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Double_t | TMath::ACos (Double_t) |
| Returns the principal value of the arc cosine of x , expressed in radians.
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Double_t | TMath::ACosH (Double_t) |
| Returns the nonnegative area hyperbolic cosine of x .
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Bool_t | TMath::AreEqualAbs (Double_t af, Double_t bf, Double_t epsilon) |
| Comparing floating points.
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Bool_t | TMath::AreEqualRel (Double_t af, Double_t bf, Double_t relPrec) |
| Comparing floating points.
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Double_t | TMath::ASin (Double_t) |
| Returns the principal value of the arc sine of x , expressed in radians.
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Double_t | TMath::ASinH (Double_t) |
| Returns the area hyperbolic sine of x .
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Double_t | TMath::ATan (Double_t) |
| Returns the principal value of the arc tangent of x , expressed in radians.
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Double_t | TMath::ATan2 (Double_t y, Double_t x) |
| Returns the principal value of the arc tangent of y/x , expressed in radians.
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Double_t | TMath::ATanH (Double_t) |
| Returns the area hyperbolic tangent of x .
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Double_t | TMath::BesselI (Int_t n, Double_t x) |
| Computes the Integer Order Modified Bessel function I_n(x) for n=0,1,2,... and any real x.
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Double_t | TMath::BesselI0 (Double_t x) |
| Integer order modified Bessel function K_n(x)
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Double_t | TMath::BesselI1 (Double_t x) |
| Modified Bessel function K_0(x)
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Double_t | TMath::BesselJ0 (Double_t x) |
| Modified Bessel function K_1(x)
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Double_t | TMath::BesselJ1 (Double_t x) |
| Bessel function J0(x) for any real x.
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Double_t | TMath::BesselK (Int_t n, Double_t x) |
| Integer order modified Bessel function I_n(x)
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Double_t | TMath::BesselK0 (Double_t x) |
| Modified Bessel function I_0(x)
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Double_t | TMath::BesselK1 (Double_t x) |
| Modified Bessel function I_1(x)
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Double_t | TMath::BesselY0 (Double_t x) |
| Bessel function J1(x) for any real x.
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Double_t | TMath::BesselY1 (Double_t x) |
| Bessel function Y0(x) for positive x.
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Double_t | TMath::Beta (Double_t p, Double_t q) |
| Calculates Beta-function Gamma(p)*Gamma(q)/Gamma(p+q).
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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.
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Double_t | TMath::BetaDist (Double_t x, Double_t p, Double_t q) |
| Computes the probability density function of the Beta distribution (the cumulative distribution function is computed in BetaDistI).
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Double_t | TMath::BetaDistI (Double_t x, Double_t p, Double_t q) |
| Computes the cumulative distribution function of the Beta distribution, i.e.
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Double_t | TMath::BetaIncomplete (Double_t x, Double_t a, Double_t b) |
| Calculates the incomplete Beta-function.
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Double_t | TMath::Binomial (Int_t n, Int_t k) |
| Calculates the binomial coefficient n over k.
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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:
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Double_t | TMath::BreitWigner (Double_t x, Double_t mean=0, Double_t gamma=1) |
| Calculates a Breit Wigner function with mean and gamma.
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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.
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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.
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void | TMath::BubbleLow (Int_t Narr, Double_t *arr1, Int_t *arr2) |
| Opposite ordering of the array arr2[] to that of BubbleHigh.
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constexpr Double_t | TMath::C () |
| Velocity of light in \( m s^{-1} \).
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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)
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constexpr Double_t | TMath::Ccgs () |
| \( cm s^{-1} \)
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Double_t | TMath::Ceil (Double_t x) |
| Rounds x upward, returning the smallest integral value that is not less than x .
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Int_t | TMath::CeilNint (Double_t x) |
| Returns the nearest integer of TMath::Ceil(x) .
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Double_t | TMath::ChisquareQuantile (Double_t p, Double_t ndf) |
| Evaluate the quantiles of the chi-squared probability distribution function.
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Double_t | TMath::Cos (Double_t) |
| Returns the cosine of an angle of x radians.
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Double_t | TMath::CosH (Double_t) |
| Returns the hyperbolic cosine of x .
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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].
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constexpr Double_t | TMath::CUncertainty () |
| Speed of light uncertainty.
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constexpr Double_t | TMath::DegToRad () |
| Conversion from degree to radian: \( \frac{\pi}{180} \).
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Double_t | TMath::DiLog (Double_t x) |
| Modified Struve functions of order 1.
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constexpr Double_t | TMath::E () |
| Base of natural log: \( e \).
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Double_t | TMath::Erf (Double_t x) |
| Computation of the error function erf(x).
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Double_t | TMath::Erfc (Double_t x) |
| Computes the complementary error function erfc(x).
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Double_t | TMath::ErfcInverse (Double_t x) |
| Returns the inverse of the complementary error function.
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Double_t | TMath::ErfInverse (Double_t x) |
| Returns the inverse error function.
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constexpr Double_t | TMath::EulerGamma () |
| Euler-Mascheroni Constant.
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Double_t | TMath::Exp (Double_t x) |
| Returns the base-e exponential function of x, which is e raised to the power x .
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Double_t | TMath::Factorial (Int_t i) |
| Computes factorial(n).
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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).
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Double_t | TMath::FDistI (Double_t F, Double_t N, Double_t M) |
| Calculates the cumulative distribution function of F-distribution (see ROOT::Math::fdistribution_cdf).
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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.
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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.
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Double_t | TMath::Floor (Double_t x) |
| Rounds x downward, returning the largest integral value that is not greater than x .
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Int_t | TMath::FloorNint (Double_t x) |
| Returns the nearest integer of TMath::Floor(x) .
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Double_t | TMath::Freq (Double_t x) |
| Computation of the normal frequency function freq(x).
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constexpr Double_t | TMath::G () |
| Gravitational constant in: \( m^{3} kg^{-1} s^{-2} \).
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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 .
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Double_t | TMath::Gamma (Double_t z) |
| Computation of gamma(z) for all z.
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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.
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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.
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constexpr Double_t | TMath::Gcgs () |
| \( cm^{3} g^{-1} s^{-2} \)
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template<typename Iterator > |
Double_t | TMath::GeomMean (Iterator first, Iterator last) |
| Returns the geometric mean of an array defined by the iterators.
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template<typename T > |
Double_t | TMath::GeomMean (Long64_t n, const T *a) |
| Returns the geometric mean of an array a of size n.
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constexpr Double_t | TMath::GhbarC () |
| \( \frac{G}{\hbar C} \) in \( (GeV/c^{2})^{-2} \)
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constexpr Double_t | TMath::GhbarCUncertainty () |
| \( \frac{G}{\hbar C} \) uncertainty.
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constexpr Double_t | TMath::Gn () |
| Standard acceleration of gravity in \( m s^{-2} \).
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constexpr Double_t | TMath::GnUncertainty () |
| Standard acceleration of gravity uncertainty.
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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.
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constexpr Double_t | TMath::GUncertainty () |
| Gravitational constant uncertainty.
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constexpr Double_t | TMath::H () |
| Planck's constant in \( J s \): \( h \).
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ULong_t | TMath::Hash (const char *str) |
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ULong_t | TMath::Hash (const void *txt, Int_t ntxt) |
| Calculates hash index from any char string.
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constexpr Double_t | TMath::Hbar () |
| \( \hbar \) in \( J s \): \( \hbar = \frac{h}{2\pi} \)
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constexpr Double_t | TMath::Hbarcgs () |
| \( erg s \)
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constexpr Double_t | TMath::HbarUncertainty () |
| \( \hbar \) uncertainty.
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constexpr Double_t | TMath::HC () |
| \( hc \) in \( J m \)
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constexpr Double_t | TMath::HCcgs () |
| \( erg cm \)
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constexpr Double_t | TMath::Hcgs () |
| \( erg s \)
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constexpr Double_t | TMath::HUncertainty () |
| Planck's constant uncertainty.
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Double_t | TMath::Hypot (Double_t x, Double_t y) |
| Returns sqrt(x*x + y*y)
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Long_t | TMath::Hypot (Long_t x, Long_t y) |
| Returns sqrt(x*x + y*y)
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Double_t | TMath::Infinity () |
| Returns an infinity as defined by the IEEE standard.
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constexpr Double_t | TMath::InvPi () |
| \( \frac{1.}{\pi}\)
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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.
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Bool_t | TMath::IsNaN (Double_t x) |
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Bool_t | TMath::IsNaN (Float_t x) |
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constexpr Double_t | TMath::K () |
| Boltzmann's constant in \( J K^{-1} \): \( k \).
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constexpr Double_t | TMath::Kcgs () |
| \( erg K^{-1} \)
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Double_t | TMath::KolmogorovProb (Double_t z) |
| Calculates the Kolmogorov distribution function,.
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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.
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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).
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constexpr Double_t | TMath::KUncertainty () |
| Boltzmann's constant uncertainty.
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Double_t | TMath::Landau (Double_t x, Double_t mpv=0, Double_t sigma=1, Bool_t norm=kFALSE) |
| The LANDAU function.
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Double_t | TMath::LandauI (Double_t x) |
| Returns the cumulative (lower tail integral) of the Landau distribution function at point x.
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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.
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Double_t | TMath::LaplaceDistI (Double_t x, Double_t alpha=0, Double_t beta=1) |
| Computes the cumulative distribution function (lower tail integral) of Laplace distribution at point x, with location parameter alpha and shape parameter beta.
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template<typename T > |
T * | TMath::Laplacian (Long64_t n, T *f, double h=1) |
| Calculate the Laplacian of an array with length n.
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Double_t | TMath::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).
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constexpr Double_t | TMath::Ln10 () |
| Natural log of 10 (to convert log to ln)
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Double_t | TMath::LnGamma (Double_t z) |
| Computation of ln[gamma(z)] for all z.
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template<typename Iterator > |
Iterator | TMath::LocMax (Iterator first, Iterator last) |
| Returns index of array with the maximum element.
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template<typename T > |
Long64_t | TMath::LocMax (Long64_t n, const T *a) |
| Returns index of array with the maximum element.
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template<typename Iterator > |
Iterator | TMath::LocMin (Iterator first, Iterator last) |
| Returns index of array with the minimum element.
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template<typename T > |
Long64_t | TMath::LocMin (Long64_t n, const T *a) |
| Returns index of array with the minimum element.
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Double_t | TMath::Log (Double_t x) |
| Returns the natural logarithm of x .
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Double_t | TMath::Log10 (Double_t x) |
| Returns the common (base-10) logarithm of x .
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Double_t | TMath::Log2 (Double_t x) |
| Returns the binary (base-2) logarithm of x .
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constexpr Double_t | TMath::LogE () |
| Base-10 log of e (to convert ln to log)
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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.
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template<typename T > |
T | TMath::MaxElement (Long64_t n, const T *a) |
| Returns maximum of array a of length n.
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template<typename Iterator > |
Double_t | TMath::Mean (Iterator first, Iterator last) |
| Returns the weighted mean of an array defined by the iterators.
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template<typename Iterator , typename WeightIterator > |
Double_t | TMath::Mean (Iterator first, Iterator last, WeightIterator wfirst) |
| Returns the weighted mean of an array defined by the first and last iterators.
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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.
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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.
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template<typename T > |
T | TMath::MinElement (Long64_t n, const T *a) |
| Returns minimum of array a of length n.
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constexpr Double_t | TMath::MWair () |
| Molecular weight of dry air 1976 US Standard Atmosphere in \( kg kmol^{-1} \) or \( gm mol^{-1} \)
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constexpr Double_t | TMath::Na () |
| Avogadro constant (Avogadro's Number) in \( mol^{-1} \).
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constexpr Double_t | TMath::NaUncertainty () |
| Avogadro constant (Avogadro's Number) uncertainty.
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template<typename T > |
Int_t | TMath::Nint (T x) |
| Round to nearest integer. Rounds half integers to the nearest even integer.
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template<typename T > |
T * | TMath::Normal2Plane (const T v1[3], const T v2[3], const T v3[3], T normal[3]) |
| Calculates a normal vector of a plane.
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Double_t | TMath::Normalize (Double_t v[3]) |
| Normalize a vector v in place.
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Float_t | TMath::Normalize (Float_t v[3]) |
| Normalize a vector v in place.
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template<typename T > |
T | TMath::NormCross (const T v1[3], const T v2[3], T out[3]) |
| Calculates the Normalized Cross Product of two vectors.
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Double_t | TMath::NormQuantile (Double_t p) |
| Computes quantiles for standard normal distribution N(0, 1) at probability p.
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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.
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constexpr Double_t | TMath::Pi () |
| \( \pi\)
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constexpr Double_t | TMath::PiOver2 () |
| \( \frac{\pi}{2} \)
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constexpr Double_t | TMath::PiOver4 () |
| \( \frac{\pi}{4} \)
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Double_t | TMath::Poisson (Double_t x, Double_t par) |
| Computes the Poisson distribution function for (x,par).
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Double_t | TMath::PoissonI (Double_t x, Double_t par) |
| Computes the Discrete Poisson distribution function for (x,par).
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Double_t | TMath::Power (Double_t x, Double_t y) |
| Returns x raised to the power y .
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Double_t | TMath::Power (Double_t x, Int_t y) |
| Returns x raised to the power y .
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LongDouble_t | TMath::Power (Long64_t x, Long64_t y) |
| Returns x raised to the power y .
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LongDouble_t | TMath::Power (LongDouble_t x, Long64_t y) |
| Returns x raised to the power y .
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LongDouble_t | TMath::Power (LongDouble_t x, LongDouble_t y) |
| Returns x raised to the power y .
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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).
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constexpr Double_t | TMath::Qe () |
| Elementary charge in \( C \) .
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constexpr Double_t | TMath::QeUncertainty () |
| Elementary charge uncertainty.
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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=nullptr, Int_t type=7) |
| Computes sample quantiles, corresponding to the given probabilities.
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Double_t | TMath::QuietNaN () |
| Returns a quiet NaN as defined by IEEE 754.
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constexpr Double_t | TMath::R () |
| Universal gas constant ( \( Na K \)) in \( J K^{-1} mol^{-1} \)
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constexpr Double_t | TMath::RadToDeg () |
| Conversion from radian to degree: \( \frac{180}{\pi} \).
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constexpr Double_t | TMath::Rgair () |
| Dry Air Gas Constant (R / MWair) in \( J kg^{-1} K^{-1} \)
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template<typename Iterator > |
Double_t | TMath::RMS (Iterator first, Iterator last) |
| Returns the Standard Deviation of an array defined by the iterators.
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template<typename Iterator , typename WeightIterator > |
Double_t | TMath::RMS (Iterator first, Iterator last, WeightIterator wfirst) |
| Returns the weighted Standard Deviation of an array defined by the iterators.
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template<typename T > |
Double_t | TMath::RMS (Long64_t n, const T *a, const Double_t *w=nullptr) |
| Returns the Standard Deviation of an array a with length n.
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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.
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constexpr Double_t | TMath::RUncertainty () |
| Universal gas constant uncertainty.
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constexpr Double_t | TMath::Sigma () |
| Stefan-Boltzmann constant in \( W m^{-2} K^{-4}\): \( \sigma \).
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constexpr Double_t | TMath::SigmaUncertainty () |
| Stefan-Boltzmann constant uncertainty.
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Double_t | TMath::SignalingNaN () |
| Returns a signaling NaN as defined by IEEE 754](http://en.wikipedia.org/wiki/NaN#Signaling_NaN).
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Double_t | TMath::Sin (Double_t) |
| Returns the sine of an angle of x radians.
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Double_t | TMath::SinH (Double_t) |
| Returns the hyperbolic sine of `x.
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Double_t | TMath::Sq (Double_t x) |
| Returns x*x .
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Double_t | TMath::Sqrt (Double_t x) |
| Returns the square root of x.
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constexpr Double_t | TMath::Sqrt2 () |
| \( \sqrt{2} \)
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template<typename Iterator > |
Double_t | TMath::StdDev (Iterator first, Iterator last) |
| Same as RMS.
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template<typename Iterator , typename WeightIterator > |
Double_t | TMath::StdDev (Iterator first, Iterator last, WeightIterator wfirst) |
| Same as RMS.
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template<typename T > |
Double_t | TMath::StdDev (Long64_t n, const T *a, const Double_t *w=nullptr) |
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Double_t | TMath::StruveH0 (Double_t x) |
| Bessel function Y1(x) for positive x.
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Double_t | TMath::StruveH1 (Double_t x) |
| Struve functions of order 0.
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Double_t | TMath::StruveL0 (Double_t x) |
| Struve functions of order 1.
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Double_t | TMath::StruveL1 (Double_t x) |
| Modified Struve functions of order 0.
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Double_t | TMath::Student (Double_t T, Double_t ndf) |
| Computes density function for Student's t- distribution.
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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.
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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.
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Double_t | TMath::Tan (Double_t) |
| Returns the tangent of an angle of x radians.
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Double_t | TMath::TanH (Double_t) |
| Returns the hyperbolic tangent of x .
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constexpr Double_t | TMath::TwoPi () |
| \( 2\pi\)
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Double_t | TMath::Vavilov (Double_t x, Double_t kappa, Double_t beta2) |
| Returns the value of the Vavilov probability density function.
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Double_t | TMath::VavilovI (Double_t x, Double_t kappa, Double_t beta2) |
| Returns the value of the Vavilov cumulative distribution function (lower tail integral of the probability distribution function)
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Double_t | TMath::Voigt (Double_t x, Double_t sigma, Double_t lg, Int_t r=4) |
| Computation of Voigt function (normalised).
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