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Reference Guide
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ROOT::Math Namespace Reference

Namespaces

 Blas
 
 BrentMethods
 
 Cephes
 
 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)
 
 CholeskyDecompHelpers
 helpers for CholeskyDecomp
 
 detail
 
 GenAlgoOptUtil
 
 GenVector
 
 GenVector_detail
 
 GSLRootHelper
 Helper functions to test convergence of Root-Finding algorithms.
 
 GSLSimAn
 
 gv_detail
 
 Impl
 
 IntegMultiDim
 
 IntegOneDim
 
 IntegOptionsUtil
 
 Integration
 
 IntegrationMultiDim
 
 IntegrationOneDim
 
 internal
 
 Internal
 
 Interpolation
 
 MCIntegration
 
 Minim
 
 Minim1D
 
 Roots
 Root-Finding Algorithms.
 
 rowOffsetsUtils
 
 Sampler
 
 Util
 namespace defining Utility functions needed by mathcore
 
 VectorUtil
 
Global Helper functions for generic Vector classes.
 

Classes

class  AdaptiveIntegratorMultiDim
 Class for adaptive quadrature integration in multi-dimensions using rectangular regions. More...
 
class  AddOp
 Addition Operation Class. More...
 
struct  AddPolicy
 matrix addition policy More...
 
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...
 
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  Functor
 Documentation for class Functor class. More...
 
class  Functor1D
 Functor1D class for one-dimensional functions. More...
 
class  FunctorGradHandler
 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  GradFunctor
 GradFunctor class for Multidimensional gradient functions. More...
 
class  GradFunctor1D
 GradFunctor1D class for one-dimensional gradient functions. More...
 
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  GSLFunctionAdapter
 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...
 
struct  GSLMonteFunctionAdapter
 
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  GSLMultiFitFunctionAdapter
 
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...
 
struct  GSLMultiMinFunctionAdapter
 
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  GSLMultiRootFunctionAdapter
 
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  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...
 
class  IGradientFunctionMultiDimTempl
 Interface (abstract class) for multi-dimensional functions providing a gradient calculation. More...
 
class  IGradientFunctionOneDim
 Interface (abstract class) for one-dimensional functions providing a gradient calculation. More...
 
class  IGradientMultiDimTempl
 Gradient interface (abstract class) defining the signature for calculating the gradient of a multi-dimensional function. More...
 
class  IGradientOneDim
 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...
 
class  IParametricGradFunctionMultiDimTempl
 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...
 
class  IParametricGradFunctionOneDim
 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...
 
class  MemGradFunHandler
 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...
 
class  MultiDimParamFunctionAdapter
 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...
 
class  MultiDimParamGradFunctionAdapter
 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  MultiNumGradFunction
 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
 
class  OneDimMultiFunctionAdapter
 OneDimMultiFunctionAdapter class to wrap a multidimensional function in one dimensional one. More...
 
class  OneDimParamFunctionAdapter
 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...
 
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...
 
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 concrate 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. More...
 
typedef BasicFitMethodFunction< ROOT::Math::IMultiGenFunctionFitMethodFunction
 
typedef BasicFitMethodFunction< ROOT::Math::IMultiGradFunctionFitMethodGradFunction
 
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. More...
 
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. More...
 
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
 
typedef IGradientFunctionOneDim IGradFunction
 
using IGradientFunctionMultiDim = IGradientFunctionMultiDimTempl< double >
 
using IGradientMultiDim = IGradientMultiDimTempl< double >
 
using IMultiGenFunction = IMultiGenFunctionTempl< double >
 
template<class T >
using IMultiGenFunctionTempl = IBaseFunctionMultiDimTempl< T >
 
typedef IGradientFunctionMultiDim IMultiGradFunction
 
typedef IntegratorOneDim Integrator
 
using IParametricFunctionMultiDim = IParametricFunctionMultiDimTempl< double >
 
using IParametricGradFunctionMultiDim = IParametricGradFunctionMultiDimTempl< double >
 
typedef IParametricFunctionOneDim IParamFunction
 
typedef IParametricGradFunctionOneDim IParamGradFunction
 
typedef IParametricFunctionMultiDim IParamMultiFunction
 
template<class T >
using IParamMultiFunctionTempl = IParametricFunctionMultiDimTempl< T >
 
typedef IParametricGradFunctionMultiDim IParamMultiGradFunction
 
template<class T >
using IParamMultiGradFunctionTempl = IParametricGradFunctionMultiDimTempl< 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< double > Plane3D
 
typedef Impl::Plane3D< float > Plane3DF
 
typedef PositionVector2D< Polar2D< double >, DefaultCoordinateSystemTagPolar2DPoint
 2D Point based on the polar coordinates rho, theta, phi in double precision. More...
 
typedef Polar2DPoint Polar2DPointD
 
typedef PositionVector2D< Polar2D< float >, DefaultCoordinateSystemTagPolar2DPointF
 2D Point based on the polar coordinates rho, theta, phi in single precision. More...
 
typedef DisplacementVector2D< Polar2D< double >, DefaultCoordinateSystemTagPolar2DVector
 2D Vector based on the polar coordinates rho, phi in double precision. More...
 
typedef Polar2DVector Polar2DVectorD
 
typedef DisplacementVector2D< Polar2D< float >, DefaultCoordinateSystemTagPolar2DVectorF
 2D Vector based on the polar coordinates rho, phi in single precision. More...
 
typedef PositionVector3D< Polar3D< double >, DefaultCoordinateSystemTagPolar3DPoint
 3D Point based on the polar coordinates rho, theta, phi in double precision. More...
 
typedef Polar3DPoint Polar3DPointD
 
typedef PositionVector3D< Polar3D< float >, DefaultCoordinateSystemTagPolar3DPointF
 
3D Point based on the polar coordinates rho, theta, phi in single precision. More...
 
typedef DisplacementVector3D< Polar3D< double >, DefaultCoordinateSystemTagPolar3DVector
 3D Vector based on the polar coordinates rho, theta, phi in double precision. More...
 
typedef Polar3DVector Polar3DVectorD
 
typedef DisplacementVector3D< Polar3D< float >, DefaultCoordinateSystemTagPolar3DVectorF
 3D Vector based on the polar coordinates rho, theta, phi in single precision. More...
 
typedef LorentzVector< PtEtaPhiE4D< double > > PtEtaPhiEVector
 LorentzVector based on the cylindrical coordinates Pt, eta, phi and E (rho, eta, phi, t) in double precision. More...
 
typedef LorentzVector< PtEtaPhiM4D< double > > PtEtaPhiMVector
 LorentzVector based on the cylindrical coordinates pt, eta, phi and Mass in double precision. More...
 
typedef LorentzVector< PxPyPzE4D< double > > PxPyPzEVector
 
typedef LorentzVector< PxPyPzM4D< double > > PxPyPzMVector
 LorentzVector based on the x, y, z, and Mass in double precision. More...
 
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. More...
 
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
 
typedef PositionVector3D< CylindricalEta3D< double >, DefaultCoordinateSystemTagRhoEtaPhiPoint
 3D Point based on the eta based cylindrical coordinates rho, eta, phi in double precision. More...
 
typedef RhoEtaPhiPoint RhoEtaPhiPointD
 
typedef PositionVector3D< CylindricalEta3D< float >, DefaultCoordinateSystemTagRhoEtaPhiPointF
 3D Point based on the eta based cylindrical coordinates rho, eta, phi in single precision. More...
 
typedef DisplacementVector3D< CylindricalEta3D< double >, DefaultCoordinateSystemTagRhoEtaPhiVector
 3D Vector based on the eta based cylindrical coordinates rho, eta, phi in double precision. More...
 
typedef RhoEtaPhiVector RhoEtaPhiVectorD
 
typedef DisplacementVector3D< CylindricalEta3D< float >, DefaultCoordinateSystemTagRhoEtaPhiVectorF
 3D Vector based on the eta based cylindrical coordinates rho, eta, phi in single precision. More...
 
typedef PositionVector3D< Cylindrical3D< double >, DefaultCoordinateSystemTagRhoZPhiPoint
 3D Point based on the cylindrical coordinates rho, z, phi in double precision. More...
 
typedef RhoZPhiPoint RhoZPhiPointD
 
typedef PositionVector3D< Cylindrical3D< float >, DefaultCoordinateSystemTagRhoZPhiPointF
 3D Point based on the cylindrical coordinates rho, z, phi in single precision. More...
 
typedef DisplacementVector3D< Cylindrical3D< double >, DefaultCoordinateSystemTagRhoZPhiVector
 3D Vector based on the cylindrical coordinates rho, z, phi in double precision. More...
 
typedef RhoZPhiVector RhoZPhiVectorD
 
typedef DisplacementVector3D< Cylindrical3D< float >, DefaultCoordinateSystemTagRhoZPhiVectorF
 3D Vector based on the cylindrical coordinates rho, z, phi in single precision. More...
 
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< double > Transform3D
 
typedef Impl::Transform3D< float > Transform3DF
 
typedef Impl::Translation3D< double > Translation3D
 
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 More...
 
typedef XYPoint XYPointD
 
typedef PositionVector2D< Cartesian2D< float >, DefaultCoordinateSystemTagXYPointF
 2D Point based on the cartesian corrdinates x,y,z in single precision More...
 
typedef DisplacementVector2D< Cartesian2D< double >, DefaultCoordinateSystemTagXYVector
 2D Vector based on the cartesian coordinates x,y in double precision More...
 
typedef XYVector XYVectorD
 
typedef DisplacementVector2D< Cartesian2D< float >, DefaultCoordinateSystemTagXYVectorF
 2D Vector based on the cartesian coordinates x,y,z in single precision More...
 
typedef PositionVector3D< Cartesian3D< double >, DefaultCoordinateSystemTagXYZPoint
 3D Point based on the cartesian coordinates x,y,z in double precision More...
 
typedef XYZPoint XYZPointD
 
typedef PositionVector3D< Cartesian3D< float >, DefaultCoordinateSystemTagXYZPointF
 3D Point based on the cartesian corrdinates x,y,z in single precision More...
 
typedef LorentzVector< PxPyPzE4D< double > > XYZTVector
 LorentzVector based on x,y,x,t (or px,py,pz,E) coordinates in double precision with metric (-,-,-,+) More...
 
typedef LorentzVector< PxPyPzE4D< float > > XYZTVectorF
 
LorentzVector based on x,y,x,t (or px,py,pz,E) coordinates in float precision with metric (-,-,-,+) More...
 
typedef DisplacementVector3D< Cartesian3D< double >, DefaultCoordinateSystemTagXYZVector
 3D Vector based on the cartesian coordinates x,y,z in double precision More...
 
typedef XYZVector XYZVectorD
 
typedef DisplacementVector3D< Cartesian3D< float >, DefaultCoordinateSystemTagXYZVectorF
 3D Vector based on the cartesian corrdinates x,y,z in single precision More...
 

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. More...
 
double beta_cdf_c (double x, double a, double b)
 Complement of the cumulative distribution function of the beta distribution. More...
 
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. More...
 
double binomial_cdf_c (unsigned int k, double p, unsigned int n)
 Complement of the cumulative distribution function of the Binomial distribution. More...
 
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 ) More...
 
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 ) More...
 
double cauchy_cdf (double x, double b, double x0=0)
 Cumulative distribution function (lower tail) of the Cauchy distribution which is also Lorentzian distribution. More...
 
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. More...
 
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). More...
 
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). More...
 
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) \( \vec{c} = \vec{a}\times\vec{b} \). More...
 
template<class A , class T >
SVector< T, 3 > Cross (const VecExpr< A, T, 3 > &lhs, const SVector< T, 3 > &rhs)
 
template<class T , class A >
SVector< T, 3 > Cross (const SVector< T, 3 > &lhs, const VecExpr< A, 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. More...
 
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. More...
 
double crystalball_integral (double x, double alpha, double n, double sigma, double x0=0)
 Integral of the not-normalized Crystal Ball function. More...
 
template<class Matrix , unsigned int n, unsigned int idim>
bool Dfactir (Matrix &rhs, typename Matrix::value_type &det, unsigned int *ir)
 Dfactir. More...
 
template<class Matrix , unsigned int n, unsigned int idim>
bool Dfinv (Matrix &rhs, unsigned int *ir)
 Dfinv. More...
 
template<class R >
RotationY::Scalar Distance (const RotationY &r1, const R &r2)
 Distance between two rotations. More...
 
template<class R >
RotationZ::Scalar Distance (const RotationZ &r1, const R &r2)
 Distance between two rotations. More...
 
template<class R >
RotationX::Scalar Distance (const RotationX &r1, const R &r2)
 Distance between two rotations. More...
 
template<class R >
AxisAngle::Scalar Distance (const AxisAngle &r1, const R &r2)
 Distance between two rotations. More...
 
template<class R >
Quaternion::Scalar Distance (const Quaternion &r1, const R &r2)
 Distance between two rotations. More...
 
template<class R >
RotationZYX::Scalar Distance (const RotationZYX &r1, const R &r2)
 Distance between two rotations. More...
 
template<class R >
EulerAngles::Scalar Distance (const EulerAngles &r1, const R &r2)
 Distance between two rotations. More...
 
template<class R >
Rotation3D::Scalar Distance (const Rotation3D &r1, const R &r2)
 Distance between two rotations. More...
 
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. More...
 
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 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 T , unsigned int D>
Dot (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
 Vector dot product. More...
 
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. More...
 
long double etaMax_impl ()
 The following function could be called to provide the maximum possible value of pseudorapidity for a non-zero rho. More...
 
double expm1 (double x)
 exp(x) -1 with error cancellation when x is small More...
 
double exponential_cdf (double x, double lambda, double x0=0)
 Cumulative distribution function of the exponential distribution (lower tail). More...
 
double exponential_cdf_c (double x, double lambda, double x0=0)
 Complement of the cumulative distribution function of the exponential distribution (upper tail). More...
 
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)
 
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 More...
 
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 More...
 
double fdistribution_cdf (double x, double n, double m, double x0=0)
 Cumulative distribution function of the F-distribution (lower tail). More...
 
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). More...
 
double gamma_cdf (double x, double alpha, double theta, double x0=0)
 Cumulative distribution function of the gamma distribution (lower tail). More...
 
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). More...
 
double gaussian_cdf (double x, double sigma=1, double x0=0)
 Alternative name for same function. More...
 
double gaussian_cdf_c (double x, double sigma=1, double x0=0)
 Alternative name for same function. More...
 
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). More...
 
double landau_cdf_c (double x, double xi=1, double x0=0)
 Complement of the distribution function of the Landau distribution (upper tail). More...
 
double landau_xm1 (double x, double xi=1, double x0=0)
 First moment (mean) of the truncated Landau distribution. More...
 
double landau_xm2 (double x, double xi=1, double x0=0)
 Second moment of the truncated Landau distribution. More...
 
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: \( |\vec{v}| = \sqrt{v_0^2 - v_1^2 - v_2^2 -v_3^2} \). More...
 
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 \( |\vec{v}|^2 = v_0^2 - v_1^2 - v_2^2 -v_3^2 \). More...
 
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 More...
 
double lognormal_cdf (double x, double m, double s, double x0=0)
 Cumulative distribution function of the lognormal distribution (lower tail). More...
 
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). More...
 
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 : \( |\vec{v}| = \sqrt{\sum_iv_i^2} \). More...
 
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 \(|\vec{v}|^2 = \sum_iv_i^2 \). More...
 
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. More...
 
double minfunction (const std::vector< double > &x)
 function to return the function values at point x More...
 
TVectorD mingradfunction (TVectorD y)
 function to return the gradient values at point y More...
 
template<class T >
const T Minimum (const T &lhs, const T &rhs)
 minimum. More...
 
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. More...
 
double negative_binomial_cdf_c (unsigned int k, double p, double n)
 Complement of the cumulative distribution function of the Negative Binomial distribution. More...
 
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 \(\lambda\). More...
 
double normal_cdf (double x, double sigma=1, double x0=0)
 Cumulative distribution function of the normal (Gaussian) distribution (lower tail). More...
 
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). More...
 
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. More...
 
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 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 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 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 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 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)
 
AxisAngle operator* (RotationX const &r1, AxisAngle const &r2)
 Multiplication of an axial rotation by an AxisAngle. More...
 
AxisAngle operator* (RotationY const &r1, AxisAngle const &r2)
 
AxisAngle operator* (RotationZ const &r1, AxisAngle const &r2)
 
Quaternion operator* (RotationX const &r1, Quaternion const &r2)
 Multiplication of an axial rotation by an AxisAngle. More...
 
RotationZYX operator* (RotationX const &r1, RotationZYX const &r2)
 Multiplication of an axial rotation by an AxisAngle. More...
 
Quaternion operator* (RotationY const &r1, Quaternion const &r2)
 
RotationZYX operator* (RotationY const &r1, RotationZYX const &r2)
 
Quaternion operator* (RotationZ const &r1, Quaternion const &r2)
 
RotationZYX operator* (RotationZ const &r1, RotationZYX const &r2)
 
EulerAngles operator* (RotationX const &r1, EulerAngles const &r2)
 Multiplication of an axial rotation by an AxisAngle. More...
 
EulerAngles operator* (RotationY const &r1, EulerAngles const &r2)
 
EulerAngles operator* (RotationZ const &r1, EulerAngles const &r2)
 
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. More...
 
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. More...
 
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 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 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 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. More...
 
Rotation3D operator* (RotationX const &r1, Rotation3D const &r2)
 Multiplication of an axial rotation by a Rotation3D. More...
 
Rotation3D operator* (RotationY const &r1, Rotation3D const &r2)
 
Rotation3D operator* (RotationZ const &r1, Rotation3D const &r2)
 
Rotation3D operator* (RotationX const &r1, RotationY const &r2)
 Multiplication of an axial rotation by another axial Rotation. More...
 
Rotation3D operator* (RotationX const &r1, RotationZ const &r2)
 
Rotation3D operator* (RotationY const &r1, RotationX const &r2)
 
Rotation3D operator* (RotationY const &r1, RotationZ const &r2)
 
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. More...
 
Rotation3D operator* (RotationZ const &r1, RotationX const &r2)
 
Rotation3D operator* (RotationZ const &r1, RotationY const &r2)
 
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. More...
 
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 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 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 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 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 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. More...
 
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)
 
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 CoordSystem >
LorentzVector< CoordSystem > operator* (const typename LorentzVector< CoordSystem >::Scalar &a, const LorentzVector< CoordSystem > &v)
 Scale of a LorentzVector with a scalar quantity a. More...
 
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. More...
 
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. More...
 
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 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 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. More...
 
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 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 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 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. More...
 
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. More...
 
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 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 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. More...
 
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 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 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 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. More...
 
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. More...
 
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 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 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. More...
 
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. More...
 
template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector2D< CoordSystem1, U > operator+ (DisplacementVector2D< CoordSystem1, U > v1, const DisplacementVector2D< CoordSystem2, U > &v2)
 Addition of DisplacementVector2D vectors. More...
 
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. More...
 
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. More...
 
template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector3D< CoordSystem1, U > operator+ (DisplacementVector3D< CoordSystem1, U > v1, const DisplacementVector3D< CoordSystem2, U > &v2)
 Addition of DisplacementVector3D vectors. More...
 
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 T , unsigned int D>
VecExpr< UnaryOp< Minus< T >, SVector< T, D >, T >, T, D > operator- (const SVector< T, D > &rhs)
 Unary - operator v2 = -v1 . More...
 
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 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. More...
 
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. More...
 
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 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 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< 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. More...
 
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. More...
 
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- (const PositionVector2D< CoordSystem1, U > &v1, const PositionVector2D< CoordSystem2, U > &v2)
 Difference between two PositionVector2D vectors. More...
 
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 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. More...
 
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 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. More...
 
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 CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector2D< CoordSystem1, U > operator- (DisplacementVector2D< CoordSystem1, U > v1, DisplacementVector2D< CoordSystem2, U > const &v2)
 Difference between two DisplacementVector2D vectors. More...
 
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 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. More...
 
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. More...
 
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 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 CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector3D< CoordSystem1, U > operator- (const PositionVector3D< CoordSystem1, U > &v1, const PositionVector3D< CoordSystem2, U > &v2)
 Difference between two PositionVector3D vectors. More...
 
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. More...
 
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. More...
 
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. More...
 
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 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 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 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. More...
 
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. More...
 
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 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 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. More...
 
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. More...
 
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 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)
 
std::ostream & operator<< (std::ostream &os, const BoostY &b)
 Stream Output and Input. More...
 
std::ostream & operator<< (std::ostream &os, const BoostZ &b)
 Stream Output and Input. More...
 
std::ostream & operator<< (std::ostream &os, const BoostX &b)
 Stream Output and Input. More...
 
template<class A , class T , unsigned int D>
std::ostream & operator<< (std::ostream &os, const VecExpr< A, T, D > &rhs)
 
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 RotationX &r)
 Stream Output and Input. More...
 
std::ostream & operator<< (std::ostream &os, const RotationY &r)
 Stream Output and Input. More...
 
std::ostream & operator<< (std::ostream &os, const RotationZ &r)
 Stream Output and Input. More...
 
std::ostream & operator<< (std::ostream &os, const Boost &b)
 Stream Output and Input. More...
 
std::ostream & operator<< (std::ostream &os, const AxisAngle &a)
 Stream Output and Input. More...
 
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 Quaternion &q)
 Stream Output and Input. More...
 
std::ostream & operator<< (std::ostream &os, const RotationZYX &e)
 Stream Output and Input. More...
 
std::ostream & operator<< (std::ostream &os, const EulerAngles &e)
 Stream Output and Input. More...
 
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 >
std::basic_ostream< char_t, traits_t > & operator<< (std::basic_ostream< char_t, traits_t > &os, DisplacementVector2D< T, U > const &v)
 
std::ostream & operator<< (std::ostream &os, const LorentzRotation &r)
 Stream Output and Input. More...
 
std::ostream & operator<< (std::ostream &os, const Rotation3D &r)
 Stream Output and Input. More...
 
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)
 
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 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 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, 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, PositionVector3D< 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)
 
double Pi ()
 Mathematical constants. More...
 
double poisson_cdf (unsigned int n, double mu)
 Cumulative distribution function of the Poisson distribution Lower tail of the integral of the poisson_pdf. More...
 
double poisson_cdf_c (unsigned int n, double mu)
 Complement of the cumulative distribution function of the Poisson distribution. More...
 
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. More...
 
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. More...
 
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 \( s = \sum_{i,j} v(i) * A(i,j) * v(j)\). More...
 
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 T , unsigned int D, class R >
Similarity (const SMatrix< T, D, D, R > &lhs, const VecExpr< A, T, D > &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 D, class R >
Similarity (const SVector< T, D > &lhs, const Expr< A, T, D, D, R > &rhs)
 
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 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 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: \( B(i,j) = \sum_{k,l} U(i,k) * A(k,l) * U(j,l) \). More...
 
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 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: \( B(i,j) = \sum_{k,l} U(k,i) * A(k,l) * U(l,j) \). More...
 
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 D>
bool SolveChol (SMatrix< T, D, D, MatRepSym< T, D > > &mat, SVector< T, D > &vec)
 
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) More...
 
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 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) . More...
 
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 More...
 
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 , 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 More...
 
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 More...
 
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 More...
 
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). More...
 
double tdistribution_cdf_c (double x, double r, double x0=0)
 Complement of the cumulative distribution function of Student's t-distribution (upper tail). More...
 
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. More...
 
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 >
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 , 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 More...
 
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. More...
 
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 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 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. More...
 
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)
 
double uniform_cdf (double x, double a, double b, double x0=0)
 Cumulative distribution function of the uniform (flat) distribution (lower tail). More...
 
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). More...
 
template<class T , unsigned int D>
SVector< T, D > Unit (const SVector< T, D > &rhs)
 Unit. More...
 
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. More...
 
double vavilov_accurate_cdf_c (double x, double kappa, double beta2)
 The Vavilov complementary cumulative probability density function. More...
 
double vavilov_accurate_pdf (double x, double kappa, double beta2)
 The Vavilov probability density function. More...
 
double vavilov_accurate_quantile (double z, double kappa, double beta2)
 The inverse of the Vavilov cumulative probability density function. More...
 
double vavilov_accurate_quantile_c (double z, double kappa, double beta2)
 The inverse of the complementary Vavilov cumulative probability density function. More...
 
double vavilov_fast_cdf (double x, double kappa, double beta2)
 The Vavilov cumulative probability density function. More...
 
double vavilov_fast_cdf_c (double x, double kappa, double beta2)
 The Vavilov complementary cumulative probability density function. More...
 
double vavilov_fast_pdf (double x, double kappa, double beta2)
 The Vavilov probability density function. More...
 
double vavilov_fast_quantile (double z, double kappa, double beta2)
 The inverse of the Vavilov cumulative probability density function. More...
 
double vavilov_fast_quantile_c (double z, double kappa, double beta2)
 The inverse of the complementary Vavilov cumulative probability density function. More...
 
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. More...
 
double binomial_pdf (unsigned int k, double p, unsigned int n)
 Probability density function of the binomial distribution. More...
 
double negative_binomial_pdf (unsigned int k, double p, double n)
 Probability density function of the negative binomial distribution. More...
 
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 ) More...
 
double cauchy_pdf (double x, double b=1, double x0=0)
 Probability density function of the Cauchy distribution which is also called Lorentzian distribution. More...
 
double chisquared_pdf (double x, double r, double x0=0)
 Probability density function of the \(\chi^2\) distribution with \(r\) degrees of freedom. More...
 
double crystalball_function (double x, double alpha, double n, double sigma, double mean=0)
 Crystal ball function. More...
 
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 More...
 
double exponential_pdf (double x, double lambda, double x0=0)
 Probability density function of the exponential distribution. More...
 
double fdistribution_pdf (double x, double n, double m, double x0=0)
 Probability density function of the F-distribution. More...
 
double gamma_pdf (double x, double alpha, double theta, double x0=0)
 Probability density function of the gamma distribution. More...
 
double gaussian_pdf (double x, double sigma=1, double x0=0)
 Probability density function of the normal (Gaussian) distribution. More...
 
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. More...
 
double landau_pdf (double x, double xi=1, double x0=0)
 Probability density function of the Landau distribution:

\[ p(x) = \frac{1}{\xi} \phi (\lambda) \]

with

\[ \phi(\lambda) = \frac{1}{2 \pi i}\int_{c-i\infty}^{c+i\infty} e^{\lambda s + s \log{s}} ds\]

where \(\lambda = (x-x_0)/\xi\). More...

 
double lognormal_pdf (double x, double m, double s, double x0=0)
 Probability density function of the lognormal distribution. More...
 
double normal_pdf (double x, double sigma=1, double x0=0)
 Probability density function of the normal (Gaussian) distribution. More...
 
double poisson_pdf (unsigned int n, double mu)
 Probability density function of the Poisson distribution. More...
 
double tdistribution_pdf (double x, double r, double x0=0)
 Probability density function of Student's t-distribution. More...
 
double uniform_pdf (double x, double a, double b, double x0=0)
 Probability density function of the uniform (flat) distribution. More...
 
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). More...
 
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). More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
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). More...
 
Special Functions from MathCore
double erf (double x)
 Error function encountered in integrating the normal distribution. More...
 
double erfc (double x)
 Complementary error function. More...
 
double tgamma (double x)
 The gamma function is defined to be the extension of the factorial to real numbers. More...
 
double lgamma (double x)
 Calculates the logarithm of the gamma function. More...
 
double inc_gamma (double a, double x)
 Calculates the normalized (regularized) lower incomplete gamma function (lower integral) More...
 
double inc_gamma_c (double a, double x)
 Calculates the normalized (regularized) upper incomplete gamma function (upper integral) More...
 
double beta (double x, double y)
 Calculates the beta function. More...
 
double inc_beta (double x, double a, double b)
 Calculates the normalized (regularized) incomplete beta function. More...
 
double sinint (double x)
 Calculates the sine integral. More...
 
double cosint (double x)
 Calculates the real part of the cosine integral Re(Ci). More...
 
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). More...
 
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). More...
 
Special Functions from MathMore
double assoc_laguerre (unsigned n, double m, double x)
 Computes the generalized Laguerre polynomials for \( n \geq 0, m > -1 \). More...
 
double assoc_legendre (unsigned l, unsigned m, double x)
 Computes the associated Legendre polynomials. More...
 
double comp_ellint_1 (double k)
 Calculates the complete elliptic integral of the first kind. More...
 
double comp_ellint_2 (double k)
 Calculates the complete elliptic integral of the second kind. More...
 
double comp_ellint_3 (double n, double k)
 Calculates the complete elliptic integral of the third kind. More...
 
double conf_hyperg (double a, double b, double z)
 Calculates the confluent hypergeometric functions of the first kind. More...
 
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. More...
 
double cyl_bessel_i (double nu, double x)
 Calculates the modified Bessel function of the first kind (also called regular modified (cylindrical) Bessel function). More...
 
double cyl_bessel_j (double nu, double x)
 Calculates the (cylindrical) Bessel functions of the first kind (also called regular (cylindrical) Bessel functions). More...
 
double cyl_bessel_k (double nu, double x)
 Calculates the modified Bessel functions of the second kind (also called irregular modified (cylindrical) Bessel functions). More...
 
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). More...
 
double ellint_1 (double k, double phi)
 Calculates the incomplete elliptic integral of the first kind. More...
 
double ellint_2 (double k, double phi)
 Calculates the complete elliptic integral of the second kind. More...
 
double ellint_3 (double n, double k, double phi)
 Calculates the complete elliptic integral of the third kind. More...
 
double expint (double x)
 Calculates the exponential integral. More...
 
double expint_n (int n, double x)
 
double hyperg (double a, double b, double c, double x)
 Calculates Gauss' hypergeometric function. More...
 
double laguerre (unsigned n, double x)
 Calculates the Laguerre polynomials. More...
 
double legendre (unsigned l, double x)
 Calculates the Legendre polynomials. More...
 
double riemann_zeta (double x)
 Calculates the Riemann zeta function. More...
 
double sph_bessel (unsigned n, double x)
 Calculates the spherical Bessel functions of the first kind (also called regular spherical Bessel functions). More...
 
double sph_legendre (unsigned l, unsigned m, double theta)
 Computes the spherical (normalized) associated Legendre polynomials, or spherical harmonic without azimuthal dependence ( \(e^(im\phi)\)). More...
 
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). More...
 
double airy_Ai (double x)
 Calculates the Airy function Ai. More...
 
double airy_Bi (double x)
 Calculates the Airy function Bi. More...
 
double airy_Ai_deriv (double x)
 Calculates the derivative of the Airy function Ai. More...
 
double airy_Bi_deriv (double x)
 Calculates the derivative of the Airy function Bi. More...
 
double airy_zero_Ai (unsigned int s)
 Calculates the zeroes of the Airy function Ai. More...
 
double airy_zero_Bi (unsigned int s)
 Calculates the zeroes of the Airy function Bi. More...
 
double airy_zero_Ai_deriv (unsigned int s)
 Calculates the zeroes of the derivative of the Airy function Ai. More...
 
double airy_zero_Bi_deriv (unsigned int s)
 Calculates the zeroes of the derivative of the Airy function Bi. More...
 
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. More...
 
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. More...
 
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. More...
 

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 More...
 
const ROOT::Math::IMultiGradFunctiongGradFunction
 function wrapper for the gradient of the function to be minimized More...
 
int gNCalls = 0
 integer for the number of function calls More...
 
double kEulerGamma = 0.577215664901532860606512090082402431042
 
double kPi = 3.14159265358979323846
 
static const double kSqrt2 = 1.41421356237309515
 

Typedef Documentation

◆ FitMethodFunction

Definition at line 40 of file Fitter.h.

◆ FitMethodGradFunction

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 369 of file GSLRndmEngines.h.

◆ GSLRngRanLux2

Definition at line 384 of file GSLRndmEngines.h.

◆ GSLRngRanLux48

Definition at line 413 of file GSLRndmEngines.h.

◆ IBaseFunctionMultiDim

Definition at line 31 of file IFunctionfwd.h.

◆ IGenFunction

Definition at line 37 of file IFunctionfwd.h.

◆ IGradFunction

Definition at line 40 of file IFunctionfwd.h.

◆ IGradientFunctionMultiDim

Definition at line 34 of file IFunctionfwd.h.

◆ IGradientMultiDim

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<T>

Definition at line 30 of file IFunctionfwd.h.

◆ IMultiGradFunction

Definition at line 41 of file IFunctionfwd.h.

◆ Integrator

Definition at line 476 of file Integrator.h.

◆ IParametricFunctionMultiDim

Definition at line 26 of file IParamFunctionfwd.h.

◆ IParametricGradFunctionMultiDim

Definition at line 29 of file IParamFunctionfwd.h.

◆ IParamFunction

Definition at line 31 of file IParamFunctionfwd.h.

◆ IParamGradFunction

Definition at line 36 of file IParamFunctionfwd.h.

◆ IParamMultiFunction

Definition at line 32 of file IParamFunctionfwd.h.

◆ IParamMultiFunctionTempl

Definition at line 34 of file IParamFunctionfwd.h.

◆ IParamMultiGradFunction

Definition at line 37 of file IParamFunctionfwd.h.

◆ IParamMultiGradFunctionTempl

Definition at line 39 of file IParamFunctionfwd.h.

◆ MathMoreLibrary

Definition at line 68 of file PdfFuncMathMore.h.

◆ MixMaxEngine17

Definition at line 177 of file MixMaxEngine.h.

◆ MixMaxEngine240

Definition at line 175 of file MixMaxEngine.h.

◆ MixMaxEngine256

Definition at line 176 of file MixMaxEngine.h.

◆ MultiRootFinder

Definition at line 292 of file GSLMultiRootFinder.h.

◆ OptionsMap

typedef std::map<std::string, ROOT::Math::GenAlgoOptions > ROOT::Math::OptionsMap

Definition at line 25 of file GenAlgoOptions.cxx.

◆ ParamFunctor

Definition at line 388 of file ParamFunctor.h.

◆ Plane3D

Definition at line 302 of file Plane3D.h.

◆ Plane3DF

Definition at line 303 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

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.

Definition at line 49 of file Vector2Dfwd.h.

◆ Polar2DVectorD

Definition at line 50 of file Vector2Dfwd.h.

◆ Polar2DVectorF

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

Definition at line 55 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


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.

Definition at line 60 of file Vector3Dfwd.h.

◆ Polar3DVectorD

Definition at line 65 of file Vector3Dfwd.h.

◆ Polar3DVectorF

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

Definition at line 64 of file Vector3Dfwd.h.

◆ PtEtaPhiEVector

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

Definition at line 61 of file Vector4Dfwd.h.

◆ PtEtaPhiMVector

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

Definition at line 66 of file Vector4Dfwd.h.

◆ PxPyPzEVector

Definition at line 44 of file Vector4Dfwd.h.

◆ PxPyPzMVector

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

Definition at line 56 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

Useful typedef definitions.

Definition at line 243 of file Random.h.

◆ RandomMT

Definition at line 11 of file GSLRandom.h.

◆ RandomMT19937

Definition at line 244 of file Random.h.

◆ RandomMT64

Definition at line 245 of file Random.h.

◆ RandomRanLux

Definition at line 13 of file GSLRandom.h.

◆ RandomRanlux48

Definition at line 246 of file Random.h.

◆ RandomTaus

Definition at line 12 of file GSLRandom.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

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.

Definition at line 50 of file Vector3Dfwd.h.

◆ RhoEtaPhiVectorD

Definition at line 55 of file Vector3Dfwd.h.

◆ RhoEtaPhiVectorF

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

Definition at line 54 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

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.

Definition at line 70 of file Vector3Dfwd.h.

◆ RhoZPhiVectorD

Definition at line 75 of file Vector3Dfwd.h.

◆ RhoZPhiVectorF

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

Definition at line 74 of file Vector3Dfwd.h.

◆ Scalar

Definition at line 69 of file Rotation3DxAxial.cxx.

◆ SMatrix2D

typedef SMatrix<double,2,2,MatRepStd<double,2,2> > ROOT::Math::SMatrix2D

Definition at line 14 of file SMatrixDfwd.h.

◆ SMatrix2F

typedef SMatrix<float,2,2,MatRepStd<float,2,2> > ROOT::Math::SMatrix2F

Definition at line 14 of file SMatrixFfwd.h.

◆ SMatrix3D

typedef SMatrix<double,3,3,MatRepStd<double,3,3> > ROOT::Math::SMatrix3D

Definition at line 17 of file SMatrixDfwd.h.

◆ SMatrix3F

typedef SMatrix<float,3,3,MatRepStd<float,3,3> > ROOT::Math::SMatrix3F

Definition at line 17 of file SMatrixFfwd.h.

◆ SMatrix4D

typedef SMatrix<double,4,4,MatRepStd<double,4,4> > ROOT::Math::SMatrix4D

Definition at line 18 of file SMatrixDfwd.h.

◆ SMatrix4F

typedef SMatrix<float,4,4,MatRepStd<float,4,4> > ROOT::Math::SMatrix4F

Definition at line 18 of file SMatrixFfwd.h.

◆ SMatrix5D

typedef SMatrix<double,5,5,MatRepStd<double,5,5> > ROOT::Math::SMatrix5D

Definition at line 19 of file SMatrixDfwd.h.

◆ SMatrix5F

typedef SMatrix<float,5,5,MatRepStd<float,5,5> > ROOT::Math::SMatrix5F

Definition at line 19 of file SMatrixFfwd.h.

◆ SMatrix6D

typedef SMatrix<double,6,6,MatRepStd<double,6,6> > ROOT::Math::SMatrix6D

Definition at line 20 of file SMatrixDfwd.h.

◆ SMatrix6F

typedef SMatrix<float,6,6,MatRepStd<float,6,6> > ROOT::Math::SMatrix6F

Definition at line 20 of file SMatrixFfwd.h.

◆ SMatrix7D

typedef SMatrix<double,7,7,MatRepStd<double,7,7> > ROOT::Math::SMatrix7D

Definition at line 21 of file SMatrixDfwd.h.

◆ SMatrix7F

typedef SMatrix<float,7,7,MatRepStd<float,7,7> > ROOT::Math::SMatrix7F

Definition at line 21 of file SMatrixFfwd.h.

◆ SMatrixSym2D

typedef SMatrix<double,2,2,MatRepSym<double,2> > ROOT::Math::SMatrixSym2D

Definition at line 24 of file SMatrixDfwd.h.

◆ SMatrixSym2F

typedef SMatrix<float,2,2,MatRepSym<float,2> > ROOT::Math::SMatrixSym2F

Definition at line 23 of file SMatrixFfwd.h.

◆ SMatrixSym3D

typedef SMatrix<double,3,3,MatRepSym<double,3> > ROOT::Math::SMatrixSym3D

Definition at line 25 of file SMatrixDfwd.h.

◆ SMatrixSym3F

typedef SMatrix<float,3,3,MatRepSym<float,3> > ROOT::Math::SMatrixSym3F

Definition at line 24 of file SMatrixFfwd.h.

◆ SMatrixSym4D

typedef SMatrix<double,4,4,MatRepSym<double,4> > ROOT::Math::SMatrixSym4D

Definition at line 26 of file SMatrixDfwd.h.

◆ SMatrixSym4F

typedef SMatrix<float,4,4,MatRepSym<float,4> > ROOT::Math::SMatrixSym4F

Definition at line 25 of file SMatrixFfwd.h.

◆ SMatrixSym5D

typedef SMatrix<double,5,5,MatRepSym<double,5> > ROOT::Math::SMatrixSym5D

Definition at line 27 of file SMatrixDfwd.h.

◆ SMatrixSym5F

typedef SMatrix<float,5,5,MatRepSym<float,5> > ROOT::Math::SMatrixSym5F

Definition at line 26 of file SMatrixFfwd.h.

◆ SMatrixSym6D

typedef SMatrix<double,6,6,MatRepSym<double,6> > ROOT::Math::SMatrixSym6D

Definition at line 28 of file SMatrixDfwd.h.

◆ SMatrixSym6F

typedef SMatrix<float,6,6,MatRepSym<float,6> > ROOT::Math::SMatrixSym6F

Definition at line 27 of file SMatrixFfwd.h.

◆ SMatrixSym7D

typedef SMatrix<double,7,7,MatRepSym<double,7> > ROOT::Math::SMatrixSym7D

Definition at line 29 of file SMatrixDfwd.h.

◆ SMatrixSym7F

typedef SMatrix<float,7,7,MatRepSym<float,7> > ROOT::Math::SMatrixSym7F

Definition at line 28 of file SMatrixFfwd.h.

◆ TDataPoint1D

Definition at line 60 of file TDataPoint.h.

◆ TDataPoint1F

Definition at line 57 of file TDataPoint.h.

◆ TDataPoint2D

Definition at line 61 of file TDataPoint.h.

◆ TDataPoint2F

Definition at line 58 of file TDataPoint.h.

◆ TDataPoint3D

Definition at line 62 of file TDataPoint.h.

◆ TDataPoint3F

Definition at line 59 of file TDataPoint.h.

◆ Transform3D

Definition at line 1318 of file Transform3D.h.

◆ Transform3DF

Definition at line 1319 of file Transform3D.h.

◆ Translation3D

Definition at line 307 of file Translation3D.h.

◆ Translation3DF

Definition at line 308 of file Translation3D.h.

◆ WrappedMultiTF1

Definition at line 335 of file WrappedMultiTF1.h.

◆ XYPoint

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

Definition at line 30 of file Point2Dfwd.h.

◆ XYPointD

Definition at line 36 of file Point2Dfwd.h.

◆ 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

Definition at line 31 of file Vector2Dfwd.h.

◆ XYVectorD

Definition at line 38 of file Vector2Dfwd.h.

◆ XYVectorF

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

Definition at line 43 of file Vector2Dfwd.h.

◆ XYZPoint

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

Definition at line 33 of file Point3Dfwd.h.

◆ XYZPointD

Definition at line 44 of file Point3Dfwd.h.

◆ XYZPointF

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

Definition at line 43 of file Point3Dfwd.h.

◆ XYZTVector

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

Definition at line 33 of file Vector4Dfwd.h.

◆ XYZTVectorF


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

Definition at line 50 of file Vector4Dfwd.h.

◆ XYZVector

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

Definition at line 34 of file Vector3Dfwd.h.

◆ XYZVectorD

Definition at line 45 of file Vector3Dfwd.h.

◆ XYZVectorF

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

Definition at line 44 of file Vector3Dfwd.h.

Enumeration Type Documentation

◆ 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

◆ adkTestStat()

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

Definition at line 546 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 A , class T >
SVector<T,3> ROOT::Math::Cross ( const VecExpr< A, T, 3 > &  lhs,
const SVector< T, 3 > &  rhs 
)
inline

Definition at line 335 of file Functions.h.

◆ Cross() [2/3]

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 348 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 361 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.

Author
T. Glebe

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!

Author
T. Glebe

Definition at line 47 of file Dfinv.h.

◆ Distance() [1/8]

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() [2/8]

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() [3/8]

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() [4/8]

template<class R >
AxisAngle::Scalar ROOT::Math::Distance ( const AxisAngle r1,
const R r2 
)
inline

Distance between two rotations.

Definition at line 326 of file AxisAngle.h.

◆ Distance() [5/8]

template<class R >
Quaternion::Scalar ROOT::Math::Distance ( const Quaternion r1,
const R r2 
)
inline

Distance between two rotations.

Definition at line 334 of file Quaternion.h.

◆ Distance() [6/8]

template<class R >
RotationZYX::Scalar ROOT::Math::Distance ( const RotationZYX r1,
const R r2 
)
inline

Distance between two rotations.

Definition at line 335 of file RotationZYX.h.

◆ Distance() [7/8]

template<class R >
EulerAngles::Scalar ROOT::Math::Distance ( const EulerAngles r1,
const R r2 
)
inline

Distance between two rotations.

Definition at line 362 of file EulerAngles.h.

◆ Distance() [8/8]

template<class R >
Rotation3D::Scalar ROOT::Math::Distance ( const Rotation3D r1,
const R r2 
)
inline

Distance between two rotations.

Definition at line 496 of file Rotation3D.h.

◆ Div() [1/3]

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() [2/3]

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.

◆ Div() [3/3]

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.

◆ 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 172 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 180 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 189 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 50 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>
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.

◆ fabs() [2/2]

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.

◆ 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 520 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 534 of file GoFTest.cxx.

◆ human_readable()

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 307 of file Functions.h.

◆ Lmag2()

template<class A , class T >
T ROOT::Math::Lmag2 ( const VecExpr< A, T, 4 > &  rhs)
inline

Definition at line 283 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.

◆ machine_readable()

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 260 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 237 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.

◆ mingradfunction()

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 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 221 of file MatrixFunctions.h.

◆ operator*() [2/45]

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 231 of file MatrixFunctions.h.

◆ operator*() [3/45]

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 241 of file MatrixFunctions.h.

◆ operator*() [4/45]

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 251 of file MatrixFunctions.h.

◆ operator*() [5/45]

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 261 of file MatrixFunctions.h.

◆ operator*() [6/45]

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 271 of file MatrixFunctions.h.

◆ operator*() [7/45]

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 281 of file MatrixFunctions.h.

◆ operator*() [8/45]

AxisAngle ROOT::Math::operator* ( RotationX const &  r1,
AxisAngle const &  r2 
)

Multiplication of an axial rotation by an AxisAngle.

Definition at line 182 of file AxisAngleXother.cxx.

◆ operator*() [9/45]

AxisAngle ROOT::Math::operator* ( RotationY const &  r1,
AxisAngle const &  r2 
)

Definition at line 186 of file AxisAngleXother.cxx.

◆ operator*() [10/45]

AxisAngle ROOT::Math::operator* ( RotationZ const &  r1,
AxisAngle const &  r2 
)

Definition at line 190 of file AxisAngleXother.cxx.

◆ operator*() [11/45]

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*() [12/45]

RotationZYX ROOT::Math::operator* ( RotationX const &  r1,
RotationZYX const &  r2 
)

Multiplication of an axial rotation by an AxisAngle.

Definition at line 96 of file RotationZYX.cxx.

◆ operator*() [13/45]

Quaternion ROOT::Math::operator* ( RotationY const &  r1,
Quaternion const &  r2 
)

Definition at line 68 of file QuaternionXaxial.cxx.

◆ operator*() [14/45]

RotationZYX ROOT::Math::operator* ( RotationY const &  r1,
RotationZYX const &  r2 
)

Definition at line 100 of file RotationZYX.cxx.

◆ operator*() [15/45]

Quaternion ROOT::Math::operator* ( RotationZ const &  r1,
Quaternion const &  r2 
)

Definition at line 73 of file QuaternionXaxial.cxx.

◆ operator*() [16/45]

RotationZYX ROOT::Math::operator* ( RotationZ const &  r1,
RotationZYX const &  r2 
)

Definition at line 105 of file RotationZYX.cxx.

◆ operator*() [17/45]

EulerAngles ROOT::Math::operator* ( RotationX const &  r1,
EulerAngles const &  r2 
)

Multiplication of an axial rotation by an AxisAngle.

Definition at line 113 of file EulerAngles.cxx.

◆ operator*() [18/45]

EulerAngles ROOT::Math::operator* ( RotationY const &  r1,
EulerAngles const &  r2 
)

Definition at line 117 of file EulerAngles.cxx.

◆ operator*() [19/45]

EulerAngles ROOT::Math::operator* ( RotationZ const &  r1,
EulerAngles const &  r2 
)

Definition at line 122 of file EulerAngles.cxx.

◆ operator*() [20/45]

template<class CoordSystem , class U >
PositionVector2D<CoordSystem> ROOT::Math::operator* ( typename PositionVector2D< CoordSystem, U >::Scalar  a,
PositionVector2D< CoordSystem, U >  v 
)
inline

Multiplication of a position vector by real number a*v.

Definition at line 376 of file PositionVector2D.h.

◆ operator*() [21/45]

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 397 of file MatrixFunctions.h.

◆ operator*() [22/45]

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 408 of file MatrixFunctions.h.

◆ operator*() [23/45]

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 419 of file MatrixFunctions.h.

◆ operator*() [24/45]

template<class CoordSystem , class U >
DisplacementVector2D<CoordSystem,U> ROOT::Math::operator* ( typename DisplacementVector2D< CoordSystem, U >::Scalar  a,
DisplacementVector2D< CoordSystem, U >  v 
)
inline

Multiplication of a displacement vector by real number a*v.

Definition at line 461 of file DisplacementVector2D.h.

◆ operator*() [25/45]

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*() [26/45]

Rotation3D ROOT::Math::operator* ( RotationY const &  r1,
Rotation3D const &  r2 
)

Definition at line 57 of file Rotation3DxAxial.cxx.

◆ operator*() [27/45]

Rotation3D ROOT::Math::operator* ( RotationZ const &  r1,
Rotation3D const &  r2 
)

Definition at line 63 of file Rotation3DxAxial.cxx.

◆ operator*() [28/45]

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*() [29/45]

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

Definition at line 84 of file Rotation3DxAxial.cxx.

◆ operator*() [30/45]

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

Definition at line 96 of file Rotation3DxAxial.cxx.

◆ operator*() [31/45]

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

Definition at line 108 of file Rotation3DxAxial.cxx.

◆ operator*() [32/45]

template<class CoordSystem , class U >
PositionVector3D<CoordSystem> ROOT::Math::operator* ( typename PositionVector3D< CoordSystem, U >::Scalar  a,
PositionVector3D< CoordSystem, U >  v 
)
inline

Multiplication of a position vector by real number a*v.

Definition at line 513 of file PositionVector3D.h.

◆ operator*() [33/45]

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

Definition at line 120 of file Rotation3DxAxial.cxx.

◆ operator*() [34/45]

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

Definition at line 132 of file Rotation3DxAxial.cxx.

◆ operator*() [35/45]

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*() [36/45]

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*() [37/45]

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*() [38/45]

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*() [39/45]

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*() [40/45]

template<class CoordSystem , class U >
DisplacementVector3D<CoordSystem,U> ROOT::Math::operator* ( typename DisplacementVector3D< CoordSystem, U >::Scalar  a,
DisplacementVector3D< CoordSystem, U >  v 
)
inline

Multiplication of a displacement vector by real number a*v.

Definition at line 622 of file DisplacementVector3D.h.

◆ operator*() [41/45]

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*() [42/45]

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*() [43/45]

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
ascalar quantity of typpe a
vmathcore::LorentzVector based on any coordinate system
Returns
a new mathcoreLorentzVector q = v * a same type as v

Definition at line 693 of file LorentzVector.h.

◆ operator*() [44/45]

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*() [45/45]

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+() [1/16]

template<class A , class T , unsigned int D>
VecExpr<BinaryOp<AddOp<T>, VecExpr<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 74 of file BinaryOperators.h.

◆ operator+() [2/16]

template<class A , class T , unsigned int D>
VecExpr<BinaryOp<AddOp<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 86 of file BinaryOperators.h.

◆ operator+() [3/16]

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> ROOT::Math::operator+ ( const VecExpr< A, T, D > &  lhs,
const VecExpr< B, T, D > &  rhs 
)
inline

Definition at line 98 of file BinaryOperators.h.

◆ operator+() [4/16]

template<class A , class B , class T , unsigned int D>
VecExpr<BinaryOpCopyR<AddOp<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 145 of file BinaryOperators.h.

◆ operator+() [5/16]

template<class A , class B , class T , unsigned int D>
VecExpr<BinaryOpCopyL<AddOp<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 156 of file BinaryOperators.h.

◆ operator+() [6/16]

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> ROOT::Math::operator+ ( const Expr< A, T, D, D2, R1 > &  lhs,
const SMatrix< T, D, D2, R2 > &  rhs 
)
inline

Definition at line 186 of file BinaryOperators.h.

◆ operator+() [7/16]

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> ROOT::Math::operator+ ( const SMatrix< T, D, D2, R1 > &  lhs,
const Expr< A, T, D, D2, R2 > &  rhs 
)
inline

Definition at line 198 of file BinaryOperators.h.

◆ operator+() [8/16]

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 > ROOT::Math::operator+ ( const Expr< A, T, D, D2, R1 > &  lhs,
const Expr< B, T, D, D2, R2 > &  rhs 
)
inline

Definition at line 210 of file BinaryOperators.h.

◆ operator+() [9/16]

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, R> ROOT::Math::operator+ ( const Expr< B, T, D, D2, R > &  lhs,
const A &  rhs 
)
inline

Definition at line 258 of file BinaryOperators.h.

◆ operator+() [10/16]

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, R> ROOT::Math::operator+ ( const A &  lhs,
const Expr< B, T, D, D2, R > &  rhs 
)
inline

Definition at line 270 of file BinaryOperators.h.

◆ operator+() [11/16]

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector2D<CoordSystem2,U> ROOT::Math::operator+ ( PositionVector2D< CoordSystem2, U >  p1,
const DisplacementVector2D< CoordSystem1, U > &  v2 
)
inline

Addition of a PositionVector2D and a DisplacementVector2D.

The return type is a PositionVector2D, of the same (coordinate system) type as the input PositionVector2D.

Definition at line 408 of file PositionVector2D.h.

◆ operator+() [12/16]

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector2D<CoordSystem2,U> ROOT::Math::operator+ ( DisplacementVector2D< CoordSystem1, U > const &  v1,
PositionVector2D< CoordSystem2, U >  p2 
)
inline

Addition of a DisplacementVector2D and a PositionVector2D.

The return type is a PositionVector2D, of the same (coordinate system) type as the input PositionVector2D.

Definition at line 421 of file PositionVector2D.h.

◆ operator+() [13/16]

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

Addition of DisplacementVector2D vectors.

The (coordinate system) type of the returned vector is defined to be identical to that of the first vector, which is passed by value

Definition at line 433 of file DisplacementVector2D.h.

◆ operator+() [14/16]

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector3D<CoordSystem2,U> ROOT::Math::operator+ ( PositionVector3D< CoordSystem2, U >  p1,
const DisplacementVector3D< CoordSystem1, U > &  v2 
)
inline

Addition of a PositionVector3D and a DisplacementVector3D.

The return type is a PositionVector3D, of the same (coordinate system) type as the input PositionVector3D.

Definition at line 545 of file PositionVector3D.h.

◆ operator+() [15/16]

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector3D<CoordSystem2,U> ROOT::Math::operator+ ( DisplacementVector3D< CoordSystem1, U > const &  v1,
PositionVector3D< CoordSystem2, U >  p2 
)
inline

Addition of a DisplacementVector3D and a PositionVector3D.

The return type is a PositionVector3D, of the same (coordinate system) type as the input PositionVector3D.

Definition at line 558 of file PositionVector3D.h.

◆ operator+() [16/16]

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

Addition of DisplacementVector3D vectors.

The (coordinate system) type of the returned vector is defined to be identical to that of the first vector, which is passed by value

Definition at line 596 of file DisplacementVector3D.h.

◆ operator-() [1/18]

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

Definition at line 56 of file UnaryOperators.h.

◆ operator-() [2/18]

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,R> ROOT::Math::operator- ( const Expr< A, T, D, D2, R > &  rhs)
inline

Definition at line 85 of file UnaryOperators.h.

◆ operator-() [3/18]

template<class A , class T , unsigned int D>
VecExpr<BinaryOp<MinOp<T>, VecExpr<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 318 of file BinaryOperators.h.

◆ operator-() [4/18]

template<class A , class T , unsigned int D>
VecExpr<BinaryOp<MinOp<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 330 of file BinaryOperators.h.

◆ operator-() [5/18]

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> ROOT::Math::operator- ( const VecExpr< A, T, D > &  lhs,
const VecExpr< B, T, D > &  rhs 
)
inline

Definition at line 342 of file BinaryOperators.h.

◆ operator-() [6/18]

template<class A , class B , class T , unsigned int D>
VecExpr<BinaryOpCopyR<MinOp<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 389 of file BinaryOperators.h.

◆ operator-() [7/18]

template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector2D<CoordSystem1,U> ROOT::Math::operator- ( const PositionVector2D< CoordSystem1, U > &  v1,
const PositionVector2D< CoordSystem2, U > &  v2 
)
inline

Difference between two PositionVector2D vectors.

The result is a DisplacementVector2D. The (coordinate system) type of the returned vector is defined to be identical to that of the first position vector.

Definition at line 393 of file PositionVector2D.h.

◆ operator-() [8/18]

template<class A , class B , class T , unsigned int D>
VecExpr<BinaryOpCopyL<MinOp<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 400 of file BinaryOperators.h.

◆ operator-() [9/18]

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> ROOT::Math::operator- ( const Expr< A, T, D, D2, R1 > &  lhs,
const SMatrix< T, D, D2, R2 > &  rhs 
)
inline

Definition at line 430 of file BinaryOperators.h.

◆ operator-() [10/18]

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector2D<CoordSystem2,U> ROOT::Math::operator- ( PositionVector2D< CoordSystem2, U >  p1,
DisplacementVector2D< CoordSystem1, U > const &  v2 
)
inline

Subtraction of a DisplacementVector2D from a PositionVector2D.

The return type is a PositionVector2D, of the same (coordinate system) type as the input PositionVector2D.

Definition at line 434 of file PositionVector2D.h.

◆ operator-() [11/18]

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> ROOT::Math::operator- ( const SMatrix< T, D, D2, R1 > &  lhs,
const Expr< A, T, D, D2, R2 > &  rhs 
)
inline

Definition at line 442 of file BinaryOperators.h.

◆ operator-() [12/18]

template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector2D<CoordSystem1,U> ROOT::Math::operator- ( DisplacementVector2D< CoordSystem1, U >  v1,
DisplacementVector2D< CoordSystem2, U > const &  v2 
)
inline

Difference between two DisplacementVector2D vectors.

The (coordinate system) type of the returned vector is defined to be identical to that of the first vector.

Definition at line 446 of file DisplacementVector2D.h.

◆ operator-() [13/18]

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> ROOT::Math::operator- ( const Expr< A, T, D, D2, R1 > &  lhs,
const Expr< B, T, D, D2, R2 > &  rhs 
)
inline

Definition at line 454 of file BinaryOperators.h.

◆ operator-() [14/18]

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, R> ROOT::Math::operator- ( const Expr< B, T, D, D2, R > &  lhs,
const A &  rhs 
)
inline

Definition at line 501 of file BinaryOperators.h.

◆ operator-() [15/18]

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, R> ROOT::Math::operator- ( const A &  lhs,
const Expr< B, T, D, D2, R > &  rhs 
)
inline

Definition at line 512 of file BinaryOperators.h.

◆ operator-() [16/18]

template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector3D<CoordSystem1,U> ROOT::Math::operator- ( const PositionVector3D< CoordSystem1, U > &  v1,
const PositionVector3D< CoordSystem2, U > &  v2 
)
inline

Difference between two PositionVector3D vectors.

The result is a DisplacementVector3D. The (coordinate system) type of the returned vector is defined to be identical to that of the first position vector.

Definition at line 530 of file PositionVector3D.h.

◆ operator-() [17/18]

template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector3D<CoordSystem2,U> ROOT::Math::operator- ( PositionVector3D< CoordSystem2, U >  p1,
DisplacementVector3D< CoordSystem1, U > const &  v2 
)
inline

Subtraction of a DisplacementVector3D from a PositionVector3D.

The return type is a PositionVector3D, of the same (coordinate system) type as the input PositionVector3D.

Definition at line 571 of file PositionVector3D.h.

◆ operator-() [18/18]

template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector3D<CoordSystem1,U> ROOT::Math::operator- ( DisplacementVector3D< CoordSystem1, U >  v1,
DisplacementVector3D< CoordSystem2, U > const &  v2 
)
inline

Difference between two DisplacementVector3D vectors.

The (coordinate system) type of the returned vector is defined to be identical to that of the first vector.

Definition at line 609 of file DisplacementVector3D.h.

◆ operator/() [1/7]

template<class A , class T , unsigned int D>
VecExpr<BinaryOp<DivOp<T>, VecExpr<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 796 of file BinaryOperators.h.

◆ operator/() [2/7]

template<class A , class T , unsigned int D>
VecExpr<BinaryOp<DivOp<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 807 of file BinaryOperators.h.

◆ operator/() [3/7]

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> ROOT::Math::operator/ ( const VecExpr< A, T, D > &  lhs,
const VecExpr< B, T, D > &  rhs 
)
inline

Definition at line 819 of file BinaryOperators.h.

◆ operator/() [4/7]

template<class A , class B , class T , unsigned int D>
VecExpr<BinaryOpCopyR<DivOp<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 866 of file BinaryOperators.h.

◆ operator/() [5/7]

template<class A , class B , class T , unsigned int D>
VecExpr<BinaryOpCopyL<DivOp<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 877 of file BinaryOperators.h.

◆ operator/() [6/7]

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, R> ROOT::Math::operator/ ( const Expr< B, T, D, D2, R > &  lhs,
const A &  rhs 
)
inline

Definition at line 980 of file BinaryOperators.h.

◆ operator/() [7/7]

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,R> ROOT::Math::operator/ ( const A &  lhs,
const Expr< B, T, D, D2, R > &  rhs 
)
inline

Definition at line 992 of file BinaryOperators.h.

◆ operator<<() [1/22]

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const BoostY b 
)

Stream Output and Input.

Definition at line 107 of file BoostY.cxx.

◆ operator<<() [2/22]

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const BoostZ b 
)

Stream Output and Input.

Definition at line 108 of file BoostZ.cxx.

◆ operator<<() [3/22]

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const BoostX b 
)

Stream Output and Input.

Definition at line 108 of file BoostX.cxx.

◆ operator<<() [4/22]

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

Definition at line 210 of file Expression.h.

◆ operator<<() [5/22]

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

Definition at line 215 of file Expression.h.

◆ operator<<() [6/22]

std::ostream& ROOT::Math::operator<< ( std::ostream &  os,
const RotationZ r 
)
inline

Stream Output and Input.

Definition at line 243 of file RotationZ.h.

◆ operator<<() [7/22]

std::ostream& ROOT::Math::operator<< ( std::ostream &  os,
const RotationY r 
)
inline

Stream Output and Input.

Definition at line 243 of file RotationY.h.

◆ operator<<() [8/22]

std::ostream& ROOT::Math::operator<< ( std::ostream &  os,
const RotationX r 
)
inline

Stream Output and Input.

Definition at line 243 of file RotationX.h.

◆ operator<<() [9/22]

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const Boost b 
)

Stream Output and Input.

Definition at line 173 of file Boost.cxx.

◆ operator<<() [10/22]

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const AxisAngle a 
)

Stream Output and Input.

Definition at line 91 of file AxisAngle.cxx.

◆ operator<<() [11/22]

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

Definition at line 640 of file SVector.icc.

◆ operator<<() [12/22]

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const Quaternion q 
)

Stream Output and Input.

Definition at line 101 of file Quaternion.cxx.

◆ operator<<() [13/22]

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const RotationZYX e 
)

Stream Output and Input.

Definition at