ROOT   Reference Guide
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ROOT::Math Namespace Reference

## Namespaces

namespace  Blas

namespace  BrentMethods

namespace  Cephes

namespace  Chebyshev
template recursive functions for defining evaluation of Chebyshev polynomials T_n(x) and the series S(x) = Sum_i c_i* T_i(x)

namespace  CholeskyDecompHelpers
helpers for CholeskyDecomp

namespace  detail

namespace  GenAlgoOptUtil

namespace  GenVector

namespace  GenVector_detail

namespace  GSLRootHelper
Helper functions to test convergence of Root-Finding algorithms.

namespace  GSLSimAn

namespace  gv_detail

namespace  Impl

namespace  IntegMultiDim

namespace  IntegOneDim

namespace  IntegOptionsUtil

namespace  Integration

namespace  IntegrationMultiDim

namespace  IntegrationOneDim

namespace  Internal

namespace  internal

namespace  Interpolation

namespace  MCIntegration

namespace  Minim

namespace  Minim1D

namespace  Roots
Root-Finding Algorithms.

namespace  rowOffsetsUtils

namespace  Sampler

namespace  Util
namespace defining Utility functions needed by mathcore

namespace  VectorUtil
Global Helper functions for generic Vector classes.

## Classes

struct  AddPolicy< T, D1, D2, MatRepSym< T, D1 >, MatRepSym< T, D1 > >

struct  Assign
Structure to assign from an expression based to general matrix to general matrix. More...

struct  Assign< T, D1, D2, A, MatRepSym< T, D1 >, MatRepStd< T, D1, D2 > >
Dummy Structure which flags an error to avoid assigment from expression based on a general matrix to a symmetric matrix. More...

struct  Assign< T, D1, D2, A, MatRepSym< T, D1 >, MatRepSym< T, D1 > >
Structure to assign from an expression based to symmetric matrix to symmetric matrix. More...

struct  AssignItr
Structure for assignment to a general matrix from iterator. More...

struct  AssignItr< T, D1, D2, MatRepSym< T, D1 > >
Specialized structure for assignment to a symmetrix matrix from iterator. More...

struct  AssignSym
Force Expression evaluation from general to symmetric. More...

class  AxisAngle
AxisAngle class describing rotation represented with direction axis (3D Vector) and an angle of rotation around that axis. More...

class  BaseIntegratorOptions
Base class for Numerical integration options common in 1D and multi-dimension This is an internal class and is not supposed to be instantiated by the user. More...

class  BasicFitMethodFunction
FitMethodFunction class Interface for objective functions (like chi2 and likelihood used in the fit) In addition to normal function interface provide interface for calculating each data contrinution to the function which is required by some algorithm (like Fumili) More...

class  BasicMinimizer
Base Minimizer class, which defines the basic funcionality of various minimizer implementations (apart from Minuit and Minuit2) It provides support for storing parameter values, step size, parameter transofrmation etc. More...

class  BinaryOp
BinaryOperation class A class representing binary operators in the parse tree. More...

class  BinaryOpCopyL
Binary Operation class with value storage for the left argument. More...

class  BinaryOpCopyR
Binary Operation class with value storage for the right argument. More...

class  Boost
Lorentz boost class with the (4D) transformation represented internally by a 4x4 orthosymplectic matrix. More...

class  BoostX
Class representing a Lorentz Boost along the X axis, by beta. More...

class  BoostY
Class representing a Lorentz Boost along the Y axis, by beta. More...

class  BoostZ
Class representing a Lorentz Boost along the Z axis, by beta. More...

class  BrentMinimizer1D
User class for performing function minimization. More...

class  BrentRootFinder
Class for finding the root of a one dimensional function using the Brent algorithm. More...

class  Cartesian2D
Class describing a 2D cartesian coordinate system (x, y coordinates) More...

class  Cartesian3D
Class describing a 3D cartesian coordinate system (x, y, z coordinates) More...

struct  CDFWrapper

class  ChebyshevApprox
Class describing a Chebyshev series which can be used to approximate a function in a defined range [a,b] using Chebyshev polynomials. More...

class  ChebyshevPol

class  CholeskyDecomp
class to compute the Cholesky decomposition of a matrix More...

class  CholeskyDecompGenDim
class to compute the Cholesky decomposition of a matrix More...

class  CholInverter

struct  CompileTimeChecker

struct  CompileTimeChecker< false >

class  Constant
Constant expression class A class representing constant expressions (literals) in the parse tree. More...

class  Cylindrical3D
Class describing a cylindrical coordinate system based on rho, z and phi. More...

class  CylindricalEta3D
Class describing a cylindrical coordinate system based on eta (pseudorapidity) instead of z. More...

class  DefaultCoordinateSystemTag
DefaultCoordinateSystemTag Default tag for identifying any coordinate system. More...

class  Delaunay2D
Class to generate a Delaunay triangulation of a 2D set of points. More...

class  Derivator
Class for computing numerical derivative of a function. More...

class  Determinant
Detrminant for a general squared matrix Function to compute the determinant from a square matrix ( $$\det(A)$$) of dimension idim and order n. More...

class  DisplacementVector2D
Class describing a generic displacement vector in 2 dimensions. More...

class  DisplacementVector3D
Class describing a generic displacement vector in 3 dimensions. More...

class  DistSampler
Interface class for generic sampling of a distribution, i.e. More...

class  DistSamplerOptions
DistSampler options class. More...

class  DivOp
Division (element-wise) Operation Class. More...

class  EulerAngles
EulerAngles class describing rotation as three angles (Euler Angles). More...

struct  EvaluatorOneDim

struct  EvaluatorOneDim< const ROOT::Math::IParamMultiFunction & >

class  Expr

class  Fabs
Unary abs Operation Class. More...

class  Factory
Factory class holding static functions to create the interfaces like ROOT::Math::Minimizer via the Plugin Manager. More...

class  FastInverter
Fast Matrix Inverter class Class to specialize calls to Dinv. More...

class  FastInverter< 3 >
3x3 direct matrix inversion using Cramer Rule use only for FastInverter More...

class  FastInverter< 4 >
4x4 matrix inversion using Cramers rule. More...

class  FastInverter< 5 >
5x5 Matrix inversion using Cramers rule. More...

class  FitTransformFunction

class  Functor
Documentation for class Functor class. More...

class  Functor1D
Functor1D class for one-dimensional functions. More...

Functor Handler class for gradient functions where both callable objects are provided for the function evaluation (type Func) and for the gradient (type GradFunc) . More...

class  FunctorHandler
Functor Handler class is responsible for wrapping any other functor and pointer to free C functions. More...

class  FunctorImpl
FunctorImpl is a base class for the functor handler implementation class. More...

class  GaussIntegrator
User class for performing function integration. More...

class  GaussLegendreIntegrator
User class for performing function integration. More...

class  GenAlgoOptions
class implementing generic options for a numerical algorithm Just store the options in a map of string-value pairs More...

struct  GeneralLinearFunctionDerivation
Auxiliar class to bypass the (provisional) lack of vectorization in TFormula::EvalPar. More...

struct  GeneralLinearFunctionDerivation< double >

class  GeneticMinimizer
GeneticMinimizer. More...

struct  GeneticMinimizerParameters

class  GenVector_exception

class  GlobalCoordinateSystemTag
Tag for identifying vectors based on a global coordinate system. More...

class  GoFTest

class  GSL1DMinimizerWrapper
wrapper class for gsl_min_fminimizer structure More...

class  GSLChebSeries
wrapper class for C struct gsl_cheb_series More...

class  GSLDerivator
Class for computing numerical derivative of a function based on the GSL numerical algorithm This class is implemented using the numerical derivatives algorithms provided by GSL (see GSL Online Manual ). More...

class  GSLError
class to change GSL Error handler to use ROOT one. More...

Class for adapting any C++ functor class to C function pointers used by GSL. More...

class  GSLFunctionDerivWrapper
class to wrap a gsl_function_fdf (with derivatives) More...

class  GSLFunctionWrapper
Wrapper class to the gsl_function C structure. More...

class  GSLIntegrationWorkspace

class  GSLIntegrator
Class for performing numerical integration of a function in one dimension. More...

class  GSLInterpolator
Interpolation class based on GSL interpolation functions. More...

class  GSLMCIntegrationWorkspace

class  GSLMCIntegrator

class  GSLMinimizer
GSLMinimizer class. More...

class  GSLMinimizer1D
Minimizer for arbitrary one dimensional functions. More...

class  GSLMiserIntegrationWorkspace
Workspace for MISER. More...

class  GSLMonteFunctionWrapper
wrapper to a multi-dim function withtout derivatives for Monte Carlo multi-dimensional integration algorithm More...

class  GSLMultiFit
GSLMultiFit, internal class for implementing GSL non linear least square GSL fitting. More...

Class for adapting a C++ functor class to C function pointers used by GSL MultiFit Algorithm The templated C++ function class must implement: More...

class  GSLMultiFitFunctionWrapper
wrapper to a multi-dim function withtout derivatives for multi-dimensional minimization algorithm More...

class  GSLMultiMinDerivFunctionWrapper
Wrapper for a multi-dimensional function with derivatives used in GSL multidim minimization algorithm. More...

Class for adapting any multi-dimension C++ functor class to C function pointers used by GSL MultiMin algorithms. More...

class  GSLMultiMinFunctionWrapper
wrapper to a multi-dim function withtout derivatives for multi-dimensional minimization algorithm More...

class  GSLMultiMinimizer
GSLMultiMinimizer class , for minimizing multi-dimensional function using derivatives. More...

class  GSLMultiRootBaseSolver
GSLMultiRootBaseSolver, internal class for implementing GSL multi-root finders This is the base class for GSLMultiRootSolver (solver not using derivatives) and GSLMUltiRootDerivSolver (solver using derivatives) More...

class  GSLMultiRootDerivFunctionWrapper
wrapper to a multi-dim function with derivatives for multi roots algorithm More...

class  GSLMultiRootDerivSolver
GSLMultiRootDerivSolver, internal class for implementing GSL multi-root finders using derivatives. More...

class  GSLMultiRootFinder
Class for Multidimensional root finding algorithms bassed on GSL. More...

Class for adapting a C++ functor class to C function pointers used by GSL MultiRoot Algorithm The templated C++ function class must implement: More...

class  GSLMultiRootFunctionWrapper
wrapper to a multi-dim function without derivatives for multi roots algorithm More...

class  GSLMultiRootSolver
GSLMultiRootSolver, internal class for implementing GSL multi-root finders not using derivatives. More...

class  GSLNLSMinimizer
GSLNLSMinimizer class for Non Linear Least Square fitting It Uses the Levemberg-Marquardt algorithm from GSL Non Linear Least Square fitting. More...

class  GSLPlainIntegrationWorkspace

class  GSLQRngNiederreiter2
Niederreiter generator gsl_qrng_niederreiter_2 from here More...

class  GSLQRngSobol
Sobol generator gsl_qrng_sobol from here More...

class  GSLQRngWrapper
GSLQRngWrapper class to wrap gsl_qrng structure. More...

class  GSLQuasiRandomEngine
GSLQuasiRandomEngine Base class for all GSL quasi random engines, normally user instantiate the derived classes which creates internally the generator and uses the class ROOT::Math::QuasiRandom. More...

class  GSLRandomEngine
GSLRandomEngine Base class for all GSL random engines, normally user instantiate the derived classes which creates internally the generator. More...

class  GSLRngCMRG
Combined multiple recursive generator (L'Ecuyer) see here More...

class  GSLRngGFSR4
Lagged Fibonacci generator by Ziff see here More...

class  GSLRngMinStd
MINSTD generator (Park and Miller) see here More...

class  GSLRngMixMax
MixMax generator based on ROOT::Math::MixMaxEngine of N=240. More...

class  GSLRngMRG
5-th order multiple recursive generator (L'Ecuyer, Blouin and Coutre) see here More...

class  GSLRngMT
Mersenne-Twister generator gsl_rng_mt19937 from here More...

class  GSLRngRand
BSD rand() generator gsl_rmg_rand from here More...

class  GSLRngRanLux
Old Ranlux generator (James, Luscher) (default luxury level, p = 223) (This is eequivalent to TRandom1 with default luxury level) see here More...

class  GSLRngRanLuxD1
Double precision (48 bits) version of Second generation of Ranlux generator with luxury level of 1 (It throws away 202 value for every 12 used) see here More...

class  GSLRngRanLuxD2
Double precision (48 bits) version of Second generation of Ranlux generator with luxury level of 2 (It throws away 397 value for every 12 used) see here More...

class  GSLRngRanLuxS1
Second generation of Ranlux generator for single precision with luxury level of 1 (It throws away 202 values for every 12 used) see here More...

class  GSLRngRanLuxS2
Second generation of Ranlux generator for Single precision with luxury level of 2 (It throws away 397 value for every 12 used) see here More...

class  GSLRngRanMar
RANMAR generator see here More...

struct  GSLRngROOTWrapper
class for wrapping ROOT Engines in gsl_rng types which can be used as extra GSL random number generators For this we need to implment functions which will be called by gsl_rng. More...

class  GSLRngTaus
Tausworthe generator by L'Ecuyer see here More...

class  GSLRngWrapper
GSLRngWrapper class to wrap gsl_rng structure. More...

class  GSLRootFdFSolver
Root-Finder with derivatives implementation class using GSL. More...

class  GSLRootFinder
Base class for GSL Root-Finding algorithms for one dimensional functions which do not use function derivatives. More...

class  GSLRootFinderDeriv
Base class for GSL Root-Finding algorithms for one dimensional functions which use function derivatives. More...

class  GSLRootFSolver
Root-Finder implementation class using GSL. More...

class  GSLSimAnFunc
GSLSimAnFunc class description. More...

class  GSLSimAnMinimizer
GSLSimAnMinimizer class for minimization using simulated annealing using the algorithm from GSL. More...

class  GSLSimAnnealing
GSLSimAnnealing class for performing a simulated annealing search of a multidimensional function. More...

struct  GSLSimAnParams
structure holding the simulated annealing parameters More...

class  GSLVegasIntegrationWorkspace
workspace for VEGAS More...

class  IBaseFunctionMultiDimTempl
Documentation for the abstract class IBaseFunctionMultiDim. More...

class  IBaseFunctionOneDim
Interface (abstract class) for generic functions objects of one-dimension Provides a method to evaluate the function given a value (simple double) by implementing operator() (const double ). More...

class  IBaseParam
Documentation for the abstract class IBaseParam. More...

Interface (abstract class) for multi-dimensional functions providing a gradient calculation. More...

Interface (abstract class) for one-dimensional functions providing a gradient calculation. More...

Gradient interface (abstract class) defining the signature for calculating the gradient of a multi-dimensional function. More...

Specialized Gradient interface(abstract class) for one dimensional functions It provides a method to evaluate the derivative of the function, Derivative and a method to evaluate at the same time the function and the derivative FdF. More...

class  IMinimizer1D
Interface class for numerical methods for one-dimensional minimization. More...

class  IntegrandTransform
Auxiliary inner class for mapping infinite and semi-infinite integrals. More...

class  IntegratorMultiDim
User class for performing multidimensional integration. More...

class  IntegratorMultiDimOptions
Numerical multi dimensional integration options. More...

class  IntegratorOneDim
User Class for performing numerical integration of a function in one dimension. More...

class  IntegratorOneDimOptions
Numerical one dimensional integration options. More...

class  Interpolator
Class for performing function interpolation of points. More...

class  Inverter
Matrix Inverter class Class to specialize calls to Dinv. More...

class  Inverter< 0 >
Inverter<0>. More...

class  Inverter< 1 >
1x1 matrix inversion $$a_{11} \to 1/a_{11}$$ More...

class  Inverter< 2 >
2x2 matrix inversion using Cramers rule. More...

class  IOptions
Generic interface for defining configuration options of a numerical algorithm. More...

class  IParametricFunctionMultiDimTempl
IParamFunction interface (abstract class) describing multi-dimensional parameteric functions It is a derived class from ROOT::Math::IBaseFunctionMultiDim and ROOT::Math::IBaseParam. More...

class  IParametricFunctionOneDim
Specialized IParamFunction interface (abstract class) for one-dimensional parametric functions It is a derived class from ROOT::Math::IBaseFunctionOneDim and ROOT::Math::IBaseParam. More...

Interface (abstract class) for parametric gradient multi-dimensional functions providing in addition to function evaluation with respect to the coordinates also the gradient with respect to the parameters, via the method ParameterGradient. More...

Interface (abstract class) for parametric one-dimensional gradient functions providing in addition to function evaluation with respect the coordinates also the gradient with respect to the parameters, via the method ParameterGradient. More...

class  IRootFinderMethod
Interface for finding function roots of one-dimensional functions. More...

class  KahanSum
The Kahan summation is a compensated summation algorithm, which significantly reduces numerical errors when adding a sequence of finite-precision floating point numbers. More...

class  KDTree

class  KelvinFunctions
This class calculates the Kelvin functions Ber(x), Bei(x), Ker(x), Kei(x), and their first derivatives. More...

class  LCGEngine

class  LocalCoordinateSystemTag
Tag for identifying vectors based on a local coordinate system. More...

class  LorentzRotation
Lorentz transformation class with the (4D) transformation represented by a 4x4 orthosymplectic matrix. More...

class  LorentzVector
Class describing a generic LorentzVector in the 4D space-time, using the specified coordinate system for the spatial vector part. More...

class  LSResidualFunc
LSResidualFunc class description. More...

class  MathMoreLib

class  MatRepStd
Expression wrapper class for Matrix objects. More...

class  MatRepSym
MatRepSym Matrix storage representation for a symmetric matrix of dimension NxN This class is a template on the contained type and on the symmetric matrix size, N. More...

class  MatrixMulOp
Class for Matrix-Matrix multiplication. More...

class  MemFunHandler
Functor Handler to Wrap pointers to member functions The member function type must be (XXX means any name is allowed) : double XXX ( double x) for 1D functions and double XXXX (const double *x) for multi-dimensional functions. More...

Functor Handler to Wrap pointers to member functions for the evaluation of the function and the gradient. More...

class  MersenneTwisterEngine
Random number generator class based on M. More...

struct  meta_col_dot

struct  meta_col_dot< 0 >

struct  meta_dot

struct  meta_dot< 0 >

struct  meta_mag

struct  meta_mag< 0 >

struct  meta_matrix_dot

struct  meta_matrix_dot< 0 >

struct  meta_row_dot

struct  meta_row_dot< 0 >

class  Minimizer
Abstract Minimizer class, defining the interface for the various minimizer (like Minuit2, Minuit, GSL, etc..) Plug-in's exist in ROOT to be able to instantiate the derived classes like ROOT::Math::GSLMinimizer or ROOT::Math::Minuit2Minimizer via the plug-in manager. More...

class  MinimizerOptions
Minimizer options. More...

class  MinimizerVariableTransformation
Base class for MinimizerVariable transformations defining the functions to deal with bounded parameters. More...

class  MinimTransformFunction
MinimTransformFunction class to perform a transformations on the variables to deal with fixed or limited variables (support both double and single bounds) The class manages the passed function pointer. More...

class  MinimTransformVariable
MinimTransformVariable class Contains meta information of the variables such as bounds, fix flags and deals with transformation of the variable The class does not contain the values and the step size (error) of the variable This is an internal class used by the MinimTransformFunction class. More...

class  MinOp
Subtraction Operation Class. More...

class  Minus
Unary Minus Operation Class. More...

struct  MinusEquals
Evaluate the expression performing a -= operation Need to check whether creating a temporary object with the expression result (like in op: A -= A * B ) More...

struct  MinusEquals< T, D1, D2, A, MatRepSym< T, D1 >, MatRepStd< T, D1, D2 > >
Specialization for symmetrix -= general : NOT Allowed operation. More...

struct  MinusEquals< T, D1, D2, A, MatRepSym< T, D1 >, MatRepSym< T, D1 > >
Specialization for symmetric matrices. More...

struct  MiserParameters
structures collecting parameters for MISER multidimensional integration More...

class  MixMaxEngine
MixMaxEngine is a wrapper class for the MIXMAX Random number generator. More...

class  MixMaxEngineImpl

class  MixMaxEngineImpl< ROOT_MM_N >

class  MulOp
Multiplication (element-wise) Operation Class. More...

MultiDimParamFunctionAdapter class to wrap a one-dimensional parametric function in a multi dimensional parameteric function interface This is used typically in fitting where internally the function is stored as multidimension. More...

MultiDimParamGradFunctionAdapter class to wrap a one-dimensional parametric gradient function in a multi dimensional parameteric gradient function interface This is used typically in fitting where internally the function is stored as multidimension. More...

class  MultiGenFunctionFitness

MultiNumGradFunction class to wrap a normal function in a gradient function using numerical gradient calculation provided by the class Derivator (based on GSL numerical derivation) More...

struct  MultPolicy
matrix-matrix multiplication policy More...

struct  NullTypeFunc1D

OneDimMultiFunctionAdapter class to wrap a multidimensional function in one dimensional one. More...

OneDimParamFunctionAdapter class to wrap a multi-dim parameteric function in one dimensional one. More...

class  ParamFunction
Base template class for all Parametric Functions. More...

class  ParamFunctionBase
class defining the signature for multi-dim parametric functions More...

class  ParamFunctorHandler
ParamFunctor Handler class is responsible for wrapping any other functor and pointer to free C functions. More...

class  ParamFunctorTempl
Param Functor class for Multidimensional functions. More...

class  ParamMemFunHandler
ParamFunctor Handler to Wrap pointers to member functions. More...

class  PDFIntegral

struct  PlaceExpr

struct  PlaceExpr< T, D1, D2, D3, D4, A, MatRepSym< T, D1 >, MatRepStd< T, D3, D4 > >

struct  PlaceExpr< T, D1, D2, D3, D4, A, MatRepSym< T, D1 >, MatRepSym< T, D3 > >

struct  PlaceMatrix
Structure to deal when a submatrix is placed in a matrix. More...

struct  PlaceMatrix< T, D1, D2, D3, D4, MatRepSym< T, D1 >, MatRepStd< T, D3, D4 > >

struct  PlaceMatrix< T, D1, D2, D3, D4, MatRepSym< T, D1 >, MatRepSym< T, D3 > >

struct  PlainParameters

struct  PlusEquals
Evaluate the expression performing a += operation Need to check whether creating a temporary object with the expression result (like in op: A += A * B ) More...

struct  PlusEquals< T, D1, D2, A, MatRepSym< T, D1 >, MatRepStd< T, D1, D2 > >
Specialization for symmetrix += general : NOT Allowed operation. More...

struct  PlusEquals< T, D1, D2, A, MatRepSym< T, D1 >, MatRepSym< T, D1 > >
Specialization for symmetric matrices Evaluate the expression performing a += operation for symmetric matrices Need to have a separate functions to avoid to modify two times the off-diagonal elements (i.e applying two times the expression) Need to check whether creating a temporary object with the expression result (like in op: A += A * B ) More...

class  Polar2D
Class describing a polar 2D coordinate system based on r and phi Phi is restricted to be in the range [-PI,PI) More...

class  Polar3D
Class describing a polar coordinate system based on r, theta and phi Phi is restricted to be in the range [-PI,PI) More...

class  Polynomial
Parametric Function class describing polynomials of order n. More...

class  PositionVector2D
Class describing a generic position vector (point) in 2 dimensions. More...

class  PositionVector3D
Class describing a generic position vector (point) in 3 dimensions. More...

class  PtEtaPhiE4D
Class describing a 4D cylindrical coordinate system using Pt , Phi, Eta and E (or rho, phi, eta , T) The metric used is (-,-,-,+). More...

class  PtEtaPhiM4D
Class describing a 4D cylindrical coordinate system using Pt , Phi, Eta and M (mass) The metric used is (-,-,-,+). More...

class  PxPyPzE4D
Class describing a 4D cartesian coordinate system (x, y, z, t coordinates) or momentum-energy vectors stored as (Px, Py, Pz, E). More...

class  PxPyPzM4D
Class describing a 4D coordinate system or momentum-energy vectors stored as (Px, Py, Pz, M). More...

class  QuasiRandom
User class for MathMore random numbers template on the Engine type. More...

class  Quaternion
Rotation class with the (3D) rotation represented by a unit quaternion (u, i, j, k). More...

class  Random
Documentation for the Random class. More...

class  RandomFunctions

class  RandomFunctions< EngineType, ROOT::Math::GSLRandomEngine >
Specialized implementation of the Random functions based on the GSL library. More...

class  RandomFunctionsImpl
Definition of the generic impelmentation class for the RandomFunctions. More...

class  RandomFunctionsImpl< TRandomEngine >
Implementation class for the RandomFunction for all the engined that derives from TRandomEngine class, which defines an interface which has TRandomEngine::Rndm() In this way we can have a common implementation for the RandomFunctions. More...

class  RanluxppCompatEngineGslRanlxd
Compatibility engine for gsl_rng_ranlxd* from the GNU Scientific Library. More...

class  RanluxppCompatEngineGslRanlxs
Compatibility engine for gsl_rng_ranlxs* from the GNU Scientific Library. More...

class  RanluxppCompatEngineJames

class  RanluxppCompatEngineLuescherImpl

class  RanluxppCompatEngineLuescherRanlxd
Compatibility engine for LÃ¼scher's ranlxd implementation written in C. More...

class  RanluxppCompatEngineLuescherRanlxs
Compatibility engine for LÃ¼scher's ranlxs implementation written in C. More...

class  RanluxppCompatEngineStdRanlux24
Compatibility engine for std::ranlux24 from the C++ standard. More...

class  RanluxppCompatEngineStdRanlux48
Compatibility engine for std::ranlux48 from the C++ standard. More...

class  RanluxppEngine
Implementation of the RANLUX++ generator. More...

class  RanluxppEngineImpl

struct  RetrieveMatrix
Structure for getting sub matrices We have different cases according to the matrix representations. More...

struct  RetrieveMatrix< T, D1, D2, D3, D4, MatRepSym< T, D1 >, MatRepStd< T, D3, D4 > >

struct  RetrieveMatrix< T, D1, D2, D3, D4, MatRepSym< T, D1 >, MatRepSym< T, D3 > >

class  RichardsonDerivator
User class for calculating the derivatives of a function. More...

class  RMinimizer
RMinimizer class. More...

class  RootFinder
User Class to find the Root of one dimensional functions. More...

class  Rotation3D
Rotation class with the (3D) rotation represented by a 3x3 orthogonal matrix. More...

class  RotationX
Rotation class representing a 3D rotation about the X axis by the angle of rotation. More...

class  RotationY
Rotation class representing a 3D rotation about the Y axis by the angle of rotation. More...

class  RotationZ
Rotation class representing a 3D rotation about the Z axis by the angle of rotation. More...

class  RotationZYX
Rotation class with the (3D) rotation represented by angles describing first a rotation of an angle phi (yaw) about the Z axis, followed by a rotation of an angle theta (pitch) about the Y axis, followed by a third rotation of an angle psi (roll) about the X axis. More...

struct  RowOffsets
Static structure to keep the conversion from (i,j) to offsets in the storage data for a symmetric matrix. More...

class  SDeterminant
Dsfact. More...

class  SinVariableTransformation
Sin Transformation class for dealing with double bounded variables. More...

class  SInverter
Dsinv. More...

struct  SkipFunction

struct  SkipFunction< 0 >

class  SMatrix
SMatrix: a generic fixed size D1 x D2 Matrix class. More...

struct  SMatrixIdentity

struct  SMatrixNoInit

class  Sqr
Unary Square Operation Class. More...

class  Sqrt
Unary Square Root Operation Class. More...

class  SqrtLowVariableTransformation
Sqrt Transformation class for dealing with lower bounded variables. More...

class  SqrtUpVariableTransformation
Sqrt Transformation class for dealing with upper bounded variables. More...

class  StdEngine
Class to wrap engines fron the C++ standard random library in the ROOT Random interface. More...

struct  StdEngineType

struct  StdEngineType< std::knuth_b >

struct  StdEngineType< std::minstd_rand >

struct  StdEngineType< std::mt19937 >

struct  StdEngineType< std::mt19937_64 >

struct  StdEngineType< std::random_device >

struct  StdEngineType< std::ranlux24 >

struct  StdEngineType< std::ranlux48 >

class  StdRandomEngine

class  SVector
SVector: a generic fixed size Vector class. More...

class  TDataPoint

class  TDataPointN

class  TensorMulOp
Class for Tensor Multiplication (outer product) of two vectors giving a matrix. More...

class  TRandomEngine

class  TransposeOp
Class for Transpose Operations. More...

struct  TranspPolicy
matrix transpose policy More...

struct  TranspPolicy< T, D1, D2, MatRepSym< T, D1 > >

class  UnaryOp
UnaryOperation class A class representing unary operators in the parse tree. More...

class  Vavilov
Base class describing a Vavilov distribution. More...

class  VavilovAccurate
Class describing a Vavilov distribution. More...

class  VavilovAccurateCdf
Class describing the Vavilov cdf. More...

class  VavilovAccuratePdf
Class describing the Vavilov pdf. More...

class  VavilovAccurateQuantile
Class describing the Vavilov quantile function. More...

class  VavilovFast
Class describing a Vavilov distribution. More...

class  VecExpr
Expression wrapper class for Vector objects. More...

class  VectorMatrixColOp
Class for Vector-Matrix multiplication. More...

class  VectorMatrixRowOp

struct  VegasParameters
structures collecting parameters for VEGAS multidimensional integration FOr implementation of default parameters see file mathmore/src/GSLMCIntegrationWorkspace.h More...

class  VirtualIntegrator
Abstract class for all numerical integration methods (1D and multi-dim) Interface defining the common methods for the numerical integrator classes of one and multi dimensions The derived class VirtualIntegratorOneDim defines the methods for one-dimensional integration. More...

class  VirtualIntegratorMultiDim
Interface (abstract) class for multi numerical integration It must be implemented by the concrete Integrator classes like ROOT::Math::GSLMCIntegrator. More...

class  VirtualIntegratorOneDim
Interface (abstract) class for 1D numerical integration It must be implemented by the concrete Integrator classes like ROOT::Math::GSLIntegrator. More...

class  WrappedFunction
Template class to wrap any C++ callable object which takes one argument i.e. More...

class  WrappedMemFunction
Template class to wrap any member function of a class taking a double and returning a double in a 1D function interface For example, if you have a class like: struct X { double Eval(double x); }; you can wrapped in the following way: WrappedMemFunction<X, double ( X::* ) (double) > f;. More...

class  WrappedMemMultiFunction

class  WrappedMultiFunction
Template class to wrap any C++ callable object implementing operator() (const double * x) in a multi-dimensional function interface. More...

class  WrappedMultiTF1Templ
Class to Wrap a ROOT Function class (like TF1) in a IParamMultiFunction interface of multi-dimensions to be used in the ROOT::Math numerical algorithm. More...

class  WrappedParamFunction
WrappedParamFunction class to wrap any multi-dimensional function pbject implementing the operator()(const double * x, const double * p) in an interface-like IParamFunction with a vector storing and caching internally the parameter values. More...

class  WrappedParamFunctionGen
WrappedParamGenFunction class to wrap any multi-dimensional function implementing the operator()(const double * ) in an interface-like IParamFunction, by fixing some of the variables and define them as parameters. More...

class  WrappedTF1
Class to Wrap a ROOT Function class (like TF1) in a IParamFunction interface of one dimensions to be used in the ROOT::Math numerical algorithms The wrapper does not own bby default the TF1 pointer, so it assumes it exists during the wrapper lifetime. More...

## Typedefs

typedef TRandomEngine DefaultEngineType
Documentation for the RandomFunction class.

typedef BasicFitMethodFunction< ROOT::Math::IMultiGenFunctionFitMethodFunction

typedef double(* FreeFunctionPtr) (double)

typedef double(* FreeMultiFunctionPtr) (const double *)

typedef double(* FreeParamMultiFunctionPtr) (const double *, const double *)

typedef void(* GSLFdfPointer) (double, void *, double *, double *)

typedef double(* GSLFuncPointer) (double, void *)
Function pointer corresponding to gsl_function signature.

typedef double(* GSLMonteFuncPointer) (double *, size_t, void *)
Class for adapting any multi-dimension C++ functor class to C function pointers used by GSL MonteCarlo integration algorithms.

typedef void(* GSLMultiFitDfPointer) (const gsl_vector *, void *, gsl_matrix *)

typedef void(* GSLMultiFitFdfPointer) (const gsl_vector *, void *, gsl_vector *, gsl_matrix *)

typedef double(* GSLMultiFitFPointer) (const gsl_vector *, void *, gsl_vector *)

typedef void(* GSLMultiMinDfPointer) (const gsl_vector *, void *, gsl_vector *)

typedef void(* GSLMultiMinFdfPointer) (const gsl_vector *, void *, double *, gsl_vector *)

typedef double(* GSLMultiMinFuncPointer) (const gsl_vector *, void *)

typedef void(* GSLMultiRootDfPointer) (const gsl_vector *, void *, gsl_matrix *)

typedef void(* GSLMultiRootFdfPointer) (const gsl_vector *, void *, gsl_vector *, gsl_matrix *)

typedef double(* GSLMultiRootFPointer) (const gsl_vector *, void *, gsl_vector *)

typedef GSLRngRanLuxS1 GSLRngRanLux1

typedef GSLRngRanLuxS2 GSLRngRanLux2

typedef GSLRngRanLuxD2 GSLRngRanLux48

using IBaseFunctionMultiDim = IBaseFunctionMultiDimTempl< double >

typedef IBaseFunctionOneDim IGenFunction

using IMultiGenFunction = IMultiGenFunctionTempl< double >

template<class T >
using IMultiGenFunctionTempl = IBaseFunctionMultiDimTempl< T >

typedef IntegratorOneDim Integrator

using IParametricFunctionMultiDim = IParametricFunctionMultiDimTempl< double >

typedef IParametricFunctionOneDim IParamFunction

typedef IParametricFunctionMultiDim IParamMultiFunction

template<class T >
using IParamMultiFunctionTempl = IParametricFunctionMultiDimTempl< T >

template<class T >

typedef MathMoreLib MathMoreLibrary

typedef MixMaxEngine< 17, 0 > MixMaxEngine17

typedef MixMaxEngine< 240, 0 > MixMaxEngine240

typedef MixMaxEngine< 256, 2 > MixMaxEngine256

typedef GSLMultiRootFinder MultiRootFinder

typedef std::map< std::string, ROOT::Math::GenAlgoOptionsOptionsMap

using ParamFunctor = ParamFunctorTempl< double >

typedef Impl::Plane3D< doublePlane3D

typedef Impl::Plane3D< float > Plane3DF

typedef PositionVector2D< Polar2D< double >, DefaultCoordinateSystemTagPolar2DPoint
2D Point based on the polar coordinates rho, theta, phi in double precision.

typedef Polar2DPoint Polar2DPointD

typedef PositionVector2D< Polar2D< float >, DefaultCoordinateSystemTagPolar2DPointF
2D Point based on the polar coordinates rho, theta, phi in single precision.

typedef DisplacementVector2D< Polar2D< double >, DefaultCoordinateSystemTagPolar2DVector
2D Vector based on the polar coordinates rho, phi in double precision.

typedef Polar2DVector Polar2DVectorD

typedef DisplacementVector2D< Polar2D< float >, DefaultCoordinateSystemTagPolar2DVectorF
2D Vector based on the polar coordinates rho, phi in single precision.

typedef PositionVector3D< Polar3D< double >, DefaultCoordinateSystemTagPolar3DPoint
3D Point based on the polar coordinates rho, theta, phi in double precision.

typedef Polar3DPoint Polar3DPointD

typedef PositionVector3D< Polar3D< float >, DefaultCoordinateSystemTagPolar3DPointF
3D Point based on the polar coordinates rho, theta, phi in single precision.

typedef DisplacementVector3D< Polar3D< double >, DefaultCoordinateSystemTagPolar3DVector
3D Vector based on the polar coordinates rho, theta, phi in double precision.

typedef Polar3DVector Polar3DVectorD

typedef DisplacementVector3D< Polar3D< float >, DefaultCoordinateSystemTagPolar3DVectorF
3D Vector based on the polar coordinates rho, theta, phi in single precision.

typedef LorentzVector< PtEtaPhiE4D< double > > PtEtaPhiEVector
LorentzVector based on the cylindrical coordinates Pt, eta, phi and E (rho, eta, phi, t) in double precision.

typedef LorentzVector< PtEtaPhiM4D< double > > PtEtaPhiMVector
LorentzVector based on the cylindrical coordinates pt, eta, phi and Mass in double precision.

typedef LorentzVector< PxPyPzE4D< double > > PxPyPzEVector

typedef LorentzVector< PxPyPzM4D< double > > PxPyPzMVector
LorentzVector based on the x, y, z, and Mass in double precision.

typedef QuasiRandom< ROOT::Math::GSLQRngNiederreiter2QuasiRandomNiederreiter

typedef QuasiRandom< ROOT::Math::GSLQRngSobolQuasiRandomSobol

typedef Random< ROOT::Math::GSLRngGFSR4RandomGFSR4

typedef Random< ROOT::Math::MixMaxEngine< 240, 0 > > RandomMixMax
Useful typedef definitions.

typedef Random< ROOT::Math::GSLRngMTRandomMT

typedef Random< ROOT::Math::MersenneTwisterEngineRandomMT19937

typedef Random< ROOT::Math::StdEngine< std::mt19937_64 > > RandomMT64

typedef Random< ROOT::Math::GSLRngRanLuxRandomRanLux

typedef Random< ROOT::Math::StdEngine< std::ranlux48 > > RandomRanlux48

typedef Random< ROOT::Math::GSLRngTausRandomTaus

using RanluxppCompatEngineGslRanlxd1 = RanluxppCompatEngineGslRanlxd< 404 >

using RanluxppCompatEngineGslRanlxd2 = RanluxppCompatEngineGslRanlxd< 794 >

using RanluxppCompatEngineGslRanlxs0 = RanluxppCompatEngineGslRanlxs< 218 >

using RanluxppCompatEngineGslRanlxs1 = RanluxppCompatEngineGslRanlxs< 404 >

using RanluxppCompatEngineGslRanlxs2 = RanluxppCompatEngineGslRanlxs< 794 >

using RanluxppCompatEngineJamesP3 = RanluxppCompatEngineJames< 223 >
Compatibility engine for original RANLUX implementation by James, luxury level 3 (p = 223).

using RanluxppCompatEngineJamesP4 = RanluxppCompatEngineJames< 389 >
Compatibility engine for original RANLUX implementation by James, luxury level 4 (p = 389).

using RanluxppCompatEngineLuescherRanlxd1 = RanluxppCompatEngineLuescherRanlxd< 404 >

using RanluxppCompatEngineLuescherRanlxd2 = RanluxppCompatEngineLuescherRanlxd< 794 >

using RanluxppCompatEngineLuescherRanlxs0 = RanluxppCompatEngineLuescherRanlxs< 218 >

using RanluxppCompatEngineLuescherRanlxs1 = RanluxppCompatEngineLuescherRanlxs< 404 >

using RanluxppCompatEngineLuescherRanlxs2 = RanluxppCompatEngineLuescherRanlxs< 794 >

using RanluxppEngine2048 = RanluxppEngine< 2048 >

using RanluxppEngine24 = RanluxppEngine< 24 >

typedef PositionVector3D< CylindricalEta3D< double >, DefaultCoordinateSystemTagRhoEtaPhiPoint
3D Point based on the eta based cylindrical coordinates rho, eta, phi in double precision.

typedef RhoEtaPhiPoint RhoEtaPhiPointD

typedef PositionVector3D< CylindricalEta3D< float >, DefaultCoordinateSystemTagRhoEtaPhiPointF
3D Point based on the eta based cylindrical coordinates rho, eta, phi in single precision.

typedef DisplacementVector3D< CylindricalEta3D< double >, DefaultCoordinateSystemTagRhoEtaPhiVector
3D Vector based on the eta based cylindrical coordinates rho, eta, phi in double precision.

typedef RhoEtaPhiVector RhoEtaPhiVectorD

typedef DisplacementVector3D< CylindricalEta3D< float >, DefaultCoordinateSystemTagRhoEtaPhiVectorF
3D Vector based on the eta based cylindrical coordinates rho, eta, phi in single precision.

typedef PositionVector3D< Cylindrical3D< double >, DefaultCoordinateSystemTagRhoZPhiPoint
3D Point based on the cylindrical coordinates rho, z, phi in double precision.

typedef RhoZPhiPoint RhoZPhiPointD

typedef PositionVector3D< Cylindrical3D< float >, DefaultCoordinateSystemTagRhoZPhiPointF
3D Point based on the cylindrical coordinates rho, z, phi in single precision.

typedef DisplacementVector3D< Cylindrical3D< double >, DefaultCoordinateSystemTagRhoZPhiVector
3D Vector based on the cylindrical coordinates rho, z, phi in double precision.

typedef RhoZPhiVector RhoZPhiVectorD

typedef DisplacementVector3D< Cylindrical3D< float >, DefaultCoordinateSystemTagRhoZPhiVectorF
3D Vector based on the cylindrical coordinates rho, z, phi in single precision.

typedef Rotation3D::Scalar Scalar

typedef SMatrix< double, 2, 2, MatRepStd< double, 2, 2 > > SMatrix2D

typedef SMatrix< float, 2, 2, MatRepStd< float, 2, 2 > > SMatrix2F

typedef SMatrix< double, 3, 3, MatRepStd< double, 3, 3 > > SMatrix3D

typedef SMatrix< float, 3, 3, MatRepStd< float, 3, 3 > > SMatrix3F

typedef SMatrix< double, 4, 4, MatRepStd< double, 4, 4 > > SMatrix4D

typedef SMatrix< float, 4, 4, MatRepStd< float, 4, 4 > > SMatrix4F

typedef SMatrix< double, 5, 5, MatRepStd< double, 5, 5 > > SMatrix5D

typedef SMatrix< float, 5, 5, MatRepStd< float, 5, 5 > > SMatrix5F

typedef SMatrix< double, 6, 6, MatRepStd< double, 6, 6 > > SMatrix6D

typedef SMatrix< float, 6, 6, MatRepStd< float, 6, 6 > > SMatrix6F

typedef SMatrix< double, 7, 7, MatRepStd< double, 7, 7 > > SMatrix7D

typedef SMatrix< float, 7, 7, MatRepStd< float, 7, 7 > > SMatrix7F

typedef SMatrix< double, 2, 2, MatRepSym< double, 2 > > SMatrixSym2D

typedef SMatrix< float, 2, 2, MatRepSym< float, 2 > > SMatrixSym2F

typedef SMatrix< double, 3, 3, MatRepSym< double, 3 > > SMatrixSym3D

typedef SMatrix< float, 3, 3, MatRepSym< float, 3 > > SMatrixSym3F

typedef SMatrix< double, 4, 4, MatRepSym< double, 4 > > SMatrixSym4D

typedef SMatrix< float, 4, 4, MatRepSym< float, 4 > > SMatrixSym4F

typedef SMatrix< double, 5, 5, MatRepSym< double, 5 > > SMatrixSym5D

typedef SMatrix< float, 5, 5, MatRepSym< float, 5 > > SMatrixSym5F

typedef SMatrix< double, 6, 6, MatRepSym< double, 6 > > SMatrixSym6D

typedef SMatrix< float, 6, 6, MatRepSym< float, 6 > > SMatrixSym6F

typedef SMatrix< double, 7, 7, MatRepSym< double, 7 > > SMatrixSym7D

typedef SMatrix< float, 7, 7, MatRepSym< float, 7 > > SMatrixSym7F

typedef TDataPoint< 1, Double_tTDataPoint1D

typedef TDataPoint< 1, Float_tTDataPoint1F

typedef TDataPoint< 2, Double_tTDataPoint2D

typedef TDataPoint< 2, Float_tTDataPoint2F

typedef TDataPoint< 3, Double_tTDataPoint3D

typedef TDataPoint< 3, Float_tTDataPoint3F

typedef Impl::Transform3D< doubleTransform3D

typedef Impl::Transform3D< float > Transform3DF

typedef Impl::Translation3D< doubleTranslation3D

typedef Impl::Translation3D< float > Translation3DF

using WrappedMultiTF1 = WrappedMultiTF1Templ< double >

typedef PositionVector2D< Cartesian2D< double >, DefaultCoordinateSystemTagXYPoint
2D Point based on the cartesian coordinates x,y,z in double precision

typedef XYPoint XYPointD

typedef PositionVector2D< Cartesian2D< float >, DefaultCoordinateSystemTagXYPointF
2D Point based on the cartesian corrdinates x,y,z in single precision

typedef DisplacementVector2D< Cartesian2D< double >, DefaultCoordinateSystemTagXYVector
2D Vector based on the cartesian coordinates x,y in double precision

typedef XYVector XYVectorD

typedef DisplacementVector2D< Cartesian2D< float >, DefaultCoordinateSystemTagXYVectorF
2D Vector based on the cartesian coordinates x,y,z in single precision

typedef PositionVector3D< Cartesian3D< double >, DefaultCoordinateSystemTagXYZPoint
3D Point based on the cartesian coordinates x,y,z in double precision

typedef XYZPoint XYZPointD

typedef PositionVector3D< Cartesian3D< float >, DefaultCoordinateSystemTagXYZPointF
3D Point based on the cartesian corrdinates x,y,z in single precision

typedef LorentzVector< PxPyPzE4D< double > > XYZTVector
LorentzVector based on x,y,x,t (or px,py,pz,E) coordinates in double precision with metric (-,-,-,+)

typedef LorentzVector< PxPyPzE4D< float > > XYZTVectorF
LorentzVector based on x,y,x,t (or px,py,pz,E) coordinates in float precision with metric (-,-,-,+)

typedef DisplacementVector3D< Cartesian3D< double >, DefaultCoordinateSystemTagXYZVector
3D Vector based on the cartesian coordinates x,y,z in double precision

typedef XYZVector XYZVectorD

typedef DisplacementVector3D< Cartesian3D< float >, DefaultCoordinateSystemTagXYZVectorF
3D Vector based on the cartesian coordinates x,y,z in single precision

## Enumerations

enum  EGSLMinimizerType {
kConjugateFR , kConjugatePR , kVectorBFGS , kVectorBFGS2 ,
kSteepestDescent
}
enumeration specifying the types of GSL minimizers More...

enum  EMinimVariableType {
kDefault , kFix , kBounds , kLowBound ,
kUpBound
}
Enumeration describing the status of the variable The enumeration are used in the minimizer classes to categorize the variables. More...

enum  ERotation3DMatrixIndex {
kXX = 0 , kXY = 1 , kXZ = 2 , kYX = 3 ,
kYY = 4 , kYZ = 5 , kZX = 6 , kZY = 7 ,
kZZ = 8
}

## Functions

void adkTestStat (double *adk, const std::vector< std::vector< double > > &samples, const std::vector< double > &zstar)

double beta_cdf (double x, double a, double b)
Cumulative distribution function of the beta distribution Upper tail of the integral of the beta_pdf.

double beta_cdf_c (double x, double a, double b)
Complement of the cumulative distribution function of the beta distribution.

double binomial_cdf (unsigned int k, double p, unsigned int n)
Cumulative distribution function of the Binomial distribution Lower tail of the integral of the binomial_pdf.

double binomial_cdf_c (unsigned int k, double p, unsigned int n)
Complement of the cumulative distribution function of the Binomial distribution.

double breitwigner_cdf (double x, double gamma, double x0=0)
Cumulative distribution function (lower tail) of the Breit_Wigner distribution and it is similar (just a different parameter definition) to the Cauchy distribution (see cauchy_cdf )

double breitwigner_cdf_c (double x, double gamma, double x0=0)
Complement of the cumulative distribution function (upper tail) of the Breit_Wigner distribution and it is similar (just a different parameter definition) to the Cauchy distribution (see cauchy_cdf_c )

double cauchy_cdf (double x, double b, double x0=0)
Cumulative distribution function (lower tail) of the Cauchy distribution which is also Lorentzian distribution.

double cauchy_cdf_c (double x, double b, double x0=0)
Complement of the cumulative distribution function (upper tail) of the Cauchy distribution which is also Lorentzian distribution.

double Chebyshev0 (double, double c0)

double Chebyshev1 (double x, double c0, double c1)

double Chebyshev10 (double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7, double c8, double c9, double c10)

double Chebyshev2 (double x, double c0, double c1, double c2)

double Chebyshev3 (double x, double c0, double c1, double c2, double c3)

double Chebyshev4 (double x, double c0, double c1, double c2, double c3, double c4)

double Chebyshev5 (double x, double c0, double c1, double c2, double c3, double c4, double c5)

double Chebyshev6 (double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6)

double Chebyshev7 (double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7)

double Chebyshev8 (double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7, double c8)

double Chebyshev9 (double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7, double c8, double c9)

double ChebyshevN (unsigned int n, double x, const double *c)

double chisquared_cdf (double x, double r, double x0=0)
Cumulative distribution function of the $$\chi^2$$ distribution with $$r$$ degrees of freedom (lower tail).

double chisquared_cdf_c (double x, double r, double x0=0)
Complement of the cumulative distribution function of the $$\chi^2$$ distribution with $$r$$ degrees of freedom (upper tail).

template<class T >
SVector< T, 3 > Cross (const SVector< T, 3 > &lhs, const SVector< T, 3 > &rhs)
Vector Cross Product (only for 3-dim vectors) $$\vec{c} = \vec{a}\times\vec{b}$$.

template<class T , class A >
SVector< T, 3 > Cross (const SVector< T, 3 > &lhs, const VecExpr< A, T, 3 > &rhs)

template<class A , class T >
SVector< T, 3 > Cross (const VecExpr< A, T, 3 > &lhs, const SVector< T, 3 > &rhs)

template<class A , class B , class T >
SVector< T, 3 > Cross (const VecExpr< A, T, 3 > &lhs, const VecExpr< B, T, 3 > &rhs)

double crystalball_cdf (double x, double alpha, double n, double sigma, double x0=0)
Cumulative distribution for the Crystal Ball distribution function.

double crystalball_cdf_c (double x, double alpha, double n, double sigma, double x0=0)
Complement of the Cumulative distribution for the Crystal Ball distribution.

double crystalball_integral (double x, double alpha, double n, double sigma, double x0=0)
Integral of the not-normalized Crystal Ball function.

template<class Matrix , unsigned int n, unsigned int idim>
bool Dfactir (Matrix &rhs, typename Matrix::value_type &det, unsigned int *ir)
Dfactir.

template<class Matrix , unsigned int n, unsigned int idim>
bool Dfinv (Matrix &rhs, unsigned int *ir)
Dfinv.

template<class R >
AxisAngle::Scalar Distance (const AxisAngle &r1, const R &r2)
Distance between two rotations.

template<class R >
EulerAngles::Scalar Distance (const EulerAngles &r1, const R &r2)
Distance between two rotations.

template<class R >
Quaternion::Scalar Distance (const Quaternion &r1, const R &r2)
Distance between two rotations.

template<class R >
Rotation3D::Scalar Distance (const Rotation3D &r1, const R &r2)
Distance between two rotations.

template<class R >
RotationX::Scalar Distance (const RotationX &r1, const R &r2)
Distance between two rotations.

template<class R >
RotationY::Scalar Distance (const RotationY &r1, const R &r2)
Distance between two rotations.

template<class R >
RotationZ::Scalar Distance (const RotationZ &r1, const R &r2)
Distance between two rotations.

template<class R >
RotationZYX::Scalar Distance (const RotationZYX &r1, const R &r2)
Distance between two rotations.

template<class A , class B , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< DivOp< T >, Expr< A, T, D, D2, R1 >, Expr< B, T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > Div (const Expr< A, T, D, D2, R1 > &lhs, const Expr< B, T, D, D2, R2 > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< DivOp< T >, Expr< A, T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > Div (const Expr< A, T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< DivOp< T >, SMatrix< T, D, D2, R1 >, Expr< A, T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > Div (const SMatrix< T, D, D2, R1 > &lhs, const Expr< A, T, D, D2, R2 > &rhs)

template<class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< DivOp< T >, SMatrix< T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > Div (const SMatrix< T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs)
Division (element wise) of two matrices of the same dimensions: C(i,j) = A(i,j) / B(i,j) returning a matrix expression.

template<class T , unsigned int D>
Dot (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
Vector dot product.

template<class A , class T , unsigned int D>
Dot (const SVector< T, D > &lhs, const VecExpr< A, T, D > &rhs)

template<class A , class T , unsigned int D>
Dot (const VecExpr< A, T, D > &lhs, const SVector< T, D > &rhs)

template<class A , class B , class T , unsigned int D>
Dot (const VecExpr< A, T, D > &lhs, const VecExpr< B, T, D > &rhs)

template<class T >
etaMax ()
Function providing the maximum possible value of pseudorapidity for a non-zero rho, in the Scalar type with the largest dynamic range.

long double etaMax_impl ()
The following function could be called to provide the maximum possible value of pseudorapidity for a non-zero rho.

double expm1 (double x)
exp(x) -1 with error cancellation when x is small

double exponential_cdf (double x, double lambda, double x0=0)
Cumulative distribution function of the exponential distribution (lower tail).

double exponential_cdf_c (double x, double lambda, double x0=0)
Complement of the cumulative distribution function of the exponential distribution (upper tail).

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< UnaryOp< Fabs< T >, Expr< A, T, D, D2, R >, T >, T, D, D2, Rfabs (const Expr< A, T, D, D2, R > &rhs)

template<class T , unsigned int D, unsigned int D2, class R >
Expr< UnaryOp< Fabs< T >, SMatrix< T, D, D2, R >, T >, T, D, D2, Rfabs (const SMatrix< T, D, D2, R > &rhs)
abs of a matrix m2(i,j) = | m1(i,j) | returning a matrix epression

template<class T , unsigned int D>
VecExpr< UnaryOp< Fabs< T >, SVector< T, D >, T >, T, D > fabs (const SVector< T, D > &rhs)
abs of a vector : v2(i) = | v1(i) | returning a vector expression

template<class A , class T , unsigned int D>
VecExpr< UnaryOp< Fabs< T >, VecExpr< A, T, D >, T >, T, D > fabs (const VecExpr< A, T, D > &rhs)

double fdistribution_cdf (double x, double n, double m, double x0=0)
Cumulative distribution function of the F-distribution (lower tail).

double fdistribution_cdf_c (double x, double n, double m, double x0=0)
Complement of the cumulative distribution function of the F-distribution (upper tail).

double gamma_cdf (double x, double alpha, double theta, double x0=0)
Cumulative distribution function of the gamma distribution (lower tail).

double gamma_cdf_c (double x, double alpha, double theta, double x0=0)
Complement of the cumulative distribution function of the gamma distribution (upper tail).

double gaussian_cdf (double x, double sigma=1, double x0=0)
Alternative name for same function.

double gaussian_cdf_c (double x, double sigma=1, double x0=0)
Alternative name for same function.

int getCount (double z, const double *dat, int n)

const gsl_multiroot_fdfsolver_type * GetGSLDerivType (GSLMultiRootFinder::EDerivType type)

const gsl_multiroot_fsolver_type * GetGSLType (GSLMultiRootFinder::EType type)

int getSum (const int *x, int n)

template<class char_t , class traits_t >
std::basic_ios< char_t, traits_t > & human_readable (std::basic_ios< char_t, traits_t > &ios)

double landau_cdf (double x, double xi=1, double x0=0)
Cumulative distribution function of the Landau distribution (lower tail).

double landau_cdf_c (double x, double xi=1, double x0=0)
Complement of the distribution function of the Landau distribution (upper tail).

double landau_xm1 (double x, double xi=1, double x0=0)
First moment (mean) of the truncated Landau distribution.

double landau_xm2 (double x, double xi=1, double x0=0)
Second moment of the truncated Landau distribution.

template<class T >
Lmag (const SVector< T, 4 > &rhs)
Lmag: Minkowski Lorentz-Vector norm (only for 4-dim vectors) Length of a vector Lorentz-Vector: $$|\vec{v}| = \sqrt{v_0^2 - v_1^2 - v_2^2 -v_3^2}$$.

template<class A , class T >
Lmag (const VecExpr< A, T, 4 > &rhs)

template<class T >
Lmag2 (const SVector< T, 4 > &rhs)
Lmag2: Square of Minkowski Lorentz-Vector norm (only for 4D Vectors) Template to compute $$|\vec{v}|^2 = v_0^2 - v_1^2 - v_2^2 -v_3^2$$.

template<class A , class T >
Lmag2 (const VecExpr< A, T, 4 > &rhs)

double log1p (double x)
declarations for functions which are not implemented by some compilers

double lognormal_cdf (double x, double m, double s, double x0=0)
Cumulative distribution function of the lognormal distribution (lower tail).

double lognormal_cdf_c (double x, double m, double s, double x0=0)
Complement of the cumulative distribution function of the lognormal distribution (upper tail).

template<class char_t , class traits_t >
std::basic_ios< char_t, traits_t > & machine_readable (std::basic_ios< char_t, traits_t > &ios)

template<class T , unsigned int D>
Mag (const SVector< T, D > &rhs)
Vector magnitude (Euclidian norm) Compute : $$|\vec{v}| = \sqrt{\sum_iv_i^2}$$.

template<class A , class T , unsigned int D>
Mag (const VecExpr< A, T, D > &rhs)

template<class T , unsigned int D>
Mag2 (const SVector< T, D > &rhs)
Vector magnitude square Template to compute $$|\vec{v}|^2 = \sum_iv_i^2$$.

template<class A , class T , unsigned int D>
Mag2 (const VecExpr< A, T, D > &rhs)

template<class T >
const T Maximum (const T &lhs, const T &rhs)
maximum.

double minfunction (const std::vector< double > &x)
function to return the function values at point x

function to return the gradient values at point y

template<class T >
const T Minimum (const T &lhs, const T &rhs)
minimum.

double negative_binomial_cdf (unsigned int k, double p, double n)
Cumulative distribution function of the Negative Binomial distribution Lower tail of the integral of the negative_binomial_pdf.

double negative_binomial_cdf_c (unsigned int k, double p, double n)
Complement of the cumulative distribution function of the Negative Binomial distribution.

double noncentral_chisquared_pdf (double x, double r, double lambda)
Probability density function of the non central $$\chi^2$$ distribution with $$r$$ degrees of freedom and the noon-central parameter $$\lambda$$.

double normal_cdf (double x, double sigma=1, double x0=0)
Cumulative distribution function of the normal (Gaussian) distribution (lower tail).

double normal_cdf_c (double x, double sigma=1, double x0=0)
Complement of the cumulative distribution function of the normal (Gaussian) distribution (upper tail).

template<class A , class B , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyL< MulOp< T >, Constant< A >, Expr< B, T, D, D2, R >, T >, T, D, D2, Roperator* (const A &lhs, const Expr< B, T, D, D2, R > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyL< MulOp< T >, Constant< A >, SMatrix< T, D, D2, R >, T >, T, D, D2, Roperator* (const A &lhs, const SMatrix< T, D, D2, R > &rhs)
Multiplication (element wise) of a matrix and a scalar, B(i,j) = s * A(i,j) returning a matrix expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyL< MulOp< T >, Constant< A >, SVector< T, D >, T >, T, D > operator* (const A &lhs, const SVector< T, D > &rhs)

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOpCopyL< MulOp< T >, Constant< A >, VecExpr< B, T, D >, T >, T, D > operator* (const A &lhs, const VecExpr< B, T, D > &rhs)

template<class A , class B , class T , unsigned int D1, unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< MatrixMulOp< Expr< A, T, D1, D, R1 >, Expr< B, T, D, D2, R2 >, T, D >, T, D1, D2, typename MultPolicy< T, R1, R2 >::RepType > operator* (const Expr< A, T, D1, D, R1 > &lhs, const Expr< B, T, D, D2, R2 > &rhs)

template<class A , class T , unsigned int D1, unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< MatrixMulOp< Expr< A, T, D1, D, R1 >, SMatrix< T, D, D2, R2 >, T, D >, T, D1, D2, typename MultPolicy< T, R1, R2 >::RepType > operator* (const Expr< A, T, D1, D, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs)

template<class A , class T , unsigned int D1, unsigned int D2, class R >
VecExpr< VectorMatrixRowOp< Expr< A, T, D1, D2, R >, SVector< T, D2 >, D2 >, T, D1 > operator* (const Expr< A, T, D1, D2, R > &lhs, const SVector< T, D2 > &rhs)

template<class A , class B , class T , unsigned int D1, unsigned int D2, class R >
VecExpr< VectorMatrixRowOp< Expr< A, T, D1, D2, R >, VecExpr< B, T, D2 >, D2 >, T, D1 > operator* (const Expr< A, T, D1, D2, R > &lhs, const VecExpr< B, T, D2 > &rhs)

template<class A , class B , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyR< MulOp< T >, Expr< B, T, D, D2, R >, Constant< A >, T >, T, D, D2, Roperator* (const Expr< B, T, D, D2, R > &lhs, const A &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyR< MulOp< T >, SMatrix< T, D, D2, R >, Constant< A >, T >, T, D, D2, Roperator* (const SMatrix< T, D, D2, R > &lhs, const A &rhs)
Multiplication (element wise) of a matrix and a scalar, B(i,j) = A(i,j) * s returning a matrix expression.

template<class A , class T , unsigned int D1, unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< MatrixMulOp< SMatrix< T, D1, D, R1 >, Expr< A, T, D, D2, R2 >, T, D >, T, D1, D2, typename MultPolicy< T, R1, R2 >::RepType > operator* (const SMatrix< T, D1, D, R1 > &lhs, const Expr< A, T, D, D2, R2 > &rhs)

template<class T , unsigned int D1, unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< MatrixMulOp< SMatrix< T, D1, D, R1 >, SMatrix< T, D, D2, R2 >, T, D >, T, D1, D2, typename MultPolicy< T, R1, R2 >::RepType > operator* (const SMatrix< T, D1, D, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs)
Matrix * Matrix multiplication , $$C(i,j) = \sum_{k} A(i,k) * B(k,j)$$ returning a matrix expression.

template<class T , unsigned int D1, unsigned int D2, class R >
VecExpr< VectorMatrixRowOp< SMatrix< T, D1, D2, R >, SVector< T, D2 >, D2 >, T, D1 > operator* (const SMatrix< T, D1, D2, R > &lhs, const SVector< T, D2 > &rhs)
Matrix * Vector multiplication $$a(i) = \sum_{j} M(i,j) * b(j)$$ returning a vector expression.

template<class A , class T , unsigned int D1, unsigned int D2, class R >
VecExpr< VectorMatrixRowOp< SMatrix< T, D1, D2, R >, VecExpr< A, T, D2 >, D2 >, T, D1 > operator* (const SMatrix< T, D1, D2, R > &lhs, const VecExpr< A, T, D2 > &rhs)

template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyR< MulOp< T >, SVector< T, D >, Constant< A >, T >, T, D > operator* (const SVector< T, D > &lhs, const A &rhs)

template<class T , unsigned int D>
VecExpr< BinaryOp< MulOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D > operator* (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
Element by element vector product v3(i) = v1(i)*v2(i) returning a vector expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOp< MulOp< T >, SVector< T, D >, VecExpr< A, T, D >, T >, T, D > operator* (const SVector< T, D > &lhs, const VecExpr< A, T, D > &rhs)

template<class A , class T , unsigned int D1, unsigned int D2, class R >
VecExpr< VectorMatrixColOp< SVector< T, D1 >, Expr< A, T, D1, D2, R >, D1 >, T, D2 > operator* (const SVector< T, D1 > &lhs, const Expr< A, T, D1, D2, R > &rhs)

template<class T , unsigned int D1, unsigned int D2, class R >
VecExpr< VectorMatrixColOp< SVector< T, D1 >, SMatrix< T, D1, D2, R >, D1 >, T, D2 > operator* (const SVector< T, D1 > &lhs, const SMatrix< T, D1, D2, R > &rhs)

template<class CoordSystem >
LorentzVector< CoordSystem > operator* (const typename LorentzVector< CoordSystem >::Scalar &a, const LorentzVector< CoordSystem > &v)
Scale of a LorentzVector with a scalar quantity a.

template<class A , class T , unsigned int D>
VecExpr< BinaryOp< MulOp< T >, Expr< A, T, D >, SVector< T, D >, T >, T, D > operator* (const VecExpr< A, T, D > &lhs, const SVector< T, D > &rhs)

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOp< MulOp< T >, VecExpr< A, T, D >, VecExpr< B, T, D >, T >, T, D > operator* (const VecExpr< A, T, D > &lhs, const VecExpr< B, T, D > &rhs)

template<class A , class B , class T , unsigned int D1, unsigned int D2, class R >
VecExpr< VectorMatrixColOp< VecExpr< A, T, D1 >, Expr< B, T, D1, D2, R >, D1 >, T, D2 > operator* (const VecExpr< A, T, D1 > &lhs, const Expr< B, T, D1, D2, R > &rhs)

template<class A , class T , unsigned int D1, unsigned int D2, class R >
VecExpr< VectorMatrixColOp< VecExpr< A, T, D1 >, SMatrix< T, D1, D2, R >, D1 >, T, D2 > operator* (const VecExpr< A, T, D1 > &lhs, const SMatrix< T, D1, D2, R > &rhs)

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOpCopyR< MulOp< T >, VecExpr< B, T, D >, Constant< A >, T >, T, D > operator* (const VecExpr< B, T, D > &lhs, const A &rhs)

AxisAngle operator* (RotationX const &r1, AxisAngle const &r2)
Multiplication of an axial rotation by an AxisAngle.

EulerAngles operator* (RotationX const &r1, EulerAngles const &r2)
Multiplication of an axial rotation by an AxisAngle.

Quaternion operator* (RotationX const &r1, Quaternion const &r2)
Multiplication of an axial rotation by an AxisAngle.

Rotation3D operator* (RotationX const &r1, Rotation3D const &r2)
Multiplication of an axial rotation by a Rotation3D.

Rotation3D operator* (RotationX const &r1, RotationY const &r2)
Multiplication of an axial rotation by another axial Rotation.

Rotation3D operator* (RotationX const &r1, RotationZ const &r2)

RotationZYX operator* (RotationX const &r1, RotationZYX const &r2)
Multiplication of an axial rotation by an AxisAngle.

AxisAngle operator* (RotationY const &r1, AxisAngle const &r2)

EulerAngles operator* (RotationY const &r1, EulerAngles const &r2)

Quaternion operator* (RotationY const &r1, Quaternion const &r2)

Rotation3D operator* (RotationY const &r1, Rotation3D const &r2)

Rotation3D operator* (RotationY const &r1, RotationX const &r2)

Rotation3D operator* (RotationY const &r1, RotationZ const &r2)

RotationZYX operator* (RotationY const &r1, RotationZYX const &r2)

AxisAngle operator* (RotationZ const &r1, AxisAngle const &r2)

EulerAngles operator* (RotationZ const &r1, EulerAngles const &r2)

Quaternion operator* (RotationZ const &r1, Quaternion const &r2)

Rotation3D operator* (RotationZ const &r1, Rotation3D const &r2)

Rotation3D operator* (RotationZ const &r1, RotationX const &r2)

Rotation3D operator* (RotationZ const &r1, RotationY const &r2)

RotationZYX operator* (RotationZ const &r1, RotationZYX const &r2)

template<class CoordSystem , class U >
DisplacementVector2D< CoordSystem, U > operator* (typename DisplacementVector2D< CoordSystem, U >::Scalar a, DisplacementVector2D< CoordSystem, U > v)
Multiplication of a displacement vector by real number a*v.

template<class CoordSystem , class U >
DisplacementVector3D< CoordSystem, U > operator* (typename DisplacementVector3D< CoordSystem, U >::Scalar a, DisplacementVector3D< CoordSystem, U > v)
Multiplication of a displacement vector by real number a*v.

template<class CoordSystem , class U >
PositionVector2D< CoordSystem > operator* (typename PositionVector2D< CoordSystem, U >::Scalar a, PositionVector2D< CoordSystem, U > v)
Multiplication of a position vector by real number a*v.

template<class CoordSystem , class U >
PositionVector3D< CoordSystem > operator* (typename PositionVector3D< CoordSystem, U >::Scalar a, PositionVector3D< CoordSystem, U > v)
Multiplication of a position vector by real number a*v.

template<class A , class B , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyL< AddOp< T >, Constant< A >, Expr< B, T, D, D2, R >, T >, T, D, D2, Roperator+ (const A &lhs, const Expr< B, T, D, D2, R > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyL< AddOp< T >, Constant< A >, SMatrix< T, D, D2, R >, T >, T, D, D2, Roperator+ (const A &lhs, const SMatrix< T, D, D2, R > &rhs)
Addition element by element of matrix and a scalar C(i,j) = s + A(i,j) returning a matrix expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyL< AddOp< T >, Constant< A >, SVector< T, D >, T >, T, D > operator+ (const A &lhs, const SVector< T, D > &rhs)
Addition of a scalar to each vector element v2(i) = a + v1(i) returning a vector expression.

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOpCopyL< AddOp< T >, Constant< A >, VecExpr< B, T, D >, T >, T, D > operator+ (const A &lhs, const VecExpr< B, T, D > &rhs)

template<class A , class B , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< AddOp< T >, Expr< A, T, D, D2, R1 >, Expr< B, T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > operator+ (const Expr< A, T, D, D2, R1 > &lhs, const Expr< B, T, D, D2, R2 > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< AddOp< T >, Expr< A, T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > operator+ (const Expr< A, T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs)

template<class A , class B , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyR< AddOp< T >, Expr< B, T, D, D2, R >, Constant< A >, T >, T, D, D2, Roperator+ (const Expr< B, T, D, D2, R > &lhs, const A &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyR< AddOp< T >, SMatrix< T, D, D2, R >, Constant< A >, T >, T, D, D2, Roperator+ (const SMatrix< T, D, D2, R > &lhs, const A &rhs)
Addition element by element of matrix and a scalar C(i,j) = A(i,j) + s returning a matrix expression.

template<class A , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< AddOp< T >, SMatrix< T, D, D2, R1 >, Expr< A, T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > operator+ (const SMatrix< T, D, D2, R1 > &lhs, const Expr< A, T, D, D2, R2 > &rhs)

template<class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< AddOp< T >, SMatrix< T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > operator+ (const SMatrix< T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs)
Addition of two matrices C = A+B returning a matrix expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyR< AddOp< T >, SVector< T, D >, Constant< A >, T >, T, D > operator+ (const SVector< T, D > &lhs, const A &rhs)
Addition of a scalar to a each vector element: v2(i) = v1(i) + a returning a vector expression.

template<class T , unsigned int D>
VecExpr< BinaryOp< AddOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D > operator+ (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
Addition of two vectors v3 = v1+v2 returning a vector expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOp< AddOp< T >, SVector< T, D >, VecExpr< A, T, D >, T >, T, D > operator+ (const SVector< T, D > &lhs, const VecExpr< A, T, D > &rhs)

template<class A , class T , unsigned int D>
VecExpr< BinaryOp< AddOp< T >, VecExpr< A, T, D >, SVector< T, D >, T >, T, D > operator+ (const VecExpr< A, T, D > &lhs, const SVector< T, D > &rhs)

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOp< AddOp< T >, VecExpr< A, T, D >, VecExpr< B, T, D >, T >, T, D > operator+ (const VecExpr< A, T, D > &lhs, const VecExpr< B, T, D > &rhs)

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOpCopyR< AddOp< T >, VecExpr< B, T, D >, Constant< A >, T >, T, D > operator+ (const VecExpr< B, T, D > &lhs, const A &rhs)

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector2D< CoordSystem2, U > operator+ (DisplacementVector2D< CoordSystem1, U > const &v1, PositionVector2D< CoordSystem2, U > p2)
Addition of a DisplacementVector2D and a PositionVector2D.

template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector2D< CoordSystem1, U > operator+ (DisplacementVector2D< CoordSystem1, U > v1, const DisplacementVector2D< CoordSystem2, U > &v2)

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector3D< CoordSystem2, U > operator+ (DisplacementVector3D< CoordSystem1, U > const &v1, PositionVector3D< CoordSystem2, U > p2)
Addition of a DisplacementVector3D and a PositionVector3D.

template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector3D< CoordSystem1, U > operator+ (DisplacementVector3D< CoordSystem1, U > v1, const DisplacementVector3D< CoordSystem2, U > &v2)

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector2D< CoordSystem2, U > operator+ (PositionVector2D< CoordSystem2, U > p1, const DisplacementVector2D< CoordSystem1, U > &v2)
Addition of a PositionVector2D and a DisplacementVector2D.

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector3D< CoordSystem2, U > operator+ (PositionVector3D< CoordSystem2, U > p1, const DisplacementVector3D< CoordSystem1, U > &v2)
Addition of a PositionVector3D and a DisplacementVector3D.

template<class A , class B , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyL< MinOp< T >, Constant< A >, Expr< B, T, D, D2, R >, T >, T, D, D2, Roperator- (const A &lhs, const Expr< B, T, D, D2, R > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyL< MinOp< T >, Constant< A >, SMatrix< T, D, D2, R >, T >, T, D, D2, Roperator- (const A &lhs, const SMatrix< T, D, D2, R > &rhs)
Subtraction of a scalar and a matrix (element wise) B(i,j) = s - A(i,j) returning a matrix expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyL< MinOp< T >, Constant< A >, SVector< T, D >, T >, T, D > operator- (const A &lhs, const SVector< T, D > &rhs)
Subtraction scalar vector (for each vector element) v2(i) = a - v1(i) returning a vector expression.

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOpCopyL< MinOp< T >, Constant< A >, VecExpr< B, T, D >, T >, T, D > operator- (const A &lhs, const VecExpr< B, T, D > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< UnaryOp< Minus< T >, Expr< A, T, D, D2, R >, T >, T, D, D2, Roperator- (const Expr< A, T, D, D2, R > &rhs)

template<class A , class B , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< MinOp< T >, Expr< A, T, D, D2, R1 >, Expr< B, T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > operator- (const Expr< A, T, D, D2, R1 > &lhs, const Expr< B, T, D, D2, R2 > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< MinOp< T >, Expr< A, T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > operator- (const Expr< A, T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs)

template<class A , class B , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyR< MinOp< T >, Expr< B, T, D, D2, R >, Constant< A >, T >, T, D, D2, Roperator- (const Expr< B, T, D, D2, R > &lhs, const A &rhs)

template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector2D< CoordSystem1, U > operator- (const PositionVector2D< CoordSystem1, U > &v1, const PositionVector2D< CoordSystem2, U > &v2)
Difference between two PositionVector2D vectors.

template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector3D< CoordSystem1, U > operator- (const PositionVector3D< CoordSystem1, U > &v1, const PositionVector3D< CoordSystem2, U > &v2)
Difference between two PositionVector3D vectors.

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyR< MinOp< T >, SMatrix< T, D, D2, R >, Constant< A >, T >, T, D, D2, Roperator- (const SMatrix< T, D, D2, R > &lhs, const A &rhs)
Subtraction of a scalar and a matrix (element wise) B(i,j) = A(i,j) - s returning a matrix expression.

template<class T , unsigned int D, unsigned int D2, class R >
Expr< UnaryOp< Minus< T >, SMatrix< T, D, D2, R >, T >, T, D, D2, Roperator- (const SMatrix< T, D, D2, R > &rhs)
Unary - operator B = - A returning a matrix expression.

template<class A , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< MinOp< T >, SMatrix< T, D, D2, R1 >, Expr< A, T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > operator- (const SMatrix< T, D, D2, R1 > &lhs, const Expr< A, T, D, D2, R2 > &rhs)

template<class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< MinOp< T >, SMatrix< T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > operator- (const SMatrix< T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs)
Subtraction of two matrices C = A-B returning a matrix expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyR< MinOp< T >, SVector< T, D >, Constant< A >, T >, T, D > operator- (const SVector< T, D > &lhs, const A &rhs)
Subtraction of a scalar from each vector element: v2(i) = v1(i) - a returning a vector expression.

template<class T , unsigned int D>
VecExpr< BinaryOp< MinOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D > operator- (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
Vector Subtraction: v3 = v1 - v2 returning a vector expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOp< MinOp< T >, SVector< T, D >, VecExpr< A, T, D >, T >, T, D > operator- (const SVector< T, D > &lhs, const VecExpr< A, T, D > &rhs)

template<class T , unsigned int D>
VecExpr< UnaryOp< Minus< T >, SVector< T, D >, T >, T, D > operator- (const SVector< T, D > &rhs)
Unary - operator v2 = -v1 .

template<class A , class T , unsigned int D>
VecExpr< BinaryOp< MinOp< T >, VecExpr< A, T, D >, SVector< T, D >, T >, T, D > operator- (const VecExpr< A, T, D > &lhs, const SVector< T, D > &rhs)

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOp< MinOp< T >, VecExpr< A, T, D >, VecExpr< B, T, D >, T >, T, D > operator- (const VecExpr< A, T, D > &lhs, const VecExpr< B, T, D > &rhs)

template<class A , class T , unsigned int D>
VecExpr< UnaryOp< Minus< T >, VecExpr< A, T, D >, T >, T, D > operator- (const VecExpr< A, T, D > &rhs)

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOpCopyR< MinOp< T >, VecExpr< B, T, D >, Constant< A >, T >, T, D > operator- (const VecExpr< B, T, D > &lhs, const A &rhs)

template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector2D< CoordSystem1, U > operator- (DisplacementVector2D< CoordSystem1, U > v1, DisplacementVector2D< CoordSystem2, U > const &v2)
Difference between two DisplacementVector2D vectors.

template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector3D< CoordSystem1, U > operator- (DisplacementVector3D< CoordSystem1, U > v1, DisplacementVector3D< CoordSystem2, U > const &v2)
Difference between two DisplacementVector3D vectors.

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector2D< CoordSystem2, U > operator- (PositionVector2D< CoordSystem2, U > p1, DisplacementVector2D< CoordSystem1, U > const &v2)
Subtraction of a DisplacementVector2D from a PositionVector2D.

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector3D< CoordSystem2, U > operator- (PositionVector3D< CoordSystem2, U > p1, DisplacementVector3D< CoordSystem1, U > const &v2)
Subtraction of a DisplacementVector3D from a PositionVector3D.

template<class A , class B , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyL< DivOp< T >, Constant< A >, Expr< B, T, D, D2, R >, T >, T, D, D2, Roperator/ (const A &lhs, const Expr< B, T, D, D2, R > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyL< DivOp< T >, Constant< A >, SMatrix< T, D, D2, R >, T >, T, D, D2, Roperator/ (const A &lhs, const SMatrix< T, D, D2, R > &rhs)
Division (element wise) of a matrix and a scalar, B(i,j) = s / A(i,j) returning a matrix expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyL< DivOp< T >, Constant< A >, SVector< T, D >, T >, T, D > operator/ (const A &lhs, const SVector< T, D > &rhs)
Division of a scalar value by the vector element: v2(i) = a/v1(i) returning a vector expression.

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOpCopyL< DivOp< T >, Constant< A >, VecExpr< B, T, D >, T >, T, D > operator/ (const A &lhs, const VecExpr< B, T, D > &rhs)

template<class A , class B , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyR< DivOp< T >, Expr< B, T, D, D2, R >, Constant< A >, T >, T, D, D2, Roperator/ (const Expr< B, T, D, D2, R > &lhs, const A &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< BinaryOpCopyR< DivOp< T >, SMatrix< T, D, D2, R >, Constant< A >, T >, T, D, D2, Roperator/ (const SMatrix< T, D, D2, R > &lhs, const A &rhs)
Division (element wise) of a matrix and a scalar, B(i,j) = A(i,j) / s returning a matrix expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyR< DivOp< T >, SVector< T, D >, Constant< A >, T >, T, D > operator/ (const SVector< T, D > &lhs, const A &rhs)
Division of the vector element by a scalar value: v2(i) = v1(i)/a returning a vector expression.

template<class T , unsigned int D>
VecExpr< BinaryOp< DivOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D > operator/ (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
Element by element division of vectors of the same dimension: v3(i) = v1(i)/v2(i) returning a vector expression.

template<class A , class T , unsigned int D>
VecExpr< BinaryOp< DivOp< T >, SVector< T, D >, VecExpr< A, T, D >, T >, T, D > operator/ (const SVector< T, D > &lhs, const VecExpr< A, T, D > &rhs)

template<class A , class T , unsigned int D>
VecExpr< BinaryOp< DivOp< T >, VecExpr< A, T, D >, SVector< T, D >, T >, T, D > operator/ (const VecExpr< A, T, D > &lhs, const SVector< T, D > &rhs)

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOp< DivOp< T >, VecExpr< A, T, D >, VecExpr< B, T, D >, T >, T, D > operator/ (const VecExpr< A, T, D > &lhs, const VecExpr< B, T, D > &rhs)

template<class A , class B , class T , unsigned int D>
VecExpr< BinaryOpCopyR< DivOp< T >, VecExpr< B, T, D >, Constant< A >, T >, T, D > operator/ (const VecExpr< B, T, D > &lhs, const A &rhs)

template<class char_t , class traits_t , class T , class U >
std::basic_ostream< char_t, traits_t > & operator<< (std::basic_ostream< char_t, traits_t > &os, DisplacementVector2D< T, U > const &v)

template<class char_t , class traits_t , class T , class U , typename std::enable_if< std::is_arithmetic< typename DisplacementVector3D< T, U >::Scalar >::value >::type * = nullptr>
std::basic_ostream< char_t, traits_t > & operator<< (std::basic_ostream< char_t, traits_t > &os, DisplacementVector3D< T, U > const &v)

template<class char_t , class traits_t , class Coords >
std::basic_ostream< char_t, traits_t > & operator<< (std::basic_ostream< char_t, traits_t > &os, LorentzVector< Coords > const &v)

template<class char_t , class traits_t , class T , class U >
std::basic_ostream< char_t, traits_t > & operator<< (std::basic_ostream< char_t, traits_t > &os, PositionVector2D< T, U > const &v)

template<class char_t , class traits_t , class T , class U , typename std::enable_if< std::is_arithmetic< typename PositionVector3D< T, U >::Scalar >::value >::type * = nullptr>
std::basic_ostream< char_t, traits_t > & operator<< (std::basic_ostream< char_t, traits_t > &os, PositionVector3D< T, U > const &v)

std::ostream & operator<< (std::ostream &os, const AxisAngle &a)
Stream Output and Input.

std::ostream & operator<< (std::ostream &os, const Boost &b)
Stream Output and Input.

std::ostream & operator<< (std::ostream &os, const BoostX &b)
Stream Output and Input.

std::ostream & operator<< (std::ostream &os, const BoostY &b)
Stream Output and Input.

std::ostream & operator<< (std::ostream &os, const BoostZ &b)
Stream Output and Input.

std::ostream & operator<< (std::ostream &os, const EulerAngles &e)
Stream Output and Input.

template<class A , class T , unsigned int D1, unsigned int D2, class R1 >
std::ostream & operator<< (std::ostream &os, const Expr< A, T, D1, D2, R1 > &rhs)

std::ostream & operator<< (std::ostream &os, const LorentzRotation &r)
Stream Output and Input.

std::ostream & operator<< (std::ostream &os, const Quaternion &q)
Stream Output and Input.

template<class T , unsigned int D1, unsigned int D2, class R >
std::ostream & operator<< (std::ostream &os, const ROOT::Math::SMatrix< T, D1, D2, R > &rhs)

template<class T , unsigned int D>
std::ostream & operator<< (std::ostream &os, const ROOT::Math::SVector< T, D > &rhs)

std::ostream & operator<< (std::ostream &os, const Rotation3D &r)
Stream Output and Input.

std::ostream & operator<< (std::ostream &os, const RotationX &r)
Stream Output and Input.

std::ostream & operator<< (std::ostream &os, const RotationY &r)
Stream Output and Input.

std::ostream & operator<< (std::ostream &os, const RotationZ &r)
Stream Output and Input.

std::ostream & operator<< (std::ostream &os, const RotationZYX &e)
Stream Output and Input.

template<class A , class T , unsigned int D>
std::ostream & operator<< (std::ostream &os, const VecExpr< A, T, D > &rhs)

template<class char_t , class traits_t , class T , class U >
std::basic_istream< char_t, traits_t > & operator>> (std::basic_istream< char_t, traits_t > &is, DisplacementVector2D< T, U > &v)

template<class char_t , class traits_t , class T , class U >
std::basic_istream< char_t, traits_t > & operator>> (std::basic_istream< char_t, traits_t > &is, DisplacementVector3D< T, U > &v)

template<class char_t , class traits_t , class Coords >
std::basic_istream< char_t, traits_t > & operator>> (std::basic_istream< char_t, traits_t > &is, LorentzVector< Coords > &v)

template<class char_t , class traits_t , class T , class U >
std::basic_istream< char_t, traits_t > & operator>> (std::basic_istream< char_t, traits_t > &is, PositionVector2D< T, U > &v)

template<class char_t , class traits_t , class T , class U >
std::basic_istream< char_t, traits_t > & operator>> (std::basic_istream< char_t, traits_t > &is, PositionVector3D< T, U > &v)

double Pi ()
Mathematical constants.

double poisson_cdf (unsigned int n, double mu)
Cumulative distribution function of the Poisson distribution Lower tail of the integral of the poisson_pdf.

double poisson_cdf_c (unsigned int n, double mu)
Complement of the cumulative distribution function of the Poisson distribution.

double Polynomial1eval (double x, double *a, unsigned int N)

double Polynomialeval (double x, double *a, unsigned int N)

template<class T >
int Round (const T &x)
round.

template<class char_t >
detail::manipulator< char_t > set_close (char_t ch)

template<class char_t >
detail::manipulator< char_t > set_open (char_t ch)

template<class char_t >
detail::manipulator< char_t > set_separator (char_t ch)

template<class T >
int Sign (const T &x)
sign.

template<class A , class T , unsigned int D, class R >
Similarity (const Expr< A, T, D, D, R > &lhs, const SVector< T, D > &rhs)

template<class A , class B , class T , unsigned int D, class R >
Similarity (const Expr< A, T, D, D, R > &lhs, const VecExpr< B, T, D > &rhs)

template<class A , class T , unsigned int D1, unsigned int D2, class R >
SMatrix< T, D1, D1, MatRepSym< T, D1 > > Similarity (const Expr< A, T, D1, D2, R > &lhs, const SMatrix< T, D2, D2, MatRepSym< T, D2 > > &rhs)

template<class T , unsigned int D, class R >
Similarity (const SMatrix< T, D, D, R > &lhs, const SVector< T, D > &rhs)
Similarity Vector - Matrix Product: v^T * A * v returning a scalar value of type T $$s = \sum_{i,j} v(i) * A(i,j) * v(j)$$.

template<class A , class T , unsigned int D, class R >
Similarity (const SMatrix< T, D, D, R > &lhs, const VecExpr< A, T, D > &rhs)

template<class T , unsigned int D1, unsigned int D2, class R >
SMatrix< T, D1, D1, MatRepSym< T, D1 > > Similarity (const SMatrix< T, D1, D2, R > &lhs, const SMatrix< T, D2, D2, MatRepSym< T, D2 > > &rhs)
Similarity Matrix Product : B = U * A * U^T for A symmetric returning a symmetric matrix expression: $$B(i,j) = \sum_{k,l} U(i,k) * A(k,l) * U(j,l)$$.

template<class A , class T , unsigned int D, class R >
Similarity (const SVector< T, D > &lhs, const Expr< A, T, D, D, R > &rhs)

template<class T , unsigned int D, class R >
Similarity (const SVector< T, D > &lhs, const SMatrix< T, D, D, R > &rhs)

template<class A , class B , class T , unsigned int D, class R >
Similarity (const VecExpr< A, T, D > &lhs, const Expr< B, T, D, D, R > &rhs)

template<class A , class T , unsigned int D, class R >
Similarity (const VecExpr< A, T, D > &lhs, const SMatrix< T, D, D, R > &rhs)

template<class A , class T , unsigned int D1, unsigned int D2, class R >
SMatrix< T, D2, D2, MatRepSym< T, D2 > > SimilarityT (const Expr< A, T, D1, D2, R > &lhs, const SMatrix< T, D1, D1, MatRepSym< T, D1 > > &rhs)

template<class T , unsigned int D1, unsigned int D2, class R >
SMatrix< T, D2, D2, MatRepSym< T, D2 > > SimilarityT (const SMatrix< T, D1, D2, R > &lhs, const SMatrix< T, D1, D1, MatRepSym< T, D1 > > &rhs)
Transpose Similarity Matrix Product : B = U^T * A * U for A symmetric returning a symmetric matrix expression: $$B(i,j) = \sum_{k,l} U(k,i) * A(k,l) * U(l,j)$$.

template<class T , unsigned int D>
SVector< T, D > SolveChol (const SMatrix< T, D, D, MatRepSym< T, D > > &mat, const SVector< T, D > &vec, int &ifail)
same function as before but not overwriting the matrix and returning a copy of the vector (this is the slow version)

template<class T , unsigned int D>
bool SolveChol (SMatrix< T, D, D, MatRepSym< T, D > > &mat, SVector< T, D > &vec)

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< UnaryOp< Sqr< T >, Expr< A, T, D, D2, R >, T >, T, D, D2, Rsqr (const Expr< A, T, D, D2, R > &rhs)

template<class T , unsigned int D, unsigned int D2, class R >
Expr< UnaryOp< Sqr< T >, SMatrix< T, D, D2, R >, T >, T, D, D2, Rsqr (const SMatrix< T, D, D2, R > &rhs)
square of a matrix B(i,j) = A(i,j)*A(i,j) returning a matrix expression

template<class T , unsigned int D>
VecExpr< UnaryOp< Sqr< T >, SVector< T, D >, T >, T, D > sqr (const SVector< T, D > &rhs)
square of a vector v2(i) = v1(i)*v1(i) .

template<class A , class T , unsigned int D>
VecExpr< UnaryOp< Sqr< T >, VecExpr< A, T, D >, T >, T, D > sqr (const VecExpr< A, T, D > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R >
Expr< UnaryOp< Sqrt< T >, Expr< A, T, D, D2, R >, T >, T, D, D2, Rsqrt (const Expr< A, T, D, D2, R > &rhs)

template<class T , unsigned int D, unsigned int D2, class R >
Expr< UnaryOp< Sqrt< T >, SMatrix< T, D, D2, R >, T >, T, D, D2, Rsqrt (const SMatrix< T, D, D2, R > &rhs)
square root of a matrix (element by element) m2(i,j) = sqrt ( m1(i,j) ) returning a matrix expression

template<class T , unsigned int D>
VecExpr< UnaryOp< Sqrt< T >, SVector< T, D >, T >, T, D > sqrt (const SVector< T, D > &rhs)
square root of a vector (element by element) v2(i) = sqrt( v1(i) ) returning a vector expression

template<class A , class T , unsigned int D>
VecExpr< UnaryOp< Sqrt< T >, VecExpr< A, T, D >, T >, T, D > sqrt (const VecExpr< A, T, D > &rhs)

template<class T >
const T Square (const T &x)
square Template function to compute $$x\cdot x$$, for any type T returning a type T

static void swap (double &a, double &b)

double tdistribution_cdf (double x, double r, double x0=0)
Cumulative distribution function of Student's t-distribution (lower tail).

double tdistribution_cdf_c (double x, double r, double x0=0)
Complement of the cumulative distribution function of Student's t-distribution (upper tail).

template<class T , unsigned int D1, unsigned int D2>
Expr< TensorMulOp< SVector< T, D1 >, SVector< T, D2 > >, T, D1, D2 > TensorProd (const SVector< T, D1 > &lhs, const SVector< T, D2 > &rhs)
Tensor Vector Product : M(i,j) = v(i) * v(j) returning a matrix expression.

template<class T , unsigned int D1, unsigned int D2, class A >
Expr< TensorMulOp< SVector< T, D1 >, VecExpr< A, T, D2 > >, T, D1, D2 > TensorProd (const SVector< T, D1 > &lhs, const VecExpr< A, T, D2 > &rhs)

template<class T , unsigned int D1, unsigned int D2, class A >
Expr< TensorMulOp< VecExpr< A, T, D1 >, SVector< T, D2 > >, T, D1, D2 > TensorProd (const VecExpr< A, T, D1 > &lhs, const SVector< T, D2 > &rhs)

template<class T , unsigned int D1, unsigned int D2, class A , class B >
Expr< TensorMulOp< VecExpr< A, T, D1 >, VecExpr< B, T, D2 > >, T, D1, D2 > TensorProd (const VecExpr< A, T, D1 > &lhs, const VecExpr< B, T, D2 > &rhs)

void Throw (GenVector_exception &e)
throw explicity GenVector exceptions

template<class A , class B , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< MulOp< T >, Expr< A, T, D, D2, R1 >, Expr< B, T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > Times (const Expr< A, T, D, D2, R1 > &lhs, const Expr< B, T, D, D2, R2 > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< MulOp< T >, Expr< A, T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > Times (const Expr< A, T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs)

template<class A , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< MulOp< T >, SMatrix< T, D, D2, R1 >, Expr< A, T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > Times (const SMatrix< T, D, D2, R1 > &lhs, const Expr< A, T, D, D2, R2 > &rhs)

template<class T , unsigned int D, unsigned int D2, class R1 , class R2 >
Expr< BinaryOp< MulOp< T >, SMatrix< T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > Times (const SMatrix< T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs)
Element by element matrix multiplication C(i,j) = A(i,j)*B(i,j) returning a matrix expression.

template<class A , class T , unsigned int D1, unsigned int D2, class R >
Expr< TransposeOp< Expr< A, T, D1, D2, R >, T, D1, D2 >, T, D2, D1, typename TranspPolicy< T, D1, D2, R >::RepType > Transpose (const Expr< A, T, D1, D2, R > &rhs)

template<class T , unsigned int D1, unsigned int D2, class R >
Expr< TransposeOp< SMatrix< T, D1, D2, R >, T, D1, D2 >, T, D2, D1, typename TranspPolicy< T, D1, D2, R >::RepType > Transpose (const SMatrix< T, D1, D2, R > &rhs)
Matrix Transpose B(i,j) = A(j,i) returning a matrix expression.

double uniform_cdf (double x, double a, double b, double x0=0)
Cumulative distribution function of the uniform (flat) distribution (lower tail).

double uniform_cdf_c (double x, double a, double b, double x0=0)
Complement of the cumulative distribution function of the uniform (flat) distribution (upper tail).

template<class T , unsigned int D>
SVector< T, D > Unit (const SVector< T, D > &rhs)
Unit.

template<class A , class T , unsigned int D>
SVector< T, D > Unit (const VecExpr< A, T, D > &rhs)

double vavilov_accurate_cdf (double x, double kappa, double beta2)
The Vavilov cumulative probability density function.

double vavilov_accurate_cdf_c (double x, double kappa, double beta2)
The Vavilov complementary cumulative probability density function.

double vavilov_accurate_pdf (double x, double kappa, double beta2)
The Vavilov probability density function.

double vavilov_accurate_quantile (double z, double kappa, double beta2)
The inverse of the Vavilov cumulative probability density function.

double vavilov_accurate_quantile_c (double z, double kappa, double beta2)
The inverse of the complementary Vavilov cumulative probability density function.

double vavilov_fast_cdf (double x, double kappa, double beta2)
The Vavilov cumulative probability density function.

double vavilov_fast_cdf_c (double x, double kappa, double beta2)
The Vavilov complementary cumulative probability density function.

double vavilov_fast_pdf (double x, double kappa, double beta2)
The Vavilov probability density function.

double vavilov_fast_quantile (double z, double kappa, double beta2)
The inverse of the Vavilov cumulative probability density function.

double vavilov_fast_quantile_c (double z, double kappa, double beta2)
The inverse of the complementary Vavilov cumulative probability density function.

Probability Density Functions from MathCore

Additional PDF's are provided in the MathMore library (see PDF functions from MathMore)

double beta_pdf (double x, double a, double b)
Probability density function of the beta distribution.

double binomial_pdf (unsigned int k, double p, unsigned int n)
Probability density function of the binomial distribution.

double negative_binomial_pdf (unsigned int k, double p, double n)
Probability density function of the negative binomial distribution.

double breitwigner_pdf (double x, double gamma, double x0=0)
Probability density function of Breit-Wigner distribution, which is similar, just a different definition of the parameters, to the Cauchy distribution (see cauchy_pdf )

double cauchy_pdf (double x, double b=1, double x0=0)
Probability density function of the Cauchy distribution which is also called Lorentzian distribution.

double chisquared_pdf (double x, double r, double x0=0)
Probability density function of the $$\chi^2$$ distribution with $$r$$ degrees of freedom.

double crystalball_function (double x, double alpha, double n, double sigma, double mean=0)
Crystal ball function.

double crystalball_pdf (double x, double alpha, double n, double sigma, double mean=0)
pdf definition of the crystal_ball which is defined only for n > 1 otherwise integral is diverging

double exponential_pdf (double x, double lambda, double x0=0)
Probability density function of the exponential distribution.

double fdistribution_pdf (double x, double n, double m, double x0=0)
Probability density function of the F-distribution.

double gamma_pdf (double x, double alpha, double theta, double x0=0)
Probability density function of the gamma distribution.

double gaussian_pdf (double x, double sigma=1, double x0=0)
Probability density function of the normal (Gaussian) distribution.

double bigaussian_pdf (double x, double y, double sigmax=1, double sigmay=1, double rho=0, double x0=0, double y0=0)
Probability density function of the bi-dimensional (Gaussian) distribution.

double landau_pdf (double x, double xi=1, double x0=0)
Probability density function of the Landau distribution:

double lognormal_pdf (double x, double m, double s, double x0=0)
Probability density function of the lognormal distribution.

double normal_pdf (double x, double sigma=1, double x0=0)
Probability density function of the normal (Gaussian) distribution.

double poisson_pdf (unsigned int n, double mu)
Probability density function of the Poisson distribution.

double tdistribution_pdf (double x, double r, double x0=0)
Probability density function of Student's t-distribution.

double uniform_pdf (double x, double a, double b, double x0=0)
Probability density function of the uniform (flat) distribution.

Quantile Functions from MathCore

The implementation is provided in MathCore and for the majority of the function comes from Cephes.

double beta_quantile (double x, double a, double b)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the beta distribution (beta_cdf_c).

double beta_quantile_c (double x, double a, double b)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the beta distribution (beta_cdf).

double cauchy_quantile_c (double z, double b)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the Cauchy distribution (cauchy_cdf_c) which is also called Lorentzian distribution.

double cauchy_quantile (double z, double b)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the Cauchy distribution (cauchy_cdf) which is also called Breit-Wigner or Lorentzian distribution.

double breitwigner_quantile_c (double z, double gamma)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the Breit-Wigner distribution (breitwigner_cdf_c) which is similar to the Cauchy distribution.

double breitwigner_quantile (double z, double gamma)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the Breit_Wigner distribution (breitwigner_cdf) which is similar to the Cauchy distribution.

double chisquared_quantile_c (double z, double r)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the $$\chi^2$$ distribution with $$r$$ degrees of freedom (chisquared_cdf_c).

double chisquared_quantile (double z, double r)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the $$\chi^2$$ distribution with $$r$$ degrees of freedom (chisquared_cdf).

double exponential_quantile_c (double z, double lambda)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the exponential distribution (exponential_cdf_c).

double exponential_quantile (double z, double lambda)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the exponential distribution (exponential_cdf).

double fdistribution_quantile (double z, double n, double m)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the f distribution (fdistribution_cdf).

double fdistribution_quantile_c (double z, double n, double m)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the f distribution (fdistribution_cdf_c).

double gamma_quantile_c (double z, double alpha, double theta)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the gamma distribution (gamma_cdf_c).

double gamma_quantile (double z, double alpha, double theta)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the gamma distribution (gamma_cdf).

double gaussian_quantile_c (double z, double sigma)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the normal (Gaussian) distribution (gaussian_cdf_c).

double gaussian_quantile (double z, double sigma)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the normal (Gaussian) distribution (gaussian_cdf).

double lognormal_quantile_c (double x, double m, double s)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the lognormal distribution (lognormal_cdf_c).

double lognormal_quantile (double x, double m, double s)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the lognormal distribution (lognormal_cdf).

double normal_quantile_c (double z, double sigma)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the normal (Gaussian) distribution (normal_cdf_c).

double normal_quantile (double z, double sigma)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the normal (Gaussian) distribution (normal_cdf).

double uniform_quantile_c (double z, double a, double b)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the uniform (flat) distribution (uniform_cdf_c).

double uniform_quantile (double z, double a, double b)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the uniform (flat) distribution (uniform_cdf).

double landau_quantile (double z, double xi=1)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of the Landau distribution (landau_cdf).

double landau_quantile_c (double z, double xi=1)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of the landau distribution (landau_cdf_c).

Special Functions from MathCore
double erf (double x)
Error function encountered in integrating the normal distribution.

double erfc (double x)
Complementary error function.

double tgamma (double x)
The gamma function is defined to be the extension of the factorial to real numbers.

double lgamma (double x)
Calculates the logarithm of the gamma function.

double inc_gamma (double a, double x)
Calculates the normalized (regularized) lower incomplete gamma function (lower integral)

double inc_gamma_c (double a, double x)
Calculates the normalized (regularized) upper incomplete gamma function (upper integral)

double beta (double x, double y)
Calculates the beta function.

double inc_beta (double x, double a, double b)
Calculates the normalized (regularized) incomplete beta function.

double sinint (double x)
Calculates the sine integral.

double cosint (double x)
Calculates the real part of the cosine integral Re(Ci).

Quantile Functions from MathMore

The implementation used is that of GSL.

double tdistribution_quantile_c (double z, double r)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the upper tail of Student's t-distribution (tdistribution_cdf_c).

double tdistribution_quantile (double z, double r)
Inverse ( $$D^{-1}(z)$$) of the cumulative distribution function of the lower tail of Student's t-distribution (tdistribution_cdf).

Special Functions from MathMore
double assoc_laguerre (unsigned n, double m, double x)
Computes the generalized Laguerre polynomials for $$n \geq 0, m > -1$$.

double assoc_legendre (unsigned l, unsigned m, double x)
Computes the associated Legendre polynomials.

double comp_ellint_1 (double k)
Calculates the complete elliptic integral of the first kind.

double comp_ellint_2 (double k)
Calculates the complete elliptic integral of the second kind.

double comp_ellint_3 (double n, double k)
Calculates the complete elliptic integral of the third kind.

double conf_hyperg (double a, double b, double z)
Calculates the confluent hypergeometric functions of the first kind.

double conf_hypergU (double a, double b, double z)
Calculates the confluent hypergeometric functions of the second kind, known also as Kummer function of the second kind, it is related to the confluent hypergeometric functions of the first kind.

double cyl_bessel_i (double nu, double x)
Calculates the modified Bessel function of the first kind (also called regular modified (cylindrical) Bessel function).

double cyl_bessel_j (double nu, double x)
Calculates the (cylindrical) Bessel functions of the first kind (also called regular (cylindrical) Bessel functions).

double cyl_bessel_k (double nu, double x)
Calculates the modified Bessel functions of the second kind (also called irregular modified (cylindrical) Bessel functions).

double cyl_neumann (double nu, double x)
Calculates the (cylindrical) Bessel functions of the second kind (also called irregular (cylindrical) Bessel functions or (cylindrical) Neumann functions).

double ellint_1 (double k, double phi)
Calculates the incomplete elliptic integral of the first kind.

double ellint_2 (double k, double phi)
Calculates the complete elliptic integral of the second kind.

double ellint_3 (double n, double k, double phi)
Calculates the complete elliptic integral of the third kind.

double expint (double x)
Calculates the exponential integral.

double expint_n (int n, double x)

double hyperg (double a, double b, double c, double x)
Calculates Gauss' hypergeometric function.

double laguerre (unsigned n, double x)
Calculates the Laguerre polynomials.

double lambert_W0 (double x)
Calculates the Lambert W function on branch 0.

double lambert_Wm1 (double x)
Calculates the Lambert W function on branch -1.

double legendre (unsigned l, double x)
Calculates the Legendre polynomials.

double riemann_zeta (double x)
Calculates the Riemann zeta function.

double sph_bessel (unsigned n, double x)
Calculates the spherical Bessel functions of the first kind (also called regular spherical Bessel functions).

double sph_legendre (unsigned l, unsigned m, double theta)
Computes the spherical (normalized) associated Legendre polynomials, or spherical harmonic without azimuthal dependence ( $$e^(im\phi)$$).

double sph_neumann (unsigned n, double x)
Calculates the spherical Bessel functions of the second kind (also called irregular spherical Bessel functions or spherical Neumann functions).

double airy_Ai (double x)
Calculates the Airy function Ai.

double airy_Bi (double x)
Calculates the Airy function Bi.

double airy_Ai_deriv (double x)
Calculates the derivative of the Airy function Ai.

double airy_Bi_deriv (double x)
Calculates the derivative of the Airy function Bi.

double airy_zero_Ai (unsigned int s)
Calculates the zeroes of the Airy function Ai.

double airy_zero_Bi (unsigned int s)
Calculates the zeroes of the Airy function Bi.

double airy_zero_Ai_deriv (unsigned int s)
Calculates the zeroes of the derivative of the Airy function Ai.

double airy_zero_Bi_deriv (unsigned int s)
Calculates the zeroes of the derivative of the Airy function Bi.

double wigner_3j (int two_ja, int two_jb, int two_jc, int two_ma, int two_mb, int two_mc)
Calculates the Wigner 3j coupling coefficients.

double wigner_6j (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf)
Calculates the Wigner 6j coupling coefficients.

double wigner_9j (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf, int two_jg, int two_jh, int two_ji)
Calculates the Wigner 9j coupling coefficients.

## Variables

static const double eu = 0.577215664901532860606

double gDefaultAbsTolerance = 1.E-6

int gDefaultMaxIter = 100

static int gDefaultNpx = 100

static int gDefaultNpx = 100

static int gDefaultNSearch = 10

static int gDefaultNSearch = 10

double gDefaultRelTolerance = 1.E-10

const ROOT::Math::IMultiGenFunctiongFunction
function wrapper for the function to be minimized

function wrapper for the gradient of the function to be minimized

int gNCalls = 0
integer for the number of function calls

double kEulerGamma = 0.577215664901532860606512090082402431042

double kPi = 3.14159265358979323846

static const double kSqrt2 = 1.41421356237309515

## ◆ FitMethodFunction

Definition at line 43 of file Fitter.h.

Definition at line 44 of file Fitter.h.

## ◆ FreeFunctionPtr

 typedef double(* ROOT::Math::FreeFunctionPtr) (double)

Definition at line 39 of file WrappedFunction.h.

## ◆ FreeMultiFunctionPtr

 typedef double(* ROOT::Math::FreeMultiFunctionPtr)(const double *)

Definition at line 41 of file WrappedFunction.h.

## ◆ FreeParamMultiFunctionPtr

 typedef double(* ROOT::Math::FreeParamMultiFunctionPtr) (const double *, const double *)

Definition at line 29 of file WrappedParamFunction.h.

## ◆ GSLFdfPointer

 typedef void(* ROOT::Math::GSLFdfPointer) (double, void *, double *, double *)

Definition at line 46 of file GSLFunctionWrapper.h.

## ◆ GSLFuncPointer

 typedef double(* ROOT::Math::GSLFuncPointer)(double, void *)

Function pointer corresponding to gsl_function signature.

Definition at line 45 of file GSLFunctionAdapter.h.

## ◆ GSLMultiFitDfPointer

 typedef void(* ROOT::Math::GSLMultiFitDfPointer) (const gsl_vector *, void *, gsl_matrix *)

Definition at line 47 of file GSLMultiFitFunctionWrapper.h.

## ◆ GSLMultiFitFdfPointer

 typedef void(* ROOT::Math::GSLMultiFitFdfPointer) (const gsl_vector *, void *, gsl_vector *, gsl_matrix *)

Definition at line 48 of file GSLMultiFitFunctionWrapper.h.

## ◆ GSLMultiFitFPointer

 typedef double(* ROOT::Math::GSLMultiFitFPointer) (const gsl_vector *, void *, gsl_vector *)

Definition at line 46 of file GSLMultiFitFunctionWrapper.h.

## ◆ GSLMultiMinDfPointer

 typedef void(* ROOT::Math::GSLMultiMinDfPointer) (const gsl_vector *, void *, gsl_vector *)

Definition at line 47 of file GSLMultiMinFunctionWrapper.h.

## ◆ GSLMultiMinFdfPointer

 typedef void(* ROOT::Math::GSLMultiMinFdfPointer) (const gsl_vector *, void *, double *, gsl_vector *)

Definition at line 48 of file GSLMultiMinFunctionWrapper.h.

## ◆ GSLMultiMinFuncPointer

 typedef double(* ROOT::Math::GSLMultiMinFuncPointer) (const gsl_vector *, void *)

Definition at line 46 of file GSLMultiMinFunctionWrapper.h.

## ◆ GSLMultiRootDfPointer

 typedef void(* ROOT::Math::GSLMultiRootDfPointer) (const gsl_vector *, void *, gsl_matrix *)

Definition at line 49 of file GSLMultiRootFunctionWrapper.h.

## ◆ GSLMultiRootFdfPointer

 typedef void(* ROOT::Math::GSLMultiRootFdfPointer) (const gsl_vector *, void *, gsl_vector *, gsl_matrix *)

Definition at line 50 of file GSLMultiRootFunctionWrapper.h.

## ◆ GSLMultiRootFPointer

 typedef double(* ROOT::Math::GSLMultiRootFPointer) (const gsl_vector *, void *, gsl_vector *)

Definition at line 48 of file GSLMultiRootFunctionWrapper.h.

## ◆ GSLRngRanLux1

Definition at line 374 of file GSLRndmEngines.h.

## ◆ GSLRngRanLux2

Definition at line 389 of file GSLRndmEngines.h.

## ◆ GSLRngRanLux48

Definition at line 418 of file GSLRndmEngines.h.

## ◆ IBaseFunctionMultiDim

 using ROOT::Math::IBaseFunctionMultiDim = typedef IBaseFunctionMultiDimTempl

Definition at line 31 of file IFunctionfwd.h.

## ◆ IGenFunction

Definition at line 37 of file IFunctionfwd.h.

Definition at line 40 of file IFunctionfwd.h.

Definition at line 34 of file IFunctionfwd.h.

Definition at line 35 of file IFunctionfwd.h.

## ◆ IMultiGenFunction

Definition at line 32 of file IFunctionfwd.h.

## ◆ IMultiGenFunctionTempl

template<class T >
 using ROOT::Math::IMultiGenFunctionTempl = typedef IBaseFunctionMultiDimTempl

Definition at line 30 of file IFunctionfwd.h.

Definition at line 41 of file IFunctionfwd.h.

## ◆ Integrator

Definition at line 480 of file Integrator.h.

## ◆ IParametricFunctionMultiDim

Definition at line 26 of file IParamFunctionfwd.h.

Definition at line 29 of file IParamFunctionfwd.h.

## ◆ IParamFunction

Definition at line 31 of file IParamFunctionfwd.h.

Definition at line 36 of file IParamFunctionfwd.h.

## ◆ IParamMultiFunction

Definition at line 32 of file IParamFunctionfwd.h.

## ◆ IParamMultiFunctionTempl

template<class T >
 using ROOT::Math::IParamMultiFunctionTempl = typedef IParametricFunctionMultiDimTempl

Definition at line 34 of file IParamFunctionfwd.h.

Definition at line 37 of file IParamFunctionfwd.h.

template<class T >

Definition at line 39 of file IParamFunctionfwd.h.

## ◆ MathMoreLibrary

Definition at line 68 of file PdfFuncMathMore.h.

## ◆ MixMaxEngine17

 typedef MixMaxEngine<17,0> ROOT::Math::MixMaxEngine17

Definition at line 176 of file MixMaxEngine.h.

## ◆ MixMaxEngine240

 typedef MixMaxEngine<240,0> ROOT::Math::MixMaxEngine240

Definition at line 174 of file MixMaxEngine.h.

## ◆ MixMaxEngine256

 typedef MixMaxEngine<256,2> ROOT::Math::MixMaxEngine256

Definition at line 175 of file MixMaxEngine.h.

## ◆ MultiRootFinder

Definition at line 294 of file GSLMultiRootFinder.h.

## ◆ OptionsMap

 typedef std::map ROOT::Math::OptionsMap

Definition at line 25 of file GenAlgoOptions.cxx.

## ◆ ParamFunctor

 using ROOT::Math::ParamFunctor = typedef ParamFunctorTempl

Definition at line 387 of file ParamFunctor.h.

## ◆ Plane3D

 typedef Impl::Plane3D ROOT::Math::Plane3D

Definition at line 304 of file Plane3D.h.

## ◆ Plane3DF

 typedef Impl::Plane3D ROOT::Math::Plane3DF

Definition at line 305 of file Plane3D.h.

## ◆ Polar2DPoint

2D Point based on the polar coordinates rho, theta, phi in double precision.

Definition at line 47 of file Point2Dfwd.h.

## ◆ Polar2DPointD

Definition at line 48 of file Point2Dfwd.h.

## ◆ Polar2DPointF

 typedef PositionVector2D< Polar2D, DefaultCoordinateSystemTag > ROOT::Math::Polar2DPointF

2D Point based on the polar coordinates rho, theta, phi in single precision.

Definition at line 53 of file Point2Dfwd.h.

## ◆ Polar2DVector

2D Vector based on the polar coordinates rho, phi in double precision.

To use it add the line #include <Vector2D.h>

See the documentation on the DisplacementVector2D page.

Definition at line 61 of file Vector2Dfwd.h.

## ◆ Polar2DVectorD

Definition at line 62 of file Vector2Dfwd.h.

## ◆ Polar2DVectorF

 typedef DisplacementVector2D< Polar2D, DefaultCoordinateSystemTag > ROOT::Math::Polar2DVectorF

2D Vector based on the polar coordinates rho, phi in single precision.

To use it add the line #include <Vector2D.h>

See the documentation on the DisplacementVector2D page.

Definition at line 71 of file Vector2Dfwd.h.

## ◆ Polar3DPoint

3D Point based on the polar coordinates rho, theta, phi in double precision.

Definition at line 59 of file Point3Dfwd.h.

## ◆ Polar3DPointD

Definition at line 64 of file Point3Dfwd.h.

## ◆ Polar3DPointF

 typedef PositionVector3D< Polar3D, DefaultCoordinateSystemTag > ROOT::Math::Polar3DPointF

3D Point based on the polar coordinates rho, theta, phi in single precision.

Definition at line 63 of file Point3Dfwd.h.

## ◆ Polar3DVector

3D Vector based on the polar coordinates rho, theta, phi in double precision.

To use it add the line #include <Vector3D.h>

See the documentation on the DisplacementVector3D page.

Definition at line 80 of file Vector3Dfwd.h.

## ◆ Polar3DVectorD

Definition at line 89 of file Vector3Dfwd.h.

## ◆ Polar3DVectorF

 typedef DisplacementVector3D< Polar3D, DefaultCoordinateSystemTag > ROOT::Math::Polar3DVectorF

3D Vector based on the polar coordinates rho, theta, phi in single precision.

To use it add the line #include <Vector3D.h>

See the documentation on the DisplacementVector3D page.

Definition at line 88 of file Vector3Dfwd.h.

## ◆ PtEtaPhiEVector

LorentzVector based on the cylindrical coordinates Pt, eta, phi and E (rho, eta, phi, t) in double precision.

To use it add the line #include <Vector4D.h>

See the documentation on the LorentzVector page.

Definition at line 77 of file Vector4Dfwd.h.

## ◆ PtEtaPhiMVector

LorentzVector based on the cylindrical coordinates pt, eta, phi and Mass in double precision.

To use it add the line #include <Vector4D.h>

See the documentation on the LorentzVector page.

Definition at line 86 of file Vector4Dfwd.h.

## ◆ PxPyPzEVector

 typedef LorentzVector > ROOT::Math::PxPyPzEVector

Definition at line 48 of file Vector4Dfwd.h.

## ◆ PxPyPzMVector

 typedef LorentzVector > ROOT::Math::PxPyPzMVector

LorentzVector based on the x, y, z, and Mass in double precision.

To use it add the line #include <Vector4D.h>

See the documentation on the LorentzVector page.

Definition at line 68 of file Vector4Dfwd.h.

## ◆ QuasiRandomNiederreiter

Definition at line 179 of file QuasiRandom.h.

## ◆ QuasiRandomSobol

Definition at line 178 of file QuasiRandom.h.

## ◆ RandomGFSR4

Definition at line 14 of file GSLRandom.h.

## ◆ RandomMixMax

 typedef Random > ROOT::Math::RandomMixMax

Useful typedef definitions.

Definition at line 247 of file Random.h.

## ◆ RandomMT

Definition at line 11 of file GSLRandom.h.

## ◆ RandomMT19937

Definition at line 248 of file Random.h.

## ◆ RandomMT64

 typedef Random > ROOT::Math::RandomMT64

Definition at line 249 of file Random.h.

## ◆ RandomRanLux

Definition at line 13 of file GSLRandom.h.

## ◆ RandomRanlux48

 typedef Random > ROOT::Math::RandomRanlux48

Definition at line 250 of file Random.h.

## ◆ RandomTaus

Definition at line 12 of file GSLRandom.h.

## ◆ RanluxppCompatEngineGslRanlxd1

 using ROOT::Math::RanluxppCompatEngineGslRanlxd1 = typedef RanluxppCompatEngineGslRanlxd<404>

Definition at line 163 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineGslRanlxd2

 using ROOT::Math::RanluxppCompatEngineGslRanlxd2 = typedef RanluxppCompatEngineGslRanlxd<794>

Definition at line 164 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineGslRanlxs0

 using ROOT::Math::RanluxppCompatEngineGslRanlxs0 = typedef RanluxppCompatEngineGslRanlxs<218>

Definition at line 126 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineGslRanlxs1

 using ROOT::Math::RanluxppCompatEngineGslRanlxs1 = typedef RanluxppCompatEngineGslRanlxs<404>

Definition at line 127 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineGslRanlxs2

 using ROOT::Math::RanluxppCompatEngineGslRanlxs2 = typedef RanluxppCompatEngineGslRanlxs<794>

Definition at line 128 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineJamesP3

 using ROOT::Math::RanluxppCompatEngineJamesP3 = typedef RanluxppCompatEngineJames<223>

Compatibility engine for original RANLUX implementation by James, luxury level 3 (p = 223).

The sequence of numbers also matches gsl_rng_ranlux.

Definition at line 89 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineJamesP4

 using ROOT::Math::RanluxppCompatEngineJamesP4 = typedef RanluxppCompatEngineJames<389>

Compatibility engine for original RANLUX implementation by James, luxury level 4 (p = 389).

The sequence of numbers also matches gsl_rng_ranlux389.

Definition at line 92 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineLuescherRanlxd1

 using ROOT::Math::RanluxppCompatEngineLuescherRanlxd1 = typedef RanluxppCompatEngineLuescherRanlxd<404>

Definition at line 237 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineLuescherRanlxd2

 using ROOT::Math::RanluxppCompatEngineLuescherRanlxd2 = typedef RanluxppCompatEngineLuescherRanlxd<794>

Definition at line 238 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineLuescherRanlxs0

 using ROOT::Math::RanluxppCompatEngineLuescherRanlxs0 = typedef RanluxppCompatEngineLuescherRanlxs<218>

Definition at line 201 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineLuescherRanlxs1

 using ROOT::Math::RanluxppCompatEngineLuescherRanlxs1 = typedef RanluxppCompatEngineLuescherRanlxs<404>

Definition at line 202 of file RanluxppEngine.h.

## ◆ RanluxppCompatEngineLuescherRanlxs2

 using ROOT::Math::RanluxppCompatEngineLuescherRanlxs2 = typedef RanluxppCompatEngineLuescherRanlxs<794>

Definition at line 203 of file RanluxppEngine.h.

## ◆ RanluxppEngine2048

 using ROOT::Math::RanluxppEngine2048 = typedef RanluxppEngine<2048>

Definition at line 54 of file RanluxppEngine.h.

## ◆ RanluxppEngine24

 using ROOT::Math::RanluxppEngine24 = typedef RanluxppEngine<24>

Definition at line 53 of file RanluxppEngine.h.

## ◆ RhoEtaPhiPoint

3D Point based on the eta based cylindrical coordinates rho, eta, phi in double precision.

Definition at line 49 of file Point3Dfwd.h.

## ◆ RhoEtaPhiPointD

Definition at line 54 of file Point3Dfwd.h.

## ◆ RhoEtaPhiPointF

 typedef PositionVector3D< CylindricalEta3D, DefaultCoordinateSystemTag > ROOT::Math::RhoEtaPhiPointF

3D Point based on the eta based cylindrical coordinates rho, eta, phi in single precision.

Definition at line 53 of file Point3Dfwd.h.

## ◆ RhoEtaPhiVector

3D Vector based on the eta based cylindrical coordinates rho, eta, phi in double precision.

To use it add the line #include <Vector3D.h>

See the documentation on the DisplacementVector3D page.

Definition at line 62 of file Vector3Dfwd.h.

## ◆ RhoEtaPhiVectorD

Definition at line 71 of file Vector3Dfwd.h.

## ◆ RhoEtaPhiVectorF

3D Vector based on the eta based cylindrical coordinates rho, eta, phi in single precision.

To use it add the line #include <Vector3D.h>

See the documentation on the DisplacementVector3D page.

Definition at line 70 of file Vector3Dfwd.h.

## ◆ RhoZPhiPoint

3D Point based on the cylindrical coordinates rho, z, phi in double precision.

Definition at line 69 of file Point3Dfwd.h.

## ◆ RhoZPhiPointD

Definition at line 74 of file Point3Dfwd.h.

## ◆ RhoZPhiPointF

 typedef PositionVector3D< Cylindrical3D, DefaultCoordinateSystemTag > ROOT::Math::RhoZPhiPointF

3D Point based on the cylindrical coordinates rho, z, phi in single precision.

Definition at line 73 of file Point3Dfwd.h.

## ◆ RhoZPhiVector

3D Vector based on the cylindrical coordinates rho, z, phi in double precision.

To use it add the line #include <Vector3D.h>

See the documentation on the DisplacementVector3D page.

Definition at line 98 of file Vector3Dfwd.h.

## ◆ RhoZPhiVectorD

Definition at line 107 of file Vector3Dfwd.h.

## ◆ RhoZPhiVectorF

 typedef DisplacementVector3D< Cylindrical3D, DefaultCoordinateSystemTag > ROOT::Math::RhoZPhiVectorF

3D Vector based on the cylindrical coordinates rho, z, phi in single precision.

To use it add the line #include <Vector3D.h>

See the documentation on the DisplacementVector3D page.

Definition at line 106 of file Vector3Dfwd.h.

## ◆ Scalar

 typedef Rotation3D::Scalar ROOT::Math::Scalar

Definition at line 69 of file Rotation3DxAxial.cxx.

## ◆ SMatrix2D

 typedef SMatrix > ROOT::Math::SMatrix2D

Definition at line 16 of file SMatrixDfwd.h.

## ◆ SMatrix2F

 typedef SMatrix > ROOT::Math::SMatrix2F

Definition at line 16 of file SMatrixFfwd.h.

## ◆ SMatrix3D

 typedef SMatrix > ROOT::Math::SMatrix3D

Definition at line 17 of file SMatrixDfwd.h.

## ◆ SMatrix3F

 typedef SMatrix > ROOT::Math::SMatrix3F

Definition at line 17 of file SMatrixFfwd.h.

## ◆ SMatrix4D

 typedef SMatrix > ROOT::Math::SMatrix4D

Definition at line 18 of file SMatrixDfwd.h.

## ◆ SMatrix4F

 typedef SMatrix > ROOT::Math::SMatrix4F

Definition at line 18 of file SMatrixFfwd.h.

## ◆ SMatrix5D

 typedef SMatrix > ROOT::Math::SMatrix5D

Definition at line 19 of file SMatrixDfwd.h.

## ◆ SMatrix5F

 typedef SMatrix > ROOT::Math::SMatrix5F

Definition at line 19 of file SMatrixFfwd.h.

## ◆ SMatrix6D

 typedef SMatrix > ROOT::Math::SMatrix6D

Definition at line 20 of file SMatrixDfwd.h.

## ◆ SMatrix6F

 typedef SMatrix > ROOT::Math::SMatrix6F

Definition at line 20 of file SMatrixFfwd.h.

## ◆ SMatrix7D

 typedef SMatrix > ROOT::Math::SMatrix7D

Definition at line 21 of file SMatrixDfwd.h.

## ◆ SMatrix7F

 typedef SMatrix > ROOT::Math::SMatrix7F

Definition at line 21 of file SMatrixFfwd.h.

## ◆ SMatrixSym2D

 typedef SMatrix > ROOT::Math::SMatrixSym2D

Definition at line 24 of file SMatrixDfwd.h.

## ◆ SMatrixSym2F

 typedef SMatrix > ROOT::Math::SMatrixSym2F

Definition at line 23 of file SMatrixFfwd.h.

## ◆ SMatrixSym3D

 typedef SMatrix > ROOT::Math::SMatrixSym3D

Definition at line 25 of file SMatrixDfwd.h.

## ◆ SMatrixSym3F

 typedef SMatrix > ROOT::Math::SMatrixSym3F

Definition at line 24 of file SMatrixFfwd.h.

## ◆ SMatrixSym4D

 typedef SMatrix > ROOT::Math::SMatrixSym4D

Definition at line 26 of file SMatrixDfwd.h.

## ◆ SMatrixSym4F

 typedef SMatrix > ROOT::Math::SMatrixSym4F

Definition at line 25 of file SMatrixFfwd.h.

## ◆ SMatrixSym5D

 typedef SMatrix > ROOT::Math::SMatrixSym5D

Definition at line 27 of file SMatrixDfwd.h.

## ◆ SMatrixSym5F

 typedef SMatrix > ROOT::Math::SMatrixSym5F

Definition at line 26 of file SMatrixFfwd.h.

## ◆ SMatrixSym6D

 typedef SMatrix > ROOT::Math::SMatrixSym6D

Definition at line 28 of file SMatrixDfwd.h.

## ◆ SMatrixSym6F

 typedef SMatrix > ROOT::Math::SMatrixSym6F

Definition at line 27 of file SMatrixFfwd.h.

## ◆ SMatrixSym7D

 typedef SMatrix > ROOT::Math::SMatrixSym7D

Definition at line 29 of file SMatrixDfwd.h.

## ◆ SMatrixSym7F

 typedef SMatrix > ROOT::Math::SMatrixSym7F

Definition at line 28 of file SMatrixFfwd.h.

## ◆ TDataPoint1D

 typedef TDataPoint<1,Double_t> ROOT::Math::TDataPoint1D

Definition at line 60 of file TDataPoint.h.

## ◆ TDataPoint1F

 typedef TDataPoint<1,Float_t> ROOT::Math::TDataPoint1F

Definition at line 57 of file TDataPoint.h.

## ◆ TDataPoint2D

 typedef TDataPoint<2,Double_t> ROOT::Math::TDataPoint2D

Definition at line 61 of file TDataPoint.h.

## ◆ TDataPoint2F

 typedef TDataPoint<2,Float_t> ROOT::Math::TDataPoint2F

Definition at line 58 of file TDataPoint.h.

## ◆ TDataPoint3D

 typedef TDataPoint<3,Double_t> ROOT::Math::TDataPoint3D

Definition at line 62 of file TDataPoint.h.

## ◆ TDataPoint3F

 typedef TDataPoint<3,Float_t> ROOT::Math::TDataPoint3F

Definition at line 59 of file TDataPoint.h.

## ◆ Transform3D

Definition at line 1312 of file Transform3D.h.

## ◆ Transform3DF

 typedef Impl::Transform3D ROOT::Math::Transform3DF

Definition at line 1313 of file Transform3D.h.

## ◆ Translation3D

Definition at line 307 of file Translation3D.h.

## ◆ Translation3DF

 typedef Impl::Translation3D ROOT::Math::Translation3DF

Definition at line 308 of file Translation3D.h.

## ◆ WrappedMultiTF1

 using ROOT::Math::WrappedMultiTF1 = typedef WrappedMultiTF1Templ

Definition at line 337 of file WrappedMultiTF1.h.

## ◆ XYPoint

2D Point based on the cartesian coordinates x,y,z in double precision

Definition at line 35 of file Point2Dfwd.h.

## ◆ XYPointD

 typedef XYPoint ROOT::Math::XYPointD

Definition at line 36 of file Point2Dfwd.h.

## ◆ XYPointF

 typedef PositionVector2D< Cartesian2D, DefaultCoordinateSystemTag > ROOT::Math::XYPointF

2D Point based on the cartesian corrdinates x,y,z in single precision

Definition at line 41 of file Point2Dfwd.h.

## ◆ XYVector

2D Vector based on the cartesian coordinates x,y in double precision

To use it add the line #include <Vector2D.h>

See the documentation on the DisplacementVector2D page.

Definition at line 41 of file Vector2Dfwd.h.

## ◆ XYVectorD

 typedef XYVector ROOT::Math::XYVectorD

Definition at line 42 of file Vector2Dfwd.h.

## ◆ XYVectorF

 typedef DisplacementVector2D< Cartesian2D, DefaultCoordinateSystemTag > ROOT::Math::XYVectorF

2D Vector based on the cartesian coordinates x,y,z in single precision

To use it add the line #include <Vector2D.h>

See the documentation on the DisplacementVector2D page.

Definition at line 51 of file Vector2Dfwd.h.

## ◆ XYZPoint

3D Point based on the cartesian coordinates x,y,z in double precision

Definition at line 38 of file Point3Dfwd.h.

## ◆ XYZPointD

 typedef XYZPoint ROOT::Math::XYZPointD

Definition at line 44 of file Point3Dfwd.h.

## ◆ XYZPointF

 typedef PositionVector3D< Cartesian3D, DefaultCoordinateSystemTag > ROOT::Math::XYZPointF

3D Point based on the cartesian corrdinates x,y,z in single precision

Definition at line 43 of file Point3Dfwd.h.

## ◆ XYZTVector

 typedef LorentzVector > ROOT::Math::XYZTVector

LorentzVector based on x,y,x,t (or px,py,pz,E) coordinates in double precision with metric (-,-,-,+)

To use it add the line #include <Vector4D.h>

See the documentation on the LorentzVector page.

Definition at line 46 of file Vector4Dfwd.h.

## ◆ XYZTVectorF

 typedef LorentzVector< PxPyPzE4D > ROOT::Math::XYZTVectorF

LorentzVector based on x,y,x,t (or px,py,pz,E) coordinates in float precision with metric (-,-,-,+)

To use it add the line #include <Vector4D.h>

See the documentation on the LorentzVector page.

Definition at line 58 of file Vector4Dfwd.h.

## ◆ XYZVector

3D Vector based on the cartesian coordinates x,y,z in double precision

To use it add the line #include <Vector3D.h>

See the documentation on the DisplacementVector3D page.

Definition at line 44 of file Vector3Dfwd.h.

## ◆ XYZVectorD

 typedef XYZVector ROOT::Math::XYZVectorD

Definition at line 53 of file Vector3Dfwd.h.

## ◆ XYZVectorF

 typedef DisplacementVector3D< Cartesian3D, DefaultCoordinateSystemTag > ROOT::Math::XYZVectorF

3D Vector based on the cartesian coordinates x,y,z in single precision

To use it add the line #include <Vector3D.h>

See the documentation on the DisplacementVector3D page.

Definition at line 52 of file Vector3Dfwd.h.

## ◆ EMinimVariableType

Enumeration describing the status of the variable The enumeration are used in the minimizer classes to categorize the variables.

Enumerator
kDefault
kFix
kBounds
kLowBound
kUpBound

Definition at line 27 of file MinimTransformVariable.h.

## ◆ ERotation3DMatrixIndex

Enumerator
kXX
kXY
kXZ
kYX
kYY
kYZ
kZX
kZY
kZZ

Definition at line 64 of file AxisAngle.cxx.

## Function Documentation

 void ROOT::Math::adkTestStat ( double * adk, const std::vector< std::vector< double > > & samples, const std::vector< double > & zstar )

Definition at line 545 of file GoFTest.cxx.

## ◆ Chebyshev0()

 double ROOT::Math::Chebyshev0 ( double , double c0 )
inline

Definition at line 57 of file ChebyshevPol.h.

## ◆ Chebyshev1()

 double ROOT::Math::Chebyshev1 ( double x, double c0, double c1 )
inline

Definition at line 60 of file ChebyshevPol.h.

## ◆ Chebyshev10()

 double ROOT::Math::Chebyshev10 ( double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7, double c8, double c9, double c10 )
inline

Definition at line 87 of file ChebyshevPol.h.

## ◆ Chebyshev2()

 double ROOT::Math::Chebyshev2 ( double x, double c0, double c1, double c2 )
inline

Definition at line 63 of file ChebyshevPol.h.

## ◆ Chebyshev3()

 double ROOT::Math::Chebyshev3 ( double x, double c0, double c1, double c2, double c3 )
inline

Definition at line 66 of file ChebyshevPol.h.

## ◆ Chebyshev4()

 double ROOT::Math::Chebyshev4 ( double x, double c0, double c1, double c2, double c3, double c4 )
inline

Definition at line 69 of file ChebyshevPol.h.

## ◆ Chebyshev5()

 double ROOT::Math::Chebyshev5 ( double x, double c0, double c1, double c2, double c3, double c4, double c5 )
inline

Definition at line 72 of file ChebyshevPol.h.

## ◆ Chebyshev6()

 double ROOT::Math::Chebyshev6 ( double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6 )
inline

Definition at line 75 of file ChebyshevPol.h.

## ◆ Chebyshev7()

 double ROOT::Math::Chebyshev7 ( double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7 )
inline

Definition at line 78 of file ChebyshevPol.h.

## ◆ Chebyshev8()

 double ROOT::Math::Chebyshev8 ( double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7, double c8 )
inline

Definition at line 81 of file ChebyshevPol.h.

## ◆ Chebyshev9()

 double ROOT::Math::Chebyshev9 ( double x, double c0, double c1, double c2, double c3, double c4, double c5, double c6, double c7, double c8, double c9 )
inline

Definition at line 84 of file ChebyshevPol.h.

## ◆ ChebyshevN()

 double ROOT::Math::ChebyshevN ( unsigned int n, double x, const double * c )
inline

Definition at line 93 of file ChebyshevPol.h.

## ◆ Cross() [1/3]

template<class T , class A >
 SVector< T, 3 > ROOT::Math::Cross ( const SVector< T, 3 > & lhs, const VecExpr< A, T, 3 > & rhs )
inline

Definition at line 349 of file Functions.h.

## ◆ Cross() [2/3]

template<class A , class T >
 SVector< T, 3 > ROOT::Math::Cross ( const VecExpr< A, T, 3 > & lhs, const SVector< T, 3 > & rhs )
inline

Definition at line 336 of file Functions.h.

## ◆ Cross() [3/3]

template<class A , class B , class T >
 SVector< T, 3 > ROOT::Math::Cross ( const VecExpr< A, T, 3 > & lhs, const VecExpr< B, T, 3 > & rhs )
inline

Definition at line 362 of file Functions.h.

## ◆ Dfactir()

template<class Matrix , unsigned int n, unsigned int idim>
 bool ROOT::Math::Dfactir ( Matrix & rhs, typename Matrix::value_type & det, unsigned int * ir )

Dfactir.

Function to compute the determinant from a square matrix, Det(A) of dimension idim and order n. A working area ir is returned which is needed by the Dfinv routine.

Definition at line 46 of file Dfactir.h.

## ◆ Dfinv()

template<class Matrix , unsigned int n, unsigned int idim>
 bool ROOT::Math::Dfinv ( Matrix & rhs, unsigned int * ir )

Dfinv.

Function to compute the inverse of a square matrix ( $$A^{-1}$$) of dimension $$idim$$ and order $$n$$. The routine Dfactir must be called before Dfinv!

Definition at line 47 of file Dfinv.h.

## ◆ Distance() [1/8]

template<class R >
 AxisAngle::Scalar ROOT::Math::Distance ( const AxisAngle & r1, const R & r2 )
inline

Distance between two rotations.

Definition at line 320 of file AxisAngle.h.

## ◆ Distance() [2/8]

template<class R >
 EulerAngles::Scalar ROOT::Math::Distance ( const EulerAngles & r1, const R & r2 )
inline

Distance between two rotations.

Definition at line 356 of file EulerAngles.h.

## ◆ Distance() [3/8]

template<class R >
 Quaternion::Scalar ROOT::Math::Distance ( const Quaternion & r1, const R & r2 )
inline

Distance between two rotations.

Definition at line 328 of file Quaternion.h.

## ◆ Distance() [4/8]

template<class R >
 Rotation3D::Scalar ROOT::Math::Distance ( const Rotation3D & r1, const R & r2 )
inline

Distance between two rotations.

Definition at line 490 of file Rotation3D.h.

## ◆ Distance() [5/8]

template<class R >
 RotationX::Scalar ROOT::Math::Distance ( const RotationX & r1, const R & r2 )
inline

Distance between two rotations.

Definition at line 235 of file RotationX.h.

## ◆ Distance() [6/8]

template<class R >
 RotationY::Scalar ROOT::Math::Distance ( const RotationY & r1, const R & r2 )
inline

Distance between two rotations.

Definition at line 235 of file RotationY.h.

## ◆ Distance() [7/8]

template<class R >
 RotationZ::Scalar ROOT::Math::Distance ( const RotationZ & r1, const R & r2 )
inline

Distance between two rotations.

Definition at line 235 of file RotationZ.h.

## ◆ Distance() [8/8]

template<class R >
 RotationZYX::Scalar ROOT::Math::Distance ( const RotationZYX & r1, const R & r2 )
inline

Distance between two rotations.

Definition at line 329 of file RotationZYX.h.

## ◆ Div() [1/3]

template<class A , class B , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
 Expr< BinaryOp< DivOp< T >, Expr< A, T, D, D2, R1 >, Expr< B, T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > ROOT::Math::Div ( const Expr< A, T, D, D2, R1 > & lhs, const Expr< B, T, D, D2, R2 > & rhs )
inline

Definition at line 931 of file BinaryOperators.h.

## ◆ Div() [2/3]

template<class A , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
 Expr< BinaryOp< DivOp< T >, Expr< A, T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > ROOT::Math::Div ( const Expr< A, T, D, D2, R1 > & lhs, const SMatrix< T, D, D2, R2 > & rhs )
inline

Definition at line 907 of file BinaryOperators.h.

## ◆ Div() [3/3]

template<class A , class T , unsigned int D, unsigned int D2, class R1 , class R2 >
 Expr< BinaryOp< DivOp< T >, SMatrix< T, D, D2, R1 >, Expr< A, T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > ROOT::Math::Div ( const SMatrix< T, D, D2, R1 > & lhs, const Expr< A, T, D, D2, R2 > & rhs )
inline

Definition at line 919 of file BinaryOperators.h.

## ◆ Dot() [1/3]

template<class A , class T , unsigned int D>
 T ROOT::Math::Dot ( const SVector< T, D > & lhs, const VecExpr< A, T, D > & rhs )
inline

Definition at line 173 of file Functions.h.

## ◆ Dot() [2/3]

template<class A , class T , unsigned int D>
 T ROOT::Math::Dot ( const VecExpr< A, T, D > & lhs, const SVector< T, D > & rhs )
inline

Definition at line 181 of file Functions.h.

## ◆ Dot() [3/3]

template<class A , class B , class T , unsigned int D>
 T ROOT::Math::Dot ( const VecExpr< A, T, D > & lhs, const VecExpr< B, T, D > & rhs )
inline

Definition at line 190 of file Functions.h.

## ◆ etaMax()

template<class T >
 T ROOT::Math::etaMax ( )
inline

Function providing the maximum possible value of pseudorapidity for a non-zero rho, in the Scalar type with the largest dynamic range.

Definition at line 51 of file etaMax.h.

## ◆ etaMax_impl()

 long double ROOT::Math::etaMax_impl ( )
inline

The following function could be called to provide the maximum possible value of pseudorapidity for a non-zero rho.

This is log ( max/min ) where max and min are the extrema of positive values for type long double.

Definition at line 36 of file etaMax.h.

## ◆ expm1()

 double ROOT::Math::expm1 ( double x )
inline

exp(x) -1 with error cancellation when x is small

Definition at line 110 of file Math.h.

## ◆ fabs() [1/2]

template<class A , class T , unsigned int D, unsigned int D2, class R >
 Expr< UnaryOp< Fabs< T >, Expr< A, T, D, D2, R >, T >, T, D, D2, R > ROOT::Math::fabs ( const Expr< A, T, D, D2, R > & rhs )
inline

Definition at line 160 of file UnaryOperators.h.

## ◆ fabs() [2/2]

template<class A , class T , unsigned int D>
 VecExpr< UnaryOp< Fabs< T >, VecExpr< A, T, D >, T >, T, D > ROOT::Math::fabs ( const VecExpr< A, T, D > & rhs )
inline

Definition at line 131 of file UnaryOperators.h.

## ◆ gaussian_cdf()

 double ROOT::Math::gaussian_cdf ( double x, double sigma = 1, double x0 = 0 )
inline

Alternative name for same function.

Definition at line 485 of file ProbFuncMathCore.h.

## ◆ gaussian_cdf_c()

 double ROOT::Math::gaussian_cdf_c ( double x, double sigma = 1, double x0 = 0 )
inline

Alternative name for same function.

Definition at line 463 of file ProbFuncMathCore.h.

## ◆ getCount()

 int ROOT::Math::getCount ( double z, const double * dat, int n )

Definition at line 519 of file GoFTest.cxx.

## ◆ GetGSLDerivType()

 const gsl_multiroot_fdfsolver_type * ROOT::Math::GetGSLDerivType ( GSLMultiRootFinder::EDerivType type )

Definition at line 201 of file GSLMultiRootFinder.cxx.

## ◆ GetGSLType()

 const gsl_multiroot_fsolver_type * ROOT::Math::GetGSLType ( GSLMultiRootFinder::EType type )

Definition at line 183 of file GSLMultiRootFinder.cxx.

## ◆ getSum()

 int ROOT::Math::getSum ( const int * x, int n )

Definition at line 533 of file GoFTest.cxx.

template<class char_t , class traits_t >
 std::basic_ios< char_t, traits_t > & ROOT::Math::human_readable ( std::basic_ios< char_t, traits_t > & ios )
inline

Definition at line 197 of file GenVectorIO.h.

## ◆ Lmag()

template<class A , class T >
 T ROOT::Math::Lmag ( const VecExpr< A, T, 4 > & rhs )
inline

Definition at line 308 of file Functions.h.

## ◆ Lmag2()

template<class A , class T >
 T ROOT::Math::Lmag2 ( const VecExpr< A, T, 4 > & rhs )
inline

Definition at line 284 of file Functions.h.

## ◆ log1p()

 double ROOT::Math::log1p ( double x )
inline

declarations for functions which are not implemented by some compilers

log(1+x) with error cancelatio when x is small

Definition at line 98 of file Math.h.

template<class char_t , class traits_t >
 std::basic_ios< char_t, traits_t > & ROOT::Math::machine_readable ( std::basic_ios< char_t, traits_t > & ios )
inline

Definition at line 208 of file GenVectorIO.h.

## ◆ Mag()

template<class A , class T , unsigned int D>
 T ROOT::Math::Mag ( const VecExpr< A, T, D > & rhs )
inline

Definition at line 261 of file Functions.h.

## ◆ Mag2()

template<class A , class T , unsigned int D>
 T ROOT::Math::Mag2 ( const VecExpr< A, T, D > & rhs )
inline

Definition at line 238 of file Functions.h.

## ◆ minfunction()

 double ROOT::Math::minfunction ( const std::vector< double > & x )

function to return the function values at point x

Definition at line 19 of file RMinimizer.cxx.

 TVectorD ROOT::Math::mingradfunction ( TVectorD y )

function to return the gradient values at point y

Definition at line 25 of file RMinimizer.cxx.

## ◆ operator*() [1/45]

template<class A , class B , class T , unsigned int D, unsigned int D2, class R >
 Expr< BinaryOpCopyL< MulOp< T >, Constant< A >, Expr< B, T, D, D2, R >, T >, T, D, D2, R > ROOT::Math::operator* ( const A & lhs, const Expr< B, T, D, D2, R > & rhs )
inline

Definition at line 749 of file BinaryOperators.h.

## ◆ operator*() [2/45]

template<class A , class T , unsigned int D>
 VecExpr< BinaryOpCopyL< MulOp< T >, Constant< A >, SVector< T, D >, T >, T, D > ROOT::Math::operator* ( const A & lhs, const SVector< T, D > & rhs )
inline

Definition at line 610 of file BinaryOperators.h.

## ◆ operator*() [3/45]

template<class A , class B , class T , unsigned int D>
 VecExpr< BinaryOpCopyL< MulOp< T >, Constant< A >, VecExpr< B, T, D >, T >, T, D > ROOT::Math::operator* ( const A & lhs, const VecExpr< B, T, D > & rhs )
inline

Definition at line 633 of file BinaryOperators.h.

## ◆ operator*() [4/45]

template<class A , class B , class T , unsigned int D1, unsigned int D, unsigned int D2, class R1 , class R2 >
 Expr< MatrixMulOp< Expr< A, T, D1, D, R1 >, Expr< B, T, D, D2, R2 >, T, D >, T, D1, D2, typename MultPolicy< T, R1, R2 >::RepType > ROOT::Math::operator* ( const Expr< A, T, D1, D, R1 > & lhs, const Expr< B, T, D, D2, R2 > & rhs )
inline

Definition at line 421 of file MatrixFunctions.h.

## ◆ operator*() [5/45]

template<class A , class T , unsigned int D1, unsigned int D, unsigned int D2, class R1 , class R2 >
 Expr< MatrixMulOp< Expr< A, T, D1, D, R1 >, SMatrix< T, D, D2, R2 >, T, D >, T, D1, D2, typename MultPolicy< T, R1, R2 >::RepType > ROOT::Math::operator* ( const Expr< A, T, D1, D, R1 > & lhs, const SMatrix< T, D, D2, R2 > & rhs )
inline

Definition at line 410 of file MatrixFunctions.h.

## ◆ operator*() [6/45]

template<class A , class T , unsigned int D1, unsigned int D2, class R >
 VecExpr< VectorMatrixRowOp< Expr< A, T, D1, D2, R >, SVector< T, D2 >, D2 >, T, D1 > ROOT::Math::operator* ( const Expr< A, T, D1, D2, R > & lhs, const SVector< T, D2 > & rhs )
inline

Definition at line 233 of file MatrixFunctions.h.

## ◆ operator*() [7/45]

template<class A , class B , class T , unsigned int D1, unsigned int D2, class R >
 VecExpr< VectorMatrixRowOp< Expr< A, T, D1, D2, R >, VecExpr< B, T, D2 >, D2 >, T, D1 > ROOT::Math::operator* ( const Expr< A, T, D1, D2, R > & lhs, const VecExpr< B, T, D2 > & rhs )
inline

Definition at line 243 of file MatrixFunctions.h.

## ◆ operator*() [8/45]

template<class A , class B , class T , unsigned int D, unsigned int D2, class R >
 Expr< BinaryOpCopyR< MulOp< T >, Expr< B, T, D, D2, R >, Constant< A >, T >, T, D, D2, R > ROOT::Math::operator* ( const Expr< B, T, D, D2, R > & lhs, const A & rhs )
inline

Definition at line 737 of file BinaryOperators.h.

## ◆ operator*() [9/45]

template<class A , class T , unsigned int D1, unsigned int D, unsigned int D2, class R1 , class R2 >
 Expr< MatrixMulOp< SMatrix< T, D1, D, R1 >, Expr< A, T, D, D2, R2 >, T, D >, T, D1, D2, typename MultPolicy< T, R1, R2 >::RepType > ROOT::Math::operator* ( const SMatrix< T, D1, D, R1 > & lhs, const Expr< A, T, D, D2, R2 > & rhs )
inline

Definition at line 399 of file MatrixFunctions.h.

## ◆ operator*() [10/45]

template<class A , class T , unsigned int D1, unsigned int D2, class R >
 VecExpr< VectorMatrixRowOp< SMatrix< T, D1, D2, R >, VecExpr< A, T, D2 >, D2 >, T, D1 > ROOT::Math::operator* ( const SMatrix< T, D1, D2, R > & lhs, const VecExpr< A, T, D2 > & rhs )
inline

Definition at line 223 of file MatrixFunctions.h.

## ◆ operator*() [11/45]

template<class A , class T , unsigned int D>
 VecExpr< BinaryOpCopyR< MulOp< T >, SVector< T, D >, Constant< A >, T >, T, D > ROOT::Math::operator* ( const SVector< T, D > & lhs, const A & rhs )
inline

Definition at line 599 of file BinaryOperators.h.

## ◆ operator*() [12/45]

template<class A , class T , unsigned int D>
 VecExpr< BinaryOp< MulOp< T >, SVector< T, D >, VecExpr< A, T, D >, T >, T, D > ROOT::Math::operator* ( const SVector< T, D > & lhs, const VecExpr< A, T, D > & rhs )
inline

Definition at line 577 of file BinaryOperators.h.

## ◆ operator*() [13/45]

template<class A , class T , unsigned int D1, unsigned int D2, class R >
 VecExpr< VectorMatrixColOp< SVector< T, D1 >, Expr< A, T, D1, D2, R >, D1 >, T, D2 > ROOT::Math::operator* ( const SVector< T, D1 > & lhs, const Expr< A, T, D1, D2, R > & rhs )
inline

Definition at line 263 of file MatrixFunctions.h.

## ◆ operator*() [14/45]

template<class T , unsigned int D1, unsigned int D2, class R >
 VecExpr< VectorMatrixColOp< SVector< T, D1 >, SMatrix< T, D1, D2, R >, D1 >, T, D2 > ROOT::Math::operator* ( const SVector< T, D1 > & lhs, const SMatrix< T, D1, D2, R > & rhs )
inline

Definition at line 253 of file MatrixFunctions.h.

## ◆ operator*() [15/45]

template<class CoordSystem >
 LorentzVector< CoordSystem > ROOT::Math::operator* ( const typename LorentzVector< CoordSystem >::Scalar & a, const LorentzVector< CoordSystem > & v )
inline

Scale of a LorentzVector with a scalar quantity a.

Parameters
 a scalar quantity of typpe a v mathcore::LorentzVector based on any coordinate system
Returns
a new mathcoreLorentzVector q = v * a same type as v

Definition at line 685 of file LorentzVector.h.

## ◆ operator*() [16/45]

template<class A , class T , unsigned int D>
 VecExpr< BinaryOp< MulOp< T >, Expr< A, T, D >, SVector< T, D >, T >, T, D > ROOT::Math::operator* ( const VecExpr< A, T, D > & lhs, const SVector< T, D > & rhs )
inline

Definition at line 566 of file BinaryOperators.h.

## ◆ operator*() [17/45]

template<class A , class B , class T , unsigned int D>
 VecExpr< BinaryOp< MulOp< T >, VecExpr< A, T, D >, VecExpr< B, T, D >, T >, T, D > ROOT::Math::operator* ( const VecExpr< A, T, D > & lhs, const VecExpr< B, T, D > & rhs )
inline

Definition at line 588 of file BinaryOperators.h.

## ◆ operator*() [18/45]

template<class A , class B , class T , unsigned int D1, unsigned int D2, class R >
 VecExpr< VectorMatrixColOp< VecExpr< A, T, D1 >, Expr< B, T, D1, D2, R >, D1 >, T, D2 > ROOT::Math::operator* ( const VecExpr< A, T, D1 > & lhs, const Expr< B, T, D1, D2, R > & rhs )
inline

Definition at line 283 of file MatrixFunctions.h.

## ◆ operator*() [19/45]

template<class A , class T , unsigned int D1, unsigned int D2, class R >
 VecExpr< VectorMatrixColOp< VecExpr< A, T, D1 >, SMatrix< T, D1, D2, R >, D1 >, T, D2 > ROOT::Math::operator* ( const VecExpr< A, T, D1 > & lhs, const SMatrix< T, D1, D2, R > & rhs )
inline

Definition at line 273 of file MatrixFunctions.h.

## ◆ operator*() [20/45]

template<class A , class B , class T , unsigned int D>
 VecExpr< BinaryOpCopyR< MulOp< T >, VecExpr< B, T, D >, Constant< A >, T >, T, D > ROOT::Math::operator* ( const VecExpr< B, T, D > & lhs, const A & rhs )
inline

Definition at line 622 of file BinaryOperators.h.

## ◆ operator*() [21/45]

 AxisAngle ROOT::Math::operator* ( RotationX const & r1, AxisAngle const & r2 )

Multiplication of an axial rotation by an AxisAngle.

Definition at line 181 of file AxisAngleXother.cxx.

## ◆ operator*() [22/45]

 EulerAngles ROOT::Math::operator* ( RotationX const & r1, EulerAngles const & r2 )

Multiplication of an axial rotation by an AxisAngle.

Definition at line 112 of file EulerAngles.cxx.

## ◆ operator*() [23/45]

 Quaternion ROOT::Math::operator* ( RotationX const & r1, Quaternion const & r2 )

Multiplication of an axial rotation by an AxisAngle.

Definition at line 63 of file QuaternionXaxial.cxx.

## ◆ operator*() [24/45]

 Rotation3D ROOT::Math::operator* ( RotationX const & r1, Rotation3D const & r2 )

Multiplication of an axial rotation by a Rotation3D.

Definition at line 51 of file Rotation3DxAxial.cxx.

## ◆ operator*() [25/45]

 Rotation3D ROOT::Math::operator* ( RotationX const & r1, RotationY const & r2 )

Multiplication of an axial rotation by another axial Rotation.

Definition at line 72 of file Rotation3DxAxial.cxx.

## ◆ operator*() [26/45]

 Rotation3D ROOT::Math::operator* ( RotationX const & r1, RotationZ const & r2 )

Definition at line 84 of file Rotation3DxAxial.cxx.

## ◆ operator*() [27/45]

 RotationZYX ROOT::Math::operator* ( RotationX const & r1, RotationZYX const & r2 )

Multiplication of an axial rotation by an AxisAngle.

Definition at line 95 of file RotationZYX.cxx.

## ◆ operator*() [28/45]

 AxisAngle ROOT::Math::operator* ( RotationY const & r1, AxisAngle const & r2 )

Definition at line 185 of file AxisAngleXother.cxx.

## ◆ operator*() [29/45]

 EulerAngles ROOT::Math::operator* ( RotationY const & r1, EulerAngles const & r2 )

Definition at line 116 of file EulerAngles.cxx.

## ◆ operator*() [30/45]

 Quaternion ROOT::Math::operator* ( RotationY const & r1, Quaternion const & r2 )

Definition at line 68 of file QuaternionXaxial.cxx.

## ◆ operator*() [31/45]

 Rotation3D ROOT::Math::operator* ( RotationY const & r1, Rotation3D const & r2 )

Definition at line 57 of file Rotation3DxAxial.cxx.

## ◆ operator*() [32/45]

 Rotation3D ROOT::Math::operator* ( RotationY const & r1, RotationX const & r2 )

Definition at line 96 of file Rotation3DxAxial.cxx.

## ◆ operator*() [33/45]

 Rotation3D ROOT::Math::operator* ( RotationY const & r1, RotationZ const & r2 )

Definition at line 108 of file Rotation3DxAxial.cxx.

## ◆ operator*() [34/45]

 RotationZYX ROOT::Math::operator* ( RotationY const & r1, RotationZYX const & r2 )

Definition at line 99 of file RotationZYX.cxx.

## ◆ operator*() [35/45]

 AxisAngle ROOT::Math::operator* ( RotationZ const & r1, AxisAngle const & r2 )

Definition at line 189 of file AxisAngleXother.cxx.

## ◆ operator*() [36/45]

 EulerAngles ROOT::Math::operator* ( RotationZ const & r1, EulerAngles const & r2 )

Definition at line 121 of file EulerAngles.cxx.

## ◆ operator*() [37/45]

 Quaternion ROOT::Math::operator* ( RotationZ const & r1, Quaternion const & r2 )

Definition at line 73 of file QuaternionXaxial.cxx.

## ◆ operator*() [38/45]

 Rotation3D ROOT::Math::operator* ( RotationZ const & r1, Rotation3D const & r2 )

Definition at line 63 of file Rotation3DxAxial.cxx.

## ◆ operator*() [39/45]

 Rotation3D ROOT::Math::operator* ( RotationZ const & r1, RotationX const & r2 )

Definition at line 120 of file Rotation3DxAxial.cxx.

## ◆ operator*() [40/45]

 Rotation3D ROOT::Math::operator* ( RotationZ const & r1, RotationY const & r2 )

Definition at line 132 of file Rotation3DxAxial.cxx.

## ◆ operator*() [41/45]

 RotationZYX ROOT::Math::operator* ( RotationZ const & r1