Classes
struct	Limits

Functions
Short_t	Abs (Short_t d)

Int_t	Abs (Int_t d)

Long_t	Abs (Long_t d)

Long64_t	Abs (Long64_t d)

Float_t	Abs (Float_t d)

Double_t	Abs (Double_t d)

LongDouble_t	Abs (LongDouble_t d)

Bool_t	Even (Long_t a)

Bool_t	Odd (Long_t a)

template<typename Integer >
Bool_t	SignBit (Integer a)

Bool_t	SignBit (Float_t a)

Bool_t	SignBit (Double_t a)

Bool_t	SignBit (LongDouble_t a)

template<typename T1 , typename T2 >
T1	Sign (T1 a, T2 b)

Float_t	Sign (Float_t a, Float_t b)

Double_t	Sign (Double_t a, Double_t b)

LongDouble_t	Sign (LongDouble_t a, LongDouble_t b)

Short_t	Min (Short_t a, Short_t b)

UShort_t	Min (UShort_t a, UShort_t b)

Int_t	Min (Int_t a, Int_t b)

UInt_t	Min (UInt_t a, UInt_t b)

Long_t	Min (Long_t a, Long_t b)

ULong_t	Min (ULong_t a, ULong_t b)

Long64_t	Min (Long64_t a, Long64_t b)

ULong64_t	Min (ULong64_t a, ULong64_t b)

Float_t	Min (Float_t a, Float_t b)

Double_t	Min (Double_t a, Double_t b)

Short_t	Max (Short_t a, Short_t b)

UShort_t	Max (UShort_t a, UShort_t b)

Int_t	Max (Int_t a, Int_t b)

UInt_t	Max (UInt_t a, UInt_t b)

Long_t	Max (Long_t a, Long_t b)

ULong_t	Max (ULong_t a, ULong_t b)

Long64_t	Max (Long64_t a, Long64_t b)

ULong64_t	Max (ULong64_t a, ULong64_t b)

Float_t	Max (Float_t a, Float_t b)

Double_t	Max (Double_t a, Double_t b)

Short_t	Range (Short_t lb, Short_t ub, Short_t x)

Int_t	Range (Int_t lb, Int_t ub, Int_t x)

Long_t	Range (Long_t lb, Long_t ub, Long_t x)

ULong_t	Range (ULong_t lb, ULong_t ub, ULong_t x)

Double_t	Range (Double_t lb, Double_t ub, Double_t x)

Long_t	NextPrime (Long_t x)
	TMath Base functions. More...

Double_t	Pi ()

Double_t	TwoPi ()

Double_t	PiOver2 ()

Double_t	PiOver4 ()

Double_t	InvPi ()

Double_t	RadToDeg ()

Double_t	DegToRad ()

Double_t	Sqrt2 ()

Double_t	E ()

Double_t	Ln10 ()

Double_t	LogE ()

Double_t	C ()

Double_t	Ccgs ()

Double_t	CUncertainty ()

Double_t	G ()

Double_t	Gcgs ()

Double_t	GUncertainty ()

Double_t	GhbarC ()

Double_t	GhbarCUncertainty ()

Double_t	Gn ()

Double_t	GnUncertainty ()

Double_t	H ()

Double_t	Hcgs ()

Double_t	HUncertainty ()

Double_t	Hbar ()

Double_t	Hbarcgs ()

Double_t	HbarUncertainty ()

Double_t	HC ()

Double_t	HCcgs ()

Double_t	K ()

Double_t	Kcgs ()

Double_t	KUncertainty ()

Double_t	Sigma ()

Double_t	SigmaUncertainty ()

Double_t	Na ()

Double_t	NaUncertainty ()

Double_t	R ()

Double_t	RUncertainty ()

Double_t	MWair ()

Double_t	Rgair ()

Double_t	EulerGamma ()

Double_t	Qe ()

Double_t	QeUncertainty ()

Double_t	Sin (Double_t)

Double_t	Cos (Double_t)

Double_t	Tan (Double_t)

Double_t	SinH (Double_t)

Double_t	CosH (Double_t)

Double_t	TanH (Double_t)

Double_t	ASin (Double_t)

Double_t	ACos (Double_t)

Double_t	ATan (Double_t)

Double_t	ATan2 (Double_t, Double_t)

Double_t	ASinH (Double_t)

Double_t	ACosH (Double_t)

Double_t	ATanH (Double_t)

Double_t	Hypot (Double_t x, Double_t y)

Double_t	Ceil (Double_t x)

Int_t	CeilNint (Double_t x)

Double_t	Floor (Double_t x)

Int_t	FloorNint (Double_t x)

template<typename T >
Int_t	Nint (T x)

Double_t	Sq (Double_t x)

Double_t	Sqrt (Double_t x)

Double_t	Exp (Double_t x)

Double_t	Ldexp (Double_t x, Int_t exp)

Double_t	Factorial (Int_t i)
	Compute factorial(n). More...

LongDouble_t	Power (LongDouble_t x, LongDouble_t y)

LongDouble_t	Power (LongDouble_t x, Long64_t y)

LongDouble_t	Power (Long64_t x, Long64_t y)

Double_t	Power (Double_t x, Double_t y)

Double_t	Power (Double_t x, Int_t y)

Double_t	Log (Double_t x)

Double_t	Log2 (Double_t x)

Double_t	Log10 (Double_t x)

Int_t	Finite (Double_t x)

Int_t	IsNaN (Double_t x)

Double_t	QuietNaN ()

Double_t	SignalingNaN ()

Double_t	Infinity ()

Long_t	Hypot (Long_t x, Long_t y)

Bool_t	AreEqualAbs (Double_t af, Double_t bf, Double_t epsilon)

Bool_t	AreEqualRel (Double_t af, Double_t bf, Double_t relPrec)

template<typename T >
T	MinElement (Long64_t n, const T *a)

template<typename T >
T	MaxElement (Long64_t n, const T *a)

template<typename T >
Long64_t	LocMin (Long64_t n, const T *a)

template<typename Iterator >
Iterator	LocMin (Iterator first, Iterator last)

template<typename T >
Long64_t	LocMax (Long64_t n, const T *a)

template<typename Iterator >
Iterator	LocMax (Iterator first, Iterator last)

template<typename T >
Long64_t	BinarySearch (Long64_t n, const T *array, T value)

template<typename T >
Long64_t	BinarySearch (Long64_t n, const T **array, T value)

template<typename Iterator , typename Element >
Iterator	BinarySearch (Iterator first, Iterator last, Element value)

ULong_t	Hash (const void *txt, Int_t ntxt)
	Calculates hash index from any char string. More...

ULong_t	Hash (const char *str)
	Return a case-sensitive hash value (endian independent). More...

template<typename Element , typename Index >
void	Sort (Index n, const Element a, Index index, Bool_t down=kTRUE)

template<typename Iterator , typename IndexIterator >
void	SortItr (Iterator first, Iterator last, IndexIterator index, Bool_t down=kTRUE)

void	BubbleHigh (Int_t Narr, Double_t arr1, Int_t arr2)
	Bubble sort variant to obtain the order of an array's elements into an index in order to do more useful things than the standard built in functions. More...

void	BubbleLow (Int_t Narr, Double_t arr1, Int_t arr2)
	Opposite ordering of the array arr2[] to that of BubbleHigh. More...

Bool_t	Permute (Int_t n, Int_t *a)
	Simple recursive algorithm to find the permutations of n natural numbers, not necessarily all distinct adapted from CERNLIB routine PERMU. More...

void	Quantiles (Int_t n, Int_t nprob, Double_t x, Double_t quantiles, Double_t prob, Bool_t isSorted=kTRUE, Int_t index=0, Int_t type=7)
	Computes sample quantiles, corresponding to the given probabilities Parameters: x -the data sample n - its size quantiles - computed quantiles are returned in there prob - probabilities where to compute quantiles nprob - size of prob array isSorted - is the input array x sorted? NOTE, that when the input is not sorted, an array of integers of size n needs to be allocated. More...

template<typename T >
Bool_t	IsInside (T xp, T yp, Int_t np, T x, T y)

template<typename T >
T *	Cross (const T v1[3], const T v2[3], T out[3])

Float_t	Normalize (Float_t v[3])
	Normalize a vector v in place. More...

Double_t	Normalize (Double_t v[3])
	Normalize a vector v in place. More...

template<typename T >
T	NormCross (const T v1[3], const T v2[3], T out[3])

template<typename T >
T *	Normal2Plane (const T v1[3], const T v2[3], const T v3[3], T normal[3])

Bool_t	RootsCubic (const Double_t coef[4], Double_t &a, Double_t &b, Double_t &c)
	Calculates roots of polynomial of 3rd order ax^3 + bx^2 + cx + d, where a == coef[3], b == coef[2], c == coef[1], d == coef[0] coef[3] must be different from 0 If the boolean returned by the method is false: ==> there are 3 real roots a,b,c If the boolean returned by the method is true: ==> there is one real root a and 2 complex conjugates roots (b+ic,b-i*c) Author: Francois-Xavier Gentit. More...

Double_t	Binomial (Int_t n, Int_t k)
	Calculate the binomial coefficient n over k. More...

Double_t	BinomialI (Double_t p, Int_t n, Int_t k)
	Suppose an event occurs with probability p per trial Then the probability P of its occuring k or more times in n trials is termed a cumulative binomial probability the formula is P = sum_from_j=k_to_n(TMath::Binomial(n, j)* TMath::Power(p, j)TMathPower(1-p, n-j) For n larger than 12 BetaIncomplete is a much better way to evaluate the sum than would be the straightforward sum calculation for n smaller than 12 either method is acceptable ("Numerical Recipes") –implementation by Anna Kreshuk. More...

Double_t	BreitWigner (Double_t x, Double_t mean=0, Double_t gamma=1)
	Calculate a Breit Wigner function with mean and gamma. More...

Double_t	CauchyDist (Double_t x, Double_t t=0, Double_t s=1)
	Computes the density of Cauchy distribution at point x by default, standard Cauchy distribution is used (t=0, s=1) t is the location parameter s is the scale parameter The Cauchy distribution, also called Lorentzian distribution, is a continuous distribution describing resonance behavior The mean and standard deviation of the Cauchy distribution are undefined. More...

Double_t	ChisquareQuantile (Double_t p, Double_t ndf)
	Evaluate the quantiles of the chi-squared probability distribution function. More...

Double_t	FDist (Double_t F, Double_t N, Double_t M)
	Computes the density function of F-distribution (probability function, integral of density, is computed in FDistI). More...

Double_t	FDistI (Double_t F, Double_t N, Double_t M)
	Calculates the cumulative distribution function of F-distribution, this function occurs in the statistical test of whether two observed samples have the same variance. More...

Double_t	Gaus (Double_t x, Double_t mean=0, Double_t sigma=1, Bool_t norm=kFALSE)
	Calculate a gaussian function with mean and sigma. More...

Double_t	KolmogorovProb (Double_t z)
	Calculates the Kolmogorov distribution function, Begin_Html. More...

Double_t	KolmogorovTest (Int_t na, const Double_t a, Int_t nb, const Double_t b, Option_t *option)
	Statistical test whether two one-dimensional sets of points are compatible with coming from the same parent distribution, using the Kolmogorov test. More...

Double_t	Landau (Double_t x, Double_t mpv=0, Double_t sigma=1, Bool_t norm=kFALSE)
	The LANDAU function. More...

Double_t	LandauI (Double_t x)
	Returns the value of the Landau distribution function at point x. More...

Double_t	LaplaceDist (Double_t x, Double_t alpha=0, Double_t beta=1)
	Computes the probability density function of Laplace distribution at point x, with location parameter alpha and shape parameter beta. More...

Double_t	LaplaceDistI (Double_t x, Double_t alpha=0, Double_t beta=1)
	Computes the distribution function of Laplace distribution at point x, with location parameter alpha and shape parameter beta. More...

Double_t	LogNormal (Double_t x, Double_t sigma, Double_t theta=0, Double_t m=1)
	Computes the density of LogNormal distribution at point x. More...

Double_t	NormQuantile (Double_t p)
	Computes quantiles for standard normal distribution N(0, 1) at probability p ALGORITHM AS241 APPL. More...

Double_t	Poisson (Double_t x, Double_t par)
	compute the Poisson distribution function for (x,par) The Poisson PDF is implemented by means of Euler's Gamma-function (for the factorial), so for any x integer argument it is correct. More...

Double_t	PoissonI (Double_t x, Double_t par)
	compute the Poisson distribution function for (x,par) This is a non-smooth function. More...

Double_t	Prob (Double_t chi2, Int_t ndf)
	Computation of the probability for a certain Chi-squared (chi2) and number of degrees of freedom (ndf). More...

Double_t	Student (Double_t T, Double_t ndf)
	Computes density function for Student's t- distribution (the probability function (integral of density) is computed in StudentI). More...

Double_t	StudentI (Double_t T, Double_t ndf)
	Calculates the cumulative distribution function of Student's t-distribution second parameter stands for number of degrees of freedom, not for the number of samples if x has Student's t-distribution, the function returns the probability of x being less than T. More...

Double_t	StudentQuantile (Double_t p, Double_t ndf, Bool_t lower_tail=kTRUE)
	Computes quantiles of the Student's t-distribution 1st argument is the probability, at which the quantile is computed 2nd argument - the number of degrees of freedom of the Student distribution When the 3rd argument lower_tail is kTRUE (default)- the algorithm returns such x0, that P(x < x0)=p upper tail (lower_tail is kFALSE)- the algorithm returns such x0, that P(x > x0)=p the algorithm was taken from G.W.Hill, "Algorithm 396, Student's t-quantiles" "Communications of the ACM", 13(10), October 1970. More...

Double_t	Vavilov (Double_t x, Double_t kappa, Double_t beta2)
	Returns the value of the Vavilov density function Parameters: 1st - the point were the density function is evaluated 2nd - value of kappa (distribution parameter) 3rd - value of beta2 (distribution parameter) The algorithm was taken from the CernLib function vavden(G115) Reference: A.Rotondi and P.Montagna, Fast Calculation of Vavilov distribution Nucl.Instr. More...

Double_t	VavilovI (Double_t x, Double_t kappa, Double_t beta2)
	Returns the value of the Vavilov distribution function Parameters: 1st - the point were the density function is evaluated 2nd - value of kappa (distribution parameter) 3rd - value of beta2 (distribution parameter) The algorithm was taken from the CernLib function vavden(G115) Reference: A.Rotondi and P.Montagna, Fast Calculation of Vavilov distribution Nucl.Instr. More...

Double_t	Voigt (Double_t x, Double_t sigma, Double_t lg, Int_t r=4)
	Computation of Voigt function (normalised). More...

template<typename T >
Double_t	Mean (Long64_t n, const T a, const Double_t w=0)

template<typename Iterator >
Double_t	Mean (Iterator first, Iterator last)

template<typename Iterator , typename WeightIterator >
Double_t	Mean (Iterator first, Iterator last, WeightIterator wfirst)

template<typename T >
Double_t	GeomMean (Long64_t n, const T *a)

template<typename Iterator >
Double_t	GeomMean (Iterator first, Iterator last)

template<typename T >
Double_t	RMS (Long64_t n, const T a, const Double_t w=0)

template<typename Iterator >
Double_t	RMS (Iterator first, Iterator last)

template<typename Iterator , typename WeightIterator >
Double_t	RMS (Iterator first, Iterator last, WeightIterator wfirst)

template<typename T >
Double_t	StdDev (Long64_t n, const T a, const Double_t w=0)

template<typename Iterator >
Double_t	StdDev (Iterator first, Iterator last)

template<typename Iterator , typename WeightIterator >
Double_t	StdDev (Iterator first, Iterator last, WeightIterator wfirst)

template<typename T >
Double_t	Median (Long64_t n, const T a, const Double_t w=0, Long64_t *work=0)

template<class Element , typename Size >
Element	KOrdStat (Size n, const Element a, Size k, Size work=0)

Double_t	Beta (Double_t p, Double_t q)
	Calculates Beta-function Gamma(p)*Gamma(q)/Gamma(p+q). More...

Double_t	BetaCf (Double_t x, Double_t a, Double_t b)
	Continued fraction evaluation by modified Lentz's method used in calculation of incomplete Beta function. More...

Double_t	BetaDist (Double_t x, Double_t p, Double_t q)
	Computes the probability density function of the Beta distribution (the distribution function is computed in BetaDistI). More...

Double_t	BetaDistI (Double_t x, Double_t p, Double_t q)
	Computes the distribution function of the Beta distribution. More...

Double_t	BetaIncomplete (Double_t x, Double_t a, Double_t b)
	Calculates the incomplete Beta-function. More...

Double_t	BesselI (Int_t n, Double_t x)
	Compute the Integer Order Modified Bessel function I_n(x) for n=0,1,2,... More...

Double_t	BesselK (Int_t n, Double_t x)
	Compute the Integer Order Modified Bessel function K_n(x) for n=0,1,2,... More...

Double_t	BesselI0 (Double_t x)
	Compute the modified Bessel function I_0(x) for any real x. More...

Double_t	BesselK0 (Double_t x)
	Compute the modified Bessel function K_0(x) for positive real x. More...

Double_t	BesselI1 (Double_t x)
	Compute the modified Bessel function I_1(x) for any real x. More...

Double_t	BesselK1 (Double_t x)
	Compute the modified Bessel function K_1(x) for positive real x. More...

Double_t	BesselJ0 (Double_t x)
	Returns the Bessel function J0(x) for any real x. More...

Double_t	BesselJ1 (Double_t x)
	Returns the Bessel function J1(x) for any real x. More...

Double_t	BesselY0 (Double_t x)
	Returns the Bessel function Y0(x) for positive x. More...

Double_t	BesselY1 (Double_t x)
	Returns the Bessel function Y1(x) for positive x. More...

Double_t	StruveH0 (Double_t x)
	Struve Functions of Order 0. More...

Double_t	StruveH1 (Double_t x)
	Struve Functions of Order 1. More...

Double_t	StruveL0 (Double_t x)
	Modified Struve Function of Order 0. More...

Double_t	StruveL1 (Double_t x)
	Modified Struve Function of Order 1. More...

Double_t	DiLog (Double_t x)
	The DiLogarithm function Code translated by R.Brun from CERNLIB DILOG function C332. More...

Double_t	Erf (Double_t x)
	Computation of the error function erf(x). More...

Double_t	ErfInverse (Double_t x)
	returns the inverse error function x must be <-1<x<1 More...

Double_t	Erfc (Double_t x)
	Compute the complementary error function erfc(x). More...

Double_t	ErfcInverse (Double_t x)

Double_t	Freq (Double_t x)
	Computation of the normal frequency function freq(x). More...

Double_t	Gamma (Double_t z)
	Computation of gamma(z) for all z. More...

Double_t	Gamma (Double_t a, Double_t x)
	Computation of the normalized lower incomplete gamma function P(a,x) as defined in the Handbook of Mathematical Functions by Abramowitz and Stegun, formula 6.5.1 on page 260 . More...

Double_t	GammaDist (Double_t x, Double_t gamma, Double_t mu=0, Double_t beta=1)
	Computes the density function of Gamma distribution at point x. More...

Double_t	LnGamma (Double_t z)
	Computation of ln[gamma(z)] for all z. More...

Function Documentation

Short_t TMath::Abs ( Short_t d )

inline

Definition at line 110 of file TMathBase.h.

Int_t TMath::Abs ( Int_t d )

inline

Definition at line 113 of file TMathBase.h.

Long_t TMath::Abs ( Long_t d )

inline

Definition at line 116 of file TMathBase.h.

Long64_t TMath::Abs ( Long64_t d )

inline

Definition at line 119 of file TMathBase.h.

Float_t TMath::Abs ( Float_t d )

inline

Definition at line 126 of file TMathBase.h.

Double_t TMath::Abs ( Double_t d )

inline

Definition at line 129 of file TMathBase.h.

LongDouble_t TMath::Abs ( LongDouble_t d )

inline

Definition at line 132 of file TMathBase.h.

Referenced by Sign().

Double_t TMath::ACos ( Double_t x )

inline

Definition at line 445 of file TMath.h.

Referenced by TGLRotateManip::Angle(), TVector3::Angle(), TRotation::AngleAxis(), TGeoChecker::CheckGeometry(), TGeoChecker::CheckGeometryFull(), ClassImp(), TGeoSphere::ComputeNormal(), TGeoSphere::Contains(), TCrown::DistancetoPrimitive(), TGeoSphere::DistFromInside(), TGeoSphere::DistFromOutside(), TGLPadPainter::DrawGradient(), TTreeFormula::EvalInstance(), TText::ExecuteEvent(), TGraphPolargram::ExecuteEvent(), THelix::FindClosestPhase(), TGeoRotation::GetAngles(), TGLCamera::GetTheta(), TRotation::GetXPhi(), TRotation::GetXPsi(), TGDMLWrite::GetXYZangles(), TGeoSphere::IsOnBoundary(), TGeoSphere::IsPointInside(), TGLAxis::PaintGLAxis(), TGeoChecker::RandomRays(), RooTMathReg::RooTMathReg(), RootsCubic(), TGLCamera::RotateRad(), TGeoSphere::Safety(), TGX11::SetCharacterUp(), TGWin32::SetCharacterUp(), TGeoCtubEditor::SetModel(), TParticle::SetPolarisation(), THelix::SetRotMatrix(), TGeoChecker::ShapeDistances(), TGeoChecker::ShapeNormal(), TGeoChecker::ShapeSafety(), TEveTrackPropagator::StepRungeKutta(), TParticle::Theta(), TRotation::ThetaX(), TRotation::ThetaY(), TRotation::ThetaZ(), TGeoChecker::TimingPerVolume(), ROOT::v5::TMath_GenerInterface(), TEveTrackPropagator::Update(), and TEveTrackPropagator::Helix_t::UpdateHelix().

Double_t TMath::ACosH ( Double_t x )

Definition at line 80 of file TMath.cxx.

Referenced by ClassImp(), TTreeFormula::EvalInstance(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Bool_t TMath::AreEqualAbs	(	Double_t	af,
		Double_t	bf,
		Double_t	epsilon
	)

inline

Definition at line 192 of file TMath.h.

Referenced by RooStats::HypoTestInverterResult::Add(), RooStats::HypoTestInverterResult::FindIndex(), RooStats::HypoTestInverter::RunOnePoint(), testAnalyticalIntegrals(), testQuantiles(), and testTStatistic().

Bool_t TMath::AreEqualRel	(	Double_t	af,
		Double_t	bf,
		Double_t	relPrec
	)

inline

Definition at line 196 of file TMath.h.

Referenced by RooStats::HypoTestInverterResult::Add(), TH1::CheckAxisLimits(), TH1::CheckBinLimits(), TEfficiency::CheckBinning(), TH1::CheckConsistentSubAxes(), RooStats::HypoTestInverterResult::FindIndex(), TF1::GetQuantiles(), RooStats::SamplingDistribution::InverseCDFInterpolate(), IsEquidistantBinning(), THistPainter::PaintInit(), RooStats::HypoTestInverter::RunOnePoint(), and testTStatistic().

Double_t TMath::ASin ( Double_t x )

inline

Definition at line 439 of file TMath.h.

Referenced by ClassImp(), TTreeFormula::EvalInstance(), TText::ExecuteEvent(), TGraphPolargram::ExecuteEvent(), TGeoRotation::GetAngles(), TEveTrans::GetRotAngles(), TGLRotateManip::HandleButton(), TMinuit::mnpint(), RooTMathReg::RooTMathReg(), TGLCamera::RotateRad(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::ASinH ( Double_t x )

Definition at line 67 of file TMath.cxx.

Referenced by RooNovosibirsk::analyticalIntegral(), ClassImp(), TTreeFormula::EvalInstance(), RooNovosibirsk::evaluate(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::ATan ( Double_t x )

inline

Double_t TMath::ATan2	(	Double_t	y,
		Double_t	x
	)

inline

Definition at line 454 of file TMath.h.

Double_t TMath::ATanH ( Double_t x )

Definition at line 93 of file TMath.cxx.

Referenced by ClassImp(), TTreeFormula::EvalInstance(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BesselI	(	Int_t	n,
		Double_t	x
	)

Compute the Integer Order Modified Bessel function I_n(x) for n=0,1,2,...

and any real x.

— NvE 12-mar-2000 UU-SAP Utrecht

Definition at line 1553 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg().

Double_t TMath::BesselI0 ( Double_t x )

Compute the modified Bessel function I_0(x) for any real x.

— NvE 12-mar-2000 UU-SAP Utrecht

Definition at line 1389 of file TMath.cxx.

Referenced by BesselI(), BesselK0(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BesselI1 ( Double_t x )

Compute the modified Bessel function I_1(x) for any real x.

M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions, Applied Mathematics Series vol. 55 (1964), Washington.

— NvE 12-mar-2000 UU-SAP Utrecht

Definition at line 1457 of file TMath.cxx.

Referenced by BesselI(), BesselK1(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BesselJ0 ( Double_t x )

Returns the Bessel function J0(x) for any real x.

Definition at line 1597 of file TMath.cxx.

Referenced by BesselY0(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BesselJ1 ( Double_t x )

Returns the Bessel function J1(x) for any real x.

Definition at line 1632 of file TMath.cxx.

Referenced by BesselY1(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BesselK	(	Int_t	n,
		Double_t	x
	)

Compute the Integer Order Modified Bessel function K_n(x) for n=0,1,2,...

and positive real x.

— NvE 12-mar-2000 UU-SAP Utrecht

Definition at line 1524 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg().

Double_t TMath::BesselK0 ( Double_t x )

Compute the modified Bessel function K_0(x) for positive real x.

M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions, Applied Mathematics Series vol. 55 (1964), Washington.

— NvE 12-mar-2000 UU-SAP Utrecht

Definition at line 1423 of file TMath.cxx.

Referenced by BesselK(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BesselK1 ( Double_t x )

Compute the modified Bessel function K_1(x) for positive real x.

M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions, Applied Mathematics Series vol. 55 (1964), Washington.

— NvE 12-mar-2000 UU-SAP Utrecht

Definition at line 1492 of file TMath.cxx.

Referenced by BesselK(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BesselY0 ( Double_t x )

Returns the Bessel function Y0(x) for positive x.

Definition at line 1668 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), StruveH0(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BesselY1 ( Double_t x )

Returns the Bessel function Y1(x) for positive x.

Definition at line 1702 of file TMath.cxx.

Referenced by Functor(), RooTMathReg::RooTMathReg(), StruveH1(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Beta	(	Double_t	p,
		Double_t	q
	)

Calculates Beta-function Gamma(p)*Gamma(q)/Gamma(p+q).

Definition at line 1973 of file TMath.cxx.

Referenced by BetaDist(), RooTMathReg::RooTMathReg(), testSpecFuncBeta(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BetaCf	(	Double_t	x,
		Double_t	a,
		Double_t	b
	)

Continued fraction evaluation by modified Lentz's method used in calculation of incomplete Beta function.

Definition at line 1982 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BetaDist	(	Double_t	x,
		Double_t	p,
		Double_t	q
	)

Computes the probability density function of the Beta distribution (the distribution function is computed in BetaDistI).

The first argument is the point, where the function will be computed, second and third are the function parameters. Since the Beta distribution is bounded on both sides, it's often used to represent processes with natural lower and upper limits.

Definition at line 2033 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BetaDistI	(	Double_t	x,
		Double_t	p,
		Double_t	q
	)

Computes the distribution function of the Beta distribution.

The first argument is the point, where the function will be computed, second and third are the function parameters. Since the Beta distribution is bounded on both sides, it's often used to represent processes with natural lower and upper limits.

Definition at line 2051 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::BetaIncomplete	(	Double_t	x,
		Double_t	a,
		Double_t	b
	)

Calculates the incomplete Beta-function.

Definition at line 2064 of file TMath.cxx.

Referenced by BetaDistI(), RooStats::NumberCountingUtils::BinomialExpP(), BinomialI(), RooStats::NumberCountingUtils::BinomialObsP(), RooStats::NumberCountingUtils::BinomialWithTauExpP(), RooStats::NumberCountingUtils::BinomialWithTauObsP(), RooTMathReg::RooTMathReg(), StudentI(), testSpecFuncBetaI(), and ROOT::v5::TMath_GenerInterface().

template<typename T >

Long64_t TMath::BinarySearch	(	Long64_t	n,
		const T *	array,
		T	value
	)

Definition at line 944 of file TMath.h.

Referenced by TFileDrawMap::AnimateTree(), TGeoPcon::ComputeNormal(), TGeoPgon::ComputeNormal(), TGeoPgon::Contains(), TGeoXtru::Contains(), TEventList::ContainsRange(), TGeoPcon::DistFromInside(), TGeoPgon::DistFromInside(), TGeoXtru::DistFromInside(), TGeoPcon::DistFromOutside(), TGeoPgon::DistFromOutside(), TGeoXtru::DistFromOutside(), TEventList::Enter(), TMVA::TSpline1::Eval(), TMVA::TSpline2::Eval(), TH2::FillRandom(), TH3::FillRandom(), TH1::FillRandom(), TAxis::FindBin(), RooStats::HypoTestInverterResult::FindClosestPointIndex(), TAxis::FindFixBin(), TGeoManager::GetAlignableEntryByUID(), TH1K::GetBinContent(), TGeoVoxelFinder::GetCheckList(), TBranch::GetEntry(), TBranch::GetEntryExport(), TGLFontManager::GetFontSize(), TGeoVoxelFinder::GetIndices(), TGeoBBox::GetPointsOnFacet(), TH1::GetQuantiles(), TF1::GetQuantiles(), THnBase::GetRandom(), TH1::GetRandom(), TF1::GetRandom(), TH2::GetRandom2(), TF2::GetRandom2(), TF3::GetRandom3(), TH3::GetRandom3(), TTreeCacheUnzip::GetUnzipBuffer(), TGeoManager::InsertPNEId(), TMatrixTSparse< Element >::operator()(), TMatrixTSparseRow_const< Element >::operator()(), TMatrixTSparseRow< Element >::operator()(), TMatrixTSparseDiag_const< Element >::operator()(), TMatrixTSparseDiag< Element >::operator()(), THistPainter::PaintContour(), TGeoVoxelFinder::PrintVoxelLimits(), TFileCacheRead::ReadBufferExtNormal(), TFileCacheRead::ReadBufferExtPrefetch(), TGeoPgon::Safety(), TGeoPcon::Safety(), TGeoXtru::Safety(), TEveText::SetFontSize(), TMatrixTSparse< Element >::SetSub(), TGeoPgon::SliceCrossing(), TGeoPgon::SliceCrossingInZ(), TGeoPgon::SliceCrossingZ(), stressVector(), TTree::TClusterIterator::TClusterIterator(), testArrayFunctions(), testBinarySearch(), and testIteratorFunctions().

template<typename T >

Long64_t TMath::BinarySearch	(	Long64_t	n,
		const T **	array,
		T	value
	)

Definition at line 960 of file TMath.h.

template<typename Iterator , typename Element >

Iterator TMath::BinarySearch	(	Iterator	first,
		Iterator	last,
		Element	value
	)

Definition at line 926 of file TMath.h.

Double_t TMath::Binomial	(	Int_t	n,
		Int_t	k
	)

Calculate the binomial coefficient n over k.

Definition at line 2072 of file TMath.cxx.

Referenced by RooBernstein::analyticalIntegral(), RooBernstein::evaluate(), and RooTMathReg::RooTMathReg().

Double_t TMath::BinomialI	(	Double_t	p,
		Int_t	n,
		Int_t	k
	)

Suppose an event occurs with probability p per trial Then the probability P of its occuring k or more times in n trials is termed a cumulative binomial probability the formula is P = sum_from_j=k_to_n(TMath::Binomial(n, j)* *TMath::Power(p, j)*TMathPower(1-p, n-j) For n larger than 12 BetaIncomplete is a much better way to evaluate the sum than would be the straightforward sum calculation for n smaller than 12 either method is acceptable ("Numerical Recipes") –implementation by Anna Kreshuk.

Definition at line 2097 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg().

Double_t TMath::BreitWigner	(	Double_t	x,
		Double_t	mean = `0`,
		Double_t	gamma = `1`
	)

Calculate a Breit Wigner function with mean and gamma.

Definition at line 442 of file TMath.cxx.

Referenced by ClassImp(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

void TMath::BubbleHigh	(	Int_t	Narr,
		Double_t *	arr1,
		Int_t *	arr2
	)

Bubble sort variant to obtain the order of an array's elements into an index in order to do more useful things than the standard built in functions.

*arr1 is unchanged; *arr2 is the array of indicies corresponding to the decending value of arr1 with arr2[0] corresponding to the largest arr1 value and arr2[Narr] the smallest.

Author: Adrian Bevan (bevan.nosp@m.@sla.nosp@m.c.sta.nosp@m.nfor.nosp@m.d.edu)

Definition at line 1277 of file TMath.cxx.

void TMath::BubbleLow	(	Int_t	Narr,
		Double_t *	arr1,
		Int_t *	arr2
	)

Opposite ordering of the array arr2[] to that of BubbleHigh.

Author: Adrian Bevan (bevan.nosp@m.@sla.nosp@m.c.sta.nosp@m.nfor.nosp@m.d.edu)

Definition at line 1316 of file TMath.cxx.

Double_t TMath::C ( )

inline

Definition at line 63 of file TMath.h.

Referenced by Ccgs(), TFormula::FillDefaults(), HC(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::CauchyDist	(	Double_t	x,
		Double_t	t = `0`,
		Double_t	s = `1`
	)

Computes the density of Cauchy distribution at point x by default, standard Cauchy distribution is used (t=0, s=1) t is the location parameter s is the scale parameter The Cauchy distribution, also called Lorentzian distribution, is a continuous distribution describing resonance behavior The mean and standard deviation of the Cauchy distribution are undefined.

The practical meaning of this is that collecting 1,000 data points gives no more accurate an estimate of the mean and standard deviation than does a single point. The formula was taken from "Engineering Statistics Handbook" on site http://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm Implementation by Anna Kreshuk. Example: TF1* fc = new TF1("fc", "TMath::CauchyDist(x, [0], [1])", -5, 5); fc->SetParameters(0, 1); fc->Draw();

Definition at line 2125 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Ccgs ( )

inline

Definition at line 64 of file TMath.h.

Referenced by HCcgs(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Ceil ( Double_t x )

inline

Definition at line 467 of file TMath.h.

Referenced by TPad::DivideSquare(), ROOT::Quartz::TextLine::GetAscentDescent(), TLegend::GetNRows(), TGListBox::Layout(), TH1::RecomputeAxisLimits(), TEveTrackList::RoundMomentumLimit(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::ChisquareQuantile	(	Double_t	p,
		Double_t	ndf
	)

Evaluate the quantiles of the chi-squared probability distribution function.

Algorithm AS 91 Appl. Statist. (1975) Vol.24, P.35 implemented by Anna Kreshuk. Incorporates the suggested changes in AS R85 (vol.40(1), pp.233-5, 1991) Parameters: p - the probability value, at which the quantile is computed ndf - number of degrees of freedom

Definition at line 2141 of file TMath.cxx.

Referenced by TBackCompFitter::Contour(), RooStats::LikelihoodInterval::FindLimits(), RooStats::LikelihoodInterval::GetContourPoints(), TRolke::Interval(), and RooTMathReg::RooTMathReg().

Double_t TMath::Cos ( Double_t x )

inline

Definition at line 424 of file TMath.h.

Double_t TMath::CosH ( Double_t x )

inline

Definition at line 433 of file TMath.h.

Referenced by TEveJetCone::CalcEtaPhiVec(), ClassImp(), TComplex::Cos(), TComplex::CosH(), TTreeFormula::EvalInstance(), RooTMathReg::RooTMathReg(), TComplex::Sin(), TComplex::SinH(), and ROOT::v5::TMath_GenerInterface().

template<typename T >

T * TMath::Cross	(	const T	v1[3],
		const T	v2[3],
		T	out[3]
	)

Definition at line 1020 of file TMath.h.

Referenced by TEveJetConeGL::DirectDraw(), TEveVectorT< TT >::OrthoNormBase(), TPolyLineShape::PaintNode(), TEveBoxSetGL::RenderBoxAutoNorm(), TEveBoxGL::RenderBoxAutoNorm(), TEveQuadSetGL::RenderQuads(), and TEveTrackPropagator::Helix_t::UpdateHelix().

Double_t TMath::CUncertainty ( )

inline

Definition at line 65 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::DegToRad ( )

inline

Definition at line 50 of file TMath.h.

Referenced by TGLScenePad::AddHistoPhysical(), TGeoSphere::Capacity(), TGeoPgon::Capacity(), TGeoTubeSeg::Capacity(), TGeoConeSeg::Capacity(), TGeoSphere::ComputeBBox(), TGeoTorus::ComputeBBox(), TGeoPgon::ComputeBBox(), TGeoCtub::ComputeBBox(), TGeoPara::ComputeNormal(), TGeoSphere::ComputeNormal(), TGeoTorus::ComputeNormal(), TGeoPgon::ComputeNormal(), TGeoPgon::Contains(), TGDMLWrite::CreateFakeCtub(), TGeoPatternSphPhi::CreateSinCos(), TGeoSphere::DistFromInside(), TGeoTorus::DistFromInside(), TGeoPgon::DistFromInside(), TGeoSphere::DistFromOutside(), TGeoTorus::DistFromOutside(), TGeoPgon::DistFromOutside(), TGeoHypeEditor::DoApply(), TGeoCtubEditor::DoApply(), TGLViewer::DoDrawStereo(), TGeoHypeEditor::DoDz(), TGeoHypeEditor::DoRin(), TGeoHypeEditor::DoRout(), TGeoHypeEditor::DoStIn(), TGeoHypeEditor::DoStOut(), ROOT::Quartz::TextLine::DrawLine(), TGeoSphere::GetBoundingCylinder(), TGeoPgon::GetBoundingCylinder(), TGeoPgon::GetPhiCrossList(), TGeoTubeSeg::GetPointsOnSegments(), TGeoConeSeg::GetPointsOnSegments(), TGeoMCGeometry::GetShape(), TColorWheel::InCircles(), TGeoTubeSeg::InitTrigonometry(), TGeoConeSeg::InitTrigonometry(), TColorWheel::InRectangles(), TGeoPgon::IsCrossingSlice(), TGeoSphere::IsOnBoundary(), TColorWheel::PaintCircles(), TColorWheel::PaintRectangles(), THistPainter::ProjectAitoff2xy(), THistPainter::ProjectMercator2xy(), THistPainter::ProjectParabolic2xy(), THistPainter::ProjectSinusoidal2xy(), TGeoPainter::Raytrace(), TGeoRotation::RotateX(), TGeoCombiTrans::RotateX(), TGeoHMatrix::RotateX(), TGeoRotation::RotateY(), TGeoCombiTrans::RotateY(), TGeoHMatrix::RotateY(), TGeoRotation::RotateZ(), TGeoCombiTrans::RotateZ(), TGeoHMatrix::RotateZ(), TGeoSphere::Safety(), TGeoShape::SafetyPhi(), TGeoTubeSeg::SafetyS(), TGeoPgon::SafetyToSegment(), TGeoPara::SetDimensions(), TGeoPcon::SetDimensions(), TGeoTrap::SetDimensions(), TGeoGtra::SetDimensions(), TGeoHype::SetHypeDimensions(), TGeoEltu::SetPoints(), TGeoParaboloid::SetPoints(), TGeoTube::SetPoints(), TGeoTorus::SetPoints(), TGeoSphere::SetPoints(), TGeoCone::SetPoints(), TGeoPgon::SetPoints(), TGeoPcon::SetPoints(), TGeoHype::SetPoints(), TGeoTubeSeg::SetPoints(), TGeoConeSeg::SetPoints(), TGeoCtub::SetPoints(), TEveTransSubEditor::SetTransFromData(), TGeoPgon::SliceCrossing(), TGeoPgon::SliceCrossingIn(), TGeoPgon::SliceCrossingInZ(), TGeoPgon::SliceCrossingZ(), TGeoGtra::TGeoGtra(), TGeoPara::TGeoPara(), TGeoPatternCylPhi::TGeoPatternCylPhi(), TGeoPatternTrapZ::TGeoPatternTrapZ(), TGeoPcon::TGeoPcon(), TGeoTrap::TGeoTrap(), TGLCylinder::TGLCylinder(), ROOT::v5::TMath_GenerInterface(), TGLPerspectiveCamera::Truck(), TEveTrackPropagator::Update(), and TEveTrackPropagator::Helix_t::UpdateHelix().

Double_t TMath::DiLog ( Double_t x )

The DiLogarithm function Code translated by R.Brun from CERNLIB DILOG function C332.

Definition at line 113 of file TMath.cxx.

Referenced by Functions(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::E ( )

inline

Definition at line 54 of file TMath.h.

Double_t TMath::Erf ( Double_t x )

Computation of the error function erf(x).

Erf(x) = (2/sqrt(pi)) Integral(exp(-t^2))dt between 0 and x

Definition at line 187 of file TMath.cxx.

Referenced by RooNovosibirsk::analyticalIntegral(), RooNDKeysPdf::analyticalIntegral(), RooMath::erf(), ErfInverse(), GaussIntegral(), RooHistError::getInterval(), TMVA::VariableGaussTransform::InverseTransform(), RooNDKeysPdf::loadDataSet(), RooTMathReg::RooTMathReg(), TRolke::SetCLSigmas(), testSpecFuncErf(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Erfc ( Double_t x )

Compute the complementary error function erfc(x).

Erfc(x) = (2/sqrt(pi)) Integral(exp(-t^2))dt between x and infinity

Definition at line 197 of file TMath.cxx.

Referenced by RooCurve::calcBandInterval(), RooMath::erfc(), ErfInverse(), RooAbsReal::plotOnWithErrorBand(), RooTMathReg::RooTMathReg(), testSpecFuncErf(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::ErfcInverse ( Double_t x )

Definition at line 233 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), testSpecFuncErf(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::ErfInverse ( Double_t x )

returns the inverse error function x must be <-1<x<1

Definition at line 206 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), testSpecFuncErf(), ROOT::v5::TMath_GenerInterface(), and TMVA::VariableGaussTransform::Transform().

Double_t TMath::EulerGamma ( )

inline

Definition at line 122 of file TMath.h.

Referenced by TFormula::FillDefaults().

Bool_t TMath::Even ( Long_t a )

inline

Definition at line 102 of file TMathBase.h.

Referenced by Quantiles().

Double_t TMath::Exp ( Double_t x )

inline

Definition at line 495 of file TMath.h.

Referenced by TMVA::MethodBoost::AdaBoost(), TMVA::MethodBDT::AdaBoost(), TMVA::MethodBDT::AdaCost(), TLatex::Analyse(), TGraphSmooth::BDRksmooth(), BesselI0(), ChisquareQuantile(), ClassImp(), TKDEFGT::Compute_A_k(), TLimit::ComputeLimit(), TGeoBatemanSol::Concentration(), TPad::DrawFrame(), TNeuron::DSigmoid(), TEveCaloData::EtaToTheta(), TTreeFormula::EvalInstance(), TMVA::SVKernelFunction::Evaluate(), RooNovosibirsk::evaluate(), TPaletteAxis::ExecuteEvent(), TPad::ExecuteEventAxis(), TComplex::Exp(), TASPaletteEditor::ExpPalette(), TMVA::MethodCFMlpANN_Utils::Foncf(), Freq(), TMVA::LDA::FSub(), Gaus(), RooLognormal::generateEvent(), genPoisson(), genPoisson2(), GeomMean(), TNeuron::GetDerivative(), TMVA::LogInterval::GetElement(), TMVA::MethodSVM::GetMvaValue(), TMVA::MethodBoost::GetMvaValue(), TMVA::LogInterval::GetRndm(), TNeuron::GetValue(), KolmogorovProb(), LaplaceDist(), LaplaceDistI(), TMVA::MethodCFMlpANN::NN_fonc(), TPad::PadtoX(), TPad::PadtoY(), TRandom::Poisson(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::Poisson(), Poisson(), TRandom::PoissonD(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::PoissonD(), TComplex::Power(), TKDEFGT::Predict(), RooTMathReg::RooTMathReg(), RootsCubic(), TSpectrum3::SearchFast(), TSpectrum3::SearchHighRes(), TSpectrum2::SearchHighRes(), TSpectrum::SearchHighRes(), TVector3::SetPtEtaPhi(), TMVA::SimulatedAnnealing::ShouldGoIn(), TNeuron::Sigmoid(), TSpectrum3::SmoothMarkov(), TSpectrum2::SmoothMarkov(), TSpectrum::SmoothMarkov(), StruveL0(), StruveL1(), StudentQuantile(), ROOT::v5::TMath_GenerInterface(), and Voigt().

Double_t TMath::Factorial ( Int_t i )

Compute factorial(n).

Definition at line 250 of file TMath.cxx.

Referenced by RooLegendre::analyticalIntegral(), and RooTMathReg::RooTMathReg().

Double_t TMath::FDist	(	Double_t	F,
		Double_t	N,
		Double_t	M
	)

Computes the density function of F-distribution (probability function, integral of density, is computed in FDistI).

Parameters N and M stand for degrees of freedom of chi-squares mentioned above parameter F is the actual variable x of the density function p(x) and the point at which the density function is calculated.

About F distribution: F-distribution arises in testing whether two random samples have the same variance. It is the ratio of two chi-square distributions, with N and M degrees of freedom respectively, where each chi-square is first divided by it's number of degrees of freedom. Implementation by Anna Kreshuk.

Definition at line 2224 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::FDistI	(	Double_t	F,
		Double_t	N,
		Double_t	M
	)

Calculates the cumulative distribution function of F-distribution, this function occurs in the statistical test of whether two observed samples have the same variance.

For this test a certain statistic F, the ratio of observed dispersion of the first sample to that of the second sample, is calculated. N and M stand for numbers of degrees of freedom in the samples 1-FDistI() is the significance level at which the hypothesis "1 has smaller variance than 2" can be rejected. A small numerical value of 1 - FDistI() implies a very significant rejection, in turn implying high confidence in the hypothesis "1 has variance greater than 2". Implementation by Anna Kreshuk.

Definition at line 2242 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Int_t TMath::Finite ( Double_t x )

inline

Definition at line 532 of file TMath.h.

Referenced by TUnfoldBinning::AddAxis(), TUnfold::AddMSparse(), TF3::FindMinMax(), TF2::FindMinMax(), TComplex::Finite(), HFit::Fit(), TUnfold::InvertMSparseSymmPos(), TTable::NaN(), TPad::ResizePad(), TUnfold::ScanLcurve(), TUnfoldDensity::ScanTau(), and ROOT::Fit::UnBinFit().

Double_t TMath::Floor ( Double_t x )

inline

Definition at line 473 of file TMath.h.

Referenced by TFormula::AddVariables(), AlmostInteger(), RooPoisson::analyticalIntegral(), RooNonCentralChiSquare::analyticalIntegral(), TH1::Chi2TestX(), TPad::DivideSquare(), TH3::DoProject1D(), TH3::DoProject2D(), TH2::DoProjection(), TH3::DoProjectProfile2D(), RooNonCentralChiSquare::evaluate(), RooStats::HypoTestInverterResult::ExclusionCleanup(), ROOT::Quartz::TextLine::GetAscentDescent(), RooStats::HypoTestInverterResult::GetExpectedLimit(), RooStats::HypoTestInverterPlot::MakeExpectedPlot(), TRandom::Poisson(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::Poisson(), TRandom::PoissonD(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::PoissonD(), THnBase::ProjectionAny(), TMatrixTSparse< Element >::RandomizePD(), TGLCameraOverlay::RenderBar(), TEveTrackList::RoundMomentumLimit(), ROOT::v5::TMath_GenerInterface(), and TAxis::ZoomOut().

Int_t TMath::FloorNint ( Double_t x )

inline

Definition at line 476 of file TMath.h.

Referenced by TEveCaloLegoGL::DrawCells2D(), TEvePointSetArray::Fill(), TSpline3::FindX(), TGraphQQ::MakeQuantiles(), TMVA::MethodBDT::OptimizeTuningParameters(), TGLAxisPainter::PaintAxis(), Quantiles(), TEveCaloLegoGL::RebinAxis(), TEveLine::ReduceSegmentLengths(), TEvePointSetArray::SetRange(), TEveProjectionAxesGL::SplitIntervalByPos(), and TEveProjectionAxesGL::SplitIntervalByVal().

Double_t TMath::Freq ( Double_t x )

Computation of the normal frequency function freq(x).

Freq(x) = (1/sqrt(2pi)) Integral(exp(-t^2/2))dt between -infinity and x.

Translated from CERNLIB C300 by Rene Brun.

Definition at line 268 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::G ( )

inline

Definition at line 68 of file TMath.h.

Referenced by TFormula::FillDefaults(), Gcgs(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Gamma ( Double_t z )

Computation of gamma(z) for all z.

C.Lanczos, SIAM Journal of Numerical Analysis B1 (1964), 86.

Definition at line 352 of file TMath.cxx.

Referenced by RooLegendre::analyticalIntegral(), RooChiSquarePdf::analyticalIntegral(), RooNonCentralChiSquare::analyticalIntegral(), TMVA::MethodMLP::BFGSMinimize(), ChisquareQuantile(), RooChiSquarePdf::evaluate(), RooNonCentralChiSquare::evaluate(), TMVA::MethodPDERS::KernelNormalization(), RooTMathReg::RooTMathReg(), Student(), testSpecFuncGamma(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Gamma	(	Double_t	a,
		Double_t	x
	)

Computation of the normalized lower incomplete gamma function P(a,x) as defined in the Handbook of Mathematical Functions by Abramowitz and Stegun, formula 6.5.1 on page 260 .

Its normalization is such that TMath::Gamma(a,+infinity) = 1 .

Begin_Latex P(a, x) = #frac{1}{#Gamma(a) } #int_{0}^{x} t^{a-1} e^{-t} dt End_Latex

— Nve 14-nov-1998 UU-SAP Utrecht

Definition at line 369 of file TMath.cxx.

Double_t TMath::GammaDist	(	Double_t	x,
		Double_t	gamma,
		Double_t	mu = `0`,
		Double_t	beta = `1`
	)

Computes the density function of Gamma distribution at point x.

gamma - shape parameter mu - location parameter beta - scale parameter

The definition can be found in "Engineering Statistics Handbook" on site http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm use now implementation in ROOT::Math::gamma_pdf Begin_Html

Definition at line 2259 of file TMath.cxx.

Referenced by RooGamma::evaluate(), and RooTMathReg::RooTMathReg().

Double_t TMath::Gaus	(	Double_t	x,
		Double_t	mean = `0`,
		Double_t	sigma = `1`,
		Bool_t	norm = `kFALSE`
	)

Calculate a gaussian function with mean and sigma.

If norm=kTRUE (default is kFALSE) the result is divided by sqrt(2*Pi)*sigma.

Definition at line 453 of file TMath.cxx.

Referenced by TMVA::MethodPDERS::ApplyKernelFunction(), ClassImp(), TH2::DoQuantiles(), gaus1D(), gaus2D(), gaus3D(), gaussianPeak(), RooLognormal::generateEvent(), TMVA::MethodBoost::GetMvaValue(), myfunc(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::Poisson(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::PoissonD(), RooTMathReg::RooTMathReg(), and TMVA::PDEFoamKernelGauss::WeightGaus().

Double_t TMath::Gcgs ( )

inline

Definition at line 69 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

template<typename T >

Double_t TMath::GeomMean	(	Long64_t	n,
		const T *	a
	)

Definition at line 855 of file TMath.h.

Referenced by stressVector(), testArrayFunctions(), and testIteratorFunctions().

template<typename Iterator >

Double_t TMath::GeomMean	(	Iterator	first,
		Iterator	last
	)

Definition at line 836 of file TMath.h.

Double_t TMath::GhbarC ( )

inline

Definition at line 73 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::GhbarCUncertainty ( )

inline

Definition at line 74 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::Gn ( )

inline

Definition at line 77 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::GnUncertainty ( )

inline

Definition at line 78 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::GUncertainty ( )

inline

Definition at line 70 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::H ( )

inline

Definition at line 81 of file TMath.h.

Referenced by TFormula::FillDefaults(), HC(), Hcgs(), and ROOT::v5::TMath_GenerInterface().

ULong_t TMath::Hash	(	const void *	txt,
		Int_t	ntxt
	)

Calculates hash index from any char string.

Based on precalculated table of 256 specially selected numbers. These numbers are selected in such a way, that for string length == 4 (integer number) the hash is unambigous, i.e. from hash value we can recalculate input (no degeneration).

The quality of hash method is good enough, that "random" numbers made as R = Hash(1), Hash(2), ...Hash(N) tested by <R>, <R*R>, <Ri*Ri+1> gives the same result as for libc rand().

For string: i = TMath::Hash(string,nstring); For int: i = TMath::Hash(&intword,sizeof(int)); For pointer: i = TMath::Hash(&pointer,sizeof(void*));

         V.Perev

This function is kept for back compatibility. The code previously in this function has been moved to the static function TString::Hash

Definition at line 1371 of file TMath.cxx.

Referenced by RooHashTable::find(), RooHashTable::findArg(), and TSelEventGen::Process().

ULong_t TMath::Hash ( const char * str )

Return a case-sensitive hash value (endian independent).

Definition at line 1379 of file TMath.cxx.

Double_t TMath::Hbar ( )

inline

Definition at line 86 of file TMath.h.

Referenced by Hbarcgs(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Hbarcgs ( )

inline

Definition at line 87 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::HbarUncertainty ( )

inline

Definition at line 88 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::HC ( )

inline

Definition at line 91 of file TMath.h.

Referenced by NamespaceImp(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::HCcgs ( )

inline

Definition at line 92 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::Hcgs ( )

inline

Definition at line 82 of file TMath.h.

Referenced by HCcgs(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::HUncertainty ( )

inline

Definition at line 83 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::Hypot	(	Double_t	x,
		Double_t	y
	)

Definition at line 60 of file TMath.cxx.

Referenced by DefAplGivens(), DefGivens(), TDecompSVD::Diag_3(), TGTextLayout::DistanceToText(), TEveCaloLegoGL::GetGridStep(), TMatrixDSymEigen::MakeEigenVectors(), RooTMathReg::RooTMathReg(), TEveLegoEventHandler::Rotate(), TGLPerspectiveCamera::Setup(), and ROOT::v5::TMath_GenerInterface().

Long_t TMath::Hypot	(	Long_t	x,
		Long_t	y
	)

Definition at line 53 of file TMath.cxx.

Double_t TMath::Infinity ( )

inline

Definition at line 648 of file TMath.h.

Referenced by RooStats::SamplingDistPlot::AddSamplingDistribution(), TF1Convolution::EvalNumConv(), TFormula::FillDefaults(), RooStats::HypoTestInverterResult::FindInterpolatedLimit(), TF3::FindMinMax(), TF2::FindMinMax(), RooStats::SamplingDistPlot::GetAbsoluteInterval(), TF1::IntegralOneDim(), and TF1Convolution::SetRange().

Double_t TMath::InvPi ( )

inline

Definition at line 48 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

template<typename T >

Bool_t TMath::IsInside	(	T	xp,
		T	yp,
		Int_t	np,
		T *	x,
		T *	y
	)

Definition at line 1056 of file TMath.h.

Referenced by TText::DistancetoPrimitive(), TPolyLine::DistancetoPrimitive(), TGraphPainter::DistancetoPrimitiveHelper(), TGraphDelaunay::Enclose(), TGraph::IsInside(), TH2Poly::IsIntersectingPolygon(), and testPoints().

Int_t TMath::IsNaN ( Double_t x )

inline

Definition at line 617 of file TMath.h.

Referenced by RooGaussModel::analyticalIntegral(), TMVA::DataSetFactory::BuildEventVector(), TMVA::RuleFitParams::CalcFStar(), RooStats::HypoTestInverterResult::CalculateEstimatedError(), RooGaussModel::evaluate(), RooStats::HistFactory::RooBarlowBeestonLL::evaluate(), TMVA::Factory::EvaluateAllMethods(), TMVA::Reader::EvaluateMulticlass(), TMVA::Reader::EvaluateMVA(), TMVA::Reader::EvaluateRegression(), TH1::ExtendAxis(), RooAbsPdf::extendedTerm(), TProfile::Fill(), TProfile2D::Fill(), TProfile3D::Fill(), TProfile::FillN(), TPainter3dAlgorithms::FillPolygon(), RooStats::HypoTestInverterResult::FindInterpolatedLimit(), RooStats::AsymptoticCalculator::GenerateAsimovDataSinglePdf(), TNeuron::GetBranch(), RooStats::AsymptoticCalculator::GetHypoTest(), RooAbsPdf::getLogVal(), TMVA::Reader::GetProba(), TMVA::Reader::GetRarity(), TF1::GetSave(), TF1::Integral(), TComplex::IsNaN(), RooStats::HypoTestInverterResult::LowerLimit(), RooStats::HypoTestInverterResult::LowerLimitEstimatedError(), TVector2::Phi_0_2pi(), TVector2::Phi_mpi_pi(), TPad::ResizePad(), RooStats::HypoTestInverterOriginal::RunAutoScan(), RooStats::HypoTestInverter::RunOnePoint(), RooAbsReal::traceEval(), RooResolutionModel::traceEvalHook(), RooAbsPdf::traceEvalHook(), RooAbsPdf::traceEvalPdf(), TMultiLayerPerceptron::Train(), RooStats::HypoTestInverterResult::UpperLimit(), and RooStats::HypoTestInverterResult::UpperLimitEstimatedError().

Double_t TMath::K ( )

inline

Definition at line 95 of file TMath.h.

Referenced by TFormula::FillDefaults(), GIFencode(), TMVA::LDA::Initialize(), Kcgs(), R(), RUncertainty(), ROOT::Math::TDataPoint< K, _val_type >::TDataPoint(), test_smatrix_kalman(), test_smatrix_sym_kalman(), test_tmatrix_kalman(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Kcgs ( )

inline

Definition at line 96 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::KolmogorovProb ( Double_t z )

Calculates the Kolmogorov distribution function, Begin_Html.

Definition at line 635 of file TMath.cxx.

Referenced by ROOT::Math::GoFTest::KolmogorovSmirnovTest(), TH2::KolmogorovTest(), TH3::KolmogorovTest(), KolmogorovTest(), TH1::KolmogorovTest(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::KolmogorovTest	(	Int_t	na,
		const Double_t *	a,
		Int_t	nb,
		const Double_t *	b,
		Option_t *	option
	)

Statistical test whether two one-dimensional sets of points are compatible with coming from the same parent distribution, using the Kolmogorov test.

That is, it is used to compare two experimental distributions of unbinned data.

Input: a,b: One-dimensional arrays of length na, nb, respectively. The elements of a and b must be given in ascending order. option is a character string to specify options "D" Put out a line of "Debug" printout "M" Return the Maximum Kolmogorov distance instead of prob

Output: The returned value prob is a calculated confidence level which gives a statistical test for compatibility of a and b. Values of prob close to zero are taken as indicating a small probability of compatibility. For two point sets drawn randomly from the same parent distribution, the value of prob should be uniformly distributed between zero and one. in case of error the function return -1 If the 2 sets have a different number of points, the minimum of the two sets is used.

Method: The Kolmogorov test is used. The test statistic is the maximum deviation between the two integrated distribution functions, multiplied by the normalizing factor (rdmax*sqrt(na*nb/(na+nb)).

Code adapted by Rene Brun from CERNLIB routine TKOLMO (Fred James) (W.T. Eadie, D. Drijard, F.E. James, M. Roos and B. Sadoulet, Statistical Methods in Experimental Physics, (North-Holland, Amsterdam 1971) 269-271)

Method Improvement by Jason A Detwiler (JADet.nosp@m.wile.nosp@m.r@lbl.nosp@m..gov)

The nuts-and-bolts of the TMath::KolmogorovTest() algorithm is a for-loop over the two sorted arrays a and b representing empirical distribution functions. The for-loop handles 3 cases: when the next points to be evaluated satisfy a>b, a<b, or a=b:

for (Int_t i=0;i<na+nb;i++) { if (a[ia-1] < b[ib-1]) { rdiff -= sa; ia++; if (ia > na) {ok = kTRUE; break;} } else if (a[ia-1] > b[ib-1]) { rdiff += sb; ib++; if (ib > nb) {ok = kTRUE; break;} } else { rdiff += sb - sa; ia++; ib++; if (ia > na) {ok = kTRUE; break;} if (ib > nb) {ok = kTRUE; break;} } rdmax = TMath::Max(rdmax,TMath::Abs(rdiff)); }

For the last case, a=b, the algorithm advances each array by one index in an attempt to move through the equality. However, this is incorrect when one or the other of a or b (or both) have a repeated value, call it x. For the KS statistic to be computed properly, rdiff needs to be calculated after all of the a and b at x have been tallied (this is due to the definition of the empirical distribution function; another way to convince yourself that the old CERNLIB method is wrong is that it implies that the function defined as the difference between a and b is multi-valued at x – besides being ugly, this would invalidate Kolmogorov's theorem).

The solution is to just add while-loops into the equality-case handling to perform the tally:

  } else {
     double x = a[ia-1];
     while(a[ia-1] == x && ia <= na) {
       rdiff -= sa;
       ia++;
     }
     while(b[ib-1] == x && ib <= nb) {
       rdiff += sb;
       ib++;
     }
     if (ia > na) {ok = kTRUE; break;}
     if (ib > nb) {ok = kTRUE; break;}
  }

NOTE1 A good description of the Kolmogorov test can be seen at: http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm

Definition at line 784 of file TMath.cxx.

Referenced by ROOT::Math::GoFTest::KolmogorovSmirnov2SamplesTest().

template<class Element , typename Size >

Element TMath::KOrdStat	(	Size	n,
		const Element *	a,
		Size	k,
		Size *	work = `0`
	)

Definition at line 1167 of file TMath.h.

Referenced by TKDTree< Index, Value >::Build(), TLinearFitter::CStep(), Median(), Quantiles(), and testArrayFunctions().

Double_t TMath::KUncertainty ( )

inline

Definition at line 97 of file TMath.h.

Referenced by RUncertainty(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Landau	(	Double_t	x,
		Double_t	mu = `0`,
		Double_t	sigma = `1`,
		Bool_t	norm = `kFALSE`
	)

The LANDAU function.

mu is a location parameter and correspond approximatly to the most probable value and sigma is a scale parameter (not the sigma of the full distribution which is not defined) Note that for mu=0 and sigma=1 (default values) the exact location of the maximum of the distribution (most proble value) is at x = -0.22278 This function has been adapted from the CERNLIB routine G110 denlan. If norm=kTRUE (default is kFALSE) the result is divided by sigma

Definition at line 473 of file TMath.cxx.

Referenced by ClassImp(), RooLandau::evaluate(), and RooTMathReg::RooTMathReg().

Double_t TMath::LandauI ( Double_t x )

Returns the value of the Landau distribution function at point x.

The algorithm was taken from the Cernlib function dislan(G110) Reference: K.S.Kolbig and B.Schorr, "A program package for the Landau distribution", Computer Phys.Comm., 31(1984), 97-111

Definition at line 2682 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::LaplaceDist	(	Double_t	x,
		Double_t	alpha = `0`,
		Double_t	beta = `1`
	)

Computes the probability density function of Laplace distribution at point x, with location parameter alpha and shape parameter beta.

By default, alpha=0, beta=1 This distribution is known under different names, most common is double exponential distribution, but it also appears as the two-tailed exponential or the bilateral exponential distribution

Definition at line 2281 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::LaplaceDistI	(	Double_t	x,
		Double_t	alpha = `0`,
		Double_t	beta = `1`
	)

Computes the distribution function of Laplace distribution at point x, with location parameter alpha and shape parameter beta.

By default, alpha=0, beta=1 This distribution is known under different names, most common is double exponential distribution, but it also appears as the two-tailed exponential or the bilateral exponential distribution

Definition at line 2297 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Ldexp	(	Double_t	x,
		Int_t	exp
	)

inline

Definition at line 498 of file TMath.h.

Referenced by RooTMathReg::RooTMathReg().

Double_t TMath::Ln10 ( )

inline

Definition at line 57 of file TMath.h.

Referenced by TFormula::FillDefaults(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::LnGamma ( Double_t z )

Computation of ln[gamma(z)] for all z.

C.Lanczos, SIAM Journal of Numerical Analysis B1 (1964), 86.

The accuracy of the result is better than 2e-10.

— Nve 14-nov-1998 UU-SAP Utrecht

Definition at line 490 of file TMath.cxx.

Referenced by ChisquareQuantile(), RooNLLVar::evaluatePartition(), TFitter::FitLikelihood(), TFitter::FitLikelihoodI(), genPoisson2(), RooPoisson::getLogVal(), TRolke::LogFactorial(), TRandom::Poisson(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::Poisson(), Poisson(), TRandom::PoissonD(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::PoissonD(), RooTMathReg::RooTMathReg(), testSpecFuncGamma(), and ROOT::v5::TMath_GenerInterface().

template<typename T >

Long64_t TMath::LocMax	(	Long64_t	n,
		const T *	a
	)

Definition at line 724 of file TMath.h.

Referenced by TGeoSphere::ComputeBBox(), TGeoTorus::ComputeBBox(), TGeoPcon::ComputeBBox(), TGeoPgon::ComputeBBox(), TGeoTubeSeg::ComputeBBox(), TGeoConeSeg::ComputeBBox(), TGeoCtub::ComputeBBox(), TDecompBK::Decompose(), TGeoPcon::DistFromOutside(), TGeoPgon::DistFromOutside(), TLinearFitter::EvalRobust(), TRobustEstimator::Evaluate(), TRobustEstimator::Exact2(), TVectorT< Element >::Max(), TMatrixTBase< Element >::Max(), TGeoTrd1::Safety(), TGeoTrd2::Safety(), TGeoTube::Safety(), TGeoPara::Safety(), TGeoSphere::Safety(), TGeoArb8::Safety(), TGeoTubeSeg::Safety(), TGeoCtub::Safety(), TGeoTube::SafetyS(), TGeoTubeSeg::SafetyS(), TGeoPgon::SafetyToSegment(), TMatrixTSparse< Element >::SetMatrixArray(), testArrayFunctions(), testIteratorFunctions(), and TMatrixTSparse< Element >::TMatrixTSparse().

template<typename Iterator >

Iterator TMath::LocMax	(	Iterator	first,
		Iterator	last
	)

Definition at line 743 of file TMath.h.

template<typename T >

Long64_t TMath::LocMin	(	Long64_t	n,
		const T *	a
	)

Definition at line 695 of file TMath.h.

Referenced by TGeoSphere::ComputeBBox(), TGeoTorus::ComputeBBox(), TGeoPcon::ComputeBBox(), TGeoPgon::ComputeBBox(), TGeoTubeSeg::ComputeBBox(), TGeoConeSeg::ComputeBBox(), TGeoCtub::ComputeBBox(), TGeoTube::ComputeNormal(), TGeoBBox::ComputeNormal(), TGeoPara::ComputeNormal(), TGeoSphere::ComputeNormal(), TGeoHype::ComputeNormal(), TGeoTubeSeg::ComputeNormal(), TGeoConeSeg::ComputeNormal(), TGeoCtub::ComputeNormal(), TGeoTubeSeg::ComputeNormalS(), TGeoConeSeg::ComputeNormalS(), TGeoTrd1::DistFromInside(), TGeoTrd2::DistFromInside(), TGeoSphere::DistFromInside(), TGeoSphere::DistFromOutside(), TLinearFitter::EvalRobust(), TRobustEstimator::Evaluate(), TGeoVoxelFinder::GetNextCandidates(), TVectorT< Element >::Min(), TMatrixTBase< Element >::Min(), TGeoTrd1::Safety(), TGeoTrd2::Safety(), TGeoTube::Safety(), TGeoPara::Safety(), TGeoSphere::Safety(), TGeoCone::Safety(), TGeoArb8::Safety(), TGeoTubeSeg::Safety(), TGeoCtub::Safety(), TGeoTube::SafetyS(), TGeoCone::SafetyS(), TGeoTubeSeg::SafetyS(), TGeoPgon::SafetyToSegment(), TMatrixTSparse< Element >::SetMatrixArray(), stressVector(), testArrayFunctions(), testIteratorFunctions(), and TMatrixTSparse< Element >::TMatrixTSparse().

template<typename Iterator >

Iterator TMath::LocMin	(	Iterator	first,
		Iterator	last
	)

Definition at line 717 of file TMath.h.

Double_t TMath::Log ( Double_t x )

inline

Definition at line 526 of file TMath.h.

Referenced by TMVA::MethodBoost::AdaBoost(), TMVA::MethodBDT::AdaBoost(), TMVA::MethodBDT::AdaBoostR2(), TMVA::MethodBDT::AdaCost(), TLatex::Analyse(), RooLognormal::analyticalIntegral(), RooNovosibirsk::analyticalIntegral(), ROOT::Math::GoFTest::AndersonDarlingTest(), TGeoMixture::AverageProperties(), RooStats::MetropolisHastings::CalcNLL(), TMVA::MethodMLP::CalculateEstimator(), ChisquareQuantile(), ClassImp(), TFractionFitter::ComputeChisquareLambda(), TBinomialEfficiencyFitter::ComputeFCN(), TFractionFitter::ComputeFCN(), RooStats::MetropolisHastings::ConstructChain(), DiLog(), TPad::DrawFrame(), TEveVectorT< TT >::Eta(), TParticle::Eta(), TTreeFormula::EvalInstance(), RooLognormal::evaluate(), RooNovosibirsk::evaluate(), TRandom::Exp(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::Exp(), TASPaletteEditor::ExpPalette(), TGeoBatemanSol::FindSolution(), TSpectrumFit::FitAwmi(), TSpectrum2Fit::FitAwmi(), TFitter::FitLikelihood(), TFumili::FitLikelihood(), TFitter::FitLikelihoodI(), TFumili::FitLikelihoodI(), TSpectrumFit::FitStiefel(), TSpectrum2Fit::FitStiefel(), RooLognormal::generateEvent(), RooGamma::generateEvent(), TMVA::SimulatedAnnealing::GenerateNewTemperature(), GeomMean(), TMVA::MethodMLP::GetCEErr(), TMultiLayerPerceptron::GetCrossEntropy(), TMultiLayerPerceptron::GetCrossEntropyBinary(), TMVA::LogInterval::GetElement(), TMVA::LDA::GetLogLikelihood(), TMVA::Tools::GetMutualInformation(), TMVA::MethodBoost::GetMvaValue(), TMVA::LogInterval::GetRndm(), TGeoElementRN::GetSpecificActivity(), TFitter::GetSumLog(), TFumili::GetSumLog(), H1LeastSquareLinearFit(), TH2::KolmogorovTest(), TH3::KolmogorovTest(), TH1::KolmogorovTest(), TMultiGraph::LeastSquareLinearFit(), TGraph::LeastSquareLinearFit(), TRolke::LikeMod1(), TRolke::LikeMod2(), TRolke::LikeMod3(), TRolke::LikeMod4(), TRolke::LikeMod5(), TRolke::LikeMod6(), TRolke::LikeMod7(), TComplex::Log(), TComplex::Log10(), TComplex::Log2(), TLimit::LogLikelihood(), LogNormal(), TASPaletteEditor::LogPalette(), ROOT::Math::GoFTest::LogSample(), TMinuit::mnseek(), NormQuantile(), TGraphPolargram::PaintPolarDivisions(), TGraphPolargram::PaintRadialDivisions(), TRandom::Poisson(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::Poisson(), TRandom::PoissonD(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::PoissonD(), TComplex::Power(), THistPainter::ProjectMercator2xy(), TVector3::PseudoRapidity(), TRandom::Rannor(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::Rannor(), RooTMathReg::RooTMathReg(), RootsCubic(), TGeoMaterial::ScreenFactor(), TGeoMaterial::SetRadLen(), TGeoChecker::ShapeDistances(), RooStats::MetropolisHastings::ShouldTakeStep(), ROOT::v5::TMath_GenerInterface(), TMVA::MethodLikelihood::TransformLikelihoodOutput(), TParticle::Y(), and Yields().

Double_t TMath::Log10 ( Double_t x )

inline

Definition at line 529 of file TMath.h.

Double_t TMath::Log2 ( Double_t x )

Definition at line 104 of file TMath.cxx.

Referenced by TEveProjection::BisectBreakPoint(), ClassImp(), TGLFBO::Init(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::LogE ( )

inline

Definition at line 60 of file TMath.h.

Referenced by TFormula::FillDefaults(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::LogNormal	(	Double_t	x,
		Double_t	sigma,
		Double_t	theta = `0`,
		Double_t	m = `1`
	)

Computes the density of LogNormal distribution at point x.

Variable X has lognormal distribution if Y=Ln(X) has normal distribution sigma is the shape parameter theta is the location parameter m is the scale parameter The formula was taken from "Engineering Statistics Handbook" on site http://www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm Implementation using ROOT::Math::lognormal_pdf Begin_Html

Definition at line 2319 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg().

Short_t TMath::Max	(	Short_t	a,
		Short_t	b
	)

inline

Definition at line 202 of file TMathBase.h.

UShort_t TMath::Max	(	UShort_t	a,
		UShort_t	b
	)

inline

Definition at line 205 of file TMathBase.h.

Int_t TMath::Max	(	Int_t	a,
		Int_t	b
	)

inline

Definition at line 208 of file TMathBase.h.

UInt_t TMath::Max	(	UInt_t	a,
		UInt_t	b
	)

inline

Definition at line 211 of file TMathBase.h.

Long_t TMath::Max	(	Long_t	a,
		Long_t	b
	)

inline

Definition at line 214 of file TMathBase.h.

ULong_t TMath::Max	(	ULong_t	a,
		ULong_t	b
	)

inline

Definition at line 217 of file TMathBase.h.

Long64_t TMath::Max	(	Long64_t	a,
		Long64_t	b
	)

inline

Definition at line 220 of file TMathBase.h.

ULong64_t TMath::Max	(	ULong64_t	a,
		ULong64_t	b
	)

inline

Definition at line 223 of file TMathBase.h.

Float_t TMath::Max	(	Float_t	a,
		Float_t	b
	)

inline

Definition at line 226 of file TMathBase.h.

Double_t TMath::Max	(	Double_t	a,
		Double_t	b
	)

inline

Definition at line 229 of file TMathBase.h.

template<typename T >

T TMath::MaxElement	(	Long64_t	n,
		const T *	a
	)

Definition at line 688 of file TMath.h.

Referenced by TTreePerfStats::Finish(), TMemStatShow::Show(), and testArrayFunctions().

template<typename T >

Double_t TMath::Mean	(	Long64_t	n,
		const T *	a,
		const Double_t *	w = `0`
	)

Definition at line 824 of file TMath.h.

Referenced by FloatRandom(), TGL5DPainter::InitGeometry(), TH3::KolmogorovTest(), TMVA::Tools::Mean(), Random(), RMS(), stressVector(), testArrayFunctions(), testIteratorFunctions(), and testTStatistic().

template<typename Iterator >

Double_t TMath::Mean	(	Iterator	first,
		Iterator	last
	)

Definition at line 778 of file TMath.h.

template<typename Iterator , typename WeightIterator >

Double_t TMath::Mean	(	Iterator	first,
		Iterator	last,
		WeightIterator	wfirst
	)

Definition at line 795 of file TMath.h.

template<typename T >

Double_t TMath::Median	(	Long64_t	n,
		const T *	a,
		const Double_t *	w = `0`,
		Long64_t *	work = `0`
	)

Definition at line 1077 of file TMath.h.

Referenced by TRobustEstimator::RDist(), TH1::SmoothArray(), stressVector(), and testArrayFunctions().

Short_t TMath::Min	(	Short_t	a,
		Short_t	b
	)

inline

Definition at line 170 of file TMathBase.h.

UShort_t TMath::Min	(	UShort_t	a,
		UShort_t	b
	)

inline

Definition at line 173 of file TMathBase.h.

Int_t TMath::Min	(	Int_t	a,
		Int_t	b
	)

inline

Definition at line 176 of file TMathBase.h.

UInt_t TMath::Min	(	UInt_t	a,
		UInt_t	b
	)

inline

Definition at line 179 of file TMathBase.h.

Long_t TMath::Min	(	Long_t	a,
		Long_t	b
	)

inline

Definition at line 182 of file TMathBase.h.

ULong_t TMath::Min	(	ULong_t	a,
		ULong_t	b
	)

inline

Definition at line 185 of file TMathBase.h.

Long64_t TMath::Min	(	Long64_t	a,
		Long64_t	b
	)

inline

Definition at line 188 of file TMathBase.h.

ULong64_t TMath::Min	(	ULong64_t	a,
		ULong64_t	b
	)

inline

Definition at line 191 of file TMathBase.h.

Float_t TMath::Min	(	Float_t	a,
		Float_t	b
	)

inline

Definition at line 194 of file TMathBase.h.

Double_t TMath::Min	(	Double_t	a,
		Double_t	b
	)

inline

Definition at line 197 of file TMathBase.h.

template<typename T >

T TMath::MinElement	(	Long64_t	n,
		const T *	a
	)

Definition at line 681 of file TMath.h.

Referenced by TLinearFitter::EvalRobust(), TMemStatShow::Show(), TH1::SmoothArray(), stressVector(), and testArrayFunctions().

Double_t TMath::MWair ( )

inline

Definition at line 115 of file TMath.h.

Referenced by Rgair(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Na ( )

inline

Definition at line 104 of file TMath.h.

Referenced by TGeoMixture::AverageProperties(), TGDMLParse::GetScale(), TGDMLParse::GetScaleVal(), TGeoElementRN::GetSpecificActivity(), R(), RUncertainty(), TGeoMaterial::SetRadLen(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::NaUncertainty ( )

inline

Definition at line 105 of file TMath.h.

Referenced by RUncertainty(), and ROOT::v5::TMath_GenerInterface().

Long_t TMath::NextPrime ( Long_t x )

TMath Base functions.

Define the functions Min, Max, Abs, Sign, Range for all types. NB: These functions are unfortunately not available in a portable way in std::.

More functions are defined in TMath.h. TMathBase.h is designed to be a stable file and used in place of TMath.h in the ROOT miniCore. Return next prime number after x, unless x is a prime in which case x is returned.

Definition at line 29 of file TMathBase.cxx.

Referenced by ClassImp(), TObjectTable::Expand(), TExMap::Expand(), and RooHashTable::RooHashTable().

template<typename T >

Int_t TMath::Nint ( T x )

inline

Definition at line 480 of file TMath.h.

Referenced by TEveGValuator::CalcSliderPos(), CeilNint(), ClassImp(), TGLRect::Diagonal(), TEveRGBAPalette::DoubleToInt(), TEveCaloLegoGL::DrawAxis2D(), TEveCaloLegoGL::DrawAxis3D(), TEveCaloLegoGL::DrawCells2D(), TASImage::DrawDashZLine(), TASImage::DrawDashZTLine(), TPad::DrawDist(), TFractionFitter::FindPrediction(), FloorNint(), TEveTriangleSet::GenerateZNormalColors(), TEveCaloLegoGL::GetGridStep(), TGLColor::GetTransparency(), TGLEventHandler::HandleButton(), TRootCanvas::HandleContainerConfigure(), TGLEventHandler::HandleKey(), TGLEventHandler::HandleMotion(), TProof::HandleSubmerger(), TGLUtil::InitializeIfNeeded(), TDecompSparse::InitPivot_sub2(), KolmogorovProb(), TProof::MarkBad(), TGLAxisPainter::PaintAxis(), TMVA::TransformationHandler::PlotVariables(), TGLUtil::PointToViewport(), TH1::RecomputeAxisLimits(), TGLRnrCtx::RegisterFont(), TGLOverlayButton::Render(), TGLAnnotation::Render(), TEveBoxSetGL::RenderBoxes(), TEveCaloLegoOverlay::RenderHeader(), TEveCaloLegoOverlay::RenderLogaritmicScales(), TGLCameraOverlay::RenderPlaneIntersect(), TGPack::ResizeExistingFrames(), TGLViewer::SavePictureHeight(), TGLViewer::SavePictureScale(), TGLViewer::SavePictureWidth(), TASImage::SavePrimitive(), TGLAutoRotator::SetDt(), TEveRGBAPalette::SetLimitsScaleMinMax(), TEveRGBAPaletteSubEditor::SetModel(), TEveRGBAPalette::SetupColor(), THistPainter::ShowProjectionX(), THistPainter::ShowProjectionY(), TGLAutoRotator::Start(), TEvePointSet::TakeAction(), TEveTrack::TEveTrack(), and TMVA::MethodLikelihood::Train().

template<typename T >

T * TMath::Normal2Plane	(	const T	v1[3],
		const T	v2[3],
		const T	v3[3],
		T	normal[3]
	)

Definition at line 1032 of file TMath.h.

Referenced by TGLFaceSet::CalculateNormals(), TGLH2PolyPainter::DrawExtrusion(), Rgl::DrawTrapezoid(), Rgl::DrawTrapezoidTextured(), Rgl::DrawTrapezoidTextured2(), TGLParametricPlot::InitGeometry(), TGLAxis::PaintGLAxis(), TEveFrameBoxGL::RenderFrame(), TGLSurfacePainter::SetNormals(), testPlane(), and TGLSurfacePainter::WindowPointTo3DPoint().

Float_t TMath::Normalize ( Float_t v[3] )

Normalize a vector v in place.

Returns the norm of the original vector.

Definition at line 499 of file TMath.cxx.

Referenced by TGeoEltu::ComputeNormal(), TPolyLineShape::Gyrot(), TPolyLineShape::PaintNode(), TGeoHelix::Step(), and TCTUB::TCTUB().

Double_t TMath::Normalize ( Double_t v[3] )

Normalize a vector v in place.

Returns the norm of the original vector. This implementation (thanks Kevin Lynch krlyn.nosp@m.ch@b.nosp@m.u.edu) is protected against possible overflows.

Definition at line 516 of file TMath.cxx.

Referenced by NormCross().

template<typename T >

T TMath::NormCross	(	const T	v1[3],
		const T	v2[3],
		T	out[3]
	)

inline

Definition at line 674 of file TMath.h.

Referenced by Normal2Plane(), and testNormCross().

Double_t TMath::NormQuantile ( Double_t p )

Computes quantiles for standard normal distribution N(0, 1) at probability p ALGORITHM AS241 APPL.

STATIST. (1988) VOL. 37, NO. 3, 477-484.

Definition at line 2342 of file TMath.cxx.

Referenced by ChisquareQuantile(), ErfcInverse(), TGraphQQ::MakeFunctionQuantiles(), TGraphQQ::Quartiles(), RooTMathReg::RooTMathReg(), StudentQuantile(), and ROOT::v5::TMath_GenerInterface().

Bool_t TMath::Odd ( Long_t a )

inline

Definition at line 105 of file TMathBase.h.

Bool_t TMath::Permute	(	Int_t	n,
		Int_t *	a
	)

Simple recursive algorithm to find the permutations of n natural numbers, not necessarily all distinct adapted from CERNLIB routine PERMU.

The input array has to be initialised with a non descending sequence. The method returns kFALSE when all combinations are exhausted.

Definition at line 2443 of file TMath.cxx.

Referenced by checkPermute(), TH3::KolmogorovTest(), and permuteTime().

Double_t TMath::Pi ( )

inline

Definition at line 44 of file TMath.h.

Double_t TMath::PiOver4 ( )

inline

Definition at line 47 of file TMath.h.

Referenced by TPie::ExecuteEvent(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Poisson	(	Double_t	x,
		Double_t	par
	)

compute the Poisson distribution function for (x,par) The Poisson PDF is implemented by means of Euler's Gamma-function (for the factorial), so for any x integer argument it is correct.

BUT for non-integer x values, it IS NOT equal to the Poisson distribution. see TMath::PoissonI to get a non-smooth function. Note that for large values of par, it is better to call TMath::Gaus(x,par,sqrt(par),kTRUE) Begin_Html

Definition at line 564 of file TMath.cxx.

Referenced by RooPoisson::analyticalIntegral(), RooHistConstraint::evaluate(), RooPoisson::evaluate(), TFeldmanCousins::Prob(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::PoissonI	(	Double_t	x,
		Double_t	par
	)

compute the Poisson distribution function for (x,par) This is a non-smooth function.

This function is equivalent to ROOT::Math::poisson_pdf Begin_Html

Definition at line 592 of file TMath.cxx.

Referenced by TRolke::GetLimitsML(), TRolke::GetLimitsQuantile(), TRolke::GetSensitivity(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

LongDouble_t TMath::Power	(	LongDouble_t	x,
		LongDouble_t	y
	)

inline

Definition at line 501 of file TMath.h.

Referenced by TMVA::MethodBDT::AdaBoost(), TMVA::MethodBDT::AdaBoostR2(), RooArgusBG::analyticalIntegral(), RooCBShape::analyticalIntegral(), ROOT::Math::GoFTest::AndersonDarling2SamplesTest(), TGeoMixture::AverageProperties(), TGraphSmooth::BDRsupsmu(), BetaDist(), BinomialI(), RooGExpModel::calcDecayConv(), Roo2DKeysPdf::calculateBandWidth(), RooNDKeysPdf::calculateBandWidth(), Roo1DMomentMorphFunction::calculateFractions(), RooMomentMorph::CacheElem::calculateFractions(), ChisquareQuantile(), ClassImp(), TSpectrum3::Deconvolution(), TSpectrum2::Deconvolution(), TSpectrum::Deconvolution(), TSpectrum::DeconvolutionRL(), TMatrixTSym< Element >::Determinant(), TMatrixT< Element >::Determinant(), TEveProjectionAxesGL::DirectDraw(), TGraphPolargram::DistancetoPrimitive(), Rgl::Draw2DAxis(), Rgl::DrawPaletteAxis(), TCreatePrimitives::Ellipse(), TSpectrumTransform::Enhance(), TMVA::MethodFDA::EstimatorFunction(), TTreeFormula::EvalInstance(), RooArgusBG::evaluate(), RooDstD0BG::evaluate(), RooNovosibirsk::evaluate(), RooCBShape::evaluate(), RooBukinPdf::evaluate(), THistPainter::ExecuteEvent(), TPad::ExecuteEventAxis(), TUnfoldBinning::ExtractHistogram(), RooAbsData::fillHistogram(), TSpectrumTransform::FilterZonal(), ROOT::Fit::FitOptionsMake(), TSpectrum2Transform::General2(), RooNonCPEigenDecay::generateEvent(), TMVA::SimulatedAnnealing::GenerateNeighbour(), TUnfoldSys::GetBackground(), TPaletteAxis::GetObjectInfo(), TF1::GetRandom(), TSVDUnfold::GetUnfoldCovMatrix(), TSpectrumTransform::Haar(), TSpectrum2Transform::Haar(), TVirtualPacketizer::HandleTimer(), RooDataHist::importTH1(), RooDataHist::importTH1Set(), IncreaseReal(), Roo1DMomentMorphFunction::initialize(), RooMomentMorph::initialize(), TPostScript::Initialize(), TF1::IntegralMultiple(), TDecompLU::InvertLU(), TMVA::MethodPDERS::KernelNormalization(), TMVA::MethodPDERS::LanczosFilter(), TCreatePrimitives::Line(), Roo2DKeysPdf::loadDataSet(), RooNDKeysPdf::loadDataSet(), TPainter3dAlgorithms::Luminosity(), TMatrixDSymEigen::MakeEigenVectors(), TMatrixDEigen::MakeSchurr(), TMinuit::mnbins(), RooAbsData::moment(), TPDF::NewPage(), TMVA::MethodPDERS::NormSinc(), THLimitsFinder::Optimize(), TMVA::kNN::ModulekNN::Optimize(), TPaletteAxis::Paint(), THistPainter::PaintAxis(), TAxis3D::PaintAxis(), TGaxis::PaintAxis(), THistPainter::PaintErrors(), TGraphPainter::PaintGrapHist(), THistPainter::PaintHist(), THistPainter::PaintInit(), THistPainter::PaintInitH(), THistPainter::PaintLegoAxis(), TComplex::Power(), TQueryResult::Print(), TProofProgressDialog::Progress(), RealToDouble(), RooGrid::refine(), TUnfoldDensity::RegularizeOneDistribution(), TGLCameraOverlay::RenderBar(), TEveBoxSetGL::RenderBoxes(), TEveCaloLegoOverlay::RenderLogaritmicScales(), rescale_error(), RooTMathReg::RooTMathReg(), TEveTrackList::RoundMomentumLimit(), TH1::SavePrimitiveHelp(), TUnfold::ScanLcurve(), TUnfoldDensity::ScanTau(), TEveUtil::SetColorBrightness(), TGenPhaseSpace::SetDecay(), TMVA::SimulatedAnnealing::SetDefaultScale(), TEveProjection::SetDistortion(), TEveProjection::SetFixR(), TEveProjection::SetFixZ(), TMVA::KDEKernel::SetKernelType(), ROOT::Math::GoFTest::SetParameters(), TEveProjection::SetPastFixRFac(), TEveProjection::SetPastFixZFac(), TGeoMaterial::SetRadLen(), TGLAxisPainter::SetTextFormat(), SimpleFun(), SingularFun(), TMehrotraSolver::Solve(), TGondzioSolver::Solve(), TGeoTorus::SolveCubic(), RooAbsData::standMoment(), StrToReal(), Student(), StudentQuantile(), TUnfoldSys::SubtractBackground(), THistPainter::TableInit(), TCreatePrimitives::Text(), ROOT::v5::TMath_GenerInterface(), TSpectrumTransform::Transform(), TSpectrum::Unfolding(), and RooMCIntegrator::vegas().

LongDouble_t TMath::Power	(	LongDouble_t	x,
		Long64_t	y
	)

inline

Definition at line 504 of file TMath.h.

LongDouble_t TMath::Power	(	Long64_t	x,
		Long64_t	y
	)

inline

Definition at line 507 of file TMath.h.

Double_t TMath::Power	(	Double_t	x,
		Double_t	y
	)

inline

Definition at line 514 of file TMath.h.

Double_t TMath::Power	(	Double_t	x,
		Int_t	y
	)

inline

Definition at line 517 of file TMath.h.

Double_t TMath::Prob	(	Double_t	chi2,
		Int_t	ndf
	)

Computation of the probability for a certain Chi-squared (chi2) and number of degrees of freedom (ndf).

Calculations are based on the incomplete gamma function P(a,x), where a=ndf/2 and x=chi2/2.

P(a,x) represents the probability that the observed Chi-squared for a correct model should be less than the value chi2.

The returned probability corresponds to 1-P(a,x), which denotes the probability that an observed Chi-squared exceeds the value chi2 by chance, even for a correct model.

— NvE 14-nov-1998 UU-SAP Utrecht

Definition at line 619 of file TMath.cxx.

Referenced by TH1::Chi2TestX(), TFractionFitter::GetProb(), TF1::GetProb(), RooStats::BernsteinCorrection::ImportCorrectedPdf(), RooStats::LikelihoodInterval::IsInInterval(), TH2::KolmogorovTest(), TH3::KolmogorovTest(), TH1::KolmogorovTest(), THistPainter::PaintStat(), TGraphPainter::PaintStats(), RooChi2MCSModule::processAfterFit(), RooTMathReg::RooTMathReg(), and TMVA::PDF::ValidatePDF().

Double_t TMath::Qe ( )

inline

Definition at line 125 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::QeUncertainty ( )

inline

Definition at line 126 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

void TMath::Quantiles	(	Int_t	n,
		Int_t	nprob,
		Double_t *	x,
		Double_t *	quantiles,
		Double_t *	prob,
		Bool_t	isSorted = `kTRUE`,
		Int_t *	index = `0`,
		Int_t	type = `7`
	)

Computes sample quantiles, corresponding to the given probabilities Parameters: x -the data sample n - its size quantiles - computed quantiles are returned in there prob - probabilities where to compute quantiles nprob - size of prob array isSorted - is the input array x sorted? NOTE, that when the input is not sorted, an array of integers of size n needs to be allocated.

It can be passed by the user in parameter index, or, if not passed, it will be allocated inside the function

type - method to compute (from 1 to 9). Following types are provided: Discontinuous: type=1 - inverse of the empirical distribution function type=2 - like type 1, but with averaging at discontinuities type=3 - SAS definition: nearest even order statistic Piecwise linear continuous: In this case, sample quantiles can be obtained by linear interpolation between the k-th order statistic and p(k). type=4 - linear interpolation of empirical cdf, p(k)=k/n; type=5 - a very popular definition, p(k) = (k-0.5)/n; type=6 - used by Minitab and SPSS, p(k) = k/(n+1); type=7 - used by S-Plus and R, p(k) = (k-1)/(n-1); type=8 - resulting sample quantiles are approximately median unbiased regardless of the distribution of x. p(k) = (k-1/3)/(n+1/3); type=9 - resulting sample quantiles are approximately unbiased, when the sample comes from Normal distribution. p(k)=(k-3/8)/(n+1/4);

default type = 7

References: 1) Hyndman, R.J and Fan, Y, (1996) "Sample quantiles in statistical packages" American Statistician, 50, 361-365 2) R Project documentation for the function quantile of package {stats}

Definition at line 1173 of file TMath.cxx.

Referenced by TKDE::ComputeMidspread(), RooStats::HypoTestInverterResult::ExclusionCleanup(), RooStats::HypoTestInverterResult::GetExpectedLimit(), RooStats::HypoTestInverterResult::GetLimitDistribution(), TParallelCoordVar::GetQuantiles(), RooStats::HypoTestInverterPlot::MakeExpectedPlot(), TGraphQQ::Quartiles(), and testQuantiles().

Double_t TMath::R ( )

inline

Definition at line 109 of file TMath.h.

Referenced by TFormula::FillDefaults(), Rgair(), RUncertainty(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::RadToDeg ( )

inline

Definition at line 49 of file TMath.h.

Referenced by TGeoCtub::ComputeBBox(), TGeoPgon::ComputeNormal(), TGeoSphere::Contains(), TGeoTorus::Contains(), TGeoPcon::Contains(), TGeoPgon::Contains(), TGeoConeSeg::Contains(), TGeoCtub::Contains(), TGDMLWrite::CreateFakeCtub(), TGeoSphere::DistFromInside(), TGeoSphere::DistFromOutside(), TGeoTorus::DistFromOutside(), TGeoPgon::DistFromOutside(), TGeoConeSeg::DistToCons(), TGeoHypeEditor::DoStIn(), TGeoHypeEditor::DoStOut(), TGLPadPainter::DrawGradient(), TGeoPatternCylPhi::FindNode(), TGeoPatternSphPhi::FindNode(), TGeoRotation::GetAngles(), TGeoPgon::GetPhiCrossList(), TGDMLParse::GetScale(), TGDMLParse::GetScaleVal(), TColorWheel::InGray(), TGeoShape::IsInPhiRange(), TGeoManager::IsInPhiRange(), TGeoPatternCylPhi::IsOnBoundary(), TGeoPatternSphPhi::IsOnBoundary(), TGeoSphere::IsPointInside(), TGeoPgon::LocatePhi(), THistPainter::PaintColorLevels(), TVector2::Print(), TQuaternion::Print(), TVector3::Print(), THistPainter::ProjectAitoff2xy(), TEveBoxSetGL::RenderBoxes(), TEveLegoEventHandler::Rotate(), TGeoSphere::Safety(), TEveTransSubEditor::SetModel(), TGeoCtubEditor::SetModel(), and ROOT::v5::TMath_GenerInterface().

Short_t TMath::Range	(	Short_t	lb,
		Short_t	ub,
		Short_t	x
	)

inline

Definition at line 234 of file TMathBase.h.

Referenced by TEveTrackPropagator::ClosestPointBetweenLines(), TCollection::GrowBy(), TGLCameraGuide::Handle(), TGLAutoRotator::SetADolly(), TGLAutoRotator::SetATheta(), TGLAutoRotator::SetDt(), and ROOT::v5::TMath_GenerInterface().

Int_t TMath::Range	(	Int_t	lb,
		Int_t	ub,
		Int_t	x
	)

inline

Definition at line 237 of file TMathBase.h.

Long_t TMath::Range	(	Long_t	lb,
		Long_t	ub,
		Long_t	x
	)

inline

Definition at line 240 of file TMathBase.h.

ULong_t TMath::Range	(	ULong_t	lb,
		ULong_t	ub,
		ULong_t	x
	)

inline

Definition at line 243 of file TMathBase.h.

Double_t TMath::Range	(	Double_t	lb,
		Double_t	ub,
		Double_t	x
	)

inline

Definition at line 246 of file TMathBase.h.

Double_t TMath::Rgair ( )

inline

Definition at line 119 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

template<typename T >

Double_t TMath::RMS	(	Long64_t	n,
		const T *	a,
		const Double_t *	w = `0`
	)

Definition at line 916 of file TMath.h.

Referenced by TGL5DPainter::AddSurface(), TGL5DPainter::InitGeometry(), TMVA::Tools::RMS(), TNeuron::SetNormalisation(), stressVector(), testArrayFunctions(), testIteratorFunctions(), and testTStatistic().

template<typename Iterator >

Double_t TMath::RMS	(	Iterator	first,
		Iterator	last
	)

Definition at line 864 of file TMath.h.

template<typename Iterator , typename WeightIterator >

Double_t TMath::RMS	(	Iterator	first,
		Iterator	last,
		WeightIterator	wfirst
	)

Definition at line 889 of file TMath.h.

Bool_t TMath::RootsCubic	(	const Double_t	coef[4],
		Double_t &	a,
		Double_t &	b,
		Double_t &	c
	)

Calculates roots of polynomial of 3rd order a*x^3 + b*x^2 + c*x + d, where a == coef[3], b == coef[2], c == coef[1], d == coef[0] coef[3] must be different from 0 If the boolean returned by the method is false: ==> there are 3 real roots a,b,c If the boolean returned by the method is true: ==> there is one real root a and 2 complex conjugates roots (b+i*c,b-i*c) Author: Francois-Xavier Gentit.

Definition at line 1077 of file TMath.cxx.

Referenced by TRolke::EvalLikeMod2(), and TRolke::EvalLikeMod6().

Double_t TMath::RUncertainty ( )

inline

Definition at line 110 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

Double_t TMath::Sigma ( )

inline

Definition at line 100 of file TMath.h.

Referenced by TFormula::FillDefaults(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::SigmaUncertainty ( )

inline

Definition at line 101 of file TMath.h.

Referenced by ROOT::v5::TMath_GenerInterface().

template<typename T1 , typename T2 >

T1 TMath::Sign	(	T1	a,
		T2	b
	)

inline

Definition at line 155 of file TMathBase.h.

Float_t TMath::Sign	(	Float_t	a,
		Float_t	b
	)

inline

Definition at line 158 of file TMathBase.h.

Double_t TMath::Sign	(	Double_t	a,
		Double_t	b
	)

inline

Definition at line 161 of file TMathBase.h.

LongDouble_t TMath::Sign	(	LongDouble_t	a,
		LongDouble_t	b
	)

inline

Definition at line 164 of file TMathBase.h.

Double_t TMath::SignalingNaN ( )

inline

Definition at line 642 of file TMath.h.

Referenced by Binomial(), RooBernstein::evaluate(), and RooStats::ProfileLikelihoodTestStat::EvaluateProfileLikelihood().

template<typename Integer >

Bool_t TMath::SignBit ( Integer a )

inline

Definition at line 139 of file TMathBase.h.

Bool_t TMath::SignBit ( Float_t a )

inline

Definition at line 142 of file TMathBase.h.

Bool_t TMath::SignBit ( Double_t a )

inline

Definition at line 145 of file TMathBase.h.

Bool_t TMath::SignBit ( LongDouble_t a )

inline

Definition at line 148 of file TMathBase.h.

Referenced by Sign().

Double_t TMath::Sin ( Double_t x )

inline

Definition at line 421 of file TMath.h.

Double_t TMath::SinH ( Double_t x )

inline

Definition at line 430 of file TMath.h.

Referenced by ClassImp(), TComplex::Cos(), TComplex::CosH(), TTreeFormula::EvalInstance(), RooTMathReg::RooTMathReg(), TComplex::Sin(), TComplex::SinH(), and ROOT::v5::TMath_GenerInterface().

template<typename Element , typename Index >

void TMath::Sort	(	Index	n,
		const Element *	a,
		Index *	index,
		Bool_t	down = `kTRUE`
	)

Definition at line 1002 of file TMath.h.

Referenced by ROOT::Math::GoFTest::AndersonDarling2SamplesTest(), ClassImp(), TGeoIntersection::ComputeBBox(), RooStats::BayesianCalculator::ComputeShortestInterval(), TGraph::Eval(), TRobustEstimator::EvaluateUni(), TProofPerfAnalysis::FileProcPlot(), Memstat::TMemStatMng::FillTree(), TProofPerfAnalysis::FillWrkInfo(), TEveShape::FindConvexHull(), TFeldmanCousins::FindLimitsFromTable(), XrdProofdSandbox::GetSessionDirs(), TGraphDelaunay::Interpolate(), TProfile::LabelsOption(), TProfile2D::LabelsOption(), TH1::LabelsOption(), Median(), TGraph2DPainter::PaintTriangles_old(), TGraphSmooth::Rank(), TEveLegoEventHandler::Rotate(), TFileCacheRead::SecondSort(), TConfidenceLevel::SetTSB(), TConfidenceLevel::SetTSS(), TGLPerspectiveCamera::Setup(), TMemStatShow::Show(), TGraphSmooth::Smoothin(), TGraphSmooth::SmoothKern(), TGeoTorus::SolveQuartic(), TEventList::Sort(), TFileCacheRead::Sort(), TGeoVoxelFinder::SortAll(), TKDTreeBinning::SortOneDimBinEdges(), stressVector(), testArrayFunctions(), TestNeighbors(), TestRange(), testSort(), TGraphQQ::TGraphQQ(), and TGeoTorus::ToBoundary().

template<typename Iterator , typename IndexIterator >

void TMath::SortItr	(	Iterator	first,
		Iterator	last,
		IndexIterator	index,
		Bool_t	down = `kTRUE`
	)

Definition at line 977 of file TMath.h.

Referenced by RooStats::HypoTestInverterResult::CalculateEstimatedError(), RooStats::HypoTestInverterResult::FindClosestPointIndex(), RooStats::HypoTestInverterResult::FindInterpolatedLimit(), RooStats::HypoTestInverterResult::GetExpectedLimit(), RooStats::HypoTestInverterResult::GetLimitDistribution(), RooStats::HypoTestInverterPlot::MakeExpectedPlot(), RooStats::HypoTestInverterPlot::MakePlot(), RooStats::SamplingDistribution::SortValues(), and testIteratorFunctions().

Double_t TMath::Sq ( Double_t x )

inline

Definition at line 461 of file TMath.h.

Double_t TMath::Sqrt ( Double_t x )

inline

Definition at line 464 of file TMath.h.

Double_t TMath::Sqrt2 ( )

inline

Definition at line 51 of file TMath.h.

Referenced by TEveCaloLegoGL::DrawAxis2D(), TEveCaloLegoGL::DrawAxis3D(), and TFormula::FillDefaults().

template<typename T >

Double_t TMath::StdDev	(	Long64_t	n,
		const T *	a,
		const Double_t *	w = `0`
	)

Definition at line 311 of file TMath.h.

template<typename Iterator >

Double_t TMath::StdDev	(	Iterator	first,
		Iterator	last
	)

Definition at line 312 of file TMath.h.

template<typename Iterator , typename WeightIterator >

Double_t TMath::StdDev	(	Iterator	first,
		Iterator	last,
		WeightIterator	wfirst
	)

Definition at line 313 of file TMath.h.

Double_t TMath::StruveH0 ( Double_t x )

Struve Functions of Order 0.

Converted from CERNLIB M342 by Rene Brun.

Definition at line 1740 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::StruveH1 ( Double_t x )

Struve Functions of Order 1.

Converted from CERNLIB M342 by Rene Brun.

Definition at line 1809 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::StruveL0 ( Double_t x )

Modified Struve Function of Order 0.

By Kirill Filimonov.

Definition at line 1886 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::StruveL1 ( Double_t x )

Modified Struve Function of Order 1.

By Kirill Filimonov.

Definition at line 1932 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Student	(	Double_t	T,
		Double_t	ndf
	)

Computes density function for Student's t- distribution (the probability function (integral of density) is computed in StudentI).

First parameter stands for x - the actual variable of the density function p(x) and the point at which the density is calculated. Second parameter stands for number of degrees of freedom.

About Student distribution: Student's t-distribution is used for many significance tests, for example, for the Student's t-tests for the statistical significance of difference between two sample means and for confidence intervals for the difference between two population means.

Example: suppose we have a random sample of size n drawn from normal distribution with mean Mu and st.deviation Sigma. Then the variable

t = (sample_mean - Mu)/(sample_deviation / sqrt(n))

has Student's t-distribution with n-1 degrees of freedom.

NOTE that this function's second argument is number of degrees of freedom, not the sample size.

As the number of degrees of freedom grows, t-distribution approaches Normal(0,1) distribution. Implementation by Anna Kreshuk.

Definition at line 2508 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::StudentI	(	Double_t	T,
		Double_t	ndf
	)

Calculates the cumulative distribution function of Student's t-distribution second parameter stands for number of degrees of freedom, not for the number of samples if x has Student's t-distribution, the function returns the probability of x being less than T.

Implementation by Anna Kreshuk.

Definition at line 2529 of file TMath.cxx.

Referenced by TLinearFitter::ComputeTValues(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::StudentQuantile	(	Double_t	p,
		Double_t	ndf,
		Bool_t	lower_tail = `kTRUE`
	)

Computes quantiles of the Student's t-distribution 1st argument is the probability, at which the quantile is computed 2nd argument - the number of degrees of freedom of the Student distribution When the 3rd argument lower_tail is kTRUE (default)- the algorithm returns such x0, that P(x < x0)=p upper tail (lower_tail is kFALSE)- the algorithm returns such x0, that P(x > x0)=p the algorithm was taken from G.W.Hill, "Algorithm 396, Student's t-quantiles" "Communications of the ACM", 13(10), October 1970.

Definition at line 2553 of file TMath.cxx.

Referenced by TFitter::GetConfidenceIntervals(), TLinearFitter::GetConfidenceIntervals(), ROOT::Fit::FitResult::GetConfidenceIntervals(), and RooTMathReg::RooTMathReg().

Double_t TMath::Tan ( Double_t x )

inline

Definition at line 427 of file TMath.h.

Referenced by TRandom::BreitWigner(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::BreitWigner(), TGeoPgon::Capacity(), ClassImp(), TGeoHypeEditor::DoApply(), TGLViewer::DoDrawStereo(), TGeoHypeEditor::DoDz(), TGeoHypeEditor::DoRin(), TGeoHypeEditor::DoRout(), TGeoHypeEditor::DoStIn(), TGeoHypeEditor::DoStOut(), TTreeFormula::EvalInstance(), TGeoMCGeometry::GetShape(), TEveCaloViz::GetTransitionEta(), TEveCaloViz::GetTransitionEtaBackward(), TEveCaloViz::GetTransitionEtaForward(), TArrow::PaintArrow(), THistPainter::PaintLego(), TGraphPolargram::PaintPolarDivisions(), THistPainter::PaintSurface(), TRandom::Poisson(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::Poisson(), TRandom::PoissonD(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::PoissonD(), THistPainter::ProjectMercator2xy(), TEveCalo3DGL::RenderBarrelCell(), TEveCalo3DGL::RenderEndCapCell(), TEveCalo3DGL::RenderGridBarrel(), TEveCalo3DGL::RenderGridEndCap(), RooTMathReg::RooTMathReg(), TEveLegoEventHandler::Rotate(), TAttParticle::SampleMass(), TGeoPara::SetDimensions(), TGeoTrap::SetDimensions(), TGeoHype::SetHypeDimensions(), TPARA::SetPoints(), TGTRA::SetPoints(), TTRAP::SetPoints(), TGeoParaboloid::SetPoints(), TVector3::SetPtEtaPhi(), TVector3::SetPtThetaPhi(), TGLPerspectiveCamera::Setup(), TGeoPara::TGeoPara(), TGeoPatternTrapZ::TGeoPatternTrapZ(), TGeoTrap::TGeoTrap(), ROOT::v5::TMath_GenerInterface(), TGLPerspectiveCamera::Truck(), and XRotCreateTextItem().

Double_t TMath::TanH ( Double_t x )

inline

Definition at line 436 of file TMath.h.

Referenced by TEveJetCone::CalcEtaPhiVec(), ClassImp(), TMVA::TActivationTanh::Eval(), TTreeFormula::EvalInstance(), TMVA::SVKernelFunction::Evaluate(), TNeuron::GetDerivative(), TNeuron::GetValue(), RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::TwoPi ( )

inline

Definition at line 45 of file TMath.h.

Referenced by TEveJetConeGL::CalculatePoints(), TGeoChecker::CheckBoundaryErrors(), TRandom::Circle(), ROOT::Math::RandomFunctionsImpl< TRandomEngine >::Circle(), TEveCaloData::CellGeom_t::Configure(), TPie::DistancetoSlice(), TGLPadPainter::DrawGradient(), TPie::ExecuteEvent(), TMVA::LDA::FSub(), TEveCaloDataVec::GetCellList(), TGeoTube::GetPointsOnSegments(), TGeoCone::GetPointsOnSegments(), TGraphDelaunay::InHull(), TGLLegoPainter::InitGeometryCylindrical(), TGLSurfacePainter::InitGeometryCylindrical(), TGLLegoPainter::InitGeometryPolar(), TGLSurfacePainter::InitGeometryPolar(), TGLLegoPainter::InitGeometrySpherical(), TGLSurfacePainter::InitGeometrySpherical(), TEveUtil::IsU1IntervalContainedByMinMax(), TEveUtil::IsU1IntervalOverlappingByMinMax(), TEveTrackPropagator::LoopToBounds(), TPie::Paint(), TGLCamera::Rotate(), TGLCamera::RotateArcBall(), ROOT::v5::TMath_GenerInterface(), and TEveCaloLegoGL::WrapTwoPi().

Double_t TMath::Vavilov	(	Double_t	x,
		Double_t	kappa,
		Double_t	beta2
	)

Returns the value of the Vavilov density function Parameters: 1st - the point were the density function is evaluated 2nd - value of kappa (distribution parameter) 3rd - value of beta2 (distribution parameter) The algorithm was taken from the CernLib function vavden(G115) Reference: A.Rotondi and P.Montagna, Fast Calculation of Vavilov distribution Nucl.Instr.

and Meth. B47(1990), 215-224 Accuracy: quote from the reference above: "The resuls of our code have been compared with the values of the Vavilov density function computed numerically in an accurate way: our approximation shows a difference of less than 3% around the peak of the density function, slowly increasing going towards the extreme tails to the right and to the left" Begin_Html

Definition at line 2620 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::VavilovI	(	Double_t	x,
		Double_t	kappa,
		Double_t	beta2
	)

Returns the value of the Vavilov distribution function Parameters: 1st - the point were the density function is evaluated 2nd - value of kappa (distribution parameter) 3rd - value of beta2 (distribution parameter) The algorithm was taken from the CernLib function vavden(G115) Reference: A.Rotondi and P.Montagna, Fast Calculation of Vavilov distribution Nucl.Instr.

and Meth. B47(1990), 215-224 Accuracy: quote from the reference above: "The resuls of our code have been compared with the values of the Vavilov density function computed numerically in an accurate way: our approximation shows a difference of less than 3% around the peak of the density function, slowly increasing going towards the extreme tails to the right and to the left"

Definition at line 2653 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg(), and ROOT::v5::TMath_GenerInterface().

Double_t TMath::Voigt	(	Double_t	xx,
		Double_t	sigma,
		Double_t	lg,
		Int_t	r = `4`
	)

Computation of Voigt function (normalised).

Voigt is a convolution of gauss(xx) = 1/(sqrt(2*pi)*sigma) * exp(xx*xx/(2*sigma*sigma) and lorentz(xx) = (1/pi) * (lg/2) / (xx*xx + lg*lg/4) functions.

The Voigt function is known to be the real part of Faddeeva function also called complex error function [2].

The algoritm was developed by J. Humlicek [1]. This code is based on fortran code presented by R. J. Wells [2]. Translated and adapted by Miha D. Puc

To calculate the Faddeeva function with relative error less than 10^(-r). r can be set by the the user subject to the constraints 2 <= r <= 5.

[1] J. Humlicek, JQSRT, 21, 437 (1982). [2] R.J. Wells "Rapid Approximation to the Voigt/Faddeeva Function and its Derivatives" JQSRT 62 (1999), pp 29-48. http://www-atm.physics.ox.ac.uk/user/wells/voigt.html

Definition at line 875 of file TMath.cxx.

Referenced by RooTMathReg::RooTMathReg().

Classes

Functions

Function Documentation

Method Improvement by Jason A Detwiler (JADet.nosp@m.wile.nosp@m.r@lbl.nosp@m..gov)