TMath.h File Reference

#include "Rtypes.h"
#include "TMathBase.h"
#include "TError.h"
#include <algorithm>
#include <limits>
#include <cmath>
#include <float.h>

Include dependency graph for TMath.h:

Classes
struct	TMath::Limits< T >

Namespaces
namespace	TMath
	TMath.

Functions
double	acos (double)
Double_t	TMath::ACos (Double_t)
Double_t	TMath::ACosH (Double_t)
Bool_t	TMath::AreEqualAbs (Double_t af, Double_t bf, Double_t epsilon)
Bool_t	TMath::AreEqualRel (Double_t af, Double_t bf, Double_t relPrec)
double	asin (double)
Double_t	TMath::ASin (Double_t)
Double_t	TMath::ASinH (Double_t)
double	atan (double)
Double_t	TMath::ATan (Double_t)
double	atan2 (double, double)
Double_t	TMath::ATan2 (Double_t, Double_t)
Double_t	TMath::ATanH (Double_t)
Double_t	TMath::BesselI (Int_t n, Double_t x)
	Compute the Integer Order Modified Bessel function I_n(x) for n=0,1,2,... and any real x. More...
Double_t	TMath::BesselI0 (Double_t x)
	integer order modified Bessel function K_n(x) More...
Double_t	TMath::BesselI1 (Double_t x)
	modified Bessel function K_0(x) More...
Double_t	TMath::BesselJ0 (Double_t x)
	modified Bessel function K_1(x) More...
Double_t	TMath::BesselJ1 (Double_t x)
	Bessel function J0(x) for any real x. More...
Double_t	TMath::BesselK (Int_t n, Double_t x)
	integer order modified Bessel function I_n(x) More...
Double_t	TMath::BesselK0 (Double_t x)
	modified Bessel function I_0(x) More...
Double_t	TMath::BesselK1 (Double_t x)
	modified Bessel function I_1(x) More...
Double_t	TMath::BesselY0 (Double_t x)
	Bessel function J1(x) for any real x. More...
Double_t	TMath::BesselY1 (Double_t x)
	Bessel function Y0(x) for positive x. More...
Double_t	TMath::Beta (Double_t p, Double_t q)
	Calculates Beta-function Gamma(p)*Gamma(q)/Gamma(p+q). More...
Double_t	TMath::BetaCf (Double_t x, Double_t a, Double_t b)
	Continued fraction evaluation by modified Lentz's method used in calculation of incomplete Beta function. More...
Double_t	TMath::BetaDist (Double_t x, Double_t p, Double_t q)
	Computes the probability density function of the Beta distribution (the distribution function is computed in BetaDistI). More...
Double_t	TMath::BetaDistI (Double_t x, Double_t p, Double_t q)
	Computes the distribution function of the Beta distribution. More...
Double_t	TMath::BetaIncomplete (Double_t x, Double_t a, Double_t b)
	Calculates the incomplete Beta-function. More...
Double_t	TMath::Binomial (Int_t n, Int_t k)
	Calculate the binomial coefficient n over k. More...
Double_t	TMath::BinomialI (Double_t p, Int_t n, Int_t k)
	Suppose an event occurs with probability p per trial Then the probability P of its occurring k or more times in n trials is termed a cumulative binomial probability the formula is P = sum_from_j=k_to_n(TMath::Binomial(n, j)* *TMath::Power(p, j)*TMathPower(1-p, n-j) For n larger than 12 BetaIncomplete is a much better way to evaluate the sum than would be the straightforward sum calculation for n smaller than 12 either method is acceptable ("Numerical Recipes") –implementation by Anna Kreshuk. More...
Double_t	TMath::BreitWigner (Double_t x, Double_t mean=0, Double_t gamma=1)
	Calculate a Breit Wigner function with mean and gamma. More...
void	TMath::BubbleHigh (Int_t Narr, Double_t *arr1, Int_t *arr2)
	Bubble sort variant to obtain the order of an array's elements into an index in order to do more useful things than the standard built in functions. More...
void	TMath::BubbleLow (Int_t Narr, Double_t *arr1, Int_t *arr2)
	Opposite ordering of the array arr2[] to that of BubbleHigh. More...
constexpr Double_t	TMath::C ()
	Velocity of light in \( m s^{-1} \). More...
Double_t	TMath::CauchyDist (Double_t x, Double_t t=0, Double_t s=1)
	Computes the density of Cauchy distribution at point x by default, standard Cauchy distribution is used (t=0, s=1) More...
constexpr Double_t	TMath::Ccgs ()
	\( cm s^{-1} \) More...
double	ceil (double)
Double_t	TMath::Ceil (Double_t x)
Int_t	TMath::CeilNint (Double_t x)
Double_t	TMath::ChisquareQuantile (Double_t p, Double_t ndf)
	Evaluate the quantiles of the chi-squared probability distribution function. More...
double	cos (double)
Double_t	TMath::Cos (Double_t)
double	cosh (double)
Double_t	TMath::CosH (Double_t)
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]. More...
constexpr Double_t	TMath::CUncertainty ()
	Speed of light uncertainty. More...
constexpr Double_t	TMath::DegToRad ()
	Conversion from degree to radian: More...
Double_t	TMath::DiLog (Double_t x)
	Modified Struve functions of order 1. More...
constexpr Double_t	TMath::E ()
	Base of natural log: More...
Double_t	TMath::Erf (Double_t x)
	Computation of the error function erf(x). More...
Double_t	TMath::Erfc (Double_t x)
	Compute the complementary error function erfc(x). More...
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 More...
Double_t	TMath::ErfInverse (Double_t x)
	returns the inverse error function x must be <-1<x<1 More...
constexpr Double_t	TMath::EulerGamma ()
	Euler-Mascheroni Constant. More...
double	exp (double)
Double_t	TMath::Exp (Double_t x)
Double_t	TMath::Factorial (Int_t i)
	Compute factorial(n). More...
Double_t	TMath::FDist (Double_t F, Double_t N, Double_t M)
	Computes the density function of F-distribution (probability function, integral of density, is computed in FDistI). More...
Double_t	TMath::FDistI (Double_t F, Double_t N, Double_t M)
	Calculates the cumulative distribution function of F-distribution, this function occurs in the statistical test of whether two observed samples have the same variance. More...
int	finite (double)
Int_t	TMath::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	TMath::Finite (Float_t x)
	Check if it is finite with a mask in order to be consistent in presence of fast math. More...
double	floor (double)
Double_t	TMath::Floor (Double_t x)
Int_t	TMath::FloorNint (Double_t x)
Double_t	TMath::Freq (Double_t x)
	Computation of the normal frequency function freq(x). More...
constexpr Double_t	TMath::G ()
	Gravitational constant in: \( m^{3} kg^{-1} s^{-2} \). More...
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 . More...
Double_t	TMath::Gamma (Double_t z)
	Computation of gamma(z) for all z. More...
Double_t	TMath::GammaDist (Double_t x, Double_t gamma, Double_t mu=0, Double_t beta=1)
	Computes the density function of Gamma distribution at point x. More...
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. More...
constexpr Double_t	TMath::Gcgs ()
	\( cm^{3} g^{-1} s^{-2} \) More...
template<typename Iterator >
Double_t	TMath::GeomMean (Iterator first, Iterator last)
	Return the geometric mean of an array defined by the iterators. More...
template<typename T >
Double_t	TMath::GeomMean (Long64_t n, const T *a)
	Return the geometric mean of an array a of size n. More...
constexpr Double_t	TMath::GhbarC ()
	\( \frac{G}{\hbar C} \) in \( (GeV/c^{2})^{-2} \) More...
constexpr Double_t	TMath::GhbarCUncertainty ()
	\( \frac{G}{\hbar C} \) uncertainty. More...
constexpr Double_t	TMath::Gn ()
	Standard acceleration of gravity in \( m s^{-2} \). More...
constexpr Double_t	TMath::GnUncertainty ()
	Standard acceleration of gravity uncertainty. More...
constexpr Double_t	TMath::GUncertainty ()
	Gravitational constant uncertainty. More...
constexpr Double_t	TMath::H ()
	Planck's constant in \( J s \). More...
ULong_t	TMath::Hash (const char *str)
ULong_t	TMath::Hash (const void *txt, Int_t ntxt)
	Calculates hash index from any char string. More...
constexpr Double_t	TMath::Hbar ()
	\( \hbar \) in \( J s \) More...
constexpr Double_t	TMath::Hbarcgs ()
	\( erg s \) More...
constexpr Double_t	TMath::HbarUncertainty ()
	\( \hbar \) uncertainty. More...
constexpr Double_t	TMath::HC ()
	\( hc \) in \( J m \) More...
constexpr Double_t	TMath::HCcgs ()
	\( erg cm \) More...
constexpr Double_t	TMath::Hcgs ()
	\( erg s \) More...
constexpr Double_t	TMath::HUncertainty ()
	Planck's constant uncertainty. More...
Double_t	TMath::Hypot (Double_t x, Double_t y)
Long_t	TMath::Hypot (Long_t x, Long_t y)
Double_t	TMath::Infinity ()
	Returns an infinity as defined by the IEEE standard. More...
constexpr Double_t	TMath::InvPi ()
	\( \frac{1.}{\pi}\) More...
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. More...
int	isnan (double)
Bool_t	TMath::IsNaN (Double_t x)
Bool_t	TMath::IsNaN (Float_t x)
constexpr Double_t	TMath::K ()
	Boltzmann's constant in \( J K^{-1} \). More...
constexpr Double_t	TMath::Kcgs ()
	\( erg K^{-1} \) More...
Double_t	TMath::KolmogorovProb (Double_t z)
	Calculates the Kolmogorov distribution function,. More...
Double_t	TMath::KolmogorovTest (Int_t na, const Double_t *a, Int_t nb, const Double_t *b, Option_t *option)
	Statistical test whether two one-dimensional sets of points are compatible with coming from the same parent distribution, using the Kolmogorov test. More...
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). More...
constexpr Double_t	TMath::KUncertainty ()
	Boltzmann's constant uncertainty. More...
Double_t	TMath::Landau (Double_t x, Double_t mpv=0, Double_t sigma=1, Bool_t norm=kFALSE)
	The LANDAU function. More...
Double_t	TMath::LandauI (Double_t x)
	Returns the value of the Landau distribution function at point x. More...
Double_t	TMath::LaplaceDist (Double_t x, Double_t alpha=0, Double_t beta=1)
	Computes the probability density function of Laplace distribution at point x, with location parameter alpha and shape parameter beta. More...
Double_t	TMath::LaplaceDistI (Double_t x, Double_t alpha=0, Double_t beta=1)
	Computes the distribution function of Laplace distribution at point x, with location parameter alpha and shape parameter beta. More...
double	ldexp (double, int)
Double_t	TMath::Ldexp (Double_t x, Int_t exp)
constexpr Double_t	TMath::Ln10 ()
	Natural log of 10 (to convert log to ln) More...
Double_t	TMath::LnGamma (Double_t z)
	Computation of ln[gamma(z)] for all z. More...
template<typename Iterator >
Iterator	TMath::LocMax (Iterator first, Iterator last)
	Return index of array with the maximum element. More...
template<typename T >
Long64_t	TMath::LocMax (Long64_t n, const T *a)
	Return index of array with the maximum element. More...
template<typename Iterator >
Iterator	TMath::LocMin (Iterator first, Iterator last)
	Return index of array with the minimum element. More...
template<typename T >
Long64_t	TMath::LocMin (Long64_t n, const T *a)
	Return index of array with the minimum element. More...
double	log (double)
Double_t	TMath::Log (Double_t x)
double	log10 (double)
Double_t	TMath::Log10 (Double_t x)
Double_t	TMath::Log2 (Double_t x)
constexpr Double_t	TMath::LogE ()
	Base-10 log of e (to convert ln to log) More...
Double_t	TMath::LogNormal (Double_t x, Double_t sigma, Double_t theta=0, Double_t m=1)
	Computes the density of LogNormal distribution at point x. More...
template<typename T >
T	TMath::MaxElement (Long64_t n, const T *a)
	Return maximum of array a of length n. More...
template<typename Iterator >
Double_t	TMath::Mean (Iterator first, Iterator last)
	Return the weighted mean of an array defined by the iterators. More...
template<typename Iterator , typename WeightIterator >
Double_t	TMath::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	TMath::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 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] . More...
template<typename T >
T	TMath::MinElement (Long64_t n, const T *a)
	Return minimum of array a of length n. More...
constexpr Double_t	TMath::MWair ()
	Molecular weight of dry air 1976 US Standard Atmosphere in \( kg kmol^{-1} \) or \( gm mol^{-1} \) More...
constexpr Double_t	TMath::Na ()
	Avogadro constant (Avogadro's Number) in \( mol^{-1} \). More...
constexpr Double_t	TMath::NaUncertainty ()
	Avogadro constant (Avogadro's Number) uncertainty. More...
template<typename T >
Int_t	TMath::Nint (T x)
	Round to nearest integer. Rounds half integers to the nearest even integer. More...
template<typename T >
T *	TMath::Normal2Plane (const T v1[3], const T v2[3], const T v3[3], T normal[3])
	Calculate a normal vector of a plane. More...
Double_t	TMath::Normalize (Double_t v[3])
	Normalize a vector v in place. More...
Float_t	TMath::Normalize (Float_t v[3])
	Normalize a vector v in place. More...
template<typename T >
T	TMath::NormCross (const T v1[3], const T v2[3], T out[3])
	Calculate the Normalized Cross Product of two vectors. More...
Double_t	TMath::NormQuantile (Double_t p)
	Computes quantiles for standard normal distribution N(0, 1) at probability p. More...
Bool_t	TMath::Permute (Int_t n, Int_t *a)
	Simple recursive algorithm to find the permutations of n natural numbers, not necessarily all distinct adapted from CERNLIB routine PERMU. More...
constexpr Double_t	TMath::Pi ()
constexpr Double_t	TMath::PiOver2 ()
constexpr Double_t	TMath::PiOver4 ()
Double_t	TMath::Poisson (Double_t x, Double_t par)
	Compute the Poisson distribution function for (x,par) The Poisson PDF is implemented by means of Euler's Gamma-function (for the factorial), so for any x integer argument it is correct. More...
Double_t	TMath::PoissonI (Double_t x, Double_t par)
	Compute the Poisson distribution function for (x,par) This is a non-smooth function. More...
double	pow (double, double)
Double_t	TMath::Power (Double_t x, Double_t y)
Double_t	TMath::Power (Double_t x, Int_t y)
LongDouble_t	TMath::Power (Long64_t x, Long64_t y)
LongDouble_t	TMath::Power (LongDouble_t x, Long64_t y)
LongDouble_t	TMath::Power (LongDouble_t x, LongDouble_t y)
Double_t	TMath::Prob (Double_t chi2, Int_t ndf)
	Computation of the probability for a certain Chi-squared (chi2) and number of degrees of freedom (ndf). More...
constexpr Double_t	TMath::Qe ()
	Elementary charge in \( C \) . More...
constexpr Double_t	TMath::QeUncertainty ()
	Elementary charge uncertainty. More...
void	TMath::Quantiles (Int_t n, Int_t nprob, Double_t *x, Double_t *quantiles, Double_t *prob, Bool_t isSorted=kTRUE, Int_t *index=0, Int_t type=7)
	Computes sample quantiles, corresponding to the given probabilities. More...
Double_t	TMath::QuietNaN ()
	Returns a quiet NaN as defined by IEEE 754 More...
constexpr Double_t	TMath::R ()
	Universal gas constant ( \( Na K \)) in \( J K^{-1} mol^{-1} \) More...
constexpr Double_t	TMath::RadToDeg ()
	Conversion from radian to degree: More...
constexpr Double_t	TMath::Rgair ()
	Dry Air Gas Constant (R / MWair) in \( J kg^{-1} K^{-1} \) More...
template<typename Iterator >
Double_t	TMath::RMS (Iterator first, Iterator last)
	Return the Standard Deviation of an array defined by the iterators. More...
template<typename Iterator , typename WeightIterator >
Double_t	TMath::RMS (Iterator first, Iterator last, WeightIterator wfirst)
	Return the weighted Standard Deviation of an array defined by the iterators. More...
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. More...
Bool_t	TMath::RootsCubic (const Double_t coef[4], Double_t &a, Double_t &b, Double_t &c)
	Calculates roots of polynomial of 3rd order a*x^3 + b*x^2 + c*x + d, where. More...
constexpr Double_t	TMath::RUncertainty ()
	Universal gas constant uncertainty. More...
constexpr Double_t	TMath::Sigma ()
	Stefan-Boltzmann constant in \( W m^{-2} K^{-4}\). More...
constexpr Double_t	TMath::SigmaUncertainty ()
	Stefan-Boltzmann constant uncertainty. More...
Double_t	TMath::SignalingNaN ()
	Returns a signaling NaN as defined by IEEE 754](http://en.wikipedia.org/wiki/NaN#Signaling_NaN) More...
double	sin (double)
Double_t	TMath::Sin (Double_t)
double	sinh (double)
Double_t	TMath::SinH (Double_t)
Double_t	TMath::Sq (Double_t x)
double	sqrt (double)
Double_t	TMath::Sqrt (Double_t x)
constexpr Double_t	TMath::Sqrt2 ()
template<typename Iterator >
Double_t	TMath::StdDev (Iterator first, Iterator last)
template<typename Iterator , typename WeightIterator >
Double_t	TMath::StdDev (Iterator first, Iterator last, WeightIterator wfirst)
template<typename T >
Double_t	TMath::StdDev (Long64_t n, const T *a, const Double_t *w=0)
Double_t	TMath::StruveH0 (Double_t x)
	Bessel function Y1(x) for positive x. More...
Double_t	TMath::StruveH1 (Double_t x)
	Struve functions of order 0. More...
Double_t	TMath::StruveL0 (Double_t x)
	Struve functions of order 1. More...
Double_t	TMath::StruveL1 (Double_t x)
	Modified Struve functions of order 0. More...
Double_t	TMath::Student (Double_t T, Double_t ndf)
	Computes density function for Student's t- distribution (the probability function (integral of density) is computed in StudentI). More...
Double_t	TMath::StudentI (Double_t T, Double_t ndf)
	Calculates the cumulative distribution function of Student's t-distribution second parameter stands for number of degrees of freedom, not for the number of samples if x has Student's t-distribution, the function returns the probability of x being less than T. More...
Double_t	TMath::StudentQuantile (Double_t p, Double_t ndf, Bool_t lower_tail=kTRUE)
	Computes quantiles of the Student's t-distribution 1st argument is the probability, at which the quantile is computed 2nd argument - the number of degrees of freedom of the Student distribution When the 3rd argument lower_tail is kTRUE (default)- the algorithm returns such x0, that. More...
double	tan (double)
Double_t	TMath::Tan (Double_t)
double	tanh (double)
Double_t	TMath::TanH (Double_t)
constexpr Double_t	TMath::TwoPi ()
Double_t	TMath::Vavilov (Double_t x, Double_t kappa, Double_t beta2)
	Returns the value of the Vavilov density function. More...
Double_t	TMath::VavilovI (Double_t x, Double_t kappa, Double_t beta2)
	Returns the value of the Vavilov distribution function. More...
Double_t	TMath::Voigt (Double_t x, Double_t sigma, Double_t lg, Int_t r=4)
	Computation of Voigt function (normalised). More...

Function Documentation

acos()

double acos

(

double

)

asin()

double asin

(

double

)

atan()

double atan

(

double

)

atan2()

double atan2	(	double	,
		double
	)

ceil()

double ceil

(

double

)

cos()

double cos

(

double

)

cosh()

double cosh

(

double

)

exp()

double exp

(

double

)

finite()

int finite

(

double

)

floor()

double floor

(

double

)

isnan()

int isnan

(

double

)

ldexp()

double ldexp	(	double	,
		int
	)

log()

double log

(

double

)

log10()

double log10

(

double

)

pow()

double pow	(	double	,
		double
	)

sin()

double sin

(

double

)

sinh()

double sinh

(

double

)

sqrt()

double sqrt

(

double

)

tan()

double tan

(

double

)

tanh()

double tanh

(

double

)