBeestonLL::evaluate(), fitFunc(), TCling::FuncTempInfo_Title(), gsl_poly_complex_solve_cubic(), gsl_poly_complex_solve_quartic(), makePoints(), NormalEqn(), TOCCToStep::OCCDocCreation(), ROOT::TMetaUtils::ReSubstTemplateArg(), TPad::ShowGuidelines(), test1(), test10(), test14(), test16(), test17(), test2(), test24(), test3(), test4(), test5(), test6(), test8(), test9(), test_smatrix_op(), test_smatrix_sym_op(), test_tmatrix_op(), test_tmatrix_sym_op(), testMT_C(), testMT_S(), testMT_T(), TClingTypedefInfo::Title(), TClingMethodInfo::Title(), and TClingClassInfo::Title().

double ROOT::Math::Cephes::B[]
static
Initial value:
= {
-1.37825152569120859100E3,
-3.88016315134637840924E4,
-3.31612992738871184744E5,
-1.16237097492762307383E6,
-1.72173700820839662146E6,
-8.53555664245765465627E5
}

Definition at line 178 of file SpecFuncCephes.cxx.

Referenced by RooNovosibirsk::analyticalIntegral(), TSpline5::BuildCoeff(), counterclockwiseadapt(), ROOT::Math::crystalball_function(), ROOT::Math::crystalball_integral(), RooStats::HistFactory::RooBarlowBeestonLL::evaluate(), fitFunc(), TMVA::ROCCalc::GetSignificance(), gsl_poly_complex_solve_cubic(), gsl_poly_complex_solve_quartic(), TUnfold::InvertMSparseSymmPos(), makePoints(), TGLMatrix::MultLeft(), TGLMatrix::MultRight(), NormalEqn(), TGWin32::ReadGIF(), TEveBoxProjectedGL::RenderPoints(), TSpline3::SaveAs(), TSpline5::SaveAs(), test1(), test10(), test14(), test16(), test24(), test3(), test_smatrix_op(), test_smatrix_sym_op(), test_tmatrix_op(), test_tmatrix_sym_op(), testATBA_C(), testATBA_C2(), testATBA_S(), testATBA_S2(), testATBA_T(), testATBA_T2(), testMM(), testMM_C(), testMM_T(), TMVA::StatDialogMVAEffs::UpdateSignificanceHists(), and TGWin32::WriteGIF().

double ROOT::Math::Cephes::C[]
static
Initial value:
= {
-3.51815701436523470549E2,
-1.70642106651881159223E4,
-2.20528590553854454839E5,
-1.13933444367982507207E6,
-2.53252307177582951285E6,
-2.01889141433532773231E6
}

Definition at line 187 of file SpecFuncCephes.cxx.

Referenced by TSpline3::BuildCoeff(), TSpline5::BuildCoeff(), ROOT::Vc::Common::LogImpl< Base >::calc(), RooAbsData::corrcovMatrix(), THnBase::CreateHnAny(), ROOT::Math::crystalball_cdf(), ROOT::Math::crystalball_cdf_c(), ROOT::Math::crystalball_integral(), ROOT::Math::crystalball_pdf(), RooStats::HistFactory::RooBarlowBeestonLL::evaluate(), EvaluateExpr(), ExecAutoParse(), ROOT::Vc::Common::exp(), TClingCallbacks::FileNotFound(), fitFunc(), TGLMatrix::GetBaseVec(), TCling::GetObjectAddress(), RooAbsReal::getPropagatedError(), ROOT::Vc::Common::LogImpl< Base >::log_series(), TClingCallbacks::LookupObject(), makePoints(), TGLMatrix::MoveLF(), TGLMatrix::MultLeft(), TGLMatrix::MultRight(), ROOT::Math::CoordinateTraits< C >::name(), TClingDataMemberInfo::Offset(), RooAbsReal::plotOnWithErrorBand(), TGLMatrix::RotatePF(), TSpline3::SaveAs(), TSpline5::SaveAs(), TClingCallFunc::SetArg(), TGLMatrix::SetBaseVec(), TCling::SetDeclAttr(), test10(), test6(), test_smatrix_kalman(), test_smatrix_op(), test_smatrix_sym_kalman(), test_smatrix_sym_op(), test_tmatrix_kalman(), test_tmatrix_op(), test_tmatrix_sym_op(), testATBA_S(), testATBA_T(), TClingCallbacks::tryAutoParseInternal(), TClingCallbacks::tryFindROOTSpecialInternal(), TClingCallbacks::tryInjectImplicitAutoKeyword(), and TClingCallbacks::tryResolveAtRuntimeInternal().

double ROOT::Math::Cephes::erfP[]
static
Initial value:
= {
2.46196981473530512524E-10,
5.64189564831068821977E-1,
7.46321056442269912687E0,
4.86371970985681366614E1,
1.96520832956077098242E2,
5.26445194995477358631E2,
9.34528527171957607540E2,
1.02755188689515710272E3,
5.57535335369399327526E2
}

Definition at line 813 of file SpecFuncCephes.cxx.

double ROOT::Math::Cephes::erfQ[]
static
Initial value:
= {
1.32281951154744992508E1,
8.67072140885989742329E1,
3.54937778887819891062E2,
9.75708501743205489753E2,
1.82390916687909736289E3,
2.24633760818710981792E3,
1.65666309194161350182E3,
5.57535340817727675546E2
}

Definition at line 824 of file SpecFuncCephes.cxx.

double ROOT::Math::Cephes::erfR[]
static
Initial value:
= {
5.64189583547755073984E-1,
1.27536670759978104416E0,
5.01905042251180477414E0,
6.16021097993053585195E0,
7.40974269950448939160E0,
2.97886665372100240670E0
}

Definition at line 835 of file SpecFuncCephes.cxx.

double ROOT::Math::Cephes::erfS[]
static
Initial value:
= {
2.26052863220117276590E0,
9.39603524938001434673E0,
1.20489539808096656605E1,
1.70814450747565897222E1,
9.60896809063285878198E0,
3.36907645100081516050E0
}

Definition at line 843 of file SpecFuncCephes.cxx.

double ROOT::Math::Cephes::erfT[]
static
Initial value:
= {
9.60497373987051638749E0,
9.00260197203842689217E1,
2.23200534594684319226E3,
7.00332514112805075473E3,
5.55923013010394962768E4
}

Definition at line 852 of file SpecFuncCephes.cxx.

double ROOT::Math::Cephes::erfU[]
static
Initial value:
= {
3.35617141647503099647E1,
5.21357949780152679795E2,
4.59432382970980127987E3,
2.26290000613890934246E4,
4.92673942608635921086E4
}

Definition at line 859 of file SpecFuncCephes.cxx.

double ROOT::Math::Cephes::kBig = 4.503599627370496e15
static

Definition at line 26 of file SpecFuncCephes.cxx.

Referenced by incbcf(), and incbd().

double ROOT::Math::Cephes::kBiginv = 2.22044604925031308085e-16
static

Definition at line 27 of file SpecFuncCephes.cxx.

Referenced by igamc(), incbcf(), and incbd().

double ROOT::Math::Cephes::LS2PI = 0.91893853320467274178
static

Definition at line 30 of file SpecFuncCephes.cxx.

Referenced by lgam().

double ROOT::Math::Cephes::P[]
static
Initial value:
= {
1.60119522476751861407E-4,
1.19135147006586384913E-3,
1.04213797561761569935E-2,
4.76367800457137231464E-2,
2.07448227648435975150E-1,
4.94214826801497100753E-1,
9.99999999999999996796E-1
}

Definition at line 285 of file SpecFuncCephes.cxx.

double ROOT::Math::Cephes::P0[5]
static
Initial value:
= {
-5.99633501014107895267E1,
9.80010754185999661536E1,
-5.66762857469070293439E1,
1.39312609387279679503E1,
-1.23916583867381258016E0,
}

Definition at line 78 of file SpecFuncCephesInv.cxx.

double ROOT::Math::Cephes::P1[9]
static
Initial value:
= {
4.05544892305962419923E0,
3.15251094599893866154E1,
5.71628192246421288162E1,
4.40805073893200834700E1,
1.46849561928858024014E1,
2.18663306850790267539E0,
-1.40256079171354495875E-1,
-3.50424626827848203418E-2,
-8.57456785154685413611E-4,
}

Definition at line 95 of file SpecFuncCephesInv.cxx.

double ROOT::Math::Cephes::P2[9]
static
Initial value:
= {
3.23774891776946035970E0,
6.91522889068984211695E0,
3.93881025292474443415E0,
1.33303460815807542389E0,
2.01485389549179081538E-1,
1.23716634817820021358E-2,
3.01581553508235416007E-4,
2.65806974686737550832E-6,
6.23974539184983293730E-9,
}

Definition at line 116 of file SpecFuncCephesInv.cxx.

double ROOT::Math::Cephes::Q[]
static
Initial value:
= {
-2.31581873324120129819E-5,
5.39605580493303397842E-4,
-4.45641913851797240494E-3,
1.18139785222060435552E-2,
3.58236398605498653373E-2,
-2.34591795718243348568E-1,
7.14304917030273074085E-2,
1.00000000000000000320E0
}

Definition at line 294 of file SpecFuncCephes.cxx.

Referenced by TMVA::CostComplexityPruneTool::CalculatePruningInfo(), estimate(), ROOT::Vc::Common::exp(), fast_expansion_sum_zeroelim(), gsl_poly_complex_solve_cubic(), gsl_poly_complex_solve_quartic(), ROOT::Vc::Common::LogImpl< Base >::log_series(), and scale_expansion_zeroelim().

double ROOT::Math::Cephes::Q0[8]
static
Initial value:
= {
1.95448858338141759834E0,
4.67627912898881538453E0,
8.63602421390890590575E1,
-2.25462687854119370527E2,
2.00260212380060660359E2,
-8.20372256168333339912E1,
1.59056225126211695515E1,
-1.18331621121330003142E0,
}

Definition at line 85 of file SpecFuncCephesInv.cxx.

double ROOT::Math::Cephes::Q1[8]
static
Initial value:
= {
1.57799883256466749731E1,
4.53907635128879210584E1,
4.13172038254672030440E1,
1.50425385692907503408E1,
2.50464946208309415979E0,
-1.42182922854787788574E-1,
-3.80806407691578277194E-2,
-9.33259480895457427372E-4,
}

Definition at line 106 of file SpecFuncCephesInv.cxx.

double ROOT::Math::Cephes::Q2[8]
static
Initial value:
= {
6.02427039364742014255E0,
3.67983563856160859403E0,
1.37702099489081330271E0,
2.16236993594496635890E-1,
1.34204006088543189037E-2,
3.28014464682127739104E-4,
2.89247864745380683936E-6,
6.79019408009981274425E-9,
}

Definition at line 127 of file SpecFuncCephesInv.cxx.

double ROOT::Math::Cephes::s2pi = 2.50662827463100050242E0
static

Definition at line 76 of file SpecFuncCephesInv.cxx.

Referenced by ndtri().

double ROOT::Math::Cephes::STIR[5]
static
Initial value:
= {
7.87311395793093628397E-4,
-2.29549961613378126380E-4,
-2.68132617805781232825E-3,
3.47222221605458667310E-3,
8.33333333333482257126E-2,
}

Definition at line 306 of file SpecFuncCephes.cxx.