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)

Double_t	ACos (Double_t)

Double_t	ACosH (Double_t)

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

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

Double_t	ASin (Double_t)

Double_t	ASinH (Double_t)

Double_t	ATan (Double_t)

Double_t	ATan2 (Double_t, Double_t)

Double_t	ATanH (Double_t)

Double_t	BesselI (Int_t n, Double_t x)

Double_t	BesselI0 (Double_t x)
	integer order modified Bessel function K_n(x) More...

Double_t	BesselI1 (Double_t x)
	modified Bessel function K_0(x) More...

Double_t	BesselJ0 (Double_t x)
	modified Bessel function K_1(x) More...

Double_t	BesselJ1 (Double_t x)
	Bessel function J0(x) for any real x. More...

Double_t	BesselK (Int_t n, Double_t x)
	integer order modified Bessel function I_n(x) More...

Double_t	BesselK0 (Double_t x)
	modified Bessel function I_0(x) More...

Double_t	BesselK1 (Double_t x)
	modified Bessel function I_1(x) More...

Double_t	BesselY0 (Double_t x)
	Bessel function J1(x) for any real x. More...

Double_t	BesselY1 (Double_t x)
	Bessel function Y0(x) for positive x. More...

Double_t	Beta (Double_t p, Double_t q)

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

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

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

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

template<typename T >
Long64_t	BinarySearch (Long64_t n, const T *array, T value)
	Binary search in an array of n values to locate value. More...

template<typename T >
Long64_t	BinarySearch (Long64_t n, const T **array, T value)
	Binary search in an array of n values to locate value. More...

template<typename Iterator , typename Element >
Iterator	BinarySearch (Iterator first, Iterator last, Element value)
	Binary search in an array defined by its iterators. More...

Double_t	Binomial (Int_t n, Int_t k)

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

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

void	BubbleHigh (Int_t Narr, Double_t arr1, Int_t arr2)

void	BubbleLow (Int_t Narr, Double_t arr1, Int_t arr2)

constexpr Double_t	C ()
	Velocity of light in \( m s^{-1} \). More...

Double_t	CauchyDist (Double_t x, Double_t t=0, Double_t s=1)

constexpr Double_t	Ccgs ()
	\( cm s^{-1} \) More...

Double_t	Ceil (Double_t x)

Int_t	CeilNint (Double_t x)

Double_t	ChisquareQuantile (Double_t p, Double_t ndf)

Double_t	Cos (Double_t)

Double_t	CosH (Double_t)

template<typename T >
T *	Cross (const T v1[3], const T v2[3], T out[3])
	Calculate the Cross Product of two vectors: out = [v1 x v2]. More...

constexpr Double_t	CUncertainty ()
	Speed of light uncertainty. More...

constexpr Double_t	DegToRad ()
	Conversion from degree to radian: \[ \frac{\pi}{180} \] . More...

Double_t	DiLog (Double_t x)
	Modified Struve functions of order 1. More...

constexpr Double_t	E ()
	Base of natural log: \[ e \] . More...

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

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

Double_t	ErfcInverse (Double_t x)
	returns the inverse of the complementary error function x must be 0<x<2 implement using the quantile of the normal distribution instead of ErfInverse for better numerical precision for large x More...

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

constexpr Double_t	EulerGamma ()
	Euler-Mascheroni Constant. More...

Bool_t	Even (Long_t a)

Double_t	Exp (Double_t x)

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

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

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

Int_t	Finite (Double_t x)
	Check if it is finite with a mask in order to be consistent in presence of fast math. More...

Int_t	Finite (Float_t x)
	Check if it is finite with a mask in order to be consistent in presence of fast math. More...

Double_t	Floor (Double_t x)

Int_t	FloorNint (Double_t x)

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

constexpr Double_t	G ()
	Gravitational constant in: \( m^{3} kg^{-1} s^{-2} \). More...

Double_t	GamCf (Double_t a, Double_t x)
	Computation of the incomplete gamma function P(a,x) via its continued fraction representation. 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)

Double_t	GamSer (Double_t a, Double_t x)
	Computation of the incomplete gamma function P(a,x) via its series representation. 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...

constexpr Double_t	Gcgs ()
	\( cm^{3} g^{-1} s^{-2} \) More...

template<typename T >
Double_t	GeomMean (Long64_t n, const T *a)
	Return the geometric mean of an array a of size n. More...

template<typename Iterator >
Double_t	GeomMean (Iterator first, Iterator last)
	Return the geometric mean of an array defined by the iterators. More...

constexpr Double_t	GhbarC ()
	\( \frac{G}{\hbar C} \) in \( (GeV/c^{2})^{-2} \) More...

constexpr Double_t	GhbarCUncertainty ()
	\( \frac{G}{\hbar C} \) uncertainty. More...

constexpr Double_t	Gn ()
	Standard acceleration of gravity in \( m s^{-2} \). More...

constexpr Double_t	GnUncertainty ()
	Standard acceleration of gravity uncertainty. More...

constexpr Double_t	GUncertainty ()
	Gravitational constant uncertainty. More...

constexpr Double_t	H ()
	Planck's constant in \( J s \) \[ h \] . More...

ULong_t	Hash (const void *txt, Int_t ntxt)

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

constexpr Double_t	Hbar ()
	\( \hbar \) in \( J s \) \[ \hbar = \frac{h}{2\pi} \] More...

constexpr Double_t	Hbarcgs ()
	\( erg s \) More...

constexpr Double_t	HbarUncertainty ()
	\( \hbar \) uncertainty. More...

constexpr Double_t	HC ()
	\( hc \) in \( J m \) More...

constexpr Double_t	HCcgs ()
	\( erg cm \) More...

constexpr Double_t	Hcgs ()
	\( erg s \) More...

constexpr Double_t	HUncertainty ()
	Planck's constant uncertainty. More...

Double_t	Hypot (Double_t x, Double_t y)

Long_t	Hypot (Long_t x, Long_t y)

Double_t	Infinity ()
	Returns an infinity as defined by the IEEE standard. More...

constexpr Double_t	InvPi ()
	\( \frac{1.}{\pi}\) More...

template<typename T >
Bool_t	IsInside (T xp, T yp, Int_t np, T x, T y)
	Function which returns kTRUE if point xp,yp lies inside the polygon defined by the np points in arrays x and y, kFALSE otherwise. More...

Bool_t	IsNaN (Double_t x)

Bool_t	IsNaN (Float_t x)

constexpr Double_t	K ()
	Boltzmann's constant in \( J K^{-1} \) \[ k \] . More...

constexpr Double_t	Kcgs ()
	\( erg K^{-1} \) More...

Double_t	KolmogorovProb (Double_t z)

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

template<class Element , typename Size >
Element	KOrdStat (Size n, const Element a, Size k, Size work=0)
	Returns k_th order statistic of the array a of size n (k_th smallest element out of n elements). More...

constexpr Double_t	KUncertainty ()
	Boltzmann's constant uncertainty. 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)

Double_t	LaplaceDist (Double_t x, Double_t alpha=0, Double_t beta=1)

Double_t	LaplaceDistI (Double_t x, Double_t alpha=0, Double_t beta=1)

Double_t	Ldexp (Double_t x, Int_t exp)

constexpr Double_t	Ln10 ()
	Natural log of 10 (to convert log to ln) More...

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

template<typename T >
Long64_t	LocMax (Long64_t n, const T *a)
	Return index of array with the maximum element. More...

template<typename Iterator >
Iterator	LocMax (Iterator first, Iterator last)
	Return index of array with the maximum element. More...

template<typename T >
Long64_t	LocMin (Long64_t n, const T *a)
	Return index of array with the minimum element. More...

template<typename Iterator >
Iterator	LocMin (Iterator first, Iterator last)
	Return index of array with the minimum element. More...

Double_t	Log (Double_t x)

Double_t	Log10 (Double_t x)

Double_t	Log2 (Double_t x)

constexpr Double_t	LogE ()
	Base-10 log of e (to convert ln to log) More...

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

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)

template<typename T >
T	MaxElement (Long64_t n, const T *a)
	Return maximum of array a of length n. More...

template<typename T >
Double_t	Mean (Long64_t n, const T a, const Double_t w=0)
	Return the weighted mean of an array a with length n. More...

template<typename Iterator >
Double_t	Mean (Iterator first, Iterator last)
	Return the weighted mean of an array defined by the iterators. More...

template<typename Iterator , typename WeightIterator >
Double_t	Mean (Iterator first, Iterator last, WeightIterator wfirst)
	Return the weighted mean of an array defined by the first and last iterators. More...

template<typename T >
Double_t	Median (Long64_t n, const T a, const Double_t w=0, Long64_t *work=0)
	Return the median of the array a where each entry i has weight w[i] . More...

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)

template<typename T >
T	MinElement (Long64_t n, const T *a)
	Return minimum of array a of length n. More...

constexpr Double_t	MWair ()
	Molecular weight of dry air 1976 US Standard Atmosphere in \( kg kmol^{-1} \) or \( gm mol^{-1} \) More...

constexpr Double_t	Na ()
	Avogadro constant (Avogadro's Number) in \( mol^{-1} \). More...

constexpr Double_t	NaUncertainty ()
	Avogadro constant (Avogadro's Number) uncertainty. More...

Long_t	NextPrime (Long_t x)
	TMath Base functionsDefine the functions Min, Max, Abs, Sign, Range for all types. More...

template<typename T >
Int_t	Nint (T x)
	Round to nearest integer. Rounds half integers to the nearest even integer. More...

template<typename T >
T *	Normal2Plane (const T v1[3], const T v2[3], const T v3[3], T normal[3])
	Calculate a normal vector of a plane. More...

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])
	Calculate the Normalized Cross Product of two vectors. More...

Double_t	NormQuantile (Double_t p)

Bool_t	Odd (Long_t a)

Bool_t	Permute (Int_t n, Int_t *a)

constexpr Double_t	Pi ()
	\[ \pi\] More...

constexpr Double_t	PiOver2 ()
	\[ \frac{\pi}{2} \] More...

constexpr Double_t	PiOver4 ()
	\[ \frac{\pi}{4} \] More...

Double_t	Poisson (Double_t x, Double_t par)

Double_t	PoissonI (Double_t x, Double_t par)

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	Prob (Double_t chi2, Int_t ndf)

constexpr Double_t	Qe ()
	Elementary charge in \( C \) . More...

constexpr Double_t	QeUncertainty ()
	Elementary charge uncertainty. 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)

Double_t	QuietNaN ()
	Returns a quiet NaN as defined by IEEE 754 More...

constexpr Double_t	R ()
	Universal gas constant ( \( Na K \)) in \( J K^{-1} mol^{-1} \) More...

constexpr Double_t	RadToDeg ()
	Conversion from radian to degree: \[ \frac{180}{\pi} \] . More...

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)

constexpr Double_t	Rgair ()
	Dry Air Gas Constant (R / MWair) in \( J kg^{-1} K^{-1} \) More...

template<typename T >
Double_t	RMS (Long64_t n, const T a, const Double_t w=0)
	Return the Standard Deviation of an array a with length n. More...

template<typename Iterator >
Double_t	RMS (Iterator first, Iterator last)
	Return the Standard Deviation of an array defined by the iterators. More...

template<typename Iterator , typename WeightIterator >
Double_t	RMS (Iterator first, Iterator last, WeightIterator wfirst)
	Return the weighted Standard Deviation of an array defined by the iterators. More...

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

constexpr Double_t	RUncertainty ()
	Universal gas constant uncertainty. More...

constexpr Double_t	Sigma ()
	Stefan-Boltzmann constant in \( W m^{-2} K^{-4}\) \[ \sigma \] . More...

constexpr Double_t	SigmaUncertainty ()
	Stefan-Boltzmann constant uncertainty. More...

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)

Double_t	SignalingNaN ()
	Returns a signaling NaN as defined by IEEE 754](http://en.wikipedia.org/wiki/NaN#Signaling_NaN) More...

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)

Double_t	Sin (Double_t)

Double_t	SinH (Double_t)

template<typename Element , typename Index >
void	Sort (Index n, const Element a, Index index, Bool_t down=kTRUE)
	Sort the n elements of the array a of generic templated type Element. More...

template<typename Iterator , typename IndexIterator >
void	SortItr (Iterator first, Iterator last, IndexIterator index, Bool_t down=kTRUE)
	Sort the n1 elements of the Short_t array defined by its iterators. More...

Double_t	Sq (Double_t x)

Double_t	Sqrt (Double_t x)

constexpr Double_t	Sqrt2 ()
	\[ \sqrt{2} \] More...

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)

Double_t	StruveH0 (Double_t x)
	Bessel function Y1(x) for positive x. More...

Double_t	StruveH1 (Double_t x)
	Struve functions of order 0. More...

Double_t	StruveL0 (Double_t x)
	Struve functions of order 1. More...

Double_t	StruveL1 (Double_t x)
	Modified Struve functions of order 0. More...

Double_t	Student (Double_t T, Double_t ndf)

Double_t	StudentI (Double_t T, Double_t ndf)

Double_t	StudentQuantile (Double_t p, Double_t ndf, Bool_t lower_tail=kTRUE)

Double_t	Tan (Double_t)

Double_t	TanH (Double_t)

constexpr Double_t	TwoPi ()
	\[ 2\pi\] More...

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

Double_t	VavilovDenEval (Double_t rlam, Double_t AC, Double_t HC, Int_t itype)

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

void	VavilovSet (Double_t rkappa, Double_t beta2, Bool_t mode, Double_t WCM, Double_t AC, Double_t *HC, Int_t &itype, Int_t &npt)

Double_t	Voigt (Double_t x, Double_t sigma, Double_t lg, Int_t r=4)

Detailed Description

TMath.

Encapsulate most frequently used Math functions. NB. The basic functions Min, Max, Abs and Sign are defined in TMathBase.

Function Documentation

◆ Abs() [1/7]

Short_t TMath::Abs ( Short_t d )

inline

Definition at line 108 of file TMathBase.h.

◆ Abs() [2/7]

Int_t TMath::Abs ( Int_t d )

inline

Definition at line 111 of file TMathBase.h.

◆ Abs() [3/7]

Long_t TMath::Abs ( Long_t d )

inline

Definition at line 114 of file TMathBase.h.

◆ Abs() [4/7]

Long64_t TMath::Abs ( Long64_t d )

inline

Definition at line 117 of file TMathBase.h.

◆ Abs() [5/7]

Float_t TMath::Abs ( Float_t d )

inline

Definition at line 124 of file TMathBase.h.

◆ Abs() [6/7]

Double_t TMath::Abs ( Double_t d )

inline

Definition at line 127 of file TMathBase.h.

◆ Abs() [7/7]

LongDouble_t TMath::Abs ( LongDouble_t d )

inline

Definition at line 130 of file TMathBase.h.

◆ ACos()

Double_t TMath::ACos ( Double_t x )

inline

Definition at line 667 of file TMath.h.

◆ ACosH()

Double_t TMath::ACosH ( Double_t x )

Definition at line 77 of file TMath.cxx.

◆ AreEqualAbs()

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

inline

Definition at line 412 of file TMath.h.

◆ AreEqualRel()

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

inline

Definition at line 416 of file TMath.h.

◆ ASin()

Double_t TMath::ASin ( Double_t x )

inline

Definition at line 660 of file TMath.h.

◆ ASinH()

Double_t TMath::ASinH ( Double_t x )

Definition at line 64 of file TMath.cxx.

◆ ATan()

Double_t TMath::ATan ( Double_t x )

inline

Definition at line 674 of file TMath.h.

◆ ATan2()

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

inline

Definition at line 678 of file TMath.h.

◆ ATanH()

Double_t TMath::ATanH ( Double_t x )

Definition at line 90 of file TMath.cxx.

◆ BesselI()

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

◆ BesselI0()

Double_t TMath::BesselI0 ( Double_t x )

integer order modified Bessel function K_n(x)

◆ BesselI1()

Double_t TMath::BesselI1 ( Double_t x )

modified Bessel function K_0(x)

◆ BesselJ0()

Double_t TMath::BesselJ0 ( Double_t x )

modified Bessel function K_1(x)

◆ BesselJ1()

Double_t TMath::BesselJ1 ( Double_t x )

Bessel function J0(x) for any real x.

◆ BesselK()

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

integer order modified Bessel function I_n(x)

◆ BesselK0()

Double_t TMath::BesselK0 ( Double_t x )

modified Bessel function I_0(x)

◆ BesselK1()

Double_t TMath::BesselK1 ( Double_t x )

modified Bessel function I_1(x)

◆ BesselY0()

Double_t TMath::BesselY0 ( Double_t x )

Bessel function J1(x) for any real x.

◆ BesselY1()

Double_t TMath::BesselY1 ( Double_t x )

Bessel function Y0(x) for positive x.

◆ Beta()

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

◆ BetaCf()

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

◆ BetaDist()

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

◆ BetaDistI()

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

◆ BetaIncomplete()

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

◆ BinarySearch() [1/3]

template<typename T >

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

Binary search in an array of n values to locate value.

Array is supposed to be sorted prior to this call. If match is found, function returns position of element. If no match found, function gives nearest element smaller than value.

Definition at line 1221 of file TMath.h.

◆ BinarySearch() [2/3]

template<typename T >

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

Binary search in an array of n values to locate value.

Array is supposed to be sorted prior to this call. If match is found, function returns position of element. If no match found, function gives nearest element smaller than value.

Definition at line 1237 of file TMath.h.

◆ BinarySearch() [3/3]

template<typename Iterator , typename Element >

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

Binary search in an array defined by its iterators.

The values in the iterators range are supposed to be sorted prior to this call. If match is found, function returns position of element. If no match found, function gives nearest element smaller than value.

Definition at line 1205 of file TMath.h.

◆ Binomial()

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

◆ BinomialI()

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

◆ BreitWigner()

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 437 of file TMath.cxx.

◆ BubbleHigh()

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

◆ BubbleLow()

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

◆ C()

constexpr Double_t TMath::C ( )

Velocity of light in \( m s^{-1} \).

Definition at line 118 of file TMath.h.

◆ CauchyDist()

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

◆ Ccgs()

constexpr Double_t TMath::Ccgs ( )

\( cm s^{-1} \)

Definition at line 125 of file TMath.h.

◆ Ceil()

Double_t TMath::Ceil ( Double_t x )

inline

Definition at line 694 of file TMath.h.

◆ CeilNint()

Int_t TMath::CeilNint ( Double_t x )

inline

Definition at line 698 of file TMath.h.

◆ ChisquareQuantile()

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

◆ Cos()

Double_t TMath::Cos ( Double_t x )

inline

Definition at line 640 of file TMath.h.

◆ CosH()

Double_t TMath::CosH ( Double_t x )

inline

Definition at line 652 of file TMath.h.

◆ Cross()

template<typename T >

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

Calculate the Cross Product of two vectors: out = [v1 x v2].

Definition at line 1295 of file TMath.h.

◆ CUncertainty()

constexpr Double_t TMath::CUncertainty ( )

Speed of light uncertainty.

Definition at line 132 of file TMath.h.

◆ DegToRad()

constexpr Double_t TMath::DegToRad ( )

Conversion from degree to radian:

\[ \frac{\pi}{180} \]

.

Definition at line 82 of file TMath.h.

◆ DiLog()

Double_t TMath::DiLog ( Double_t x )

Modified Struve functions of order 1.

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

Definition at line 110 of file TMath.cxx.

◆ E()

constexpr Double_t TMath::E ( )

Base of natural log:

\[ e \]

.

Definition at line 97 of file TMath.h.

◆ Erf()

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 184 of file TMath.cxx.

◆ Erfc()

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 194 of file TMath.cxx.

◆ ErfcInverse()

Double_t TMath::ErfcInverse ( Double_t x )

returns the inverse of the complementary error function x must be 0<x<2 implement using the quantile of the normal distribution instead of ErfInverse for better numerical precision for large x

Definition at line 237 of file TMath.cxx.

◆ ErfInverse()

Double_t TMath::ErfInverse ( Double_t x )

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

Definition at line 203 of file TMath.cxx.

◆ EulerGamma()

constexpr Double_t TMath::EulerGamma ( )

Euler-Mascheroni Constant.

Definition at line 329 of file TMath.h.

◆ Even()

Bool_t TMath::Even ( Long_t a )

inline

Definition at line 100 of file TMathBase.h.

◆ Exp()

Double_t TMath::Exp ( Double_t x )

inline

Definition at line 726 of file TMath.h.

◆ Factorial()

Double_t TMath::Factorial ( Int_t i )

Compute factorial(n).

Definition at line 247 of file TMath.cxx.

◆ FDist()

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

◆ FDistI()

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

◆ Finite() [1/2]

Int_t TMath::Finite ( Double_t x )

inline

Check if it is finite with a mask in order to be consistent in presence of fast math.

Inspired from the CMSSW FWCore/Utilities package

Definition at line 770 of file TMath.h.

◆ Finite() [2/2]

Int_t TMath::Finite ( Float_t x )

inline

Check if it is finite with a mask in order to be consistent in presence of fast math.

Inspired from the CMSSW FWCore/Utilities package

Definition at line 799 of file TMath.h.

◆ Floor()

Double_t TMath::Floor ( Double_t x )

inline

Definition at line 702 of file TMath.h.

◆ FloorNint()

Int_t TMath::FloorNint ( Double_t x )

inline

Definition at line 706 of file TMath.h.

◆ Freq()

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 265 of file TMath.cxx.

◆ G()

constexpr Double_t TMath::G ( )

Gravitational constant in: \( m^{3} kg^{-1} s^{-2} \).

Definition at line 139 of file TMath.h.

◆ GamCf()

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

Computation of the incomplete gamma function P(a,x) via its continued fraction representation.

Author: NvE 14-nov-1998 UU-SAP Utrecht

Definition at line 375 of file TMath.cxx.

◆ Gamma() [1/2]

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 348 of file TMath.cxx.

◆ Gamma() [2/2]

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 .

\[ P(a, x) = \frac{1}{\Gamma(a)} \int_{0}^{x} t^{a-1} e^{-t} dt \]

Author: NvE 14-nov-1998 UU-SAP Utrecht

Definition at line 364 of file TMath.cxx.

◆ GammaDist()

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

◆ GamSer()

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

Computation of the incomplete gamma function P(a,x) via its series representation.

Author: NvE 14-nov-1998 UU-SAP Utrecht

Definition at line 412 of file TMath.cxx.

◆ Gaus()

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 448 of file TMath.cxx.

◆ Gcgs()

constexpr Double_t TMath::Gcgs ( )

\( cm^{3} g^{-1} s^{-2} \)

Definition at line 146 of file TMath.h.

◆ GeomMean() [1/2]

template<typename T >

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

Return the geometric mean of an array a of size n.

\[ GeomMean = (\prod_{i=0}^{n-1} |a[i]|)^{1/n} \]

Definition at line 1130 of file TMath.h.

◆ GeomMean() [2/2]

template<typename Iterator >

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

Return the geometric mean of an array defined by the iterators.

\[ GeomMean = (\prod_{i=0}^{n-1} |a[i]|)^{1/n} \]

Definition at line 1111 of file TMath.h.

◆ GhbarC()

constexpr Double_t TMath::GhbarC ( )

\( \frac{G}{\hbar C} \) in \( (GeV/c^{2})^{-2} \)

Definition at line 160 of file TMath.h.

◆ GhbarCUncertainty()

constexpr Double_t TMath::GhbarCUncertainty ( )

\( \frac{G}{\hbar C} \) uncertainty.

Definition at line 167 of file TMath.h.

◆ Gn()

constexpr Double_t TMath::Gn ( )

Standard acceleration of gravity in \( m s^{-2} \).

Definition at line 174 of file TMath.h.

◆ GnUncertainty()

constexpr Double_t TMath::GnUncertainty ( )

Standard acceleration of gravity uncertainty.

Definition at line 181 of file TMath.h.

◆ GUncertainty()

constexpr Double_t TMath::GUncertainty ( )

Gravitational constant uncertainty.

Definition at line 153 of file TMath.h.

◆ H()

constexpr Double_t TMath::H ( )

Planck's constant in \( J s \)

\[ h \]

.

Definition at line 189 of file TMath.h.

◆ Hash() [1/2]

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

◆ Hash() [2/2]

ULong_t TMath::Hash ( const char * str )

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

Definition at line 525 of file TString.cxx.

◆ Hbar()

constexpr Double_t TMath::Hbar ( )

\( \hbar \) in \( J s \)

\[ \hbar = \frac{h}{2\pi} \]

Definition at line 211 of file TMath.h.

◆ Hbarcgs()

constexpr Double_t TMath::Hbarcgs ( )

\( erg s \)

Definition at line 218 of file TMath.h.

◆ HbarUncertainty()

constexpr Double_t TMath::HbarUncertainty ( )

\( \hbar \) uncertainty.

Definition at line 225 of file TMath.h.

◆ HC()

constexpr Double_t TMath::HC ( )

\( hc \) in \( J m \)

Definition at line 232 of file TMath.h.

◆ HCcgs()

constexpr Double_t TMath::HCcgs ( )

\( erg cm \)

Definition at line 239 of file TMath.h.

◆ Hcgs()

constexpr Double_t TMath::Hcgs ( )

\( erg s \)

Definition at line 196 of file TMath.h.

◆ HUncertainty()

constexpr Double_t TMath::HUncertainty ( )

Planck's constant uncertainty.

Definition at line 203 of file TMath.h.

◆ Hypot() [1/2]

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

Definition at line 57 of file TMath.cxx.

◆ Hypot() [2/2]

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

Definition at line 50 of file TMath.cxx.

◆ Infinity()

Double_t TMath::Infinity ( )

inline

Returns an infinity as defined by the IEEE standard.

Definition at line 913 of file TMath.h.

◆ InvPi()

constexpr Double_t TMath::InvPi ( )

\( \frac{1.}{\pi}\)

Definition at line 66 of file TMath.h.

◆ IsInside()

template<typename T >

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

Function which returns kTRUE if point xp,yp lies inside the polygon defined by the np points in arrays x and y, kFALSE otherwise.

Note that the polygon may be open or closed.

Definition at line 1329 of file TMath.h.

◆ IsNaN() [1/2]

Bool_t TMath::IsNaN ( Double_t x )

inline

Definition at line 891 of file TMath.h.

◆ IsNaN() [2/2]

Bool_t TMath::IsNaN ( Float_t x )

inline

Definition at line 892 of file TMath.h.

◆ K()

constexpr Double_t TMath::K ( )

Boltzmann's constant in \( J K^{-1} \)

\[ k \]

.

Definition at line 247 of file TMath.h.

◆ Kcgs()

constexpr Double_t TMath::Kcgs ( )

\( erg K^{-1} \)

Definition at line 254 of file TMath.h.

◆ KolmogorovProb()

Double_t TMath::KolmogorovProb ( Double_t z )

◆ KolmogorovTest()

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

◆ KOrdStat()

template<class Element , typename Size >

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

Returns k_th order statistic of the array a of size n (k_th smallest element out of n elements).

C-convention is used for array indexing, so if you want the second smallest element, call KOrdStat(n, a, 1).

If work is supplied, it is used to store the sorting index and assumed to be >= n. If work=0, local storage is used, either on the stack if n < kWorkMax or on the heap for n >= kWorkMax. Note that the work index array will not contain the sorted indices but all indices of the smaller element in arbitrary order in work[0,...,k-1] and all indices of the larger element in arbitrary order in work[k+1,..,n-1] work[k] will contain instead the index of the returned element.

Taken from "Numerical Recipes in C++" without the index array implemented by Anna Khreshuk.

See also the declarations at the top of this file

Definition at line 1453 of file TMath.h.

◆ KUncertainty()

constexpr Double_t TMath::KUncertainty ( )

Boltzmann's constant uncertainty.

Definition at line 261 of file TMath.h.

◆ Landau()

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 approximately 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 proper 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 469 of file TMath.cxx.

◆ LandauI()

Double_t TMath::LandauI ( Double_t x )

◆ LaplaceDist()

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

◆ LaplaceDistI()

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

◆ Ldexp()

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

inline

Definition at line 730 of file TMath.h.

◆ Ln10()

constexpr Double_t TMath::Ln10 ( )

Natural log of 10 (to convert log to ln)

Definition at line 104 of file TMath.h.

◆ LnGamma()

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.

Author: NvE 14-nov-1998 UU-SAP Utrecht

Definition at line 486 of file TMath.cxx.

◆ LocMax() [1/2]

template<typename T >

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

Return index of array with the maximum element.

If more than one element is maximum returns first found.

Implement here since it is faster (see comment in LocMin function)

Definition at line 999 of file TMath.h.

◆ LocMax() [2/2]

template<typename Iterator >

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

Return index of array with the maximum element.

If more than one element is maximum returns first found.

Definition at line 1016 of file TMath.h.

◆ LocMin() [1/2]

template<typename T >

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

Return index of array with the minimum element.

If more than one element is minimum returns first found.

Implement here since this one is found to be faster (mainly on 64 bit machines) than stl generic implementation. When performing the comparison, the STL implementation needs to de-reference both the array iterator and the iterator pointing to the resulting minimum location

Definition at line 971 of file TMath.h.

◆ LocMin() [2/2]

template<typename Iterator >

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

Return index of array with the minimum element.

If more than one element is minimum returns first found.

Definition at line 988 of file TMath.h.

◆ Log()

Double_t TMath::Log ( Double_t x )

inline

Definition at line 759 of file TMath.h.

◆ Log10()

Double_t TMath::Log10 ( Double_t x )

inline

Definition at line 763 of file TMath.h.

◆ Log2()

Double_t TMath::Log2 ( Double_t x )

Definition at line 101 of file TMath.cxx.

◆ LogE()

constexpr Double_t TMath::LogE ( )

Base-10 log of e (to convert ln to log)

Definition at line 111 of file TMath.h.

◆ LogNormal()

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

◆ Max() [1/10]

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

inline

Definition at line 200 of file TMathBase.h.

◆ Max() [2/10]

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

inline

Definition at line 203 of file TMathBase.h.

◆ Max() [3/10]

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

inline

Definition at line 206 of file TMathBase.h.

◆ Max() [4/10]

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

inline

Definition at line 209 of file TMathBase.h.

◆ Max() [5/10]

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

inline

Definition at line 212 of file TMathBase.h.

◆ Max() [6/10]

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

inline

Definition at line 215 of file TMathBase.h.

◆ Max() [7/10]

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

inline

Definition at line 218 of file TMathBase.h.

◆ Max() [8/10]

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

inline

Definition at line 221 of file TMathBase.h.

◆ Max() [9/10]

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

inline

Definition at line 224 of file TMathBase.h.

◆ Max() [10/10]

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

inline

Definition at line 227 of file TMathBase.h.

◆ MaxElement()

template<typename T >

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

Return maximum of array a of length n.

Definition at line 958 of file TMath.h.

◆ Mean() [1/3]

template<typename T >

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

Return the weighted mean of an array a with length n.

Definition at line 1098 of file TMath.h.

◆ Mean() [2/3]

template<typename Iterator >

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

Return the weighted mean of an array defined by the iterators.

Definition at line 1051 of file TMath.h.

◆ Mean() [3/3]

template<typename Iterator , typename WeightIterator >

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

Return the weighted mean of an array defined by the first and last iterators.

The w iterator should point to the first element of a vector of weights of the same size as the main array.

Definition at line 1070 of file TMath.h.

◆ Median()

template<typename T >

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

Return the median of the array a where each entry i has weight w[i] .

Both arrays have a length of at least n . The median is a number obtained from the sorted array a through

median = (a[jl]+a[jh])/2. where (using also the sorted index on the array w)

sum_i=0,jl w[i] <= sumTot/2 sum_i=0,jh w[i] >= sumTot/2 sumTot = sum_i=0,n w[i]

If w=0, the algorithm defaults to the median definition where it is a number that divides the sorted sequence into 2 halves. When n is odd or n > 1000, the median is kth element k = (n + 1) / 2. when n is even and n < 1000the median is a mean of the elements k = n/2 and k = n/2 + 1.

If the weights are supplied (w not 0) all weights must be >= 0

If work is supplied, it is used to store the sorting index and assumed to be >= n . If work=0, local storage is used, either on the stack if n < kWorkMax or on the heap for n >= kWorkMax .

Definition at line 1367 of file TMath.h.

◆ Min() [1/10]

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

inline

Definition at line 168 of file TMathBase.h.

◆ Min() [2/10]

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

inline

Definition at line 171 of file TMathBase.h.

◆ Min() [3/10]

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

inline

Definition at line 174 of file TMathBase.h.

◆ Min() [4/10]

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

inline

Definition at line 177 of file TMathBase.h.

◆ Min() [5/10]

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

inline

Definition at line 180 of file TMathBase.h.

◆ Min() [6/10]

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

inline

Definition at line 183 of file TMathBase.h.

◆ Min() [7/10]

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

inline

Definition at line 186 of file TMathBase.h.

◆ Min() [8/10]

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

inline

Definition at line 189 of file TMathBase.h.

◆ Min() [9/10]

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

inline

Definition at line 192 of file TMathBase.h.

◆ Min() [10/10]

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

inline

Definition at line 195 of file TMathBase.h.

◆ MinElement()

template<typename T >

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

Return minimum of array a of length n.

Definition at line 951 of file TMath.h.

◆ MWair()

constexpr Double_t TMath::MWair ( )

Molecular weight of dry air 1976 US Standard Atmosphere in \( kg kmol^{-1} \) or \( gm mol^{-1} \)

Definition at line 314 of file TMath.h.

◆ Na()

constexpr Double_t TMath::Na ( )

Avogadro constant (Avogadro's Number) in \( mol^{-1} \).

Definition at line 283 of file TMath.h.

◆ NaUncertainty()

constexpr Double_t TMath::NaUncertainty ( )

Avogadro constant (Avogadro's Number) uncertainty.

Definition at line 290 of file TMath.h.

◆ Nint()

template<typename T >

Int_t TMath::Nint ( T x )

inline

Round to nearest integer. Rounds half integers to the nearest even integer.

Definition at line 712 of file TMath.h.

◆ Normal2Plane()

template<typename T >

T * TMath::Normal2Plane	(	const T	p1[3],
		const T	p2[3],
		const T	p3[3],
		T	normal[3]
	)

Calculate a normal vector of a plane.

Parameters

[in]	p1,p2,p3	3 3D points belonged the plane to define it.
[out]	normal	Pointer to 3D normal vector (normalized)

Definition at line 1309 of file TMath.h.

◆ Normalize() [1/2]

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

Normalize a vector v in place.

Returns the norm of the original vector.

Definition at line 495 of file TMath.cxx.

◆ Normalize() [2/2]

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 512 of file TMath.cxx.

◆ NormCross()

template<typename T >

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

inline

Calculate the Normalized Cross Product of two vectors.

Definition at line 943 of file TMath.h.

◆ NormQuantile()

Double_t TMath::NormQuantile ( Double_t p )

◆ Odd()

Bool_t TMath::Odd ( Long_t a )

inline

Definition at line 103 of file TMathBase.h.

◆ Permute()

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

◆ Pi()

constexpr Double_t TMath::Pi ( )

\[ \pi\]

Definition at line 38 of file TMath.h.

◆ PiOver2()

constexpr Double_t TMath::PiOver2 ( )

\[ \frac{\pi}{2} \]

Definition at line 52 of file TMath.h.

◆ PiOver4()

constexpr Double_t TMath::PiOver4 ( )

\[ \frac{\pi}{4} \]

Definition at line 59 of file TMath.h.

◆ Poisson()

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

◆ PoissonI()

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

◆ Power() [1/5]

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

inline

Definition at line 734 of file TMath.h.

◆ Power() [2/5]

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

inline

Definition at line 738 of file TMath.h.

◆ Power() [3/5]

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

inline

Definition at line 742 of file TMath.h.

◆ Power() [4/5]

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

inline

Definition at line 746 of file TMath.h.

◆ Power() [5/5]

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

inline

Definition at line 750 of file TMath.h.

◆ Prob()

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

◆ Qe()

constexpr Double_t TMath::Qe ( )

Elementary charge in \( C \) .

Definition at line 336 of file TMath.h.

◆ QeUncertainty()

constexpr Double_t TMath::QeUncertainty ( )

Elementary charge uncertainty.

Definition at line 343 of file TMath.h.

◆ Quantiles()

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`
	)

◆ QuietNaN()

Double_t TMath::QuietNaN ( )

inline

Returns a quiet NaN as defined by IEEE 754

Definition at line 900 of file TMath.h.

◆ R()

constexpr Double_t TMath::R ( )

Universal gas constant ( \( Na K \)) in \( J K^{-1} mol^{-1} \)

Definition at line 299 of file TMath.h.

◆ RadToDeg()

constexpr Double_t TMath::RadToDeg ( )

Conversion from radian to degree:

\[ \frac{180}{\pi} \]

.

Definition at line 74 of file TMath.h.

◆ Range() [1/5]

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

inline

Definition at line 232 of file TMathBase.h.

◆ Range() [2/5]

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

inline

Definition at line 235 of file TMathBase.h.

◆ Range() [3/5]

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

inline

Definition at line 238 of file TMathBase.h.

◆ Range() [4/5]

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

inline

Definition at line 241 of file TMathBase.h.

◆ Range() [5/5]

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

inline

Definition at line 244 of file TMathBase.h.

◆ Rgair()

constexpr Double_t TMath::Rgair ( )

Dry Air Gas Constant (R / MWair) in \( J kg^{-1} K^{-1} \)

Definition at line 322 of file TMath.h.

◆ RMS() [1/3]

template<typename T >

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

Return the Standard Deviation of an array a with length n.

Note that this function returns the sigma(standard deviation) and not the root mean square of the array.

Definition at line 1192 of file TMath.h.

◆ RMS() [2/3]

template<typename Iterator >

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

Return the Standard Deviation of an array defined by the iterators.

Note that this function returns the sigma(standard deviation) and not the root mean square of the array.

Use the two pass algorithm, which is slower (! a factor of 2) but much more precise. Since we have a vector the 2 pass algorithm is still faster than the Welford algorithm. (See also ROOT-5545)

Definition at line 1144 of file TMath.h.

◆ RMS() [3/3]

template<typename Iterator , typename WeightIterator >

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

Return the weighted Standard Deviation of an array defined by the iterators.

Note that this function returns the sigma(standard deviation) and not the root mean square of the array.

As in the unweighted case use the two pass algorithm

Definition at line 1168 of file TMath.h.

◆ RootsCubic()

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

◆ RUncertainty()

constexpr Double_t TMath::RUncertainty ( )

Universal gas constant uncertainty.

Definition at line 306 of file TMath.h.

◆ Sigma()

constexpr Double_t TMath::Sigma ( )

Stefan-Boltzmann constant in \( W m^{-2} K^{-4}\)

\[ \sigma \]

.

Definition at line 269 of file TMath.h.

◆ SigmaUncertainty()

constexpr Double_t TMath::SigmaUncertainty ( )

Stefan-Boltzmann constant uncertainty.

Definition at line 276 of file TMath.h.

◆ Sign() [1/4]

template<typename T1 , typename T2 >

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

inline

Definition at line 153 of file TMathBase.h.

◆ Sign() [2/4]

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

inline

Definition at line 156 of file TMathBase.h.

◆ Sign() [3/4]

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

inline

Definition at line 159 of file TMathBase.h.

◆ Sign() [4/4]

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

inline

Definition at line 162 of file TMathBase.h.

◆ SignalingNaN()

Double_t TMath::SignalingNaN ( )

inline

Returns a signaling NaN as defined by IEEE 754](http://en.wikipedia.org/wiki/NaN#Signaling_NaN)

Definition at line 907 of file TMath.h.

◆ SignBit() [1/4]

template<typename Integer >

Bool_t TMath::SignBit ( Integer a )

inline

Definition at line 137 of file TMathBase.h.

◆ SignBit() [2/4]

Bool_t TMath::SignBit ( Float_t a )

inline

Definition at line 140 of file TMathBase.h.

◆ SignBit() [3/4]

Bool_t TMath::SignBit ( Double_t a )

inline

Definition at line 143 of file TMathBase.h.

◆ SignBit() [4/4]

Bool_t TMath::SignBit ( LongDouble_t a )

inline

Definition at line 146 of file TMathBase.h.

◆ Sin()

Double_t TMath::Sin ( Double_t x )

inline

Definition at line 636 of file TMath.h.

◆ SinH()

Double_t TMath::SinH ( Double_t x )

inline

Definition at line 648 of file TMath.h.

◆ Sort()

template<typename Element , typename Index >

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

Sort the n elements of the array a of generic templated type Element.

In output the array index of type Index contains the indices of the sorted array. If down is false sort in increasing order (default is decreasing order).

NOTE that the array index must be created with a length >= n before calling this function. NOTE also that the size type for n must be the same type used for the index array (templated type Index)

Definition at line 1282 of file TMath.h.

◆ SortItr()

template<typename Iterator , typename IndexIterator >

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

Sort the n1 elements of the Short_t array defined by its iterators.

In output the array index contains the indices of the sorted array. If down is false sort in increasing order (default is decreasing order).

NOTE that the array index must be created with a length bigger or equal than the main array before calling this function.

Definition at line 1256 of file TMath.h.

◆ Sq()

Double_t TMath::Sq ( Double_t x )

inline

Definition at line 686 of file TMath.h.

◆ Sqrt()

Double_t TMath::Sqrt ( Double_t x )

inline

Definition at line 690 of file TMath.h.

◆ Sqrt2()

constexpr Double_t TMath::Sqrt2 ( )

\[ \sqrt{2} \]

Definition at line 89 of file TMath.h.

◆ StdDev() [1/3]

template<typename T >

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

Definition at line 527 of file TMath.h.

◆ StdDev() [2/3]

template<typename Iterator >

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

Definition at line 528 of file TMath.h.

◆ StdDev() [3/3]

template<typename Iterator , typename WeightIterator >

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

Definition at line 529 of file TMath.h.

◆ StruveH0()

Double_t TMath::StruveH0 ( Double_t x )

Bessel function Y1(x) for positive x.

◆ StruveH1()

Double_t TMath::StruveH1 ( Double_t x )

Struve functions of order 0.

◆ StruveL0()

Double_t TMath::StruveL0 ( Double_t x )

Struve functions of order 1.

◆ StruveL1()

Double_t TMath::StruveL1 ( Double_t x )

Modified Struve functions of order 0.

◆ Student()

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

◆ StudentI()

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

◆ StudentQuantile()

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

◆ Tan()

Double_t TMath::Tan ( Double_t x )

inline

Definition at line 644 of file TMath.h.

◆ TanH()

Double_t TMath::TanH ( Double_t x )

inline

Definition at line 656 of file TMath.h.

◆ TwoPi()

constexpr Double_t TMath::TwoPi ( )

\[ 2\pi\]

Definition at line 45 of file TMath.h.

◆ Vavilov()

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

◆ VavilovDenEval()

Double_t TMath::VavilovDenEval	(	Double_t	rlam,
		Double_t *	AC,
		Double_t *	HC,
		Int_t	itype
	)

◆ VavilovI()

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

◆ VavilovSet()

void TMath::VavilovSet	(	Double_t	rkappa,
		Double_t	beta2,
		Bool_t	mode,
		Double_t *	WCM,
		Double_t *	AC,
		Double_t *	HC,
		Int_t &	itype,
		Int_t &	npt
	)

◆ Voigt()

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

Classes

Functions

Detailed Description

Function Documentation

◆ Abs() [1/7]

◆ Abs() [2/7]

◆ Abs() [3/7]

◆ Abs() [4/7]

◆ Abs() [5/7]

◆ Abs() [6/7]

◆ Abs() [7/7]

◆ ACos()

◆ ACosH()

◆ AreEqualAbs()

◆ AreEqualRel()

◆ ASin()

◆ ASinH()

◆ ATan()

◆ ATan2()

◆ ATanH()

◆ BesselI()

◆ BesselI0()

◆ BesselI1()

◆ BesselJ0()

◆ BesselJ1()

◆ BesselK()

◆ BesselK0()

◆ BesselK1()

◆ BesselY0()

◆ BesselY1()

◆ Beta()

◆ BetaCf()

◆ BetaDist()

◆ BetaDistI()

◆ BetaIncomplete()

◆ BinarySearch() [1/3]

◆ BinarySearch() [2/3]

◆ BinarySearch() [3/3]

◆ Binomial()

◆ BinomialI()

◆ BreitWigner()

◆ BubbleHigh()

◆ BubbleLow()

◆ C()

◆ CauchyDist()

◆ Ccgs()

◆ Ceil()

◆ CeilNint()

◆ ChisquareQuantile()

◆ Cos()

◆ CosH()

◆ Cross()

◆ CUncertainty()

◆ DegToRad()

◆ DiLog()

◆ E()

◆ Erf()

◆ Erfc()

◆ ErfcInverse()

◆ ErfInverse()

◆ EulerGamma()

◆ Even()

◆ Exp()

◆ Factorial()

◆ FDist()

◆ FDistI()

◆ Finite() [1/2]

◆ Finite() [2/2]

◆ Floor()

◆ FloorNint()

◆ Freq()

◆ G()

◆ GamCf()

◆ Gamma() [1/2]

◆ Gamma() [2/2]

◆ GammaDist()

◆ GamSer()

◆ Gaus()

◆ Gcgs()

◆ GeomMean() [1/2]