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

§ beta()

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

Definition at line 428 of file SpecFuncCephes.cxx.

§ erf()

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

Definition at line 926 of file SpecFuncCephes.cxx.

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

§ erfc()

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

Definition at line 874 of file SpecFuncCephes.cxx.

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

§ gamma()

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

Definition at line 339 of file SpecFuncCephes.cxx.

Referenced by RooStats::HistFactory::HistoToWorkspaceFactoryFast::AddConstraintTerms(), TMath::AreEqualRel(), 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(), ParamHistFunc::createParamSet(), RooStats::HistFactory::HistoToWorkspaceFactoryFast::createStatConstraintTerms(), RooStats::HistFactory::RooBarlowBeestonLL::evaluate(), ROOT::Math::gaussian_cdf(), ROOT::Math::gaussian_quantile(), TF1::GetQuantiles(), incbet(), ROOT::Minuit2::SimplexBuilder::Minimum(), TMinuit::mnsimp(), pseries(), TMath::Quantiles(), TLorentzRotation::SetBoost(), ROOT::Math::Boost::SetComponents(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::SetEngine(), TMath::StdDev(), TMVA::SVWorkingSet::TakeStep(), TMVA::SVWorkingSet::TakeStepReg(), testStatFunc(), ROOT::Math::tgamma(), TMultiLayerPerceptron::Train(), TMVA::MethodMLP::UpdateRegulators(), and TQpLinSolverBase::~TQpLinSolverBase().

§ igam()

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().

§ igamc()

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().

§ igami()

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().

§ incbcf()

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

Definition at line 581 of file SpecFuncCephes.cxx.

Referenced by incbet().

§ incbd()

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

Definition at line 674 of file SpecFuncCephes.cxx.

Referenced by incbet().

§ 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

Definition at line 484 of file SpecFuncCephes.cxx.

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

§ 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().

§ lgam()

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().

§ ndtri()

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().

§ pseries()

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

Definition at line 766 of file SpecFuncCephes.cxx.

Referenced by incbet().

§ stirf()

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

static

Definition at line 316 of file SpecFuncCephes.cxx.

Referenced by gamma().

Variable Documentation

§ A

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(), ROOT::Math::AssignSym::Evaluate(), ROOT::Math::PlusEquals< T, D1, D2, A, MatRepSym< T, D1 >, MatRepStd< T, D1, D2 > >::Evaluate(), ROOT::Math::PlaceMatrix< T, D1, D2, D3, D4, R1, R2 >::Evaluate(), fitFunc(), TCling::FuncTempInfo_Title(), gsl_poly_complex_solve_cubic(), gsl_poly_complex_solve_quartic(), TDecompChol::Invert(), makePoints(), NormalEqn(), TOCCToStep::OCCDocCreation(), ROOT::Math::SVector< T, D >::operator<(), ROOT::Vc::AVX::Vector< T >::operator=(), ROOT::Vc::SSE::Vector< T >::operator=(), ROOT::TMetaUtils::ReSubstTemplateArg(), RosenBrock(), 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(), TClingClassInfo::Title(), TQpDataDens::TQpDataDens(), TQpDataSparse::TQpDataSparse(), ROOT::Vc::MemoryBase< V, Memory< V, 0u, 0u >, 1, void >::vector(), TQpProbDens::~TQpProbDens(), and TQpProbSparse::~TQpProbSparse().

§ B

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(), Cppyy::CallV(), counterclockwiseadapt(), ROOT::Math::crystalball_function(), ROOT::Math::crystalball_integral(), RooStats::HistFactory::RooBarlowBeestonLL::evaluate(), fitFunc(), TDecompBase::GetColLwb(), TMVA::ROCCalc::GetSignificance(), gsl_poly_complex_solve_cubic(), gsl_poly_complex_solve_quartic(), TDecompChol::Invert(), TUnfold::InvertMSparseSymmPos(), makePoints(), TGLMatrix::MultLeft(), TGLMatrix::MultRight(), NormalEqn(), TGWin32::ReadGIF(), TEveBoxProjectedGL::RenderPoints(), RosenBrock(), 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(), TVirtualMagField::TVirtualMagField(), TMVA::StatDialogMVAEffs::UpdateSignificanceHists(), and TGWin32::WriteGIF().

§ C

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(), Cppyy::CallV(), 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(), RooNonCPEigenDecay::RooNonCPEigenDecay(), 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(), TQpDataDens::TQpDataDens(), TQpDataSparse::TQpDataSparse(), RScanner::TraverseClassTemplatePartialSpecializationDecl(), TClingCallbacks::tryAutoParseInternal(), TClingCallbacks::tryFindROOTSpecialInternal(), TClingCallbacks::tryInjectImplicitAutoKeyword(), TClingCallbacks::tryResolveAtRuntimeInternal(), TQpProbDens::~TQpProbDens(), and TQpProbSparse::~TQpProbSparse().

§ erfP

double ROOT::Math::Cephes::erfP[]

static

Initial value:

= {
46196981473530512524E-10,
64189564831068821977E-1,
46321056442269912687E0,
86371970985681366614E1,
96520832956077098242E2,
26445194995477358631E2,
34528527171957607540E2,
02755188689515710272E3,
57535335369399327526E2
}

Definition at line 813 of file SpecFuncCephes.cxx.

§ erfQ

double ROOT::Math::Cephes::erfQ[]

static

Initial value:

= {
32281951154744992508E1,
67072140885989742329E1,
54937778887819891062E2,
75708501743205489753E2,
82390916687909736289E3,
24633760818710981792E3,
65666309194161350182E3,
57535340817727675546E2
}

Definition at line 824 of file SpecFuncCephes.cxx.

§ erfR

double ROOT::Math::Cephes::erfR[]

static

Initial value:

= {
64189583547755073984E-1,
27536670759978104416E0,
01905042251180477414E0,
16021097993053585195E0,
40974269950448939160E0,
97886665372100240670E0
}

Definition at line 835 of file SpecFuncCephes.cxx.

§ erfS

double ROOT::Math::Cephes::erfS[]

static

Initial value:

= {
26052863220117276590E0,
39603524938001434673E0,
20489539808096656605E1,
70814450747565897222E1,
60896809063285878198E0,
36907645100081516050E0
}

Definition at line 843 of file SpecFuncCephes.cxx.

§ erfT

double ROOT::Math::Cephes::erfT[]

static

Initial value:

= {
60497373987051638749E0,
00260197203842689217E1,
23200534594684319226E3,
00332514112805075473E3,
55923013010394962768E4
}

Definition at line 852 of file SpecFuncCephes.cxx.

§ erfU

double ROOT::Math::Cephes::erfU[]

static

Initial value:

= {
35617141647503099647E1,
21357949780152679795E2,
59432382970980127987E3,
26290000613890934246E4,
92673942608635921086E4
}

Definition at line 859 of file SpecFuncCephes.cxx.

§ kBig

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

static

Definition at line 26 of file SpecFuncCephes.cxx.

Referenced by incbcf(), and incbd().

§ kBiginv

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

static

Definition at line 27 of file SpecFuncCephes.cxx.

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

§ LS2PI

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

static

Definition at line 30 of file SpecFuncCephes.cxx.

Referenced by lgam().

§ P

double ROOT::Math::Cephes::P[]

static

Initial value:

= {
60119522476751861407E-4,
19135147006586384913E-3,
04213797561761569935E-2,
76367800457137231464E-2,
07448227648435975150E-1,
94214826801497100753E-1,
99999999999999996796E-1
}

Definition at line 285 of file SpecFuncCephes.cxx.

§ P0

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.

§ P1

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.

§ P2

double ROOT::Math::Cephes::P2[9]

static

Initial value:

= {
23774891776946035970E0,
91522889068984211695E0,
93881025292474443415E0,
33303460815807542389E0,
01485389549179081538E-1,
23716634817820021358E-2,
01581553508235416007E-4,
65806974686737550832E-6,
23974539184983293730E-9,
}

Definition at line 116 of file SpecFuncCephesInv.cxx.

§ Q

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(), TQuaternion::operator-=(), scale_expansion_zeroelim(), TQpDataDens::TQpDataDens(), TQpDataSparse::TQpDataSparse(), TQpProbDens::~TQpProbDens(), and TQpProbSparse::~TQpProbSparse().

§ Q0

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.

§ Q1

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.

§ Q2

double ROOT::Math::Cephes::Q2[8]

static

Initial value:

= {
02427039364742014255E0,
67983563856160859403E0,
37702099489081330271E0,
16236993594496635890E-1,
34204006088543189037E-2,
28014464682127739104E-4,
89247864745380683936E-6,
79019408009981274425E-9,
}

Definition at line 127 of file SpecFuncCephesInv.cxx.

§ s2pi

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

static

Definition at line 76 of file SpecFuncCephesInv.cxx.

Referenced by ndtri().

§ STIR

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.

Functions

Variables

Function Documentation

§ beta()

§ erf()

§ erfc()

§ gamma()

§ igam()

§ igamc()

§ igami()

§ incbcf()

§ incbd()

§ incbet()

§ incbi()

§ lgam()

§ ndtri()

§ pseries()

§ stirf()

Variable Documentation

§ A

§ B

§ C

§ erfP

§ erfQ

§ erfR

§ erfS

§ erfT

§ erfU

§ kBig

§ kBiginv

§ LS2PI

§ P

§ P0

§ P1

§ P2

§ Q

§ Q0

§ Q1

§ Q2

§ s2pi

§ STIR