|
| Double_t | TMath::ACos (Double_t) |
| |
| double | acos (double) |
| |
| 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_t | TMath::ASin (Double_t) |
| |
| double | asin (double) |
| |
| Double_t | TMath::ASinH (Double_t) |
| |
| Double_t | TMath::ATan (Double_t) |
| |
| double | atan (double) |
| |
| Double_t | TMath::ATan2 (Double_t, Double_t) |
| |
| double | atan2 (double, double) |
| |
| 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,... More...
|
| |
| Double_t | TMath::BesselI0 (Double_t x) |
| | Compute the modified Bessel function I_0(x) for any real x. More...
|
| |
| Double_t | TMath::BesselI1 (Double_t x) |
| | Compute the modified Bessel function I_1(x) for any real x. More...
|
| |
| Double_t | TMath::BesselJ0 (Double_t x) |
| | Returns the Bessel function J0(x) for any real x. More...
|
| |
| Double_t | TMath::BesselJ1 (Double_t x) |
| | Returns the Bessel function J1(x) for any real x. More...
|
| |
| Double_t | TMath::BesselK (Int_t n, Double_t x) |
| | Compute the Integer Order Modified Bessel function K_n(x) for n=0,1,2,... More...
|
| |
| Double_t | TMath::BesselK0 (Double_t x) |
| | Compute the modified Bessel function K_0(x) for positive real x. More...
|
| |
| Double_t | TMath::BesselK1 (Double_t x) |
| | Compute the modified Bessel function K_1(x) for positive real x. More...
|
| |
| Double_t | TMath::BesselY0 (Double_t x) |
| | Returns the Bessel function Y0(x) for positive x. More...
|
| |
| Double_t | TMath::BesselY1 (Double_t x) |
| | Returns the Bessel function Y1(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...
|
| |
| template<typename T > |
| Long64_t | TMath::BinarySearch (Long64_t n, const T *array, T value) |
| |
| template<typename T > |
| Long64_t | TMath::BinarySearch (Long64_t n, const T **array, T value) |
| |
| template<typename Iterator , typename Element > |
| Iterator | TMath::BinarySearch (Iterator first, Iterator last, Element value) |
| |
| 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...
|
| |
| Double_t | TMath::C () |
| |
| Double_t | TMath::CauchyDist (Double_t x, Double_t t=0, Double_t s=1) |
| | Computes the density of Cauchy distribution at point x by default, standard Cauchy distribution is used (t=0, s=1) t is the location parameter s is the scale parameter The Cauchy distribution, also called Lorentzian distribution, is a continuous distribution describing resonance behavior The mean and standard deviation of the Cauchy distribution are undefined. More...
|
| |
| Double_t | TMath::Ccgs () |
| |
| Double_t | TMath::Ceil (Double_t x) |
| |
| double | ceil (double) |
| |
| 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_t | TMath::Cos (Double_t) |
| |
| double | cos (double) |
| |
| Double_t | TMath::CosH (Double_t) |
| |
| double | cosh (double) |
| |
| template<typename T > |
| T * | TMath::Cross (const T v1[3], const T v2[3], T out[3]) |
| |
| Double_t | TMath::CUncertainty () |
| |
| Double_t | TMath::DegToRad () |
| |
| Double_t | TMath::DiLog (Double_t x) |
| | The DiLogarithm function Code translated by R.Brun from CERNLIB DILOG function C332. More...
|
| |
| Double_t | TMath::E () |
| |
| 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) |
| |
| Double_t | TMath::ErfInverse (Double_t x) |
| | returns the inverse error function x must be <-1<x<1 More...
|
| |
| Double_t | TMath::EulerGamma () |
| |
| Double_t | TMath::Exp (Double_t x) |
| |
| double | exp (double) |
| |
| 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_t | TMath::Finite (Double_t x) |
| |
| int | finite (double) |
| |
| Double_t | TMath::Floor (Double_t x) |
| |
| double | floor (double) |
| |
| Int_t | TMath::FloorNint (Double_t x) |
| |
| Double_t | TMath::Freq (Double_t x) |
| | Computation of the normal frequency function freq(x). More...
|
| |
| Double_t | TMath::G () |
| |
| Double_t | TMath::Gamma (Double_t z) |
| | Computation of gamma(z) for all z. 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::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...
|
| |
| Double_t | TMath::Gcgs () |
| |
| template<typename T > |
| Double_t | TMath::GeomMean (Long64_t n, const T *a) |
| |
| template<typename Iterator > |
| Double_t | TMath::GeomMean (Iterator first, Iterator last) |
| |
| Double_t | TMath::GhbarC () |
| |
| Double_t | TMath::GhbarCUncertainty () |
| |
| Double_t | TMath::Gn () |
| |
| Double_t | TMath::GnUncertainty () |
| |
| Double_t | TMath::GUncertainty () |
| |
| Double_t | TMath::H () |
| |
| ULong_t | TMath::Hash (const void *txt, Int_t ntxt) |
| | Calculates hash index from any char string. More...
|
| |
| ULong_t | TMath::Hash (const char *str) |
| | Return a case-sensitive hash value (endian independent). More...
|
| |
| Double_t | TMath::Hbar () |
| |
| Double_t | TMath::Hbarcgs () |
| |
| Double_t | TMath::HbarUncertainty () |
| |
| Double_t | TMath::HC () |
| |
| Double_t | TMath::HCcgs () |
| |
| Double_t | TMath::Hcgs () |
| |
| Double_t | TMath::HUncertainty () |
| |
| Double_t | TMath::Hypot (Double_t x, Double_t y) |
| |
| Long_t | TMath::Hypot (Long_t x, Long_t y) |
| |
| Double_t | TMath::Infinity () |
| |
| Double_t | TMath::InvPi () |
| |
| template<typename T > |
| Bool_t | TMath::IsInside (T xp, T yp, Int_t np, T *x, T *y) |
| |
| Int_t | TMath::IsNaN (Double_t x) |
| |
| int | isnan (double) |
| |
| Double_t | TMath::K () |
| |
| Double_t | TMath::Kcgs () |
| |
| 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) |
| |
| Double_t | TMath::KUncertainty () |
| |
| 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_t | TMath::Ldexp (Double_t x, Int_t exp) |
| |
| double | ldexp (double, int) |
| |
| Double_t | TMath::Ln10 () |
| |
| Double_t | TMath::LnGamma (Double_t z) |
| | Computation of ln[gamma(z)] for all z. More...
|
| |
| template<typename T > |
| Long64_t | TMath::LocMax (Long64_t n, const T *a) |
| |
| template<typename Iterator > |
| Iterator | TMath::LocMax (Iterator first, Iterator last) |
| |
| template<typename T > |
| Long64_t | TMath::LocMin (Long64_t n, const T *a) |
| |
| template<typename Iterator > |
| Iterator | TMath::LocMin (Iterator first, Iterator last) |
| |
| Double_t | TMath::Log (Double_t x) |
| |
| double | log (double) |
| |
| Double_t | TMath::Log10 (Double_t x) |
| |
| double | log10 (double) |
| |
| Double_t | TMath::Log2 (Double_t x) |
| |
| Double_t | TMath::LogE () |
| |
| 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) |
| |
| template<typename T > |
| Double_t | TMath::Mean (Long64_t n, const T *a, const Double_t *w=0) |
| |
| template<typename Iterator > |
| Double_t | TMath::Mean (Iterator first, Iterator last) |
| |
| template<typename Iterator , typename WeightIterator > |
| Double_t | TMath::Mean (Iterator first, Iterator last, WeightIterator wfirst) |
| |
| template<typename T > |
| Double_t | TMath::Median (Long64_t n, const T *a, const Double_t *w=0, Long64_t *work=0) |
| |
| template<typename T > |
| T | TMath::MinElement (Long64_t n, const T *a) |
| |
| Double_t | TMath::MWair () |
| |
| Double_t | TMath::Na () |
| |
| Double_t | TMath::NaUncertainty () |
| |
| template<typename T > |
| Int_t | TMath::Nint (T x) |
| |
| template<typename T > |
| T * | TMath::Normal2Plane (const T v1[3], const T v2[3], const T v3[3], T normal[3]) |
| |
| Float_t | TMath::Normalize (Float_t v[3]) |
| | Normalize a vector v in place. More...
|
| |
| Double_t | TMath::Normalize (Double_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]) |
| |
| Double_t | TMath::NormQuantile (Double_t p) |
| | Computes quantiles for standard normal distribution N(0, 1) at probability p ALGORITHM AS241 APPL. 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...
|
| |
| Double_t | TMath::Pi () |
| |
| Double_t | TMath::PiOver2 () |
| |
| 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) |
| |
| LongDouble_t | TMath::Power (LongDouble_t x, LongDouble_t y) |
| |
| LongDouble_t | TMath::Power (LongDouble_t x, Long64_t y) |
| |
| LongDouble_t | TMath::Power (Long64_t x, Long64_t y) |
| |
| Double_t | TMath::Power (Double_t x, Double_t y) |
| |
| Double_t | TMath::Power (Double_t x, Int_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...
|
| |
| Double_t | TMath::Qe () |
| |
| Double_t | TMath::QeUncertainty () |
| |
| void | TMath::Quantiles (Int_t n, Int_t nprob, Double_t *x, Double_t *quantiles, Double_t *prob, Bool_t isSorted=kTRUE, Int_t *index=0, Int_t type=7) |
| | Computes sample quantiles, corresponding to the given probabilities Parameters: x -the data sample n - its size quantiles - computed quantiles are returned in there prob - probabilities where to compute quantiles nprob - size of prob array isSorted - is the input array x sorted? NOTE, that when the input is not sorted, an array of integers of size n needs to be allocated. More...
|
| |
| Double_t | TMath::QuietNaN () |
| |
| Double_t | TMath::R () |
| |
| Double_t | TMath::RadToDeg () |
| |
| Double_t | TMath::Rgair () |
| |
| template<typename T > |
| Double_t | TMath::RMS (Long64_t n, const T *a, const Double_t *w=0) |
| |
| template<typename Iterator > |
| Double_t | TMath::RMS (Iterator first, Iterator last) |
| |
| template<typename Iterator , typename WeightIterator > |
| Double_t | TMath::RMS (Iterator first, Iterator last, WeightIterator wfirst) |
| |
| Bool_t | TMath::RootsCubic (const Double_t coef[4], Double_t &a, Double_t &b, Double_t &c) |
| | Calculates roots of polynomial of 3rd order a*x^3 + b*x^2 + c*x + d, where a == coef[3], b == coef[2], c == coef[1], d == coef[0] coef[3] must be different from 0 If the boolean returned by the method is false: ==> there are 3 real roots a,b,c If the boolean returned by the method is true: ==> there is one real root a and 2 complex conjugates roots (b+i*c,b-i*c) Author: Francois-Xavier Gentit. More...
|
| |
| Double_t | TMath::RUncertainty () |
| |
| Double_t | TMath::Sigma () |
| |
| Double_t | TMath::SigmaUncertainty () |
| |
| Double_t | TMath::SignalingNaN () |
| |
| Double_t | TMath::Sin (Double_t) |
| |
| double | sin (double) |
| |
| Double_t | TMath::SinH (Double_t) |
| |
| double | sinh (double) |
| |
| template<typename Element , typename Index > |
| void | TMath::Sort (Index n, const Element *a, Index *index, Bool_t down=kTRUE) |
| |
| template<typename Iterator , typename IndexIterator > |
| void | TMath::SortItr (Iterator first, Iterator last, IndexIterator index, Bool_t down=kTRUE) |
| |
| Double_t | TMath::Sq (Double_t x) |
| |
| Double_t | TMath::Sqrt (Double_t x) |
| |
| double | sqrt (double) |
| |
| Double_t | TMath::Sqrt2 () |
| |
| template<typename T > |
| Double_t | TMath::StdDev (Long64_t n, const T *a, const Double_t *w=0) |
| |
| 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) |
| |
| Double_t | TMath::StruveH0 (Double_t x) |
| | Struve Functions of Order 0. More...
|
| |
| Double_t | TMath::StruveH1 (Double_t x) |
| | Struve Functions of Order 1. More...
|
| |
| Double_t | TMath::StruveL0 (Double_t x) |
| | Modified Struve Function of Order 0. More...
|
| |
| Double_t | TMath::StruveL1 (Double_t x) |
| | Modified Struve Function of Order 1. 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 P(x < x0)=p upper tail (lower_tail is kFALSE)- the algorithm returns such x0, that P(x > x0)=p the algorithm was taken from G.W.Hill, "Algorithm 396, Student's t-quantiles" "Communications of the ACM", 13(10), October 1970. More...
|
| |
| Double_t | TMath::Tan (Double_t) |
| |
| double | tan (double) |
| |
| Double_t | TMath::TanH (Double_t) |
| |
| double | tanh (double) |
| |
| 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 Parameters: 1st - the point were the density function is evaluated 2nd - value of kappa (distribution parameter) 3rd - value of beta2 (distribution parameter) The algorithm was taken from the CernLib function vavden(G115) Reference: A.Rotondi and P.Montagna, Fast Calculation of Vavilov distribution Nucl.Instr. More...
|
| |
| Double_t | TMath::VavilovI (Double_t x, Double_t kappa, Double_t beta2) |
| | Returns the value of the Vavilov distribution function Parameters: 1st - the point were the density function is evaluated 2nd - value of kappa (distribution parameter) 3rd - value of beta2 (distribution parameter) The algorithm was taken from the CernLib function vavden(G115) Reference: A.Rotondi and P.Montagna, Fast Calculation of Vavilov distribution Nucl.Instr. More...
|
| |
| Double_t | TMath::Voigt (Double_t x, Double_t sigma, Double_t lg, Int_t r=4) |
| | Computation of Voigt function (normalised). More...
|
| |
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