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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
 
 Interpolation
 
 MCIntegration
 
 Minim
 
 Minim1D
 
 Roots
 Root-Finding Algorithms.
 
 rowOffsetsUtils
 
 Sampler
 
 test
 
 Util
 namespace defining Utility functions needed by mathcore
 
 VectorUtil
 Global Helper functions for generic Vector classes.
 

Classes

class  WrappedMultiTF1
 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 This wrapper class does not own the TF1 pointer, so it assumes it exists during the wrapper lifetime. 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...
 
struct  GeneticMinimizerParameters
 
class  GeneticMinimizer
 GeneticMinimizer. More...
 
class  AxisAngle
 AxisAngle class describing rotation represented with direction axis (3D Vector) and an angle of rotation around that axis. 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  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  DefaultCoordinateSystemTag
 DefaultCoordinateSystemTag Default tag for identifying any coordinate system. More...
 
class  GlobalCoordinateSystemTag
 Tag for identifying vectors based on a global coordinate system. More...
 
class  LocalCoordinateSystemTag
 Tag for identifying vectors based on a local coordinate system. 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  DisplacementVector2D
 Class describing a generic displacement vector in 2 dimensions. More...
 
class  DisplacementVector3D
 Class describing a generic displacement vector in 3 dimensions. More...
 
class  EulerAngles
 EulerAngles class describing rotation as three angles (Euler Angles). More...
 
class  GenVector_exception
 
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  Plane3D
 Class describing a geometrical plane in 3 dimensions. 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  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  Quaternion
 Rotation class with the (3D) rotation represented by a unit quaternion (u, i, j, k). 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 new Y' axis, followed by a third rotation of an angle psi (roll) about the final X'' axis. More...
 
class  Transform3D
 Basic 3D Transformation class describing a rotation and then a translation The internal data are a 3D rotation data (represented as a 3x3 matrix) and a 3D vector data. More...
 
class  Translation3D
 Class describing a 3 dimensional translation. More...
 
struct  CoordinateTraits
 
struct  CoordinateTraits< Cartesian3D< Scalar > >
 
struct  CoordinateTraits< CylindricalEta3D< Scalar > >
 
struct  CoordinateTraits< Cylindrical3D< Scalar > >
 
struct  CoordinateTraits< Polar3D< Scalar > >
 
struct  CoordinateTraits< PxPyPzE4D< Scalar > >
 
struct  CoordinateTraits< PxPyPzM4D< Scalar > >
 
struct  CoordinateTraits< PtEtaPhiE4D< Scalar > >
 
struct  CoordinateTraits< PtEtaPhiM4D< Scalar > >
 
struct  RotationTraits
 
struct  RotationTraits< Rotation3D >
 
struct  RotationTraits< AxisAngle >
 
struct  RotationTraits< EulerAngles >
 
struct  RotationTraits< Quaternion >
 
struct  RotationTraits< RotationX >
 
struct  RotationTraits< RotationY >
 
struct  RotationTraits< RotationZ >
 
struct  RotationTraits< LorentzRotation >
 
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  AdaptiveIntegratorMultiDim
 class for adaptive quadrature integration in multi-dimensions using rectangular regions. 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  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  ChebyshevPol
 
class  Delaunay2D
 Class to generate a Delaunay triangulation of a 2D set of points. More...
 
class  DistSampler
 Interface class for generic sampling of a distribution, i.e. More...
 
class  DistSamplerOptions
 DistSampler options class. More...
 
class  Factory
 Factory class holding static functions to create the interfaces like ROOT::Math::Minimizer via the Plugin Manager. More...
 
class  FunctorImpl
 FunctorImpl is a base class for the functor handler implementation class. More...
 
class  FunctorHandler
 Functor Handler class is responsible for wrapping any other functor and pointer to free C 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  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  Functor
 Documentation for class Functor class. More...
 
class  Functor1D
 Functor1D class for one-dimensional functions. More...
 
class  GradFunctor
 GradFunctor class for Multidimensional gradient functions. More...
 
class  GradFunctor1D
 GradFunctor1D class for one-dimensional gradient functions. More...
 
class  GaussIntegrator
 User class for performing function integration. More...
 
class  IntegrandTransform
 Auxillary inner class for mapping infinite and semi-infinite integrals. 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...
 
class  GoFTest
 
class  IBaseFunctionMultiDim
 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  IGradientMultiDim
 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  IGradientFunctionMultiDim
 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  IMinimizer1D
 Interface class for numerical methods for one-dimensional minimization. More...
 
class  IntegratorOneDim
 User Class for performing numerical integration of a function in one dimension. More...
 
class  IntegratorMultiDim
 User class for performing multidimensional integration. 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  IntegratorOneDimOptions
 Numerical one dimensional integration options. More...
 
class  IntegratorMultiDimOptions
 Numerical multi dimensional integration options. More...
 
class  IOptions
 Generic interface for defining configuration options of a numerical algorithm. More...
 
class  IBaseParam
 Documentation for the abstract class IBaseParam. More...
 
class  IParametricFunctionMultiDim
 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  IParametricGradFunctionMultiDim
 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  KDTree
 
class  MersenneTwisterEngine
 Random number generator class based on M. More...
 
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  SinVariableTransformation
 Sin Transformation class for dealing with double bounded variables. 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  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  MixMaxEngine
 MIXMAX Random number generator. 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...
 
struct  EvaluatorOneDim
 
struct  EvaluatorOneDim< const ROOT::Math::IParamMultiFunction & >
 
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  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  ParamMemFunHandler
 ParamFunctor Handler to Wrap pointers to member functions. More...
 
class  ParamFunctor
 Param Functor class for Multidimensional functions. More...
 
class  Random
 Documentation for the Random class. More...
 
class  RandomFunctionsImpl
 Definition of the generic impelmentation class for the RandomFunctions. More...
 
class  RandomFunctionsImpl< TRandomEngine >
 Implementation class for the RandomFunction for all the engined that derives from TRandomEngine class, which defines an interface which has TRandomEngine::Rndm() In this way we can have a common implementation for the RandomFunctions. More...
 
class  RandomFunctions
 
class  RichardsonDerivator
 User class for calculating the derivatives of a function. More...
 
class  RootFinder
 User Class to find the Root of one dimensional functions. More...
 
class  StdRandomEngine
 
class  StdEngine
 Wrapper class for std::random generator to be included in ROOT. More...
 
class  TDataPoint
 
class  TDataPointN
 
class  RandomBaseEngine
 
class  TRandomEngine
 
class  LCGEngine
 
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  VirtualIntegratorOneDim
 Interface (abstract) class for 1D numerical integration It must be implemented by the concrate Integrator classes like ROOT::Math::GSLIntegrator. More...
 
class  VirtualIntegratorMultiDim
 Interface (abstract) class for multi numerical integration It must be implemented by the concrete Integrator classes like ROOT::Math::GSLMCIntegrator. More...
 
struct  NullTypeFunc1D
 
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  WrappedMultiFunction
 Template class to wrap any C++ callable object implementing operator() (const double * x) in a multi-dimensional function interface. More...
 
class  WrappedMemMultiFunction
 
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  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  Derivator
 Class for computing numerical derivative of a function. More...
 
class  GSLFunctionAdapter
 Class for adapting any C++ functor class to C function pointers used by GSL. More...
 
class  GSLIntegrator
 Class for performing numerical integration of a function in one dimension. More...
 
class  GSLMCIntegrator
 
class  GSLMinimizer
 GSLMinimizer class. More...
 
class  GSLMinimizer1D
 Minimizer for arbitrary one dimensional functions. More...
 
class  GSLMultiRootFinder
 Class for Multidimensional root finding algorithms bassed on GSL. More...
 
class  LSResidualFunc
 LSResidualFunc class description. 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  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  GSLQRngSobol
 Sobol generator gsl_qrng_sobol from here More...
 
class  GSLQRngNiederreiter2
 Niederreiter generator gsl_qrng_niederreiter_2 from here More...
 
class  RandomFunctions< EngineType, ROOT::Math::GSLRandomEngine >
 Specialized implementation of the Random functions based on the GSL library. More...
 
class  GSLRandomEngine
 GSLRandomEngine Base class for all GSL random engines, normally user instantiate the derived classes which creates internally the generator. More...
 
class  GSLRngMT
 Mersenne-Twister generator gsl_rng_mt19937 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  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  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  GSLRngTaus
 Tausworthe generator by L'Ecuyer see here More...
 
class  GSLRngGFSR4
 Lagged Fibonacci generator by Ziff see here More...
 
class  GSLRngCMRG
 Combined multiple recursive generator (L'Ecuyer) see here More...
 
class  GSLRngMRG
 5-th order multiple recursive generator (L'Ecuyer, Blouin and Coutre) see here More...
 
class  GSLRngRand
 BSD rand() generator gsl_rmg_rand from here More...
 
class  GSLRngRanMar
 RANMAR generator see here More...
 
class  GSLRngMinStd
 MINSTD generator (Park and Miller) see here 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  GSLSimAnMinimizer
 GSLSimAnMinimizer class for minimization using simulated annealing using the algorithm from GSL. More...
 
class  GSLSimAnFunc
 GSLSimAnFunc class description. More...
 
struct  GSLSimAnParams
 structure holding the simulated annealing parameters More...
 
class  GSLSimAnnealing
 GSLSimAnnealing class for performing a simulated annealing search of a multidimensional function. More...
 
class  Interpolator
 Class for performing function interpolation of points. More...
 
class  KelvinFunctions
 
struct  VegasParameters
 structures collecting parameters for VEGAS multidimensional integration FOr implementation of default parameters see file mathmore/src/GSLMCIntegrationWorkspace.h More...
 
struct  MiserParameters
 structures collecting parameters for MISER multidimensional integration More...
 
struct  PlainParameters
 
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...
 
class  ParamFunction
 Base template class for all Parametric Functions. More...
 
struct  MathMoreLibrary
 
class  Polynomial
 Parametric Function class describing polynomials of order n. More...
 
class  QuasiRandom
 User class for MathMore random numbers template on the Engine type. 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  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  GSLFunctionWrapper
 Wrapper class to the gsl_function C structure. More...
 
class  GSLFunctionDerivWrapper
 class to wrap a gsl_function_fdf (with derivatives) More...
 
class  GSLIntegrationWorkspace
 
class  GSLInterpolator
 Interpolation class based on GSL interpolation functions. More...
 
class  GSLMCIntegrationWorkspace
 
class  GSLVegasIntegrationWorkspace
 workspace for VEGAS More...
 
class  GSLMiserIntegrationWorkspace
 Workspace for MISER. More...
 
class  GSLPlainIntegrationWorkspace
 
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...
 
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  GSLMultiMinDerivFunctionWrapper
 Wrapper for a multi-dimensional function with derivatives used in GSL multidim minimization algorithm. More...
 
class  GSLMultiMinimizer
 GSLMultiMinimizer class , for minimizing multi-dimensional function using derivatives. 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  GSLMultiRootDerivFunctionWrapper
 wrapper to a multi-dim function with derivatives for multi roots algorithm 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  GSLMultiRootSolver
 GSLMultiRootSolver, internal class for implementing GSL multi-root finders not using derivatives. More...
 
class  GSLMultiRootDerivSolver
 GSLMultiRootDerivSolver, internal class for implementing GSL multi-root finders using derivatives. More...
 
class  GSLQRngWrapper
 GSLQRngWrapper class to wrap gsl_qrng structure. More...
 
class  GSLRngWrapper
 GSLRngWrapper class to wrap gsl_rng structure. More...
 
class  GSLRootFdFSolver
 Root-Finder with derivatives implementation class using GSL. More...
 
class  GSLRootFSolver
 Root-Finder implementation class using GSL. More...
 
class  VavilovTest
 Test class for class Vavilov and its subclasses. More...
 
class  RMinimizer
 RMinimizer class. More...
 
class  SVector
 SVector: a generic fixed size Vector class. More...
 
class  SMatrix
 SMatrix: a generic fixed size D1 x D2 Matrix class. More...
 
class  AddOp
 Addition Operation Class. More...
 
class  MinOp
 Subtraction Operation Class. More...
 
class  MulOp
 Multiplication (element-wise) Operation Class. More...
 
class  DivOp
 Division (element-wise) Operation Class. More...
 
struct  MultPolicy
 matrix-matrix multiplication policy More...
 
struct  AddPolicy
 matrix addition policy More...
 
struct  AddPolicy< T, D1, D2, MatRepSym< T, D1 >, MatRepSym< T, D1 > >
 
struct  TranspPolicy
 matrix transpose policy More...
 
struct  TranspPolicy< T, D1, D2, MatRepSym< T, D1 > >
 
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  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  Inverter
 Matrix Inverter class Class to specialize calls to Dinv. More...
 
class  FastInverter
 Fast 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  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  CholInverter
 
class  SDeterminant
 Dsfact. More...
 
class  SInverter
 Dsinv. More...
 
class  VecExpr
 Expression wrapper class for Vector objects. More...
 
class  MatRepStd
 Expression wrapper class for Matrix objects. More...
 
class  Expr
 
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  UnaryOp
 UnaryOperation class A class representing unary operators in the parse tree. More...
 
class  Constant
 Constant expression class A class representing constant expressions (literals) in the parse tree. More...
 
struct  meta_dot
 
struct  meta_dot< 0 >
 
struct  meta_mag
 
struct  meta_mag< 0 >
 
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...
 
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 >, MatRepSym< T, D1 > >
 Structure to assign from an expression based to symmetric matrix to symmetric 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  AssignSym
 Force Expression evaluation from general to symmetric. More...
 
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 >, 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...
 
struct  PlusEquals< T, D1, D2, A, MatRepSym< T, D1 >, MatRepStd< T, D1, D2 > >
 Specialization for symmetrix += general : NOT Allowed operation. 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 >, MatRepSym< T, D1 > >
 Specialization for symmetric matrices. More...
 
struct  MinusEquals< T, D1, D2, A, MatRepSym< T, D1 >, MatRepStd< T, D1, D2 > >
 Specialization for symmetrix -= general : NOT Allowed operation. More...
 
struct  PlaceMatrix
 Structure to deal when a submatrix is placed in a matrix. More...
 
struct  PlaceExpr
 
struct  PlaceMatrix< T, D1, D2, D3, D4, MatRepSym< T, D1 >, MatRepStd< T, D3, D4 > >
 
struct  PlaceExpr< T, D1, D2, D3, D4, A, MatRepSym< T, D1 >, MatRepStd< T, D3, D4 > >
 
struct  PlaceMatrix< T, D1, D2, D3, D4, MatRepSym< T, D1 >, MatRepSym< T, D3 > >
 
struct  PlaceExpr< T, D1, D2, D3, D4, A, MatRepSym< T, D1 >, MatRepSym< T, D3 > >
 
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 > >
 
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  meta_row_dot
 
struct  meta_row_dot< 0 >
 
class  VectorMatrixRowOp
 
struct  meta_col_dot
 
struct  meta_col_dot< 0 >
 
class  VectorMatrixColOp
 Class for Vector-Matrix multiplication. More...
 
struct  meta_matrix_dot
 
struct  meta_matrix_dot< 0 >
 
class  MatrixMulOp
 Class for Matrix-Matrix multiplication. More...
 
class  TransposeOp
 Class for Transpose Operations. More...
 
class  TensorMulOp
 Class for Tensor Multiplication (outer product) of two vectors giving a matrix. More...
 
struct  RowOffsets
 Static structure to keep the conversion from (i,j) to offsets in the storage data for a symmetric matrix. More...
 
struct  SMatrixIdentity
 
struct  SMatrixNoInit
 
struct  CompileTimeChecker
 
struct  CompileTimeChecker< false >
 
class  Minus
 Unary Minus Operation Class. More...
 
class  Fabs
 Unary abs Operation Class. More...
 
class  Sqr
 Unary Square Operation Class. More...
 
class  Sqrt
 Unary Square Root Operation Class. More...
 

Typedefs

typedef PositionVector2D
< Cartesian2D< double >
, DefaultCoordinateSystemTag
XYPoint
 2D Point based on the cartesian coordinates x,y,z in double precision More...
 
typedef XYPoint XYPointD
 
typedef PositionVector2D
< Cartesian2D< float >
, DefaultCoordinateSystemTag
XYPointF
 2D Point based on the cartesian corrdinates x,y,z in single precision More...
 
typedef PositionVector2D
< Polar2D< double >
, DefaultCoordinateSystemTag
Polar2DPoint
 2D Point based on the polar coordinates rho, theta, phi in double precision. More...
 
typedef Polar2DPoint Polar2DPointD
 
typedef PositionVector2D
< Polar2D< float >
, DefaultCoordinateSystemTag
Polar2DPointF
 2D Point based on the polar coordinates rho, theta, phi in single precision. More...
 
typedef PositionVector3D
< Cartesian3D< double >
, DefaultCoordinateSystemTag
XYZPoint
 3D Point based on the cartesian coordinates x,y,z in double precision More...
 
typedef PositionVector3D
< Cartesian3D< float >
, DefaultCoordinateSystemTag
XYZPointF
 3D Point based on the cartesian corrdinates x,y,z in single precision More...
 
typedef XYZPoint XYZPointD
 
typedef PositionVector3D
< CylindricalEta3D< double >
, DefaultCoordinateSystemTag
RhoEtaPhiPoint
 3D Point based on the eta based cylindrical coordinates rho, eta, phi in double precision. More...
 
typedef PositionVector3D
< CylindricalEta3D< float >
, DefaultCoordinateSystemTag
RhoEtaPhiPointF
 3D Point based on the eta based cylindrical coordinates rho, eta, phi in single precision. More...
 
typedef RhoEtaPhiPoint RhoEtaPhiPointD
 
typedef PositionVector3D
< Polar3D< double >
, DefaultCoordinateSystemTag
Polar3DPoint
 3D Point based on the polar coordinates rho, theta, phi in double precision. More...
 
typedef PositionVector3D
< Polar3D< float >
, DefaultCoordinateSystemTag
Polar3DPointF
 3D Point based on the polar coordinates rho, theta, phi in single precision. More...
 
typedef Polar3DPoint Polar3DPointD
 
typedef PositionVector3D
< Cylindrical3D< double >
, DefaultCoordinateSystemTag
RhoZPhiPoint
 3D Point based on the cylindrical coordinates rho, z, phi in double precision. More...
 
typedef PositionVector3D
< Cylindrical3D< float >
, DefaultCoordinateSystemTag
RhoZPhiPointF
 3D Point based on the cylindrical coordinates rho, z, phi in single precision. More...
 
typedef RhoZPhiPoint RhoZPhiPointD
 
typedef DisplacementVector2D
< Cartesian2D< double >
, DefaultCoordinateSystemTag
XYVector
 2D Vector based on the cartesian coordinates x,y in double precision More...
 
typedef XYVector XYVectorD
 
typedef DisplacementVector2D
< Cartesian2D< float >
, DefaultCoordinateSystemTag
XYVectorF
 2D Vector based on the cartesian coordinates x,y,z in single precision More...
 
typedef DisplacementVector2D
< Polar2D< double >
, DefaultCoordinateSystemTag
Polar2DVector
 2D Vector based on the polar coordinates rho, phi in double precision. More...
 
typedef Polar2DVector Polar2DVectorD
 
typedef DisplacementVector2D
< Polar2D< float >
, DefaultCoordinateSystemTag
Polar2DVectorF
 2D Vector based on the polar coordinates rho, phi in single precision. More...
 
typedef DisplacementVector3D
< Cartesian3D< double >
, DefaultCoordinateSystemTag
XYZVector
 3D Vector based on the cartesian coordinates x,y,z in double precision More...
 
typedef DisplacementVector3D
< Cartesian3D< float >
, DefaultCoordinateSystemTag
XYZVectorF
 3D Vector based on the cartesian corrdinates x,y,z in single precision More...
 
typedef XYZVector XYZVectorD
 
typedef DisplacementVector3D
< CylindricalEta3D< double >
, DefaultCoordinateSystemTag
RhoEtaPhiVector
 3D Vector based on the eta based cylindrical coordinates rho, eta, phi in double precision. More...
 
typedef DisplacementVector3D
< CylindricalEta3D< float >
, DefaultCoordinateSystemTag
RhoEtaPhiVectorF
 3D Vector based on the eta based cylindrical coordinates rho, eta, phi in single precision. More...
 
typedef RhoEtaPhiVector RhoEtaPhiVectorD
 
typedef DisplacementVector3D
< Polar3D< double >
, DefaultCoordinateSystemTag
Polar3DVector
 3D Vector based on the polar coordinates rho, theta, phi in double precision. More...
 
typedef DisplacementVector3D
< Polar3D< float >
, DefaultCoordinateSystemTag
Polar3DVectorF
 3D Vector based on the polar coordinates rho, theta, phi in single precision. More...
 
typedef Polar3DVector Polar3DVectorD
 
typedef DisplacementVector3D
< Cylindrical3D< double >
, DefaultCoordinateSystemTag
RhoZPhiVector
 3D Vector based on the cylindrical coordinates rho, z, phi in double precision. More...
 
typedef DisplacementVector3D
< Cylindrical3D< float >
, DefaultCoordinateSystemTag
RhoZPhiVectorF
 3D Vector based on the cylindrical coordinates rho, z, phi in single precision. More...
 
typedef RhoZPhiVector RhoZPhiVectorD
 
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< double > > 
PxPyPzEVector
 
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 LorentzVector
< PxPyPzM4D< double > > 
PxPyPzMVector
 LorentzVector based on the x, y, z, and Mass in double 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 Plane3D::Scalar Scalar
 
typedef BasicFitMethodFunction
< ROOT::Math::IMultiGenFunction
FitMethodFunction
 
typedef BasicFitMethodFunction
< ROOT::Math::IMultiGradFunction
FitMethodGradFunction
 
typedef IBaseFunctionOneDim IGenFunction
 
typedef IBaseFunctionMultiDim IMultiGenFunction
 
typedef IGradientFunctionOneDim IGradFunction
 
typedef IGradientFunctionMultiDim IMultiGradFunction
 
typedef IntegratorOneDim Integrator
 
typedef IParametricFunctionOneDim IParamFunction
 
typedef IParametricFunctionMultiDim IParamMultiFunction
 
typedef
IParametricGradFunctionOneDim 
IParamGradFunction
 
typedef
IParametricGradFunctionMultiDim 
IParamMultiGradFunction
 
typedef Random
< ROOT::Math::MixMaxEngine
RandomMixMax
 Useful typedef definitions. More...
 
typedef Random
< ROOT::Math::MersenneTwisterEngine
RandomMT19937
 
typedef TRandomEngine DefaultEngineType
 Documentation for the RandomFunction class. More...
 
typedef TDataPoint< 1, Float_tTDataPoint1F
 
typedef TDataPoint< 2, Float_tTDataPoint2F
 
typedef TDataPoint< 3, Float_tTDataPoint3F
 
typedef TDataPoint< 1, Double_tTDataPoint1D
 
typedef TDataPoint< 2, Double_tTDataPoint2D
 
typedef TDataPoint< 3, Double_tTDataPoint3D
 
typedef double(* FreeFunctionPtr )(double)
 
typedef double(* FreeMultiFunctionPtr )(const double *)
 
typedef double(* FreeParamMultiFunctionPtr )(const double *, const double *)
 
typedef std::map< std::string,
ROOT::Math::GenAlgoOptions
OptionsMap
 
typedef double(* GSLFuncPointer )(double, void *)
 Function pointer corresponding to gsl_function signature. More...
 
typedef GSLMultiRootFinder MultiRootFinder
 
typedef Random
< ROOT::Math::GSLRngMT
RandomMT
 
typedef Random
< ROOT::Math::GSLRngTaus
RandomTaus
 
typedef Random
< ROOT::Math::GSLRngRanLux
RandomRanLux
 
typedef Random
< ROOT::Math::GSLRngGFSR4
RandomGFSR4
 
typedef GSLRngRanLuxS1 GSLRngRanLux1
 
typedef GSLRngRanLuxS2 GSLRngRanLux2
 
typedef GSLRngRanLuxD2 GSLRngRanLux48
 
typedef QuasiRandom
< ROOT::Math::GSLQRngSobol
QuasiRandomSobol
 
typedef QuasiRandom
< ROOT::Math::GSLQRngNiederreiter2
QuasiRandomNiederreiter
 
typedef void(* GSLFdfPointer )(double, void *, double *, double *)
 
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 double(* GSLMultiFitFPointer )(const gsl_vector *, void *, gsl_vector *)
 
typedef void(* GSLMultiFitDfPointer )(const gsl_vector *, void *, gsl_matrix *)
 
typedef void(* GSLMultiFitFdfPointer )(const gsl_vector *, void *, gsl_vector *, gsl_matrix *)
 
typedef double(* GSLMultiMinFuncPointer )(const gsl_vector *, void *)
 
typedef void(* GSLMultiMinDfPointer )(const gsl_vector *, void *, gsl_vector *)
 
typedef void(* GSLMultiMinFdfPointer )(const gsl_vector *, void *, double *, gsl_vector *)
 
typedef double(* GSLMultiRootFPointer )(const gsl_vector *, void *, gsl_vector *)
 
typedef void(* GSLMultiRootDfPointer )(const gsl_vector *, void *, gsl_matrix *)
 
typedef void(* GSLMultiRootFdfPointer )(const gsl_vector *, void *, gsl_vector *, gsl_matrix *)
 
typedef SMatrix< double,
2, 2, MatRepStd< double, 2, 2 > > 
SMatrix2D
 
typedef SMatrix< double,
3, 3, MatRepStd< double, 3, 3 > > 
SMatrix3D
 
typedef SMatrix< double,
4, 4, MatRepStd< double, 4, 4 > > 
SMatrix4D
 
typedef SMatrix< double,
5, 5, MatRepStd< double, 5, 5 > > 
SMatrix5D
 
typedef SMatrix< double,
6, 6, MatRepStd< double, 6, 6 > > 
SMatrix6D
 
typedef SMatrix< double,
7, 7, MatRepStd< double, 7, 7 > > 
SMatrix7D
 
typedef SMatrix< double,
2, 2, MatRepSym< double, 2 > > 
SMatrixSym2D
 
typedef SMatrix< double,
3, 3, MatRepSym< double, 3 > > 
SMatrixSym3D
 
typedef SMatrix< double,
4, 4, MatRepSym< double, 4 > > 
SMatrixSym4D
 
typedef SMatrix< double,
5, 5, MatRepSym< double, 5 > > 
SMatrixSym5D
 
typedef SMatrix< double,
6, 6, MatRepSym< double, 6 > > 
SMatrixSym6D
 
typedef SMatrix< double,
7, 7, MatRepSym< double, 7 > > 
SMatrixSym7D
 
typedef SMatrix< float,
2, 2, MatRepStd< float, 2, 2 > > 
SMatrix2F
 
typedef SMatrix< float,
3, 3, MatRepStd< float, 3, 3 > > 
SMatrix3F
 
typedef SMatrix< float,
4, 4, MatRepStd< float, 4, 4 > > 
SMatrix4F
 
typedef SMatrix< float,
5, 5, MatRepStd< float, 5, 5 > > 
SMatrix5F
 
typedef SMatrix< float,
6, 6, MatRepStd< float, 6, 6 > > 
SMatrix6F
 
typedef SMatrix< float,
7, 7, MatRepStd< float, 7, 7 > > 
SMatrix7F
 
typedef SMatrix< float,
2, 2, MatRepSym< float, 2 > > 
SMatrixSym2F
 
typedef SMatrix< float,
3, 3, MatRepSym< float, 3 > > 
SMatrixSym3F
 
typedef SMatrix< float,
4, 4, MatRepSym< float, 4 > > 
SMatrixSym4F
 
typedef SMatrix< float,
5, 5, MatRepSym< float, 5 > > 
SMatrixSym5F
 
typedef SMatrix< float,
6, 6, MatRepSym< float, 6 > > 
SMatrixSym6F
 
typedef SMatrix< float,
7, 7, MatRepSym< float, 7 > > 
SMatrixSym7F
 

Enumerations

enum  ERotation3DMatrixIndex {
  kXX = 0, kXY = 1, kXZ = 2, kYX = 3,
  kYY = 4, kYZ = 5, kZX = 6, kZY = 7,
  kZZ = 8
}
 
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  EGSLMinimizerType {
  kConjugateFR, kConjugatePR, kVectorBFGS, kVectorBFGS2,
  kSteepestDescent
}
 enumeration specifying the types of GSL minimizers More...
 

Functions

template<class R >
AxisAngle::Scalar Distance (const AxisAngle &r1, const R &r2)
 Distance between two rotations. More...
 
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)
 
std::ostream & operator<< (std::ostream &os, const AxisAngle &a)
 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 BoostX &b)
 Stream Output and Input. More...
 
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...
 
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 >
DisplacementVector2D
< CoordSystem1, U > 
operator- (DisplacementVector2D< CoordSystem1, U > v1, DisplacementVector2D< CoordSystem2, U > const &v2)
 Difference between two DisplacementVector2D vectors. More...
 
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...
 
template<class char_t , class traits_t , class T , class U >
std::basic_ostream< char_t,
traits_t > & 
operator<< (std::basic_ostream< char_t, traits_t > &os, DisplacementVector2D< T, U > const &v)
 
template<class char_t , class traits_t , class T , class U >
std::basic_istream< char_t,
traits_t > & 
operator>> (std::basic_istream< char_t, traits_t > &is, DisplacementVector2D< T, U > &v)
 
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 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 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 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, DisplacementVector3D< T, U > const &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)
 
long double etaMax_impl ()
 The following function could be called to provide the maximum possible value of pseudorapidity for a non-zero rho. More...
 
template<class T >
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...
 
template<class R >
EulerAngles::Scalar Distance (const EulerAngles &r1, const R &r2)
 Distance between two rotations. More...
 
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)
 
std::ostream & operator<< (std::ostream &os, const EulerAngles &e)
 Stream Output and Input. More...
 
void Throw (GenVector_exception &e)
 throw explicity GenVector exceptions More...
 
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 char_t >
detail::manipulator< char_t > set_close (char_t ch)
 
template<class char_t , class traits_t >
std::basic_ios< char_t,
traits_t > & 
human_readable (std::basic_ios< char_t, traits_t > &ios)
 
template<class char_t , class traits_t >
std::basic_ios< char_t,
traits_t > & 
machine_readable (std::basic_ios< char_t, traits_t > &ios)
 
std::ostream & operator<< (std::ostream &os, const LorentzRotation &r)
 Stream Output and Input. More...
 
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 char_t , class traits_t , class Coords >
std::basic_ostream< char_t,
traits_t > & 
operator<< (std::basic_ostream< char_t, traits_t > &os, LorentzVector< Coords > const &v)
 
template<class char_t , class traits_t , class Coords >
std::basic_istream< char_t,
traits_t > & 
operator>> (std::basic_istream< char_t, traits_t > &is, LorentzVector< Coords > &v)
 
std::ostream & operator<< (std::ostream &os, const Plane3D &p)
 Stream Output and Input. More...
 
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 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 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 >
PositionVector2D< CoordSystem2, U > operator- (PositionVector2D< CoordSystem2, U > p1, DisplacementVector2D< CoordSystem1, U > const &v2)
 Subtraction of a DisplacementVector2D from a PositionVector2D. 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_istream< char_t,
traits_t > & 
operator>> (std::basic_istream< char_t, traits_t > &is, PositionVector2D< T, U > &v)
 
template<class CoordSystem , class U >
PositionVector3D< CoordSystem > operator* (typename PositionVector3D< CoordSystem, U >::Scalar a, PositionVector3D< CoordSystem, U > v)
 Multiplication of a position vector by real number a*v. More...
 
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, 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 >
PositionVector3D< CoordSystem2, U > operator- (PositionVector3D< CoordSystem2, U > p1, DisplacementVector3D< CoordSystem1, U > const &v2)
 Subtraction of a DisplacementVector3D from a PositionVector3D. 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, PositionVector3D< T, U > const &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 R >
Quaternion::Scalar Distance (const Quaternion &r1, const R &r2)
 Distance between two rotations. More...
 
Quaternion operator* (RotationX const &r1, Quaternion const &r2)
 Multiplication of an axial rotation by an AxisAngle. More...
 
Quaternion operator* (RotationY const &r1, Quaternion const &r2)
 
Quaternion operator* (RotationZ const &r1, Quaternion const &r2)
 
std::ostream & operator<< (std::ostream &os, const Quaternion &q)
 Stream Output and Input. More...
 
template<class R >
Rotation3D::Scalar Distance (const Rotation3D &r1, const R &r2)
 Distance between two rotations. 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)
 
Rotation3D operator* (RotationZ const &r1, RotationX const &r2)
 
Rotation3D operator* (RotationZ const &r1, RotationY const &r2)
 
std::ostream & operator<< (std::ostream &os, const Rotation3D &r)
 Stream Output and Input. More...
 
template<class R >
RotationX::Scalar Distance (const RotationX &r1, const R &r2)
 Distance between two rotations. More...
 
std::ostream & operator<< (std::ostream &os, const RotationX &r)
 Stream Output and Input. More...
 
template<class R >
RotationY::Scalar Distance (const RotationY &r1, const R &r2)
 Distance between two rotations. More...
 
std::ostream & operator<< (std::ostream &os, const RotationY &r)
 Stream Output and Input. More...
 
template<class R >
RotationZ::Scalar Distance (const RotationZ &r1, const R &r2)
 Distance between two rotations. More...
 
std::ostream & operator<< (std::ostream &os, const RotationZ &r)
 Stream Output and Input. More...
 
template<class R >
RotationZYX::Scalar Distance (const RotationZYX &r1, const R &r2)
 Distance between two rotations. More...
 
RotationZYX operator* (RotationX const &r1, RotationZYX const &r2)
 Multiplication of an axial rotation by an AxisAngle. More...
 
RotationZYX operator* (RotationY const &r1, RotationZYX const &r2)
 
RotationZYX operator* (RotationZ const &r1, RotationZYX const &r2)
 
std::ostream & operator<< (std::ostream &os, const RotationZYX &e)
 Stream Output and Input. More...
 
Transform3D operator* (const Rotation3D &r, const Translation3D &t)
 combine a translation and a rotation to give a transform3d First the translation then the rotation More...
 
Transform3D operator* (const RotationX &r, const Translation3D &t)
 
Transform3D operator* (const RotationY &r, const Translation3D &t)
 
Transform3D operator* (const RotationZ &r, const Translation3D &t)
 
Transform3D operator* (const RotationZYX &r, const Translation3D &t)
 
Transform3D operator* (const AxisAngle &r, const Translation3D &t)
 
Transform3D operator* (const EulerAngles &r, const Translation3D &t)
 
Transform3D operator* (const Quaternion &r, const Translation3D &t)
 
Transform3D operator* (const Translation3D &t, const Rotation3D &r)
 combine a rotation and a translation to give a transform3d First a rotation then the translation More...
 
Transform3D operator* (const Translation3D &t, const RotationX &r)
 
Transform3D operator* (const Translation3D &t, const RotationY &r)
 
Transform3D operator* (const Translation3D &t, const RotationZ &r)
 
Transform3D operator* (const Translation3D &t, const RotationZYX &r)
 
Transform3D operator* (const Translation3D &t, const EulerAngles &r)
 
Transform3D operator* (const Translation3D &t, const Quaternion &r)
 
Transform3D operator* (const Translation3D &t, const AxisAngle &r)
 
Transform3D operator* (const Transform3D &t, const Translation3D &d)
 combine a transformation and a translation to give a transform3d First the translation then the transform3D More...
 
Transform3D operator* (const Translation3D &d, const Transform3D &t)
 combine a translation and a transformation to give a transform3d First the transformation then the translation More...
 
Transform3D operator* (const Transform3D &t, const Rotation3D &r)
 combine a transformation and a rotation to give a transform3d First the rotation then the transform3D More...
 
Transform3D operator* (const Transform3D &t, const RotationX &r)
 
Transform3D operator* (const Transform3D &t, const RotationY &r)
 
Transform3D operator* (const Transform3D &t, const RotationZ &r)
 
Transform3D operator* (const Transform3D &t, const RotationZYX &r)
 
Transform3D operator* (const Transform3D &t, const EulerAngles &r)
 
Transform3D operator* (const Transform3D &t, const AxisAngle &r)
 
Transform3D operator* (const Transform3D &t, const Quaternion &r)
 
Transform3D operator* (const Rotation3D &r, const Transform3D &t)
 combine a rotation and a transformation to give a transform3d First the transformation then the rotation More...
 
Transform3D operator* (const RotationX &r, const Transform3D &t)
 
Transform3D operator* (const RotationY &r, const Transform3D &t)
 
Transform3D operator* (const RotationZ &r, const Transform3D &t)
 
Transform3D operator* (const RotationZYX &r, const Transform3D &t)
 
Transform3D operator* (const EulerAngles &r, const Transform3D &t)
 
Transform3D operator* (const AxisAngle &r, const Transform3D &t)
 
Transform3D operator* (const Quaternion &r, const Transform3D &t)
 
std::ostream & operator<< (std::ostream &os, const Transform3D &t)
 print the 12 components of the Transform3D More...
 
std::ostream & operator<< (std::ostream &os, const Translation3D &t)
 
static void swap (double &a, double &b)
 
double Chebyshev0 (double, double c0)
 
double Chebyshev1 (double x, double c0, double c1)
 
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 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 ChebyshevN (unsigned int n, double x, const double *c)
 
double Pi ()
 Mathematical constants. More...
 
double log1p (double x)
 declarations for functions which are not implemented by some compilers More...
 
double expm1 (double x)
 exp(x) -1 with error cancellation when x is small More...
 
double beta_cdf_c (double x, double a, double b)
 Complement of the cumulative distribution function of the beta distribution. More...
 
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 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 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 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 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 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...
 
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 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...
 
double exponential_cdf_c (double x, double lambda, double x0=0)
 Complement of the cumulative distribution function of the exponential distribution (upper tail). More...
 
double exponential_cdf (double x, double lambda, double x0=0)
 Cumulative distribution function of the exponential 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 fdistribution_cdf (double x, double n, double m, double x0=0)
 Cumulative distribution function of the F-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 gamma_cdf (double x, double alpha, double theta, double x0=0)
 Cumulative distribution function of the gamma distribution (lower tail). More...
 
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 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...
 
double lognormal_cdf (double x, double m, double s, double x0=0)
 Cumulative distribution function of the lognormal 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...
 
double gaussian_cdf_c (double x, double sigma=1, double x0=0)
 Alternative name for same function. More...
 
double normal_cdf (double x, double sigma=1, double x0=0)
 Cumulative distribution function of the normal (Gaussian) distribution (lower tail). More...
 
double gaussian_cdf (double x, double sigma=1, double x0=0)
 Alternative name for same function. 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...
 
double tdistribution_cdf (double x, double r, double x0=0)
 Cumulative distribution function of Student's t-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...
 
double uniform_cdf (double x, double a, double b, double x0=0)
 Cumulative distribution function of the uniform (flat) distribution (lower tail). More...
 
double poisson_cdf_c (unsigned int n, double mu)
 Complement of the cumulative distribution function of the Poisson distribution. 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 binomial_cdf_c (unsigned int k, double p, unsigned int n)
 Complement of the cumulative distribution function of the Binomial 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 negative_binomial_cdf_c (unsigned int k, double p, double n)
 Complement of the cumulative distribution function of the Negative Binomial distribution. 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 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...
 
int getCount (double z, const double *dat, int n)
 
int getSum (const int *x, int n)
 
void adkTestStat (double *adk, const std::vector< std::vector< double > > &samples, const std::vector< double > &zstar)
 
double Polynomialeval (double x, double *a, unsigned int N)
 
double Polynomial1eval (double x, double *a, unsigned int N)
 
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 vavilov_accurate_pdf (double x, double kappa, double beta2)
 The Vavilov probability density function. More...
 
double vavilov_accurate_cdf (double x, double kappa, double beta2)
 The Vavilov cummulative probability density function. More...
 
double vavilov_accurate_cdf_c (double x, double kappa, double beta2)
 The Vavilov complementary cummulative probability density function. More...
 
double vavilov_accurate_quantile (double z, double kappa, double beta2)
 The inverse of the Vavilov cummulative probability density function. More...
 
double vavilov_accurate_quantile_c (double z, double kappa, double beta2)
 The inverse of the complementary Vavilov cummulative probability density function. More...
 
double vavilov_fast_pdf (double x, double kappa, double beta2)
 The Vavilov probability density function. More...
 
double vavilov_fast_cdf (double x, double kappa, double beta2)
 The Vavilov cummulative probability density function. More...
 
double vavilov_fast_cdf_c (double x, double kappa, double beta2)
 The Vavilov complementary cummulative probability density function. More...
 
double vavilov_fast_quantile (double z, double kappa, double beta2)
 The inverse of the Vavilov cummulative probability density function. More...
 
double vavilov_fast_quantile_c (double z, double kappa, double beta2)
 The inverse of the complementary Vavilov cummulative probability density function. More...
 
const gsl_multiroot_fsolver_type * GetGSLType (GSLMultiRootFinder::EType type)
 
const
gsl_multiroot_fdfsolver_type * 
GetGSLDerivType (GSLMultiRootFinder::EDerivType type)
 
static double myRound (double x, double y, double &xmantissa, int digits)
 
double myRound (double x, double y, int digits)
 
static std::string format (double x, double y, int digits, int width)
 
static void moments (ROOT::Math::Vavilov &v, double &integral, double &mean, double &variance, double &skewness, double &kurtosis)
 
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 , 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,
R
operator+ (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, R
operator+ (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,
R
operator+ (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, R
operator+ (const A &lhs, const Expr< B, T, D, D2, R > &rhs)
 
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 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 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 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,
R
operator- (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, R
operator- (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,
R
operator- (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, R
operator- (const A &lhs, const Expr< B, T, D, D2, R > &rhs)
 
template<class T , unsigned int D>
VecExpr< BinaryOp< MulOp< T >
, SVector< T, D >, SVector< T,
D >, T >, T, D > 
operator* (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
 Element by element vector product v3(i) = v1(i)*v2(i) returning a vector expression. 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 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 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 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,
R
operator* (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, R
operator* (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,
R
operator* (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, R
operator* (const A &lhs, const Expr< B, T, D, D2, R > &rhs)
 
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 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 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,
R
operator/ (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, R
operator/ (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,
R
operator/ (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, R
operator/ (const A &lhs, const Expr< B, T, D, D2, R > &rhs)
 
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 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)
 
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...
 
template<class T >
const T Maximum (const T &lhs, const T &rhs)
 maximum. More...
 
template<class T >
const T Minimum (const T &lhs, const T &rhs)
 minimum. More...
 
template<class T >
int Round (const T &x)
 round. More...
 
template<class T >
int Sign (const T &x)
 sign. More...
 
template<class T , unsigned int D>
T Dot (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
 Vector dot product. More...
 
template<class A , class T , unsigned int D>
T Dot (const SVector< T, D > &lhs, const VecExpr< A, T, D > &rhs)
 
template<class A , class T , unsigned int D>
T Dot (const VecExpr< A, T, D > &lhs, const SVector< T, D > &rhs)
 
template<class A , class B , class T , unsigned int D>
T Dot (const VecExpr< A, T, D > &lhs, const VecExpr< B, T, D > &rhs)
 
template<class T , unsigned int D>
T 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>
T Mag2 (const VecExpr< A, T, D > &rhs)
 
template<class T , unsigned int D>
T 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>
T Mag (const VecExpr< A, T, D > &rhs)
 
template<class T >
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 >
T Lmag2 (const VecExpr< A, T, 4 > &rhs)
 
template<class T >
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 >
T Lmag (const VecExpr< A, T, 4 > &rhs)
 
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)
 
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)
 
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)
 
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 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)
 
template<class T , unsigned int D, class R >
T 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 >
T Similarity (const SVector< T, D > &lhs, const SMatrix< T, D, D, R > &rhs)
 
template<class A , class T , unsigned int D, class R >
T Similarity (const SMatrix< T, D, D, R > &lhs, const VecExpr< A, T, D > &rhs)
 
template<class A , class T , unsigned int D, class R >
T Similarity (const VecExpr< A, T, D > &lhs, const SMatrix< T, D, D, R > &rhs)
 
template<class A , class T , unsigned int D, class R >
T Similarity (const SVector< T, D > &lhs, const Expr< A, T, D, D, R > &rhs)
 
template<class A , class T , unsigned int D, class R >
T 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 >
T 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 >
T 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 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)
 
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 T , unsigned int D1, unsigned int D2, class R >
std::ostream & operator<< (std::ostream &os, const ROOT::Math::SMatrix< T, D1, D2, R > &rhs)
 
template<class T , unsigned int D>
std::ostream & operator<< (std::ostream &os, const ROOT::Math::SVector< T, D > &rhs)
 
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, R
operator- (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, R
operator- (const SMatrix< T, D, D2, R > &rhs)
 Unary - operator B = - A returning a matrix expression. 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, R
fabs (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, R
fabs (const SMatrix< T, D, D2, R > &rhs)
 abs of a matrix m2(i,j) = | m1(i,j) | returning a matrix epression 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, R
sqr (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, R
sqr (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, R
sqrt (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, R
sqrt (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...
 
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 x0=0)
 Crystal ball function. More...
 
double crystalball_pdf (double x, double alpha, double n, double sigma, double x0=0)
 pdf definition of the crystal_ball which is defined only for n > 1 otehrwise 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 (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 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 int gDefaultNpx = 100
 
static int gDefaultNSearch = 10
 
static int gDefaultNpx = 100
 
static int gDefaultNSearch = 10
 
static const double kSqrt2 = 1.41421356237309515
 
int gDefaultMaxIter = 100
 
double gDefaultAbsTolerance = 1.E-6
 
double gDefaultRelTolerance = 1.E-10
 
double kPi = 3.14159265358979323846
 
double kEulerGamma = 0.577215664901532860606512090082402431042
 
static const double eu = 0.577215664901532860606
 
static const double eu = 0.577215664901532860606
 
static double vavilovPdfValues0 [45][12]
 
static double vavilovPdfValues1 [42][12]
 
static double vavilovPdfValues2 [41][12]
 
static double vavilovPdfValues3 [41][12]
 
static double vavilovPdfValues4 [28][12]
 
static double vavilovPdfValues5 [22][12]
 
static double vavilovPdfValues6 [19][12]
 
static double vavilovPdfValues7 [20][12]
 
static double vavilovPdfValues8 [21][12]
 
static double vavilovPdfValues9 [21][12]
 
static double(*[10] vavilovPdfValues )[12] ={vavilovPdfValues0, vavilovPdfValues1, vavilovPdfValues2, vavilovPdfValues3, vavilovPdfValues4, vavilovPdfValues5, vavilovPdfValues6, vavilovPdfValues7, vavilovPdfValues8, vavilovPdfValues9}
 
static double vavilovKappaValues [10] = {.01, .04, .07, .1, .4, .7, 1, 4, 7, 10}
 
static int vavilovNLambda [10] = {45, 42, 41, 41, 28, 22, 19, 20, 21, 21}
 
const
ROOT::Math::IMultiGenFunction
gFunction
 function wrapper for the function to be minimized More...
 
const
ROOT::Math::IMultiGradFunction
gGradFunction
 function wrapper for the gradient of the function to be minimized More...
 
int gNCalls = 0
 integer for the number of function calls More...
 

Typedef Documentation

Definition at line 57 of file Fitter.h.

Definition at line 61 of file Fitter.h.

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

Definition at line 41 of file WrappedFunction.h.

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

Definition at line 43 of file WrappedFunction.h.

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

Definition at line 31 of file WrappedParamFunction.h.

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

Definition at line 46 of file GSLFunctionWrapper.h.

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

Function pointer corresponding to gsl_function signature.

Definition at line 45 of file GSLFunctionAdapter.h.

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

Definition at line 47 of file GSLMultiFitFunctionWrapper.h.

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

Definition at line 48 of file GSLMultiFitFunctionWrapper.h.

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

Definition at line 46 of file GSLMultiFitFunctionWrapper.h.

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

Definition at line 47 of file GSLMultiMinFunctionWrapper.h.

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

Definition at line 48 of file GSLMultiMinFunctionWrapper.h.

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

Definition at line 46 of file GSLMultiMinFunctionWrapper.h.

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

Definition at line 49 of file GSLMultiRootFunctionWrapper.h.

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

Definition at line 50 of file GSLMultiRootFunctionWrapper.h.

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

Definition at line 48 of file GSLMultiRootFunctionWrapper.h.

Definition at line 320 of file GSLRndmEngines.h.

Definition at line 335 of file GSLRndmEngines.h.

Definition at line 364 of file GSLRndmEngines.h.

Definition at line 24 of file IFunctionfwd.h.

Definition at line 30 of file IFunctionfwd.h.

Definition at line 28 of file IFunctionfwd.h.

Definition at line 31 of file IFunctionfwd.h.

Definition at line 484 of file Integrator.h.

Definition at line 27 of file IParamFunctionfwd.h.

Definition at line 32 of file IParamFunctionfwd.h.

Definition at line 30 of file IParamFunctionfwd.h.

Definition at line 33 of file IParamFunctionfwd.h.

Definition at line 294 of file GSLMultiRootFinder.h.

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

Definition at line 24 of file GenAlgoOptions.cxx.

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

Definition at line 47 of file Point2Dfwd.h.

Definition at line 48 of file Point2Dfwd.h.

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

Definition at line 53 of file Point2Dfwd.h.

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

Definition at line 49 of file Vector2Dfwd.h.

Definition at line 50 of file Vector2Dfwd.h.

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

Definition at line 55 of file Vector2Dfwd.h.

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

Definition at line 59 of file Point3Dfwd.h.

Definition at line 64 of file Point3Dfwd.h.

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

Definition at line 63 of file Point3Dfwd.h.

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

Definition at line 60 of file Vector3Dfwd.h.

Definition at line 65 of file Vector3Dfwd.h.

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

Definition at line 64 of file Vector3Dfwd.h.

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.

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

Definition at line 66 of file Vector4Dfwd.h.

Definition at line 44 of file Vector4Dfwd.h.

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

Definition at line 56 of file Vector4Dfwd.h.

Definition at line 181 of file QuasiRandom.h.

Definition at line 180 of file QuasiRandom.h.

Definition at line 14 of file GSLRandom.h.

Useful typedef definitions.

Definition at line 220 of file Random.h.

Definition at line 11 of file GSLRandom.h.

Definition at line 221 of file Random.h.

Definition at line 13 of file GSLRandom.h.

Definition at line 12 of file GSLRandom.h.

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

Definition at line 49 of file Point3Dfwd.h.

Definition at line 54 of file Point3Dfwd.h.

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

Definition at line 53 of file Point3Dfwd.h.

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

Definition at line 50 of file Vector3Dfwd.h.

Definition at line 55 of file Vector3Dfwd.h.

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

Definition at line 54 of file Vector3Dfwd.h.

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

Definition at line 69 of file Point3Dfwd.h.

Definition at line 74 of file Point3Dfwd.h.

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

Definition at line 73 of file Point3Dfwd.h.

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

Definition at line 70 of file Vector3Dfwd.h.

Definition at line 75 of file Vector3Dfwd.h.

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

Definition at line 74 of file Vector3Dfwd.h.

Definition at line 29 of file Plane3D.cxx.

Definition at line 14 of file SMatrixDfwd.h.

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

Definition at line 14 of file SMatrixFfwd.h.

Definition at line 17 of file SMatrixDfwd.h.

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

Definition at line 17 of file SMatrixFfwd.h.

Definition at line 18 of file SMatrixDfwd.h.

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

Definition at line 18 of file SMatrixFfwd.h.

Definition at line 19 of file SMatrixDfwd.h.

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

Definition at line 19 of file SMatrixFfwd.h.

Definition at line 20 of file SMatrixDfwd.h.

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

Definition at line 20 of file SMatrixFfwd.h.

Definition at line 21 of file SMatrixDfwd.h.

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

Definition at line 21 of file SMatrixFfwd.h.

Definition at line 24 of file SMatrixDfwd.h.

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

Definition at line 23 of file SMatrixFfwd.h.

Definition at line 25 of file SMatrixDfwd.h.

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

Definition at line 24 of file SMatrixFfwd.h.

Definition at line 26 of file SMatrixDfwd.h.

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

Definition at line 25 of file SMatrixFfwd.h.

Definition at line 27 of file SMatrixDfwd.h.

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

Definition at line 26 of file SMatrixFfwd.h.

Definition at line 28 of file SMatrixDfwd.h.

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

Definition at line 27 of file SMatrixFfwd.h.

Definition at line 29 of file SMatrixDfwd.h.

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

Definition at line 28 of file SMatrixFfwd.h.

Definition at line 60 of file TDataPoint.h.

Definition at line 57 of file TDataPoint.h.

Definition at line 61 of file TDataPoint.h.

Definition at line 58 of file TDataPoint.h.

Definition at line 62 of file TDataPoint.h.

Definition at line 59 of file TDataPoint.h.

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

Definition at line 30 of file Point2Dfwd.h.

Definition at line 36 of file Point2Dfwd.h.

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

Definition at line 41 of file Point2Dfwd.h.

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

Definition at line 31 of file Vector2Dfwd.h.

Definition at line 38 of file Vector2Dfwd.h.

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

Definition at line 43 of file Vector2Dfwd.h.

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

Definition at line 33 of file Point3Dfwd.h.

Definition at line 44 of file Point3Dfwd.h.

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

Definition at line 43 of file Point3Dfwd.h.

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.

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.

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

Definition at line 34 of file Vector3Dfwd.h.

Definition at line 45 of file Vector3Dfwd.h.

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

Definition at line 44 of file Vector3Dfwd.h.

Enumeration Type Documentation

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 29 of file MinimTransformVariable.h.

Enumerator
kXX 
kXY 
kXZ 
kYX 
kYY 
kYZ 
kZX 
kZY 
kZZ 

Definition at line 64 of file AxisAngle.cxx.

Function Documentation

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

Definition at line 546 of file GoFTest.cxx.

Referenced by ROOT::Math::GoFTest::AndersonDarling2SamplesTest().

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

Definition at line 57 of file ChebyshevPol.h.

Referenced by ChebyshevN().

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

Definition at line 60 of file ChebyshevPol.h.

Referenced by ChebyshevN().

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.

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

Definition at line 63 of file ChebyshevPol.h.

Referenced by Chebyshev3(), and ChebyshevN().

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

Definition at line 66 of file ChebyshevPol.h.

Referenced by Chebyshev4(), and ChebyshevN().

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.

Referenced by Chebyshev5(), and ChebyshevN().

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.

Referenced by Chebyshev6(), and ChebyshevN().

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.

Referenced by 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.

Referenced by 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.

Referenced by 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.

Referenced by Chebyshev10().

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

Definition at line 93 of file ChebyshevPol.h.

Referenced by ROOT::Math::ChebyshevPol::operator()().

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 337 of file Functions.h.

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 350 of file Functions.h.

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 363 of file Functions.h.

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.

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.

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.

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.

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.

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

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

Distance between two rotations.

Definition at line 345 of file RotationZYX.h.

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.

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.

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 909 of file BinaryOperators.h.

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 921 of file BinaryOperators.h.

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 933 of file BinaryOperators.h.

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 174 of file Functions.h.

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 182 of file Functions.h.

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 191 of file Functions.h.

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.

Referenced by TEveCaloDataVec::AddTower(), TEveCaloData::CellGeom_t::Configure(), TEveCalo2DGL::DrawRhoZ(), TEveCaloDataVec::GetCellList(), TEveCaloDataHist::GetCellList(), TEveCalo3DGL::RenderGrid(), TEveCalo3DGL::RenderGridBarrel(), and TEveCalo3DGL::RenderGridEndCap().

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.

double ROOT::Math::expm1 ( double  x)
inline

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

Definition at line 86 of file Math.h.

Referenced by exponential_cdf().

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 133 of file UnaryOperators.h.

Referenced by RooHist::addBin(), RooNumRunningInt::RICacheElem::addRange(), RooCurve::addRange(), RooStats::SPlot::AddSWeight(), RooDataHist::adjustBinning(), RooCBShape::analyticalIntegral(), RooMultiVarGaussian::analyticalIntegral(), RooNDKeysPdf::analyticalIntegral(), RooHistFunc::areIdentical(), RooHistPdf::areIdentical(), RooUnitTest::areTHidentical(), ROOT::Math::KelvinFunctions::Bei(), ROOT::Math::KelvinFunctions::Ber(), TMath::BesselJ0(), TMath::BesselJ1(), TMVA::MethodMLP::BFGSMinimize(), RooGExpModel::calcDecayConv(), ROOT::Math::GaussLegendreIntegrator::CalcGaussLegendreSamplingPoints(), RooGExpModel::calcSinConvNorm(), RooIntegralMorph::MorphCacheElem::calculate(), RooStats::HypoTestInverterResult::CalculateEstimatedError(), ROOT::Math::VavilovTest::CdfTest(), CheckBasicTreeProperties(), CheckNearestNeighborSearches(), ClassImp(), ROOT::Minuit2::MnContours::Contour(), ROOT::Math::gv_detail::convert(), correctTicks(), ROOT::Fit::FitConfig::CreateParamsSettings(), ROOT::Math::CylindricalEta3D< T >::CylindricalEta3D(), ROOT::Math::KelvinFunctions::DBei(), ROOT::Math::KelvinFunctions::DBer(), ROOT::Minuit2::HessianGradientCalculator::DeltaGradient(), ROOT::Math::RichardsonDerivator::DerivativeForward(), ROOT::Math::Quaternion::Distance(), ROOT::Math::KelvinFunctions::DKei(), ROOT::Math::KelvinFunctions::DKer(), DoNewMinimization(), ROOT::Math::VavilovAccurate::E1plLog(), equals(), ErrorIntegral(), ROOT::Math::Impl::Eta_FromRhoZ(), RooStats::HypoTestInverter::Eval(), RooCBShape::evaluate(), RooTruthModel::evaluate(), ROOT::Minuit2::FumiliStandardMaximumLikelihoodFCN::EvaluateAll(), RooNLLVar::evaluatePartition(), RooAbsPdf::extendedTerm(), RooIntegrator1D::extrapolate(), ROOT::Math::KelvinFunctions::F1(), ROOT::Math::KelvinFunctions::F2(), vdt::fast_asin(), vdt::fast_asinf(), vdt::fast_atan(), vdt::fast_atan2(), vdt::fast_atan2f(), vdt::fast_atanf(), vdt::fast_inv_general(), vdt::fast_invf_general(), RooIntegralMorph::MorphCacheElem::fillGap(), findBin(), RooStats::HypoTestInverterResult::FindClosestPointIndex(), RooCurve::findPoint(), RooIntegralMorph::MorphCacheElem::findRange(), RooBrentRootFinder::findRoot(), format(), ROOT::Math::KelvinFunctions::G1(), ROOT::Math::KelvinFunctions::G2(), gaussian_pdf(), GaussPdf(), RooBCPEffDecay::generateEvent(), RooBCPGenDecay::generateEvent(), RooBDecay::generateEvent(), ROOT::Math::KDTree< _DataPoint >::SplitNode::GetClosestPoints(), ROOT::Minuit2::GaussianModelFunction::GetGradient(), RooStats::HybridPlot::GetHistoPvals(), RooPoisson::getLogVal(), RooAbsPdf::getLogVal(), ROOT::Math::KDTree< _DataPoint >::SplitNode::GetPointsWithinDist(), gl2psSameColorThreshold(), TMVA::MethodBDT::GradBoost(), TMVA::MethodBDT::GradBoostRegression(), gsl_integration_qk(), gsl_integration_qng(), gsl_poly_complex_solve_cubic(), gsl_poly_complex_solve_quartic(), RooHist::hasIdenticalBinning(), ROOT::Math::Cephes::igami(), ROOT::Math::Cephes::incbi(), RooAbsRealLValue::inRange(), ROOT::Minuit2::MnUserTransformation::Int2extError(), RooIntegrator1D::integral(), RooCurve::interpolate(), RooMath::interpolate(), RooCurve::isIdentical(), RooFitResult::isIdentical(), RooDataHist::isNonPoissonWeighted(), RooDataSet::isNonPoissonWeighted(), RooRealIntegral::jacobianProduct(), ROOT::Math::KelvinFunctions::Kei(), ROOT::Math::KelvinFunctions::Ker(), RooGExpModel::logErfC(), lognormal_pdf(), main(), RooExpensiveObjectCache::ExpensiveObject::matches(), ROOT::Math::BrentMethods::MinimBrent(), ROOT::Math::BrentMethods::MinimStep(), ROOT::Minuit2::SimplexBuilder::Minimum(), ROOT::Minuit2::VariableMetricBuilder::Minimum(), ROOT::Minuit2::FumiliBuilder::Minimum(), ROOT::Minuit2::mndasum(), ROOT::Minuit2::mneigen(), ROOT::Math::Vavilov::Mode(), ROOT::Math::VavilovAccurate::Mode(), myRound(), normal_pdf(), TGeoToOCC::OCC_Pgon(), ROOT::Minuit2::MnSeedGenerator::operator()(), ROOT::Minuit2::MnPosDef::operator()(), ROOT::Minuit2::SimplexSeedGenerator::operator()(), ROOT::Minuit2::InitialGradientCalculator::operator()(), ROOT::Minuit2::NegativeG2LineSearch::operator()(), ROOT::Minuit2::MnFunctionCross::operator()(), ROOT::Minuit2::MnLineSearch::operator()(), ROOT::Minuit2::Numerical2PGradientCalculator::operator()(), ROOT::Minuit2::MnHesse::operator()(), ROOT::Minuit2::GaussianModelFunction::operator()(), ROOT::Minuit2::operator<<(), operator==(), TMVA::CCPruner::Optimize(), TGLBoundingBox::Overlap(), ROOT::Math::VavilovTest::PdfTest(), printStats(), qag(), qags(), qelg(), ROOT::Math::VavilovAccurate::Quantile(), ROOT::Math::VavilovAccurate::Quantile_c(), ROOT::Math::VavilovTest::QuantileTest(), ROOT::Math::RotationY::Rectify(), ROOT::Math::RotationX::Rectify(), ROOT::Math::RotationZ::Rectify(), vdt::details::reduce2quadrant(), vdt::details::reduce2quadranttan(), rescale_error(), RooHist::RooHist(), RooHist::roundBin(), RooStats::HypoTestInverterOriginal::RunAutoScan(), RooUnitTest::runCompTests(), RooStats::HypoTestInverter::RunLimit(), TKDTreeBinning::SetCommonBinEdges(), ROOT::Fit::FitConfig::SetParamsSettings(), subinterval_too_small(), test18(), test19(), test7(), test8(), test_positivity(), testDerivation(), testIntegration(), testIntegration1D(), testIntegrationMultiDim(), testRead(), testReadSym(), testResult(), testSiCi(), testSpecFuncBeta(), testSpecFuncBetaI(), testSpecFuncErf(), testSpecFuncGamma(), testTrack(), testWrite(), testWriteSym(), ROOT::Math::Transform3D::Transform3D(), ROOT::Minuit2::FumiliErrorUpdator::Update(), RooPlot::updateFitRangeNorm(), TMVA::MethodBDT::UpdateTargetsRegression(), and TMath::Voigt().

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 162 of file UnaryOperators.h.

static std::string ROOT::Math::format ( double  x,
double  y,
int  digits,
int  width 
)
static
double ROOT::Math::gaussian_cdf ( double  x,
double  sigma = 1,
double  x0 = 0 
)
inline

Alternative name for same function.

Definition at line 497 of file ProbFuncMathCore.h.

Referenced by AnalyticalIntegral().

double ROOT::Math::gaussian_cdf_c ( double  x,
double  sigma = 1,
double  x0 = 0 
)
inline

Alternative name for same function.

Definition at line 475 of file ProbFuncMathCore.h.

Referenced by crystalball_integral().

int ROOT::Math::getCount ( double  z,
const double dat,
int  n 
)

Definition at line 520 of file GoFTest.cxx.

Referenced by adkTestStat().

const gsl_multiroot_fdfsolver_type* ROOT::Math::GetGSLDerivType ( GSLMultiRootFinder::EDerivType  type)

Definition at line 201 of file GSLMultiRootFinder.cxx.

Referenced by ROOT::Math::GSLMultiRootFinder::Solve().

const gsl_multiroot_fsolver_type* ROOT::Math::GetGSLType ( GSLMultiRootFinder::EType  type)

Definition at line 183 of file GSLMultiRootFinder.cxx.

Referenced by ROOT::Math::GSLMultiRootFinder::Solve().

int ROOT::Math::getSum ( const int *  x,
int  n 
)

Definition at line 534 of file GoFTest.cxx.

Referenced by adkTestStat().

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.

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

Definition at line 309 of file Functions.h.

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

Definition at line 285 of file Functions.h.

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 75 of file Math.h.

Referenced by beta_pdf(), binomial_pdf(), exponential_quantile(), and negative_binomial_pdf().

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.

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

Definition at line 262 of file Functions.h.

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

Definition at line 239 of file Functions.h.

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.

Referenced by ROOT::Math::RMinimizer::Minimize().

TVectorD ROOT::Math::mingradfunction ( TVectorD  y)

function to return the gradient values at point y

Definition at line 25 of file RMinimizer.cxx.

Referenced by ROOT::Math::RMinimizer::Minimize().

static void ROOT::Math::moments ( ROOT::Math::Vavilov v,
double integral,
double mean,
double variance,
double skewness,
double kurtosis 
)
static

Definition at line 568 of file VavilovTest.cxx.

Referenced by ROOT::Math::VavilovTest::PrintPdfTable().

static double ROOT::Math::myRound ( double  x,
double  y,
double xmantissa,
int  digits 
)
static

Definition at line 438 of file VavilovTest.cxx.

Referenced by myRound(), and ROOT::Math::VavilovTest::PdfTest().

double ROOT::Math::myRound ( double  x,
double  y,
int  digits 
)

Definition at line 456 of file VavilovTest.cxx.

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 229 of file MatrixFunctions.h.

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 239 of file MatrixFunctions.h.

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 249 of file MatrixFunctions.h.

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 259 of file MatrixFunctions.h.

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 269 of file MatrixFunctions.h.

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 279 of file MatrixFunctions.h.

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 289 of file MatrixFunctions.h.

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.

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

Definition at line 186 of file AxisAngleXother.cxx.

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

Definition at line 190 of file AxisAngleXother.cxx.

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.

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

Definition at line 68 of file QuaternionXaxial.cxx.

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

Definition at line 73 of file QuaternionXaxial.cxx.

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.

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

Definition at line 100 of file RotationZYX.cxx.

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

Definition at line 105 of file RotationZYX.cxx.

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.

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

Definition at line 117 of file EulerAngles.cxx.

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

Definition at line 122 of file EulerAngles.cxx.

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 384 of file PositionVector2D.h.

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 405 of file MatrixFunctions.h.

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 416 of file MatrixFunctions.h.

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 427 of file MatrixFunctions.h.

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 471 of file DisplacementVector2D.h.

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.

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

Definition at line 57 of file Rotation3DxAxial.cxx.

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

Definition at line 63 of file Rotation3DxAxial.cxx.

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.

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

Definition at line 84 of file Rotation3DxAxial.cxx.

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

Definition at line 96 of file Rotation3DxAxial.cxx.

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

Definition at line 108 of file Rotation3DxAxial.cxx.

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

Definition at line 120 of file Rotation3DxAxial.cxx.

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

Definition at line 132 of file Rotation3DxAxial.cxx.

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 521 of file PositionVector3D.h.

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 568 of file BinaryOperators.h.

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 579 of file BinaryOperators.h.

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 590 of file BinaryOperators.h.

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 601 of file BinaryOperators.h.

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 612 of file BinaryOperators.h.

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 617 of file DisplacementVector3D.h.

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 624 of file BinaryOperators.h.

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 635 of file BinaryOperators.h.

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 689 of file LorentzVector.h.

Transform3D ROOT::Math::operator* ( const Rotation3D &  r,
const Translation3D &  t 
)
inline

combine a translation and a rotation to give a transform3d First the translation then the rotation

Definition at line 704 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const RotationX &  r,
const Translation3D &  t 
)
inline

Definition at line 707 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const RotationY &  r,
const Translation3D &  t 
)
inline

Definition at line 711 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const RotationZ &  r,
const Translation3D &  t 
)
inline

Definition at line 715 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const RotationZYX &  r,
const Translation3D &  t 
)
inline

Definition at line 719 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const AxisAngle &  r,
const Translation3D &  t 
)
inline

Definition at line 723 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const EulerAngles &  r,
const Translation3D &  t 
)
inline

Definition at line 727 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Quaternion &  r,
const Translation3D &  t 
)
inline

Definition at line 731 of file Transform3D.h.

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 739 of file BinaryOperators.h.

Transform3D ROOT::Math::operator* ( const Translation3D &  t,
const Rotation3D &  r 
)
inline

combine a rotation and a translation to give a transform3d First a rotation then the translation

Definition at line 742 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Translation3D &  t,
const RotationX &  r 
)
inline

Definition at line 745 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Translation3D &  t,
const RotationY &  r 
)
inline

Definition at line 748 of file Transform3D.h.

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 751 of file BinaryOperators.h.

Transform3D ROOT::Math::operator* ( const Translation3D &  t,
const RotationZ &  r 
)
inline

Definition at line 751 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Translation3D &  t,
const RotationZYX &  r 
)
inline

Definition at line 754 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Translation3D &  t,
const EulerAngles &  r 
)
inline

Definition at line 757 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Translation3D &  t,
const Quaternion &  r 
)
inline

Definition at line 760 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Translation3D &  t,
const AxisAngle &  r 
)
inline

Definition at line 763 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Transform3D &  t,
const Translation3D &  d 
)
inline

combine a transformation and a translation to give a transform3d First the translation then the transform3D

Definition at line 773 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Translation3D &  d,
const Transform3D &  t 
)
inline

combine a translation and a transformation to give a transform3d First the transformation then the translation

Definition at line 782 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Transform3D &  t,
const Rotation3D &  r 
)
inline

combine a transformation and a rotation to give a transform3d First the rotation then the transform3D

Definition at line 793 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Transform3D &  t,
const RotationX &  r 
)
inline

Definition at line 796 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Transform3D &  t,
const RotationY &  r 
)
inline

Definition at line 799 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Transform3D &  t,
const RotationZ &  r 
)
inline

Definition at line 802 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Transform3D &  t,
const RotationZYX &  r 
)
inline

Definition at line 805 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Transform3D &  t,
const EulerAngles &  r 
)
inline

Definition at line 808 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Transform3D &  t,
const AxisAngle &  r 
)
inline

Definition at line 811 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Transform3D &  t,
const Quaternion &  r 
)
inline

Definition at line 814 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Rotation3D &  r,
const Transform3D &  t 
)
inline

combine a rotation and a transformation to give a transform3d First the transformation then the rotation

Definition at line 824 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const RotationX &  r,
const Transform3D &  t 
)
inline

Definition at line 827 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const RotationY &  r,
const Transform3D &  t 
)
inline

Definition at line 831 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const RotationZ &  r,
const Transform3D &  t 
)
inline

Definition at line 835 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const RotationZYX &  r,
const Transform3D &  t 
)
inline

Definition at line 839 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const EulerAngles &  r,
const Transform3D &  t 
)
inline

Definition at line 843 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const AxisAngle &  r,
const Transform3D &  t 
)
inline

Definition at line 847 of file Transform3D.h.

Transform3D ROOT::Math::operator* ( const Quaternion &  r,
const Transform3D &  t 
)
inline

Definition at line 851 of file Transform3D.h.

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 76 of file BinaryOperators.h.

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 88 of file BinaryOperators.h.

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 100 of file BinaryOperators.h.

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 147 of file BinaryOperators.h.

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 158 of file BinaryOperators.h.

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 188 of file BinaryOperators.h.

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 200 of file BinaryOperators.h.

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 212 of file BinaryOperators.h.

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 260 of file BinaryOperators.h.

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 272 of file BinaryOperators.h.

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 416 of file PositionVector2D.h.

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 429 of file PositionVector2D.h.

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 443 of file DisplacementVector2D.h.

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 553 of file PositionVector3D.h.

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 566 of file PositionVector3D.h.

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 591 of file DisplacementVector3D.h.

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 58 of file UnaryOperators.h.

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 87 of file UnaryOperators.h.

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 320 of file BinaryOperators.h.

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 332 of file BinaryOperators.h.

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 344 of file BinaryOperators.h.

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 391 of file BinaryOperators.h.

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 401 of file PositionVector2D.h.

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 402 of file BinaryOperators.h.

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 432 of file BinaryOperators.h.

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 442 of file PositionVector2D.h.

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 444 of file BinaryOperators.h.

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 456 of file DisplacementVector2D.h.

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 456 of file BinaryOperators.h.

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 503 of file BinaryOperators.h.

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 514 of file BinaryOperators.h.

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 538 of file PositionVector3D.h.

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 579 of file PositionVector3D.h.

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 604 of file DisplacementVector3D.h.

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 798 of file BinaryOperators.h.

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 809 of file BinaryOperators.h.

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 821 of file BinaryOperators.h.

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 868 of file BinaryOperators.h.

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 879 of file BinaryOperators.h.

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 982 of file BinaryOperators.h.

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 994 of file BinaryOperators.h.

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

Stream Output and Input.

Definition at line 107 of file BoostY.cxx.

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

Stream Output and Input.

Definition at line 108 of file BoostZ.cxx.

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

Stream Output and Input.

Definition at line 108 of file BoostX.cxx.

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.

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.

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

Stream Output and Input.

Definition at line 243 of file RotationX.h.

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

Stream Output and Input.

Definition at line 243 of file RotationZ.h.

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

Stream Output and Input.

Definition at line 243 of file RotationY.h.

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const Plane3D &  p 
)

Stream Output and Input.

Definition at line 94 of file Plane3D.cxx.

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

Stream Output and Input.

Definition at line 173 of file Boost.cxx.

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const Translation3D &  t 
)

Definition at line 50 of file Translation3D.cxx.

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

Stream Output and Input.

Definition at line 91 of file AxisAngle.cxx.

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 630 of file SVector.icc.

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

Stream Output and Input.

Definition at line 101 of file Quaternion.cxx.

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

Stream Output and Input.

Definition at line 151 of file RotationZYX.cxx.

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

Stream Output and Input.

Definition at line 128 of file EulerAngles.cxx.

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

Definition at line 454 of file PositionVector2D.h.

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

Definition at line 489 of file DisplacementVector2D.h.

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

Stream Output and Input.

Definition at line 219 of file LorentzRotation.cxx.

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const Rotation3D &  r 
)

Stream Output and Input.

Definition at line 137 of file Rotation3D.cxx.

template<class char_t , class traits_t , class T , class U >
std::basic_ostream<char_t,traits_t>& ROOT::Math::operator<< ( std::basic_ostream< char_t, traits_t > &  os,
PositionVector3D< T, U > const &  v 
)
inline

Definition at line 591 of file PositionVector3D.h.

template<class char_t , class traits_t , class T , class U >
std::basic_ostream<char_t,traits_t>& ROOT::Math::operator<< ( std::basic_ostream< char_t, traits_t > &  os,
DisplacementVector3D< T, U > const &  v 
)
inline

Definition at line 635 of file DisplacementVector3D.h.

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

Definition at line 701 of file LorentzVector.h.

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

Definition at line 724 of file SMatrix.h.

std::ostream & ROOT::Math::operator<< ( std::ostream &  os,
const Transform3D &  t 
)

print the 12 components of the Transform3D

Definition at line 214 of file Transform3D.cxx.

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

Definition at line 483 of file PositionVector2D.h.

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

Definition at line 518 of file DisplacementVector2D.h.

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

Definition at line 622 of file PositionVector3D.h.

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

Definition at line 666 of file DisplacementVector3D.h.

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

Definition at line 730 of file LorentzVector.h.

double ROOT::Math::Pi ( )
inline
double ROOT::Math::Polynomial1eval ( double  x,
double a,
unsigned int  N 
)
double ROOT::Math::Polynomialeval ( double  x,
double a,
unsigned int  N 
)
template<class char_t >
detail::manipulator<char_t> ROOT::Math::set_close ( char_t  ch)
inline

Definition at line 187 of file GenVectorIO.h.

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

Definition at line 167 of file GenVectorIO.h.

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

Definition at line 177 of file GenVectorIO.h.

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

Definition at line 679 of file MatrixFunctions.h.

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

Definition at line 687 of file MatrixFunctions.h.

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

Definition at line 695 of file MatrixFunctions.h.

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

Definition at line 703 of file MatrixFunctions.h.

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

Definition at line 711 of file MatrixFunctions.h.

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

Definition at line 719 of file MatrixFunctions.h.

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

Definition at line 727 of file MatrixFunctions.h.

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

Definition at line 758 of file MatrixFunctions.h.

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

Definition at line 808 of file MatrixFunctions.h.

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

Definition at line 991 of file MatrixFunctions.h.

Referenced by SolveChol(), and test23().

template<class T , unsigned int D>
SVector<T,D> ROOT::Math::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)

Definition at line 999 of file MatrixFunctions.h.

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

Definition at line 208 of file UnaryOperators.h.

Referenced by TEveLine::CalculateLineLength(), and TMath::NextPrime().

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

Definition at line 237 of file UnaryOperators.h.

template<class A , class T , unsigned int D>
VecExpr<UnaryOp<Sqrt<T>, VecExpr<A,T,D>, T>, T, D> ROOT::Math::sqrt ( const VecExpr< A, T, D > &  rhs)
inline
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, R> ROOT::Math::sqrt ( const Expr< A, T, D, D2, R > &  rhs)
inline

Definition at line 312 of file UnaryOperators.h.

static void ROOT::Math::swap ( double a,
double b 
)
inlinestatic
template<class T , unsigned int D1, unsigned int D2, class A >
Expr<TensorMulOp<VecExpr<A,T,D1>, SVector<T,D2> >, T, D1, D2 > ROOT::Math::TensorProd ( const VecExpr< A, T, D1 > &  lhs,
const SVector< T, D2 > &  rhs 
)
inline

Definition at line 901 of file MatrixFunctions.h.

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

Definition at line 911 of file MatrixFunctions.h.

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 > ROOT::Math::TensorProd ( const VecExpr< A, T, D1 > &  lhs,
const VecExpr< B, T, D2 > &  rhs 
)
inline

Definition at line 922 of file MatrixFunctions.h.

void ROOT::Math::Throw ( GenVector_exception &  e)

throw explicity GenVector exceptions

Definition at line 21 of file GenVector_exception.cxx.

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

Definition at line 666 of file BinaryOperators.h.

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

Definition at line 678 of file BinaryOperators.h.

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

Definition at line 690 of file BinaryOperators.h.

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> ROOT::Math::Transpose ( const Expr< A, T, D1, D2, R > &  rhs)
inline

Definition at line 557 of file MatrixFunctions.h.

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

Definition at line 391 of file Functions.h.

Variable Documentation

const double ROOT::Math::eu = 0.577215664901532860606
static
const double ROOT::Math::eu = 0.577215664901532860606
static

Definition at line 57 of file VavilovTest.cxx.

double ROOT::Math::gDefaultAbsTolerance = 1.E-6
int ROOT::Math::gDefaultMaxIter = 100
int ROOT::Math::gDefaultNpx = 100
static

Definition at line 24 of file BrentRootFinder.cxx.

int ROOT::Math::gDefaultNpx = 100
static
int ROOT::Math::gDefaultNSearch = 10
static

Definition at line 25 of file BrentRootFinder.cxx.

int ROOT::Math::gDefaultNSearch = 10
static
double ROOT::Math::gDefaultRelTolerance = 1.E-10
const ROOT::Math::IMultiGenFunction* ROOT::Math::gFunction

function wrapper for the function to be minimized

Definition at line 12 of file RMinimizer.cxx.

Referenced by minfunction(), and ROOT::Math::RMinimizer::Minimize().

const ROOT::Math::IMultiGradFunction* ROOT::Math::gGradFunction

function wrapper for the gradient of the function to be minimized

Definition at line 14 of file RMinimizer.cxx.

Referenced by mingradfunction(), and ROOT::Math::RMinimizer::Minimize().

int ROOT::Math::gNCalls = 0

integer for the number of function calls

Definition at line 16 of file RMinimizer.cxx.

Referenced by minfunction(), ROOT::Math::RMinimizer::Minimize(), and ROOT::Math::RMinimizer::NCalls().

double ROOT::Math::kEulerGamma = 0.577215664901532860606512090082402431042
double ROOT::Math::kPi = 3.14159265358979323846
double ROOT::Math::kSqrt2 = 1.41421356237309515
static
double ROOT::Math::vavilovKappaValues[10] = {.01, .04, .07, .1, .4, .7, 1, 4, 7, 10}
static

Definition at line 398 of file VavilovTest.cxx.

Referenced by ROOT::Math::VavilovTest::GetSBKappa().

int ROOT::Math::vavilovNLambda[10] = {45, 42, 41, 41, 28, 22, 19, 20, 21, 21}
static

Definition at line 400 of file VavilovTest.cxx.

Referenced by ROOT::Math::VavilovTest::GetSBNLambda().

double ROOT::Math::vavilovPdfValues0[45][12]
static

Definition at line 61 of file VavilovTest.cxx.

double ROOT::Math::vavilovPdfValues1[42][12]
static

Definition at line 110 of file VavilovTest.cxx.

double ROOT::Math::vavilovPdfValues2[41][12]
static

Definition at line 156 of file VavilovTest.cxx.

double ROOT::Math::vavilovPdfValues3[41][12]
static

Definition at line 201 of file VavilovTest.cxx.

double ROOT::Math::vavilovPdfValues4[28][12]
static
Initial value:
={
{-3.50, 1.07E-5, 1.26E-5, 1.47E-5, 1.73E-5, 2.03E-5, 2.37E-5, 2.78E-5, 3.26E-5, 3.82E-5, 4.48E-5, 5.24E-5},
{-3.00, 1.00E-3, 1.16E-3, 1.33E-3, 1.53E-3, 1.75E-3, 2.02E-3, 2.32E-3, 2.66E-3, 3.05E-3, 3.50E-3, 4.02E-3},
{-2.50, 1.44E-2, 1.62E-2, 1.83E-2, 2.06E-2, 2.32E-2, 2.61E-2, 2.93E-2, 3.30E-2, 3.71E-2, 4.17E-2, 4.68E-2},
{-2.00, 6.56E-2, 7.25E-2, 8.00E-2, 8.83E-2, 9.74E-2, 1.07E-1, 1.18E-1, 1.30E-1, 1.43E-1, 1.57E-1, 1.73E-1},
{-1.50, 1.50E-1, 1.62E-1, 1.76E-1, 1.90E-1, 2.05E-1, 2.21E-1, 2.38E-1, 2.57E-1, 2.76E-1, 2.97E-1, 3.19E-1},
{-1.00, 2.26E-1, 2.40E-1, 2.54E-1, 2.69E-1, 2.84E-1, 3.00E-1, 3.16E-1, 3.32E-1, 3.49E-1, 3.66E-1, 3.83E-1},
{-0.50, 2.65E-1, 2.75E-1, 2.85E-1, 2.96E-1, 3.05E-1, 3.15E-1, 3.24E-1, 3.32E-1, 3.40E-1, 3.47E-1, 3.52E-1},
{ 0.00, 2.66E-1, 2.71E-1, 2.76E-1, 2.79E-1, 2.82E-1, 2.84E-1, 2.84E-1, 2.84E-1, 2.82E-1, 2.78E-1, 2.73E-1},
{ 0.50, 2.44E-1, 2.43E-1, 2.42E-1, 2.39E-1, 2.36E-1, 2.31E-1, 2.25E-1, 2.18E-1, 2.09E-1, 1.99E-1, 1.88E-1},
{ 1.00, 2.07E-1, 2.03E-1, 1.97E-1, 1.91E-1, 1.83E-1, 1.75E-1, 1.65E-1, 1.55E-1, 1.44E-1, 1.31E-1, 1.18E-1},
{ 1.50, 1.66E-1, 1.59E-1, 1.51E-1, 1.43E-1, 1.34E-1, 1.24E-1, 1.14E-1, 1.03E-1, 9.21E-2, 8.05E-2, 6.86E-2},
{ 2.00, 1.26E-1, 1.18E-1, 1.10E-1, 1.01E-1, 9.25E-2, 8.35E-2, 7.43E-2, 6.51E-2, 5.58E-2, 4.66E-2, 3.75E-2},
{ 2.50, 9.11E-2, 8.37E-2, 7.62E-2, 6.87E-2, 6.11E-2, 5.36E-2, 4.63E-2, 3.91E-2, 3.22E-2, 2.56E-2, 1.94E-2},
{ 3.00, 6.35E-2, 5.71E-2, 5.09E-2, 4.48E-2, 3.88E-2, 3.31E-2, 2.77E-2, 2.26E-2, 1.78E-2, 1.35E-2, 9.60E-3},
{ 3.50, 4.28E-2, 3.77E-2, 3.29E-2, 2.82E-2, 2.39E-2, 1.98E-2, 1.60E-2, 1.26E-2, 9.52E-3, 6.84E-3, 4.55E-3},
{ 4.00, 2.79E-2, 2.41E-2, 2.06E-2, 1.72E-2, 1.42E-2, 1.14E-2, 8.95E-3, 6.78E-3, 4.91E-3, 3.35E-3, 2.08E-3},
{ 4.50, 1.77E-2, 1.50E-2, 1.25E-2, 1.02E-2, 8.21E-3, 6.42E-3, 4.87E-3, 3.55E-3, 2.46E-3, 1.59E-3, 9.22E-4},
{ 5.00, 1.10E-2, 9.10E-3, 7.42E-3, 5.93E-3, 4.63E-3, 3.51E-3, 2.58E-3, 1.81E-3, 1.20E-3, 7.34E-4, 3.96E-4},
{ 5.50, 6.65E-3, 5.39E-3, 4.30E-3, 3.35E-3, 2.55E-3, 1.88E-3, 1.33E-3, 9.02E-4, 5.72E-4, 3.30E-4, 1.66E-4},
{ 6.00, 3.93E-3, 3.13E-3, 2.44E-3, 1.85E-3, 1.37E-3, 9.83E-4, 6.75E-4, 4.39E-4, 2.66E-4, 1.45E-4, 6.73E-5},
{ 6.50, 2.28E-3, 1.78E-3, 1.35E-3, 1.01E-3, 7.25E-4, 5.04E-4, 3.34E-4, 2.09E-4, 1.21E-4, 6.24E-5, 2.68E-5},
{ 7.00, 1.30E-3, 9.91E-4, 7.38E-4, 5.35E-4, 3.76E-4, 2.53E-4, 1.63E-4, 9.79E-5, 5.41E-5, 2.64E-5, 1.05E-5},
{ 7.50, 7.27E-4, 5.43E-4, 3.96E-4, 2.80E-4, 1.91E-4, 1.25E-4, 7.76E-5, 4.49E-5, 2.36E-5, 1.08E-5, 0},
{ 8.00, 4.00E-4, 2.92E-4, 2.08E-4, 1.44E-4, 9.57E-5, 6.08E-5, 3.64E-5, 2.02E-5, 1.02E-5, 0, 0},
{ 8.50, 2.17E-4, 1.55E-4, 1.08E-4, 7.29E-5, 4.72E-5, 2.91E-5, 1.69E-5, 0, 0, 0, 0},
{ 9.00, 1.16E-4, 8.12E-5, 5.53E-5, 3.63E-5, 2.29E-5, 1.37E-5, 0, 0, 0, 0, 0},
{ 9.50, 6.08E-5, 4.19E-5, 2.79E-5, 1.79E-5, 1.09E-5, 0, 0, 0, 0, 0, 0},
{10.00, 3.17E-5, 2.13E-5, 1.39E-5, 0, 0, 0, 0, 0, 0, 0, 0}}

Definition at line 246 of file VavilovTest.cxx.

double ROOT::Math::vavilovPdfValues5[22][12]
static
Initial value:
={
{-3.50, 1.44E-5, 1.83E-5, 2.32E-5, 2.95E-5, 3.75E-5, 4.76E-5, 6.04E-5, 7.69E-5, 9.72E-5, 1.23E-4, 1.56E-4},
{-3.00, 1.36E-3, 1.67E-3, 2.04E-3, 2.50E-3, 3.07E-3, 3.76E-3, 4.60E-3, 5.62E-3, 6.87E-3, 8.39E-3, 1.02E-2},
{-2.50, 1.94E-2, 2.30E-2, 2.72E-2, 3.22E-2, 3.81E-2, 4.49E-2, 5.29E-2, 6.23E-2, 7.33E-2, 8.61E-2, 1.01E-1},
{-2.00, 8.86E-2, 1.01E-1, 1.16E-1, 1.32E-1, 1.50E-1, 1.71E-1, 1.94E-1, 2.19E-1, 2.47E-1, 2.79E-1, 3.13E-1},
{-1.50, 2.02E-1, 2.23E-1, 2.46E-1, 2.70E-1, 2.96E-1, 3.23E-1, 3.52E-1, 3.82E-1, 4.13E-1, 4.44E-1, 4.76E-1},
{-1.00, 3.03E-1, 3.23E-1, 3.42E-1, 3.62E-1, 3.81E-1, 3.99E-1, 4.15E-1, 4.30E-1, 4.42E-1, 4.52E-1, 4.57E-1},
{-0.50, 3.44E-1, 3.54E-1, 3.62E-1, 3.68E-1, 3.71E-1, 3.72E-1, 3.70E-1, 3.64E-1, 3.54E-1, 3.40E-1, 3.22E-1},
{ 0.00, 3.23E-1, 3.20E-1, 3.15E-1, 3.09E-1, 2.97E-1, 2.85E-1, 2.69E-1, 2.51E-1, 2.30E-1, 2.07E-1, 1.81E-1},
{ 0.50, 2.60E-1, 2.49E-1, 2.36E-1, 2.21E-1, 2.05E-1, 1.87E-1, 1.68E-1, 1.48E-1, 1.27E-1, 1.06E-1, 8.54E-2},
{ 1.00, 1.86E-1, 1.72E-1, 1.57E-1, 1.41E-1, 1.25E-1, 1.09E-1, 9.28E-2, 7.71E-2, 6.20E-2, 4.79E-2, 3.50E-2},
{ 1.50, 1.21E-1, 1.08E-1, 9.44E-2, 8.15E-2, 6.91E-2, 5.73E-2, 4.63E-2, 3.62E-2, 2.72E-2, 1.93E-2, 1.28E-2},
{ 2.00, 7.20E-2, 6.19E-2, 5.22E-2, 4.33E-2, 3.51E-2, 2.79E-2, 2.11E-2, 1.55E-2, 1.09E-2, 7.11E-3, 4.22E-3},
{ 2.50, 3.99E-2, 3.31E-2, 2.69E-2, 2.13E-2, 1.65E-2, 1.24E-2, 8.97E-3, 6.19E-3, 4.02E-3, 2.41E-3, 1.28E-3},
{ 3.00, 2.07E-2, 1.66E-2, 1.30E-2, 9.87E-3, 7.30E-3, 5.21E-3, 3.56E-3, 2.31E-3, 1.39E-3, 7.61E-4, 3.60E-4},
{ 3.50, 1.02E-2, 7.84E-3, 5.89E-3, 4.31E-3, 3.04E-3, 2.06E-3, 1.33E-3, 8.09E-4, 4.52E-4, 2.26E-4, 9.47E-5},
{ 4.00, 4.74E-3, 3.52E-3, 2.55E-3, 1.78E-3, 1.20E-3, 7.76E-4, 4.73E-4, 2.69E-4, 1.39E-4, 6.32E-5, 2.34E-5},
{ 4.50, 2.10E-3, 1.51E-3, 1.05E-3, 7.05E-4, 4.54E-4, 2.78E-4, 1.60E-4, 8.52E-5, 4.08E-5, 1.68E-5, 0},
{ 5.00, 8.98E-4, 6.21E-4, 4.15E-4, 2.67E-4, 1.64E-4, 9.55E-5, 5.19E-5, 2.58E-5, 1.14E-5, 0, 0},
{ 5.50, 3.68E-4, 2.45E-4, 1.58E-4, 9.71E-5, 5.70E-5, 3.15E-5, 1.61E-5, 0, 0, 0, 0},
{ 6.00, 1.45E-4, 9.32E-5, 5.76E-5, 3.41E-5, 1.91E-5, 1.00E-5, 0, 0, 0, 0, 0},
{ 6.50, 5.53E-5, 3.43E-5, 2.04E-5, 1.15E-5, 0, 0, 0, 0, 0, 0, 0},
{ 7.00, 2.04E-5, 1.22E-5, 0, 0, 0, 0, 0, 0, 0, 0, 0}}

Definition at line 278 of file VavilovTest.cxx.

double ROOT::Math::vavilovPdfValues6[19][12]
static
Initial value:
={
{-3.50, 1.94E-5, 2.64E-5, 3.59E-5, 4.87E-5, 6.61E-5, 8.96E-5, 1.21E-4, 1.64E-4, 2.22E-4, 3.00E-4, 4.05E-4},
{-3.00, 1.83E-3, 2.37E-3, 3.06E-3, 3.94E-3, 5.08E-3, 6.53E-3, 8.39E-3, 1.08E-2, 1.38E-2, 1.76E-2, 2.25E-2},
{-2.50, 2.62E-2, 3.22E-2, 3.95E-2, 4.84E-2, 5.91E-2, 7.20E-2, 8.76E-2, 1.06E-1, 1.28E-1, 1.55E-1, 1.86E-1},
{-2.00, 1.19E-1, 1.39E-1, 1.63E-1, 1.89E-1, 2.18E-1, 2.51E-1, 2.88E-1, 3.29E-1, 3.74E-1, 4.23E-1, 4.75E-1},
{-1.50, 2.69E-1, 2.99E-1, 3.31E-1, 3.64E-1, 3.97E-1, 4.31E-1, 4.65E-1, 4.97E-1, 5.26E-1, 5.52E-1, 5.73E-1},
{-1.00, 3.85E-1, 4.07E-1, 4.26E-1, 4.43E-1, 4.56E-1, 4.66E-1, 4.69E-1, 4.67E-1, 4.58E-1, 4.42E-1, 4.17E-1},
{-0.50, 4.01E-1, 4.02E-1, 4.00E-1, 3.92E-1, 3.80E-1, 3.63E-1, 3.42E-1, 3.15E-1, 2.84E-1, 2.49E-1, 2.11E-1},
{ 0.00, 3.29E-1, 3.13E-1, 2.94E-1, 2.73E-1, 2.49E-1, 2.22E-1, 1.94E-1, 1.65E-1, 1.36E-1, 1.08E-1, 8.10E-2},
{ 0.50, 2.23E-1, 2.02E-1, 1.80E-1, 1.57E-1, 1.34E-1, 1.12E-1, 9.10E-2, 7.13E-2, 5.35E-2, 3.80E-2, 2.50E-2},
{ 1.00, 1.29E-1, 1.11E-1, 9.38E-2, 7.73E-2, 6.21E-2, 4.84E-2, 3.64E-2, 2.61E-2, 1.78E-2, 1.12E-2, 6.42E-3},
{ 1.50, 6.60E-2, 5.39E-2, 4.30E-2, 3.34E-2, 2.51E-2, 1.83E-2, 1.27E-2, 8.37E-3, 5.15E-3, 2.88E-3, 1.42E-3},
{ 2.00, 3.01E-2, 2.33E-2, 1.76E-2, 1.29E-2, 9.10E-3, 6.15E-3, 3.95E-3, 2.38E-3, 1.32E-3, 6.54E-4, 2.74E-4},
{ 2.50, 1.24E-2, 9.15E-3, 6.53E-3, 4.50E-3, 2.98E-3, 1.88E-3, 1.11E-3, 6.12E-4, 3.05E-4, 1.33E-4, 4.73E-5},
{ 3.00, 4.71E-3, 3.29E-3, 2.22E-3, 1.44E-3, 8.94E-4, 5.24E-4, 2.87E-4, 1.44E-4, 6.44E-5, 2.46E-5, 0},
{ 3.50, 1.65E-3, 1.09E-3, 6.99E-4, 4.28E-4, 2.48E-4, 1.35E-4, 6.81E-5, 3.11E-5, 1.55E-5, 0, 0},
{ 4.00, 5.38E-4, 3.39E-4, 2.05E-4, 1.18E-4, 6.41E-5, 3.24E-5, 1.51E-5, 0, 0, 0, 0},
{ 4.50, 1.65E-4, 9.86E-5, 5.64E-5, 3.05E-5, 1.55E-5, 0, 0, 0, 0, 0, 0},
{ 5.00, 4.75E-5, 2.70E-5, 1.46E-5, 0, 0, 0, 0, 0, 0, 0, 0},
{ 5.50, 1.30E-5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}

Definition at line 304 of file VavilovTest.cxx.

double ROOT::Math::vavilovPdfValues7[20][12]
static
Initial value:
={
{-4.00, 0, 0, 0, 0, 0, 1.32E-5, 3.04E-5, 6.90E-5, 1.55E-4, 3.44E-4, 7.55E-4},
{-3.75, 1.38E-5, 2.98E-5, 6.38E-5, 1.35E-4, 2.83E-4, 5.85E-4, 1.20E-3, 2.41E-3, 4.78E-3, 9.35E-3, 1.80E-2},
{-3.50, 3.81E-4, 7.44E-4, 1.44E-3, 2.73E-3, 5.12E-3, 9.45E-3, 1.71E-2, 3.05E-2, 5.33E-2, 9.11E-2, 1.52E-1},
{-3.25, 4.78E-3, 8.44E-3, 1.47E-2, 2.50E-2, 4.19E-2, 6.88E-2, 1.10E-1, 1.73E-1, 2.64E-1, 3.90E-1, 5.57E-1},
{-3.00, 3.19E-2, 5.08E-2, 7.95E-2, 1.22E-1, 1.82E-1, 2.64E-1, 3.73E-1, 5.11E-1, 6.75E-1, 8.56E-1, 1.03E+0},
{-2.75, 1.27E-1, 1.83E-1, 2.56E-1, 3.51E-1, 4.66E-1, 6.00E-1, 7.44E-1, 8.86E-1, 1.01E+0, 1.08E+0, 1.09E+0},
{-2.50, 3.28E-1, 4.26E-1, 5.38E-1, 6.58E-1, 7.77E-1, 8.81E-1, 9.56E-1, 9.85E-1, 9.56E-1, 8.63E-1, 7.14E-1},
{-2.25, 5.89E-1, 6.91E-1, 7.84E-1, 8.57E-1, 8.97E-1, 8.95E-1, 8.46E-1, 7.51E-1, 6.18E-1, 4.65E-1, 3.12E-1},
{-2.00, 7.75E-1, 8.22E-1, 8.37E-1, 8.15E-1, 7.56E-1, 6.63E-1, 5.44E-1, 4.14E-1, 2.88E-1, 1.78E-1, 9.59E-2},
{-1.75, 7.79E-1, 7.45E-1, 6.81E-1, 5.91E-1, 4.85E-1, 3.73E-1, 2.65E-1, 1.72E-1, 1.01E-1, 5.10E-2, 2.17E-2},
{-1.50, 6.16E-1, 5.32E-1, 4.36E-1, 3.38E-1, 2.45E-1, 1.64E-1, 1.01E-1, 5.60E-2, 2.73E-2, 1.13E-2, 3.74E-3},
{-1.25, 3.95E-1, 3.07E-1, 2.26E-1, 1.56E-1, 9.96E-2, 5.85E-2, 3.11E-2, 1.46E-2, 5.90E-3, 1.97E-3, 5.05E-4},
{-1.00, 2.09E-1, 1.47E-1, 9.68E-2, 5.94E-2, 3.35E-2, 1.72E-2, 7.85E-3, 3.12E-3, 1.05E-3, 2.80E-4, 5.49E-5},
{-0.75, 9.33E-2, 5.91E-2, 3.49E-2, 1.91E-2, 9.47E-3, 4.23E-3, 1.66E-3, 5.59E-4, 1.54E-4, 3.29E-5, 0},
{-0.50, 3.56E-2, 2.04E-2, 1.08E-2, 5.22E-3, 2.29E-3, 8.90E-4, 3.00E-4, 8.49E-5, 1.93E-5, 0, 0},
{-0.25, 1.18E-2, 6.07E-3, 2.88E-3, 1.24E-3, 4.78E-4, 1.62E-4, 4.67E-5, 1.12E-5, 0, 0, 0},
{ 0.00, 3.41E-3, 1.59E-3, 6.74E-4, 2.58E-4, 8.75E-5, 2.57E-5, 0, 0, 0, 0, 0},
{ 0.25, 8.74E-4, 3.67E-4, 1.40E-4, 4.74E-5, 1.42E-5, 0, 0, 0, 0, 0, 0},
{ 0.50, 2.00E-4, 7.57E-5, 2.58E-5, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0.75, 4.11E-5, 1.41E-5, 0, 0, 0, 0, 0, 0, 0, 0, 0}}

Definition at line 327 of file VavilovTest.cxx.

double ROOT::Math::vavilovPdfValues8[21][12]
static
Initial value:
={
{-4.40, 0, 0, 0, 0, 0, 0, 0, 0, 1.11E-5, 3.90E-5, 1.33E-4},
{-4.20, 0, 0, 0, 0, 0, 2.17E-5, 6.93E-5, 2.15E-4, 6.46E-4, 1.88E-3, 5.28E-3},
{-4.00, 0, 1.07E-5, 3.24E-5, 9.54E-5, 2.73E-4, 7.60E-4, 2.04E-3, 5.31E-3, 1.33E-2, 3.18E-2, 7.28E-2},
{-3.80, 1.11E-4, 2.99E-4, 7.80E-4, 1.97E-3, 4.82E-3, 1.14E-2, 2.57E-2, 5.57E-2, 1.15E-1, 2.24E-1, 4.12E-1},
{-3.60, 1.77E-3, 4.11E-3, 9.26E-3, 2.01E-2, 4.18E-2, 8.32E-2, 1.58E-1, 2.83E-1, 4.78E-1, 7.51E-1, 1.09E+0},
{-3.40, 1.54E-2, 3.10E-2, 6.01E-2, 1.12E-1, 1.97E-1, 3.31E-1, 5.23E-1, 7.74E-1, 1.06E+0, 1.33E+0, 1.50E+0},
{-3.20, 7.96E-2, 1.39E-1, 2.33E-1, 3.69E-1, 5.54E-1, 7.81E-1, 1.02E+0, 1.24E+0, 1.37E+0, 1.35E+0, 1.17E+0},
{-3.00, 2.63E-1, 3.99E-1, 5.74E-1, 7.78E-1, 9.89E-1, 1.17E+0, 1.27E+0, 1.25E+0, 1.10E+0, 8.46E-1, 5.51E-1},
{-2.80, 5.86E-1, 7.71E-1, 9.54E-1, 1.10E+0, 1.18E+0, 1.17E+0, 1.04E+0, 8.35E-1, 5.83E-1, 3.46E-1, 1.68E-1},
{-2.60, 9.21E-1, 1.05E+0, 1.12E+0, 1.10E+0, 9.97E-1, 8.19E-1, 6.02E-1, 3.88E-1, 2.14E-1, 9.71E-2, 3.44E-2},
{-2.40, 1.06E+0, 1.04E+0, 9.55E-1, 8.02E-1, 6.12E-1, 4.18E-1, 2.52E-1, 1.30E-1, 5.63E-2, 1.94E-2, 4.95E-3},
{-2.20, 9.18E-1, 7.85E-1, 6.16E-1, 4.40E-1, 2.83E-1, 1.61E-1, 7.89E-2, 3.27E-2, 1.10E-2, 2.84E-3, 5.18E-4},
{-2.00, 6.17E-1, 4.57E-1, 3.08E-1, 1.87E-1, 1.01E-1, 4.75E-2, 1.90E-2, 6.29E-3, 1.64E-3, 3.16E-4, 4.05E-5},
{-1.80, 3.28E-1, 2.10E-1, 1.22E-1, 6.30E-2, 2.85E-2, 1.11E-2, 3.62E-3, 9.50E-4, 1.91E-4, 2.78E-5, 0},
{-1.60, 1.41E-1, 7.84E-2, 3.89E-2, 1.71E-2, 6.49E-3, 2.09E-3, 5.52E-4, 1.15E-4, 1.77E-5, 0, 0},
{-1.40, 4.99E-2, 2.40E-2, 1.02E-2, 3.80E-3, 1.21E-3, 3.22E-4, 6.88E-5, 1.13E-5, 0, 0, 0},
{-1.20, 1.47E-2, 6.10E-3, 2.23E-3, 7.05E-4, 1.88E-4, 4.12E-5, 0, 0, 0, 0, 0},
{-1.00, 3.64E-3, 1.31E-3, 4.11E-4, 1.10E-4, 2.46E-5, 0, 0, 0, 0, 0, 0},
{-0.80, 7.71E-4, 2.40E-4, 6.46E-5, 1.47E-5, 0, 0, 0, 0, 0, 0, 0},
{-0.60, 1.41E-4, 3.80E-5, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{-0.40, 2.24E-5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}

Definition at line 351 of file VavilovTest.cxx.

double ROOT::Math::vavilovPdfValues9[21][12]
static
Initial value:
={
{-4.60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.85E-5, 1.79E-4},
{-4.40, 0, 0, 0, 0, 0, 1.18E-5, 5.14E-5, 2.12E-4, 8.32E-4, 3.08E-3, 1.07E-2},
{-4.20, 0, 0, 1.41E-5, 5.57E-5, 2.10E-4, 7.50E-4, 2.54E-3, 8.11E-3, 2.42E-2, 6.69E-2, 1.70E-1},
{-4.00, 5.27E-5, 1.84E-4, 6.15E-4, 1.95E-3, 5.83E-3, 1.64E-2, 4.32E-2, 1.06E-1, 2.37E-1, 4.82E-1, 8.79E-1},
{-3.80, 1.43E-3, 4.07E-3, 1.10E-2, 2.78E-2, 6.61E-2, 1.46E-1, 2.96E-1, 5.49E-1, 9.16E-1, 1.35E+0, 1.73E+0},
{-3.60, 1.79E-2, 4.17E-2, 9.09E-2, 1.85E-1, 3.46E-1, 5.96E-1, 9.30E-1, 1.30E+0, 1.59E+0, 1.68E+0, 1.47E+0},
{-3.40, 1.16E-1, 2.20E-1, 3.88E-1, 6.29E-1, 9.31E-1, 1.24E+0, 1.48E+0, 1.54E+0, 1.38E+0, 1.02E+0, 5.99E-1},
{-3.20, 4.21E-1, 6.50E-1, 9.23E-1, 1.19E+0, 1.39E+0, 1.44E+0, 1.30E+0, 1.01E+0, 6.46E-1, 3.31E-1, 1.28E-1},
{-3.00, 9.12E-1, 1.15E+0, 1.31E+0, 1.35E+0, 1.24E+0, 9.87E-1, 6.74E-1, 3.84E-1, 1.76E-1, 6.16E-2, 1.53E-2},
{-2.80, 1.25E+0, 1.28E+0, 1.18E+0, 9.66E-1, 6.92E-1, 4.25E-1, 2.18E-1, 9.11E-2, 2.95E-2, 6.96E-3, 1.09E-3},
{-2.60, 1.13E+0, 9.45E-1, 7.01E-1, 4.56E-1, 2.55E-1, 1.20E-1, 4.64E-2, 1.41E-2, 3.19E-3, 5.02E-4, 4.87E-5},
{-2.40, 7.06E-1, 4.80E-1, 2.87E-1, 1.48E-1, 6.46E-2, 2.33E-2, 6.71E-3, 1.47E-3, 2.33E-4, 2.41E-5, 0},
{-2.20, 3.13E-1, 1.73E-1, 8.33E-2, 3.41E-2, 1.16E-2, 3.19E-3, 6.84E-4, 1.08E-4, 1.18E-5, 0, 0},
{-2.00, 1.02E-1, 4.59E-2, 1.77E-2, 5.74E-3, 1.52E-3, 3.19E-4, 5.06E-5, 0, 0, 0, 0},
{-1.80, 2.48E-2, 9.10E-3, 2.82E-3, 7.24E-4, 1.49E-4, 2.37E-5, 0, 0, 0, 0, 0},
{-1.60, 4.64E-3, 1.38E-3, 3.45E-4, 6.99E-5, 1.11E-5, 0, 0, 0, 0, 0, 0},
{-1.40, 6.77E-4, 1.64E-4, 3.29E-5, 0, 0, 0, 0, 0, 0, 0, 0},
{-1.20, 7.84E-5, 1.55E-5, 0, 0, 0, 0, 0, 0, 0, 0, 0}}

Definition at line 376 of file VavilovTest.cxx.