TMath. More...

Classes
struct	Limits

Functions
Double_t	Abs (Double_t d)
	Returns the absolute value of parameter Double_t d.
Float_t	Abs (Float_t d)
	Returns the absolute value of parameter Float_t d.
Int_t	Abs (Int_t d)
	Returns the absolute value of parameter Int_t d.
Long64_t	Abs (Long64_t d)
	Returns the absolute value of parameter Long64_t d.
Long_t	Abs (Long_t d)
	Returns the absolute value of parameter Long_t d.
LongDouble_t	Abs (LongDouble_t d)
	Returns the absolute value of parameter LongDouble_t d.
Short_t	Abs (Short_t d)
	Returns the absolute value of parameter Short_t d.
Double_t	ACos (Double_t)
	Returns the principal value of the arc cosine of x, expressed in radians.
Double_t	ACosH (Double_t)
	Returns the nonnegative area hyperbolic cosine of x.
Bool_t	AreEqualAbs (Double_t af, Double_t bf, Double_t epsilon)
	Comparing floating points.
Bool_t	AreEqualRel (Double_t af, Double_t bf, Double_t relPrec)
	Comparing floating points.
Double_t	ASin (Double_t)
	Returns the principal value of the arc sine of x, expressed in radians.
Double_t	ASinH (Double_t)
	Returns the area hyperbolic sine of x.
Double_t	ATan (Double_t)
	Returns the principal value of the arc tangent of x, expressed in radians.
Double_t	ATan2 (Double_t y, Double_t x)
	Returns the principal value of the arc tangent of y/x, expressed in radians.
Double_t	ATanH (Double_t)
	Returns the area hyperbolic tangent of x.
Double_t	BesselI (Int_t n, Double_t x)
Double_t	BesselI0 (Double_t x)
	Integer order modified Bessel function K_n(x).
Double_t	BesselI1 (Double_t x)
	Modified Bessel function K_0(x).
Double_t	BesselJ0 (Double_t x)
	Modified Bessel function K_1(x).
Double_t	BesselJ1 (Double_t x)
	Bessel function J0(x) for any real x.
Double_t	BesselK (Int_t n, Double_t x)
	Integer order modified Bessel function I_n(x).
Double_t	BesselK0 (Double_t x)
	Modified Bessel function I_0(x).
Double_t	BesselK1 (Double_t x)
	Modified Bessel function I_1(x).
Double_t	BesselY0 (Double_t x)
	Bessel function J1(x) for any real x.
Double_t	BesselY1 (Double_t x)
	Bessel function Y0(x) for positive x.
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.
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.
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)
	Calculates a Breit Wigner function with mean and gamma.
Double_t	BreitWignerRelativistic (Double_t x, Double_t median=0, Double_t gamma=1)
	Calculates a Relativistic Breit Wigner function with median and gamma.
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 \( m s^{-1} \).
Double_t	CauchyDist (Double_t x, Double_t t=0, Double_t s=1)
constexpr Double_t	Ccgs ()
	\( cm s^{-1} \)
Double_t	Ceil (Double_t x)
	Rounds x upward, returning the smallest integral value that is not less than x.
Int_t	CeilNint (Double_t x)
	Returns the nearest integer of TMath::Ceil(x).
Double_t	ChisquareQuantile (Double_t p, Double_t ndf)
Double_t	Cos (Double_t)
	Returns the cosine of an angle of x radians.
Double_t	CosH (Double_t)
	Returns the hyperbolic cosine of x.
template<typename T>
T *	Cross (const T v1[3], const T v2[3], T out[3])
	Calculates the Cross Product of two vectors: out = [v1 x v2].
constexpr Double_t	CUncertainty ()
	Speed of light uncertainty.
constexpr Double_t	DegToRad ()
	Conversion from degree to radian: \( \frac{\pi}{180} \).
Double_t	DiLog (Double_t x)
	Modified Struve functions of order 1.
constexpr Double_t	E ()
	Base of natural log: \( e \).
Double_t	Erf (Double_t x)
	Computation of the error function erf(x).
Double_t	Erfc (Double_t x)
	Computes the complementary error function erfc(x).
Double_t	ErfcInverse (Double_t x)
	Returns the inverse of the complementary error function.
Double_t	ErfInverse (Double_t x)
	Returns the inverse error function.
constexpr Double_t	EulerGamma ()
	Euler-Mascheroni Constant.
Bool_t	Even (Long_t a)
	Returns true if a is even.
Double_t	Exp (Double_t x)
	Returns the base-e exponential function of x, which is e raised to the power x.
Double_t	Factorial (Int_t i)
	Computes factorial(n).
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.
Int_t	Finite (Float_t x)
	Check if it is finite with a mask in order to be consistent in presence of fast math.
Double_t	Floor (Double_t x)
	Rounds x downward, returning the largest integral value that is not greater than x.
Int_t	FloorNint (Double_t x)
	Returns the nearest integer of TMath::Floor(x).
Double_t	Freq (Double_t x)
	Computation of the normal frequency function freq(x).
constexpr Double_t	G ()
	Gravitational constant in: \( m^{3} kg^{-1} s^{-2} \).
Double_t	GamCf (Double_t a, Double_t x)
	Computation of the incomplete gamma function P(a,x) via its continued fraction representation.
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 .
Double_t	Gamma (Double_t z)
	Computation of gamma(z) for all z.
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.
Double_t	Gaus (Double_t x, Double_t mean=0, Double_t sigma=1, Bool_t norm=kFALSE)
	Calculates a gaussian function with mean and sigma.
constexpr Double_t	Gcgs ()
	\( cm^{3} g^{-1} s^{-2} \)
template<typename Iterator>
Double_t	GeomMean (Iterator first, Iterator last)
	Returns the geometric mean of an array defined by the iterators.
template<typename T>
Double_t	GeomMean (Long64_t n, const T *a)
	Returns the geometric mean of an array a of size n.
constexpr Double_t	GhbarC ()
	\( \frac{G}{\hbar C} \) in \( (GeV/c^{2})^{-2} \)
constexpr Double_t	GhbarCUncertainty ()
	\( \frac{G}{\hbar C} \) uncertainty.
constexpr Double_t	Gn ()
	Standard acceleration of gravity in \( m s^{-2} \).
constexpr Double_t	GnUncertainty ()
	Standard acceleration of gravity uncertainty.
template<typename T>
T *	Gradient (Long64_t n, T *f, double h=1)
	Calculate the one-dimensional gradient of an array with length n.
constexpr Double_t	GUncertainty ()
	Gravitational constant uncertainty.
constexpr Double_t	H ()
	Planck's constant in \( J s \): \( h \).
ULong_t	Hash (const char *str)
ULong_t	Hash (const void *txt, Int_t ntxt)
constexpr Double_t	Hbar ()
	\( \hbar \) in \( J s \): \( \hbar = \frac{h}{2\pi} \)
constexpr Double_t	Hbarcgs ()
	\( erg s \)
constexpr Double_t	HbarUncertainty ()
	\( \hbar \) uncertainty.
constexpr Double_t	HC ()
	\( hc \) in \( J m \)
constexpr Double_t	HCcgs ()
	\( erg cm \)
constexpr Double_t	Hcgs ()
	\( erg s \)
constexpr Double_t	HUncertainty ()
	Planck's constant uncertainty.
Double_t	Hypot (Double_t x, Double_t y)
	Returns sqrt(xx + yy).
Long_t	Hypot (Long_t x, Long_t y)
	Returns sqrt(xx + yy).
Double_t	Infinity ()
	Returns an infinity as defined by the IEEE standard.
constexpr Double_t	InvPi ()
	\( \frac{1.}{\pi}\)
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.
Bool_t	IsNaN (Double_t x)
Bool_t	IsNaN (Float_t x)
constexpr Double_t	K ()
	Boltzmann's constant in \( J K^{-1} \): \( k \).
constexpr Double_t	Kcgs ()
	\( erg K^{-1} \)
void	KNNDensity (std::span< const double > observations, std::span< const double > queries, std::span< double > result, int k, double dmin=0.0)
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).
constexpr Double_t	KUncertainty ()
	Boltzmann's constant uncertainty.
Double_t	Landau (Double_t x, Double_t mpv=0, Double_t sigma=1, Bool_t norm=kFALSE)
	The LANDAU function.
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)
template<typename T>
T *	Laplacian (Long64_t n, T *f, double h=1)
	Calculate the Laplacian of an array with length n.
Double_t	Ldexp (Double_t x, Int_t exp)
	Returns the result of multiplying x (the significant) by 2 raised to the power of exp (the exponent).
constexpr Double_t	Ln10 ()
	Natural log of 10 (to convert log to ln).
Double_t	LnGamma (Double_t z)
	Computation of ln[gamma(z)] for all z.
template<typename Iterator>
Iterator	LocMax (Iterator first, Iterator last)
	Returns index of array with the maximum element.
template<typename T>
Long64_t	LocMax (Long64_t n, const T *a)
	Returns index of array with the maximum element.
template<typename Iterator>
Iterator	LocMin (Iterator first, Iterator last)
	Returns index of array with the minimum element.
template<typename T>
Long64_t	LocMin (Long64_t n, const T *a)
	Returns index of array with the minimum element.
Double_t	Log (Double_t x)
	Returns the natural logarithm of x.
Double_t	Log10 (Double_t x)
	Returns the common (base-10) logarithm of x.
Double_t	Log2 (Double_t x)
	Returns the binary (base-2) logarithm of x.
constexpr Double_t	LogE ()
	Base-10 log of e (to convert ln to log).
Double_t	LogNormal (Double_t x, Double_t sigma, Double_t theta=0, Double_t m=1)
Double_t	Max (Double_t a, Double_t b)
	Returns the largest of a and b.
Float_t	Max (Float_t a, Float_t b)
	Returns the largest of a and b.
Int_t	Max (Int_t a, Int_t b)
	Returns the largest of a and b.
Long64_t	Max (Long64_t a, Long64_t b)
	Returns the largest of a and b.
Long_t	Max (Long_t a, Long_t b)
	Returns the largest of a and b.
Short_t	Max (Short_t a, Short_t b)
	Returns the largest of a and b.
UInt_t	Max (UInt_t a, UInt_t b)
	Returns the largest of a and b.
ULong64_t	Max (ULong64_t a, ULong64_t b)
	Returns the largest of a and b.
ULong_t	Max (ULong_t a, ULong_t b)
	Returns the largest of a and b.
UShort_t	Max (UShort_t a, UShort_t b)
	Returns the largest of a and b.
template<typename T>
T	MaxElement (Long64_t n, const T *a)
	Returns maximum of array a of length n.
template<typename Iterator>
Double_t	Mean (Iterator first, Iterator last)
	Returns the weighted mean of an array defined by the iterators.
template<typename Iterator, typename WeightIterator>
Double_t	Mean (Iterator first, Iterator last, WeightIterator wfirst)
	Returns the weighted mean of an array defined by the first and last iterators.
template<typename T>
Double_t	Mean (Long64_t n, const T a, const Double_t w=nullptr)
	Returns the weighted mean of an array a with length n.
template<typename T>
Double_t	Median (Long64_t n, const T a, const Double_t w=nullptr, Long64_t *work=nullptr)
	Same as RMS.
Double_t	Min (Double_t a, Double_t b)
	Returns the smallest of a and b.
Float_t	Min (Float_t a, Float_t b)
	Returns the smallest of a and b.
Int_t	Min (Int_t a, Int_t b)
	Returns the smallest of a and b.
Long64_t	Min (Long64_t a, Long64_t b)
	Returns the smallest of a and b.
Long_t	Min (Long_t a, Long_t b)
	Returns the smallest of a and b.
Short_t	Min (Short_t a, Short_t b)
	Returns the smallest of a and b.
UInt_t	Min (UInt_t a, UInt_t b)
	Returns the smallest of a and b.
ULong64_t	Min (ULong64_t a, ULong64_t b)
	Returns the smallest of a and b.
ULong_t	Min (ULong_t a, ULong_t b)
	Returns the smallest of a and b.
UShort_t	Min (UShort_t a, UShort_t b)
	Returns the smallest of a and b.
template<typename T>
T	MinElement (Long64_t n, const T *a)
	Returns minimum of array a of length n.
template<typename T>
Double_t	ModeHalfSample (Long64_t n, const T a, const Double_t w=nullptr)
	Returns the half-sample mode of the array a where each entry i has weight w[i].
constexpr Double_t	MWair ()
	Molecular weight of dry air 1976 US Standard Atmosphere in \( kg kmol^{-1} \) or \( gm mol^{-1} \)
constexpr Double_t	Na ()
	Avogadro constant (Avogadro's Number) in \( mol^{-1} \).
constexpr Double_t	NaUncertainty ()
	Avogadro constant (Avogadro's Number) uncertainty.
Long_t	NextPrime (Long_t x)
	TMath Base functions.
template<typename T>
Int_t	Nint (T x)
	Round to nearest integer. Rounds half integers to the nearest even integer.
template<typename T>
T *	Normal2Plane (const T v1[3], const T v2[3], const T v3[3], T normal[3])
	Calculates a normal vector of a plane.
Double_t	Normalize (Double_t v[3])
	Normalize a vector v in place.
Float_t	Normalize (Float_t v[3])
	Normalize a vector v in place.
template<typename T>
T	NormCross (const T v1[3], const T v2[3], T out[3])
	Calculates the Normalized Cross Product of two vectors.
Double_t	NormQuantile (Double_t p)
Bool_t	Odd (Long_t a)
	Returns true if a is odd.
Bool_t	Permute (Int_t n, Int_t *a)
constexpr Double_t	Pi ()
	\( \pi\)
constexpr Double_t	PiOver2 ()
	\( \frac{\pi}{2} \)
constexpr Double_t	PiOver4 ()
	\( \frac{\pi}{4} \)
Double_t	Poisson (Double_t x, Double_t par)
Double_t	PoissonI (Double_t x, Double_t par)
Double_t	Power (Double_t x, Double_t y)
	Returns x raised to the power y.
Double_t	Power (Double_t x, Int_t y)
	Returns x raised to the power y.
LongDouble_t	Power (Long64_t x, Long64_t y)
	Returns x raised to the power y.
LongDouble_t	Power (LongDouble_t x, Long64_t y)
	Returns x raised to the power y.
LongDouble_t	Power (LongDouble_t x, LongDouble_t y)
	Returns x raised to the power y.
Double_t	Prob (Double_t chi2, Int_t ndf)
constexpr Double_t	Qe ()
	Elementary charge in \( C \) .
constexpr Double_t	QeUncertainty ()
	Elementary charge uncertainty.
void	Quantiles (Int_t n, Int_t nprob, Double_t x, Double_t quantiles, Double_t prob, Bool_t isSorted=kTRUE, Int_t index=nullptr, Int_t type=7)
Double_t	QuietNaN ()
	Returns a quiet NaN as defined by IEEE 754.
constexpr Double_t	R ()
	Universal gas constant ( \( Na K \)) in \( J K^{-1} mol^{-1} \)
constexpr Double_t	RadToDeg ()
	Conversion from radian to degree: \( \frac{180}{\pi} \).
Double_t	Range (Double_t lb, Double_t ub, Double_t x)
	Returns x if lb < x < up, lb if x < lb and ub if x > ub.
Int_t	Range (Int_t lb, Int_t ub, Int_t x)
	Returns x if lb < x < up, lb if x < lb and ub if x > ub.
Long_t	Range (Long_t lb, Long_t ub, Long_t x)
	Returns x if lb < x < up, lb if x < lb and ub if x > ub.
Short_t	Range (Short_t lb, Short_t ub, Short_t x)
	Returns x if lb < x < up, lb if x < lb and ub if x > ub.
ULong_t	Range (ULong_t lb, ULong_t ub, ULong_t x)
	Returns x if lb < x < up, lb if x < lb and ub if x > ub.
constexpr Double_t	Rgair ()
	Dry Air Gas Constant (R / MWair) in \( J kg^{-1} K^{-1} \)
template<typename Iterator>
Double_t	RMS (Iterator first, Iterator last)
	Returns the Standard Deviation of an array defined by the iterators.
template<typename Iterator, typename WeightIterator>
Double_t	RMS (Iterator first, Iterator last, WeightIterator wfirst)
	Returns the weighted Standard Deviation of an array defined by the iterators.
template<typename T>
Double_t	RMS (Long64_t n, const T a, const Double_t w=nullptr)
	Returns the Standard Deviation of an array a with length n.
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.
constexpr Double_t	Sigma ()
	Stefan-Boltzmann constant in \( W m^{-2} K^{-4}\): \( \sigma \).
constexpr Double_t	SigmaUncertainty ()
	Stefan-Boltzmann constant uncertainty.
Double_t	Sign (Double_t a, Double_t b)
	Returns a value with the magnitude of a and the sign of b.
Float_t	Sign (Float_t a, Float_t b)
	Returns a value with the magnitude of a and the sign of b.
LongDouble_t	Sign (LongDouble_t a, LongDouble_t b)
	Returns a value with the magnitude of a and the sign of b.
template<typename T1, typename T2>
T1	Sign (T1 a, T2 b)
	Returns a value with the magnitude of a and the sign of b.
Double_t	SignalingNaN ()
	Returns a signaling NaN as defined by IEEE 754](http://en.wikipedia.org/wiki/NaN#Signaling_NaN).
Bool_t	SignBit (Double_t a)
	Returns whether the sign of Double_t a is negative.
Bool_t	SignBit (Float_t a)
	Returns whether the sign of Float_t a is negative.
template<typename Integer>
Bool_t	SignBit (Integer a)
	Returns whether the sign of Integer a is negative.
Bool_t	SignBit (LongDouble_t a)
	Returns whether the sign of LongDouble_t a is negative.
Double_t	Sin (Double_t)
	Returns the sine of an angle of x radians.
Double_t	SinH (Double_t)
	Returns the hyperbolic sine of `x.
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.
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.
Double_t	Sq (Double_t x)
	Returns x*x.
Double_t	Sqrt (Double_t x)
	Returns the square root of x.
constexpr Double_t	Sqrt2 ()
	\( \sqrt{2} \)
template<typename Iterator>
Double_t	StdDev (Iterator first, Iterator last)
	Same as RMS.
template<typename Iterator, typename WeightIterator>
Double_t	StdDev (Iterator first, Iterator last, WeightIterator wfirst)
	Same as RMS.
template<typename T>
Double_t	StdDev (Long64_t n, const T a, const Double_t w=nullptr)
Double_t	StruveH0 (Double_t x)
	Bessel function Y1(x) for positive x.
Double_t	StruveH1 (Double_t x)
	Struve functions of order 0.
Double_t	StruveL0 (Double_t x)
	Struve functions of order 1.
Double_t	StruveL1 (Double_t x)
	Modified Struve functions of order 0.
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)
	Returns the tangent of an angle of x radians.
Double_t	TanH (Double_t)
	Returns the hyperbolic tangent of x.
constexpr Double_t	TwoPi ()
	\( 2\pi\)
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]

Double_t TMath::Abs ( Double_t d )

inline

Returns the absolute value of parameter Double_t d.

Definition at line 142 of file TMathBase.h.

◆ Abs() [2/7]

Float_t TMath::Abs ( Float_t d )

inline

Returns the absolute value of parameter Float_t d.

Definition at line 138 of file TMathBase.h.

◆ Abs() [3/7]

Int_t TMath::Abs ( Int_t d )

inline

Returns the absolute value of parameter Int_t d.

Definition at line 126 of file TMathBase.h.

◆ Abs() [4/7]

Long64_t TMath::Abs ( Long64_t d )

inline

Returns the absolute value of parameter Long64_t d.

Definition at line 134 of file TMathBase.h.

◆ Abs() [5/7]

Long_t TMath::Abs ( Long_t d )

inline

Returns the absolute value of parameter Long_t d.

Definition at line 130 of file TMathBase.h.

◆ Abs() [6/7]

LongDouble_t TMath::Abs ( LongDouble_t d )

inline

Returns the absolute value of parameter LongDouble_t d.

Definition at line 146 of file TMathBase.h.

◆ Abs() [7/7]

Short_t TMath::Abs ( Short_t d )

inline

Returns the absolute value of parameter Short_t d.

Definition at line 122 of file TMathBase.h.

◆ ACos()

Double_t TMath::ACos ( Double_t x )

inline

Returns the principal value of the arc cosine of x, expressed in radians.

Definition at line 643 of file TMath.h.

◆ ACosH()

Double_t TMath::ACosH ( Double_t x )

Returns the nonnegative area hyperbolic cosine of x.

Definition at line 81 of file TMath.cxx.

◆ AreEqualAbs()

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

inline

Comparing floating points.

Returns kTRUE if the absolute difference between af and bf is less than epsilon.

Definition at line 421 of file TMath.h.

◆ AreEqualRel()

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

inline

Comparing floating points.

Returns kTRUE if the relative difference between af and bf is less than relPrec.

Definition at line 429 of file TMath.h.

◆ ASin()

Double_t TMath::ASin ( Double_t x )

inline

Returns the principal value of the arc sine of x, expressed in radians.

Definition at line 635 of file TMath.h.

◆ ASinH()

Double_t TMath::ASinH ( Double_t x )

Returns the area hyperbolic sine of x.

Definition at line 67 of file TMath.cxx.

◆ ATan()

Double_t TMath::ATan ( Double_t x )

inline

Returns the principal value of the arc tangent of x, expressed in radians.

Definition at line 651 of file TMath.h.

◆ ATan2()

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

inline

Returns the principal value of the arc tangent of y/x, expressed in radians.

Definition at line 657 of file TMath.h.

◆ ATanH()

Double_t TMath::ATanH ( Double_t x )

Returns the area hyperbolic tangent of x.

Definition at line 95 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() [1/2]

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 344 of file TMathBase.h.

◆ BinarySearch() [2/2]

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 329 of file TMathBase.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 )

Calculates a Breit Wigner function with mean and gamma.

Definition at line 442 of file TMath.cxx.

◆ BreitWignerRelativistic()

Double_t TMath::BreitWignerRelativistic	(	Double_t	x,
		Double_t	median = 0,
		Double_t	gamma = 1 )

Calculates a Relativistic Breit Wigner function with median and gamma.

Definition at line 452 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()

Double_t TMath::C ( )

constexpr

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

Definition at line 117 of file TMath.h.

◆ CauchyDist()

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

◆ Ccgs()

Double_t TMath::Ccgs ( )

constexpr

\( cm s^{-1} \)

Definition at line 124 of file TMath.h.

◆ Ceil()

Double_t TMath::Ceil ( Double_t x )

inline

Rounds x upward, returning the smallest integral value that is not less than x.

Definition at line 679 of file TMath.h.

◆ CeilNint()

Int_t TMath::CeilNint ( Double_t x )

inline

Returns the nearest integer of TMath::Ceil(x).

Definition at line 685 of file TMath.h.

◆ ChisquareQuantile()

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

◆ Cos()

Double_t TMath::Cos ( Double_t x )

inline

Returns the cosine of an angle of x radians.

Definition at line 605 of file TMath.h.

◆ CosH()

Double_t TMath::CosH ( Double_t x )

inline

Returns the hyperbolic cosine of x.

Definition at line 623 of file TMath.h.

◆ Cross()

template<typename T>

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

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

Definition at line 1284 of file TMath.h.

◆ CUncertainty()

Double_t TMath::CUncertainty ( )

constexpr

Speed of light uncertainty.

Definition at line 131 of file TMath.h.

◆ DegToRad()

Double_t TMath::DegToRad ( )

constexpr

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 116 of file TMath.cxx.

◆ E()

Double_t TMath::E ( )

constexpr

Base of natural log: \( e \).

Definition at line 96 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 190 of file TMath.cxx.

◆ Erfc()

Double_t TMath::Erfc ( Double_t x )

Computes the complementary error function erfc(x).

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

Definition at line 199 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 242 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 208 of file TMath.cxx.

◆ EulerGamma()

Double_t TMath::EulerGamma ( )

constexpr

Euler-Mascheroni Constant.

Definition at line 335 of file TMath.h.

◆ Even()

Bool_t TMath::Even ( Long_t a )

inline

Returns true if a is even.

Definition at line 112 of file TMathBase.h.

◆ Exp()

Double_t TMath::Exp ( Double_t x )

inline

Returns the base-e exponential function of x, which is e raised to the power x.

Definition at line 720 of file TMath.h.

◆ Factorial()

Double_t TMath::Factorial ( Int_t i )

Computes factorial(n).

Definition at line 252 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 781 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 811 of file TMath.h.

◆ Floor()

Double_t TMath::Floor ( Double_t x )

inline

Rounds x downward, returning the largest integral value that is not greater than x.

Definition at line 691 of file TMath.h.

◆ FloorNint()

Int_t TMath::FloorNint ( Double_t x )

inline

Returns the nearest integer of TMath::Floor(x).

Definition at line 697 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 270 of file TMath.cxx.

◆ G()

Double_t TMath::G ( )

constexpr

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

Definition at line 138 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 380 of file TMath.cxx.

◆ Gamma() [1/2]

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 369 of file TMath.cxx.

◆ Gamma() [2/2]

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 353 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 417 of file TMath.cxx.

◆ Gaus()

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

Calculates 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 471 of file TMath.cxx.

◆ Gcgs()

Double_t TMath::Gcgs ( )

constexpr

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

Definition at line 146 of file TMath.h.

◆ GeomMean() [1/2]

template<typename Iterator>

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

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

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

Definition at line 1190 of file TMath.h.

◆ GeomMean() [2/2]

template<typename T>

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

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

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

Definition at line 1210 of file TMath.h.

◆ GhbarC()

Double_t TMath::GhbarC ( )

constexpr

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

Definition at line 161 of file TMath.h.

◆ GhbarCUncertainty()

Double_t TMath::GhbarCUncertainty ( )

constexpr

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

Definition at line 169 of file TMath.h.

◆ Gn()

Double_t TMath::Gn ( )

constexpr

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

Definition at line 177 of file TMath.h.

◆ GnUncertainty()

Double_t TMath::GnUncertainty ( )

constexpr

Standard acceleration of gravity uncertainty.

Definition at line 184 of file TMath.h.

◆ Gradient()

template<typename T>

T * TMath::Gradient	(	Long64_t	n,
		T *	f,
		double	h = 1 )

Calculate the one-dimensional gradient of an array with length n.

The first value in the returned array is a forward difference, the next n-2 values are central differences, and the last is a backward difference.

Note: Function leads to undefined behavior if n does not match the length of f

Parameters

n	the number of points in the array
f	the array of points.
h	the step size. The default step size is 1.

Returns: an array of size n with the gradient. Returns nullptr if n < 2 or f empty. Ownership is transferred to the caller.

Definition at line 1029 of file TMath.h.

◆ GUncertainty()

Double_t TMath::GUncertainty ( )

constexpr

Gravitational constant uncertainty.

Definition at line 153 of file TMath.h.

◆ H()

Double_t TMath::H ( )

constexpr

Planck's constant in \( J s \): \( h \).

Definition at line 191 of file TMath.h.

◆ Hash() [1/2]

ULong_t TMath::Hash ( const char * str )

◆ Hash() [2/2]

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

◆ Hbar()

Double_t TMath::Hbar ( )

constexpr

\( \hbar \) in \( J s \): \( \hbar = \frac{h}{2\pi} \)

Definition at line 214 of file TMath.h.

◆ Hbarcgs()

Double_t TMath::Hbarcgs ( )

constexpr

\( erg s \)

Definition at line 221 of file TMath.h.

◆ HbarUncertainty()

Double_t TMath::HbarUncertainty ( )

constexpr

\( \hbar \) uncertainty.

Definition at line 228 of file TMath.h.

◆ HC()

Double_t TMath::HC ( )

constexpr

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

Definition at line 236 of file TMath.h.

◆ HCcgs()

Double_t TMath::HCcgs ( )

constexpr

\( erg cm \)

Definition at line 243 of file TMath.h.

◆ Hcgs()

Double_t TMath::Hcgs ( )

constexpr

\( erg s \)

Definition at line 198 of file TMath.h.

◆ HUncertainty()

Double_t TMath::HUncertainty ( )

constexpr

Planck's constant uncertainty.

Definition at line 205 of file TMath.h.

◆ Hypot() [1/2]

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

Returns sqrt(x*x + y*y).

Definition at line 59 of file TMath.cxx.

◆ Hypot() [2/2]

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

Returns sqrt(x*x + y*y).

Definition at line 51 of file TMath.cxx.

◆ Infinity()

Double_t TMath::Infinity ( )

inline

Returns an infinity as defined by the IEEE standard.

Definition at line 928 of file TMath.h.

◆ InvPi()

Double_t TMath::InvPi ( )

constexpr

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

Definition at line 68 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 1320 of file TMath.h.

◆ IsNaN() [1/2]

Bool_t TMath::IsNaN ( Double_t x )

inline

Definition at line 903 of file TMath.h.

◆ IsNaN() [2/2]

Bool_t TMath::IsNaN ( Float_t x )

inline

Definition at line 904 of file TMath.h.

◆ K()

Double_t TMath::K ( )

constexpr

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

Definition at line 250 of file TMath.h.

◆ Kcgs()

Double_t TMath::Kcgs ( )

constexpr

\( erg K^{-1} \)

Definition at line 257 of file TMath.h.

◆ KNNDensity()

void TMath::KNNDensity	(	std::span< const double >	observations,
		std::span< const double >	queries,
		std::span< double >	result,
		int	k,
		double	dmin = 0.0 )

◆ 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 1568 of file TMath.h.

◆ KUncertainty()

Double_t TMath::KUncertainty ( )

constexpr

Boltzmann's constant uncertainty.

Definition at line 264 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 492 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 )

◆ Laplacian()

template<typename T>

T * TMath::Laplacian	(	Long64_t	n,
		T *	f,
		double	h = 1 )

Calculate the Laplacian of an array with length n.

The first value in the returned array is a forward difference, the next n-2 values are central differences, and the last is a backward difference.

Note: Function leads to undefined behavior if n does not match the length of f

Parameters

n	the number of points in the array
f	the array of points.
h	the step size. The default step size is 1.

Returns: an array of size n with the laplacian. Returns nullptr if n < 4 or f empty. Ownership is transferred to the caller.

Definition at line 1067 of file TMath.h.

◆ Ldexp()

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

inline

Returns the result of multiplying x (the significant) by 2 raised to the power of exp (the exponent).

Definition at line 726 of file TMath.h.

◆ Ln10()

Double_t TMath::Ln10 ( )

constexpr

Natural log of 10 (to convert log to ln).

Definition at line 103 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 509 of file TMath.cxx.

◆ LocMax() [1/2]

template<typename Iterator>

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

Returns index of array with the maximum element.

If more than one element is maximum returns first found.

Definition at line 1117 of file TMath.h.

◆ LocMax() [2/2]

template<typename T>

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

Returns 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 1099 of file TMath.h.

◆ LocMin() [1/2]

template<typename Iterator>

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

Returns index of array with the minimum element.

If more than one element is minimum returns first found.

Definition at line 1011 of file TMath.h.

◆ LocMin() [2/2]

template<typename T>

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

Returns 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 993 of file TMath.h.

◆ Log()

Double_t TMath::Log ( Double_t x )

inline

Returns the natural logarithm of x.

Definition at line 767 of file TMath.h.

◆ Log10()

Double_t TMath::Log10 ( Double_t x )

inline

Returns the common (base-10) logarithm of x.

Definition at line 773 of file TMath.h.

◆ Log2()

Double_t TMath::Log2 ( Double_t x )

Returns the binary (base-2) logarithm of x.

Definition at line 107 of file TMath.cxx.

◆ LogE()

Double_t TMath::LogE ( )

constexpr

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

Definition at line 110 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]

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

inline

Returns the largest of a and b.

If both are equivalent, a is returned. aand b are Double_t.

Definition at line 294 of file TMathBase.h.

◆ Max() [2/10]

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

inline

Returns the largest of a and b.

If both are equivalent, a is returned. aand b are Float_t.

Definition at line 289 of file TMathBase.h.

◆ Max() [3/10]

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

inline

Returns the largest of a and b.

If both are equivalent, a is returned. aand b are Int_t.

Definition at line 259 of file TMathBase.h.

◆ Max() [4/10]

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

inline

Returns the largest of a and b.

If both are equivalent, a is returned. aand b are Long64_t.

Definition at line 279 of file TMathBase.h.

◆ Max() [5/10]

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

inline

Returns the largest of a and b.

If both are equivalent, a is returned. aand b are Long_t.

Definition at line 269 of file TMathBase.h.

◆ Max() [6/10]

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

inline

Returns the largest of a and b.

If both are equivalent, a is returned. aand b are Short_t.

Definition at line 249 of file TMathBase.h.

◆ Max() [7/10]

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

inline

Returns the largest of a and b.

If both are equivalent, a is returned. aand b are UInt_t.

Definition at line 264 of file TMathBase.h.

◆ Max() [8/10]

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

inline

Returns the largest of a and b.

If both are equivalent, a is returned. aand b are ULong64_t.

Definition at line 284 of file TMathBase.h.

◆ Max() [9/10]

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

inline

Returns the largest of a and b.

If both are equivalent, a is returned. aand b are ULong_t.

Definition at line 274 of file TMathBase.h.

◆ Max() [10/10]

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

inline

Returns the largest of a and b.

If both are equivalent, a is returned. aand b are UShort_t.

Definition at line 254 of file TMathBase.h.

◆ MaxElement()

template<typename T>

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

Returns maximum of array a of length n.

Definition at line 979 of file TMath.h.

◆ Mean() [1/3]

template<typename Iterator>

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

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

Definition at line 1127 of file TMath.h.

◆ Mean() [2/3]

template<typename Iterator, typename WeightIterator>

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

Returns 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 1147 of file TMath.h.

◆ Mean() [3/3]

template<typename T>

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

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

Definition at line 1176 of file TMath.h.

◆ Median()

template<typename T>

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

Same as RMS.

Returns 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 1359 of file TMath.h.