ROOT::Math Namespace Reference


Namespaces
namespace	BrentMethods
namespace	Cephes
namespace	CholeskyDecompHelpers
	helpers for CholeskyDecomp
namespace	detail
namespace	GenAlgoOptUtil
namespace	GenVector
namespace	GenVector_detail
namespace	GSLRootHelper
	Helper functions to test convergence of Root-Finding algorithms.
namespace	GSLSimAn
namespace	gv_detail
namespace	Impl
namespace	IntegMultiDim
namespace	IntegOneDim
namespace	IntegOptionsUtil
namespace	Integration
namespace	IntegrationMultiDim
namespace	IntegrationOneDim
namespace	Interpolation
namespace	MCIntegration
namespace	Minim
namespace	Minim1D
namespace	Roots
	Root-Finding Algorithms.
namespace	Sampler
namespace	Util
	namespace defining Utility functions needed by mathcore
namespace	VectorUtil
	Global Helper functions for generic Vector classes.
Classes
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...
class	AdaptiveIntegratorMultiDim
	class for adaptive quadrature integration in multi-dimensions Algorithm from A.C. 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	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	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	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 otions in a maps of string-value pair 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	Minimizer
	Abstract Minimizer class, defining the interface for the various minimizer (like Minuit2, Minuit, GSL, etc. More...
class	MinimizerOptions
	Minimizer options. More...
class	MinimizerVariable
	MinimizerVariable class to perform a transformations on the variables to deal with fixed or limited variables. 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	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	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	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	FunctorCintHandler
struct	CDFWrapper
class	PDFIntegral
class	Chebyshev
	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 for performing numerical integration of a multidimensional function. More...
class	GSLMinimizer
	GSLMinimizer class. More...
class	GSLMinimizer1D
	Minimizer for arbitrary one dimensional functions. 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	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...
class	Polynomial
	Parametric Function class describing polynomials of order n. More...
class	Random
	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	FitTransformFunction
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	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	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	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 >
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...
class	MatRepStd
	MatRepStd Standard Matrix representation for a general D1 x D2 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	RowOffsets< 1 >
struct	RowOffsets< 2 >
struct	RowOffsets< 3 >
struct	RowOffsets< 4 >
struct	RowOffsets< 5 >
struct	RowOffsets< 6 >
struct	RowOffsets< 7 >
struct	RowOffsets< 8 >
struct	RowOffsets< 9 >
struct	RowOffsets< 10 >
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	SMatrixIdentity
class	SMatrix
	SMatrix: a generic fixed size D1 x D2 Matrix class. More...
struct	CompileTimeChecker
struct	CompileTimeChecker< false >
class	SVector
	SVector: a generic fixed size Vector class. More...
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
typedef XYPoint	XYPointD
typedef PositionVector2D < Cartesian2D< float > , DefaultCoordinateSystemTag >	XYPointF
	2D Point based on the cartesian corrdinates x,y,z in single precision
typedef PositionVector2D < Polar2D< double > , DefaultCoordinateSystemTag >	Polar2DPoint
	2D Point based on the polar coordinates rho, theta, phi in double precision.
typedef Polar2DPoint	Polar2DPointD
typedef PositionVector2D < Polar2D< float > , DefaultCoordinateSystemTag >	Polar2DPointF
	2D Point based on the polar coordinates rho, theta, phi in single precision.
typedef PositionVector3D < Cartesian3D< double > , DefaultCoordinateSystemTag >	XYZPoint
	3D Point based on the cartesian coordinates x,y,z in double precision
typedef PositionVector3D < Cartesian3D< float > , DefaultCoordinateSystemTag >	XYZPointF
	3D Point based on the cartesian corrdinates x,y,z in single precision
typedef XYZPoint	XYZPointD
typedef PositionVector3D < CylindricalEta3D< double > , DefaultCoordinateSystemTag >	RhoEtaPhiPoint
	3D Point based on the eta based cylindrical coordinates rho, eta, phi in double precision.
typedef PositionVector3D < CylindricalEta3D< float > , DefaultCoordinateSystemTag >	RhoEtaPhiPointF
	3D Point based on the eta based cylindrical coordinates rho, eta, phi in single precision.
typedef RhoEtaPhiPoint	RhoEtaPhiPointD
typedef PositionVector3D < Polar3D< double > , DefaultCoordinateSystemTag >	Polar3DPoint
	3D Point based on the polar coordinates rho, theta, phi in double precision.
typedef PositionVector3D < Polar3D< float > , DefaultCoordinateSystemTag >	Polar3DPointF
	3D Point based on the polar coordinates rho, theta, phi in single precision.
typedef Polar3DPoint	Polar3DPointD
typedef PositionVector3D < Cylindrical3D< double > , DefaultCoordinateSystemTag >	RhoZPhiPoint
	3D Point based on the cylindrical coordinates rho, z, phi in double precision.
typedef PositionVector3D < Cylindrical3D< float > , DefaultCoordinateSystemTag >	RhoZPhiPointF
	3D Point based on the cylindrical coordinates rho, z, phi in single precision.
typedef RhoZPhiPoint	RhoZPhiPointD
typedef DisplacementVector2D < Cartesian2D< double > , DefaultCoordinateSystemTag >	XYVector
	2D Vector based on the cartesian coordinates x,y in double precision
typedef XYVector	XYVectorD
typedef DisplacementVector2D < Cartesian2D< float > , DefaultCoordinateSystemTag >	XYVectorF
	2D Vector based on the cartesian coordinates x,y,z in single precision
typedef DisplacementVector2D < Polar2D< double > , DefaultCoordinateSystemTag >	Polar2DVector
	2D Vector based on the polar coordinates rho, phi in double precision.
typedef Polar2DVector	Polar2DVectorD
typedef DisplacementVector2D < Polar2D< float > , DefaultCoordinateSystemTag >	Polar2DVectorF
	2D Vector based on the polar coordinates rho, phi in single precision.
typedef DisplacementVector3D < Cartesian3D< double > , DefaultCoordinateSystemTag >	XYZVector
	3D Vector based on the cartesian coordinates x,y,z in double precision
typedef DisplacementVector3D < Cartesian3D< float > , DefaultCoordinateSystemTag >	XYZVectorF
	3D Vector based on the cartesian corrdinates x,y,z in single precision
typedef XYZVector	XYZVectorD
typedef DisplacementVector3D < CylindricalEta3D< double > , DefaultCoordinateSystemTag >	RhoEtaPhiVector
	3D Vector based on the eta based cylindrical coordinates rho, eta, phi in double precision.
typedef DisplacementVector3D < CylindricalEta3D< float > , DefaultCoordinateSystemTag >	RhoEtaPhiVectorF
	3D Vector based on the eta based cylindrical coordinates rho, eta, phi in single precision.
typedef RhoEtaPhiVector	RhoEtaPhiVectorD
typedef DisplacementVector3D < Polar3D< double > , DefaultCoordinateSystemTag >	Polar3DVector
	3D Vector based on the polar coordinates rho, theta, phi in double precision.
typedef DisplacementVector3D < Polar3D< float > , DefaultCoordinateSystemTag >	Polar3DVectorF
	3D Vector based on the polar coordinates rho, theta, phi in single precision.
typedef Polar3DVector	Polar3DVectorD
typedef DisplacementVector3D < Cylindrical3D< double > , DefaultCoordinateSystemTag >	RhoZPhiVector
	3D Vector based on the cylindrical coordinates rho, z, phi in double precision.
typedef DisplacementVector3D < Cylindrical3D< float > , DefaultCoordinateSystemTag >	RhoZPhiVectorF
	3D Vector based on the cylindrical coordinates rho, z, phi in single precision.
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 (-,-,-,+).
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 (-,-,-,+).
typedef LorentzVector < PxPyPzM4D< double > >	PxPyPzMVector
	LorentzVector based on the x, y, z, and Mass in double precision.
typedef LorentzVector < PtEtaPhiE4D< double > >	PtEtaPhiEVector
	LorentzVector based on the cylindrical coordinates Pt, eta, phi and E (rho, eta, phi, t) in double precision.
typedef LorentzVector < PtEtaPhiM4D< double > >	PtEtaPhiMVector
	LorentzVector based on the cylindrical coordinates pt, eta, phi and Mass in double precision.
typedef 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 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.
typedef GSLRngRanLuxS1	GSLRngRanLux1
typedef GSLRngRanLuxS2	GSLRngRanLux2
typedef GSLRngRanLuxD2	GSLRngRanLux48
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.
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 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.
AxisAngle	operator* (RotationX const &r1, AxisAngle const &r2)
	Multiplication of an axial rotation by an AxisAngle.
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.
std::ostream &	operator<< (std::ostream &os, const Boost &b)
	Stream Output and Input.
std::ostream &	operator<< (std::ostream &os, const BoostX &b)
	Stream Output and Input.
std::ostream &	operator<< (std::ostream &os, const BoostY &b)
	Stream Output and Input.
std::ostream &	operator<< (std::ostream &os, const BoostZ &b)
	Stream Output and Input.
template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector2D < CoordSystem1, U >	operator+ (DisplacementVector2D< CoordSystem1, U > v1, const DisplacementVector2D< CoordSystem2, U > &v2)
	Addition of DisplacementVector2D vectors.
template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector2D < CoordSystem1, U >	operator- (DisplacementVector2D< CoordSystem1, U > v1, DisplacementVector2D< CoordSystem2, U > const &v2)
	Difference between two DisplacementVector2D vectors.
template<class CoordSystem , class U >
DisplacementVector2D < CoordSystem, U >	operator* (typename DisplacementVector2D< CoordSystem, U >::Scalar a, DisplacementVector2D< CoordSystem, U > v)
	Multiplication of a displacement vector by real number a*v.
template<class 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.
template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector3D < CoordSystem1, U >	operator- (DisplacementVector3D< CoordSystem1, U > v1, DisplacementVector3D< CoordSystem2, U > const &v2)
	Difference between two DisplacementVector3D vectors.
template<class CoordSystem , class U >
DisplacementVector3D < CoordSystem, U >	operator* (typename DisplacementVector3D< CoordSystem, U >::Scalar a, DisplacementVector3D< CoordSystem, U > v)
	Multiplication of a displacement vector by real number a*v.
template<class 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.
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.
template<class R >
EulerAngles::Scalar	Distance (const EulerAngles &r1, const R &r2)
	Distance between two rotations.
EulerAngles	operator* (RotationX const &r1, EulerAngles const &r2)
	Multiplication of an axial rotation by an AxisAngle.
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.
void	Throw (GenVector_exception &e)
	throw explicity GenVector exceptions
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.
template<class CoordSystem >
LorentzVector< CoordSystem >	operator* (const typename LorentzVector< CoordSystem >::Scalar &a, const LorentzVector< CoordSystem > &v)
	Scale of a LorentzVector with a scalar quantity a.
template<class 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.
template<class CoordSystem , class U >
PositionVector2D< CoordSystem >	operator* (typename PositionVector2D< CoordSystem, U >::Scalar a, PositionVector2D< CoordSystem, U > v)
	Multiplication of a position vector by real number a*v.
template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector2D < CoordSystem1, U >	operator- (const PositionVector2D< CoordSystem1, U > &v1, const PositionVector2D< CoordSystem2, U > &v2)
	Difference between two PositionVector2D vectors.
template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector2D< CoordSystem2, U >	operator+ (PositionVector2D< CoordSystem2, U > p1, const DisplacementVector2D< CoordSystem1, U > &v2)
	Addition of a PositionVector2D and a DisplacementVector2D.
template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector2D< CoordSystem2, U >	operator+ (DisplacementVector2D< CoordSystem1, U > const &v1, PositionVector2D< CoordSystem2, U > p2)
	Addition of a DisplacementVector2D and a PositionVector2D.
template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector2D< CoordSystem2, U >	operator- (PositionVector2D< CoordSystem2, U > p1, DisplacementVector2D< CoordSystem1, U > const &v2)
	Subtraction of a DisplacementVector2D from a PositionVector2D.
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.
template<class CoordSystem1 , class CoordSystem2 , class U >
DisplacementVector3D < CoordSystem1, U >	operator- (const PositionVector3D< CoordSystem1, U > &v1, const PositionVector3D< CoordSystem2, U > &v2)
	Difference between two PositionVector3D vectors.
template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector3D< CoordSystem2, U >	operator+ (PositionVector3D< CoordSystem2, U > p1, const DisplacementVector3D< CoordSystem1, U > &v2)
	Addition of a PositionVector3D and a DisplacementVector3D.
template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector3D< CoordSystem2, U >	operator+ (DisplacementVector3D< CoordSystem1, U > const &v1, PositionVector3D< CoordSystem2, U > p2)
	Addition of a DisplacementVector3D and a PositionVector3D.
template<class CoordSystem1 , class CoordSystem2 , class U >
PositionVector3D< CoordSystem2, U >	operator- (PositionVector3D< CoordSystem2, U > p1, DisplacementVector3D< CoordSystem1, U > const &v2)
	Subtraction of a DisplacementVector3D from a PositionVector3D.
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.
Quaternion	operator* (RotationX const &r1, Quaternion const &r2)
	Multiplication of an axial rotation by an AxisAngle.
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.
template<class R >
Rotation3D::Scalar	Distance (const Rotation3D &r1, const R &r2)
	Distance between two rotations.
Rotation3D	operator* (RotationX const &r1, Rotation3D const &r2)
	Multiplication of an axial rotation by a Rotation3D.
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.
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.
template<class R >
RotationX::Scalar	Distance (const RotationX &r1, const R &r2)
	Distance between two rotations.
std::ostream &	operator<< (std::ostream &os, const RotationX &r)
	Stream Output and Input.
template<class R >
RotationY::Scalar	Distance (const RotationY &r1, const R &r2)
	Distance between two rotations.
std::ostream &	operator<< (std::ostream &os, const RotationY &r)
	Stream Output and Input.
template<class R >
RotationZ::Scalar	Distance (const RotationZ &r1, const R &r2)
	Distance between two rotations.
std::ostream &	operator<< (std::ostream &os, const RotationZ &r)
	Stream Output and Input.
template<class R >
RotationZYX::Scalar	Distance (const RotationZYX &r1, const R &r2)
	Distance between two rotations.
RotationZYX	operator* (RotationX const &r1, RotationZYX const &r2)
	Multiplication of an axial rotation by an AxisAngle.
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.
Transform3D	operator* (const Rotation3D &r, const Translation3D &t)
	combine a translation and a rotation to give a transform3d First the translation then the rotation
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
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
Transform3D	operator* (const Translation3D &d, const Transform3D &t)
	combine a translation and a transformation to give a transform3d First the transformation then the translation
Transform3D	operator* (const Transform3D &t, const Rotation3D &r)
	combine a transformation and a rotation to give a transform3d First the rotation then the transform3D
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
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
std::ostream &	operator<< (std::ostream &os, const Translation3D &t)
XYZVector	operator* (double a, XYZVector v)
XYZPoint	operator* (double a, XYZPoint p)
XYZTVector	operator* (double a, XYZTVector v)
double	Pi ()
	Mathematical constants.
double	log1p (double x)
	declarations for functions which are not implemented by some compilers
double	expm1 (double x)
	exp(x) -1 with error cancellation when x is small
double	beta_cdf_c (double x, double a, double b)
	Complement of the cumulative distribution function of the beta distribution.
double	beta_cdf (double x, double a, double b)
	Cumulative distribution function of the beta distribution Upper tail of the integral of the beta_pdf.
double	breitwigner_cdf_c (double x, double gamma, double x0=0)
	Complement of the cumulative distribution function (upper tail) of the Breit_Wigner distribution and it is similar (just a different parameter definition) to the Cauchy distribution (see cauchy_cdf_c ).
double	breitwigner_cdf (double x, double gamma, double x0=0)
	Cumulative distribution function (lower tail) of the Breit_Wigner distribution and it is similar (just a different parameter definition) to the Cauchy distribution (see cauchy_cdf ).
double	cauchy_cdf_c (double x, double b, double x0=0)
	Complement of the cumulative distribution function (upper tail) of the Cauchy distribution which is also Lorentzian distribution.
double	cauchy_cdf (double x, double b, double x0=0)
	Cumulative distribution function (lower tail) of the Cauchy distribution which is also Lorentzian distribution.
double	chisquared_cdf_c (double x, double r, double x0=0)
	Complement of the cumulative distribution function of the $\chi^2$ distribution with degrees of freedom (upper tail).
double	chisquared_cdf (double x, double r, double x0=0)
	Cumulative distribution function of the $\chi^2$ distribution with degrees of freedom (lower tail).
double	exponential_cdf_c (double x, double lambda, double x0=0)
	Complement of the cumulative distribution function of the exponential distribution (upper tail).
double	exponential_cdf (double x, double lambda, double x0=0)
	Cumulative distribution function of the exponential distribution (lower tail).
double	fdistribution_cdf_c (double x, double n, double m, double x0=0)
	Complement of the cumulative distribution function of the F-distribution (upper tail).
double	fdistribution_cdf (double x, double n, double m, double x0=0)
	Cumulative distribution function of the F-distribution (lower tail).
double	gamma_cdf_c (double x, double alpha, double theta, double x0=0)
	Complement of the cumulative distribution function of the gamma distribution (upper tail).
double	gamma_cdf (double x, double alpha, double theta, double x0=0)
	Cumulative distribution function of the gamma distribution (lower tail).
double	landau_cdf (double x, double xi=1, double x0=0)
	Cumulative distribution function of the Landau distribution (lower tail).
double	landau_cdf_c (double x, double xi=1, double x0=0)
	Complement of the distribution function of the Landau distribution (upper tail).
double	lognormal_cdf_c (double x, double m, double s, double x0=0)
	Complement of the cumulative distribution function of the lognormal distribution (upper tail).
double	lognormal_cdf (double x, double m, double s, double x0=0)
	Cumulative distribution function of the lognormal distribution (lower tail).
double	normal_cdf_c (double x, double sigma=1, double x0=0)
	Complement of the cumulative distribution function of the normal (Gaussian) distribution (upper tail).
double	gaussian_cdf_c (double x, double sigma=1, double x0=0)
	Alternative name for same function.
double	normal_cdf (double x, double sigma=1, double x0=0)
	Cumulative distribution function of the normal (Gaussian) distribution (lower tail).
double	gaussian_cdf (double x, double sigma=1, double x0=0)
	Alternative name for same function.
double	tdistribution_cdf_c (double x, double r, double x0=0)
	Complement of the cumulative distribution function of Student's t-distribution (upper tail).
double	tdistribution_cdf (double x, double r, double x0=0)
	Cumulative distribution function of Student's t-distribution (lower tail).
double	uniform_cdf_c (double x, double a, double b, double x0=0)
	Complement of the cumulative distribution function of the uniform (flat) distribution (upper tail).
double	uniform_cdf (double x, double a, double b, double x0=0)
	Cumulative distribution function of the uniform (flat) distribution (lower tail).
double	poisson_cdf_c (unsigned int n, double mu)
	Complement of the cumulative distribution function of the Poisson distribution.
double	poisson_cdf (unsigned int n, double mu)
	Cumulative distribution function of the Poisson distribution Lower tail of the integral of the poisson_pdf.
double	binomial_cdf_c (unsigned int k, double p, unsigned int n)
	Complement of the cumulative distribution function of the Binomial distribution.
double	binomial_cdf (unsigned int k, double p, unsigned int n)
	Cumulative distribution function of the Binomial distribution Lower tail of the integral of the binomial_pdf.
double	negative_binomial_cdf_c (unsigned int k, double p, double n)
	Complement of the cumulative distribution function of the Negative Binomial distribution.
double	negative_binomial_cdf (unsigned int k, double p, double n)
	Cumulative distribution function of the Negative Binomial distribution Lower tail of the integral of the negative_binomial_pdf.
double	landau_xm1 (double x, double xi=1, double x0=0)
	First moment (mean) of the truncated Landau distribution.
double	landau_xm2 (double x, double xi=1, double x0=0)
	Second moment of the truncated Landau distribution.
void	PrintAllDefault (std::ostream &os)
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 degrees of freedom and the noon-central parameter $\lambda$ .
double	vavilov_accurate_pdf (double x, double kappa, double beta2)
	The Vavilov probability density function.
double	vavilov_accurate_cdf (double x, double kappa, double beta2)
	The Vavilov cummulative probability density function.
double	vavilov_accurate_cdf_c (double x, double kappa, double beta2)
	The Vavilov complementary cummulative probability density function.
double	vavilov_accurate_quantile (double z, double kappa, double beta2)
	The inverse of the Vavilov cummulative probability density function.
double	vavilov_accurate_quantile_c (double z, double kappa, double beta2)
	The inverse of the complementary Vavilov cummulative probability density function.
double	vavilov_fast_pdf (double x, double kappa, double beta2)
	The Vavilov probability density function.
double	vavilov_fast_cdf (double x, double kappa, double beta2)
	The Vavilov cummulative probability density function.
double	vavilov_fast_cdf_c (double x, double kappa, double beta2)
	The Vavilov complementary cummulative probability density function.
double	vavilov_fast_quantile (double z, double kappa, double beta2)
	The inverse of the Vavilov cummulative probability density function.
double	vavilov_fast_quantile_c (double z, double kappa, double beta2)
	The inverse of the complementary Vavilov cummulative probability density function.
template<class T , unsigned int D>
VecExpr< BinaryOp< AddOp< T > , SVector< T, D >, SVector< T, D >, T >, T, D >	operator+ (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
	Addition of two vectors v3 = v1+v2 returning a vector expression.
template<class A , class T , unsigned int D>
VecExpr< BinaryOp< AddOp< T > , 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.
template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyL< AddOp < T >, Constant< A >, SVector < T, D >, T >, T, D >	operator+ (const A &lhs, const SVector< T, D > &rhs)
	Addition of a scalar to each vector element v2(i) = a + v1(i) returning a vector expression.
template<class A , class B , class T , unsigned int D>
VecExpr< 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.
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.
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.
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.
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.
template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyL< MinOp < T >, Constant< A >, SVector < T, D >, T >, T, D >	operator- (const A &lhs, const SVector< T, D > &rhs)
	Subtraction scalar vector (for each vector element) v2(i) = a - v1(i) returning a vector expression.
template<class A , class B , class T , unsigned int D>
VecExpr< 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.
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.
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.
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.
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.
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.
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.
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.
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.
template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyL< DivOp < T >, Constant< A >, SVector < T, D >, T >, T, D >	operator/ (const A &lhs, const SVector< T, D > &rhs)
	Division of a scalar value by the vector element: v2(i) = a/v1(i) returning a vector expression.
template<class A , class B , class T , unsigned int D>
VecExpr< 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.
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.
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.
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.
template<class Matrix , unsigned int n, unsigned int idim>
bool	Dfinv (Matrix &rhs, unsigned int *ir)
	Dfinv.
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
template<class T >
const T	Maximum (const T &lhs, const T &rhs)
	maximum.
template<class T >
const T	Minimum (const T &lhs, const T &rhs)
	minimum.
template<class T >
int	Round (const T &x)
	round.
template<class T >
int	Sign (const T &x)
	sign.
template<class T , unsigned int D>
T	Dot (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
	Vector dot product.
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 $\|\vec{v}\|^2 = \sum_iv_i^2$ .
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 : $\|\vec{v}\| = \sqrt{\sum_iv_i^2}$ .
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 $\|\vec{v}\|^2 = v_0^2 - v_1^2 - v_2^2 -v_3^2$ .
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: $\|\vec{v}\| = \sqrt{v_0^2 - v_1^2 - v_2^2 -v_3^2}$ .
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) $\vec{c} = \vec{a}\times\vec{b}$ .
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.
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.
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.
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.
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 $s = \sum_{i,j} v(i) * A(i,j) * v(j)$ .
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: $B(i,j) = \sum_{k,l} U(i,k) * A(k,l) * U(j,l)$ .
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: $B(i,j) = \sum_{k,l} U(k,i) * A(k,l) * U(l,j)$ .
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.
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)
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 .
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.
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
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
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) .
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
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
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
Probability Density Functions from MathCore
Additional PDF's are provided in the MathMore library (see PDF functions from MathMore)
double	beta_pdf (double x, double a, double b)
	Probability density function of the beta distribution.
double	binomial_pdf (unsigned int k, double p, unsigned int n)
	Probability density function of the binomial distribution.
double	negative_binomial_pdf (unsigned int k, double p, double n)
	Probability density function of the negative binomial distribution.
double	breitwigner_pdf (double x, double gamma, double x0=0)
	Probability density function of Breit-Wigner distribution, which is similar, just a different definition of the parameters, to the Cauchy distribution (see cauchy_pdf ).
double	cauchy_pdf (double x, double b=1, double x0=0)
	Probability density function of the Cauchy distribution which is also called Lorentzian distribution.
double	chisquared_pdf (double x, double r, double x0=0)
	Probability density function of the $\chi^2$ distribution with degrees of freedom.
double	exponential_pdf (double x, double lambda, double x0=0)
	Probability density function of the exponential distribution.
double	fdistribution_pdf (double x, double n, double m, double x0=0)
	Probability density function of the F-distribution.
double	gamma_pdf (double x, double alpha, double theta, double x0=0)
	Probability density function of the gamma distribution.
double	gaussian_pdf (double x, double sigma=1, double x0=0)
	Probability density function of the normal (Gaussian) distribution.
double	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 $\lambda = (x-x_0)/\xi$ .
double	lognormal_pdf (double x, double m, double s, double x0=0)
	Probability density function of the lognormal distribution.
double	normal_pdf (double x, double sigma=1, double x0=0)
	Probability density function of the normal (Gaussian) distribution.
double	poisson_pdf (unsigned int n, double mu)
	Probability density function of the Poisson distribution.
double	tdistribution_pdf (double x, double r, double x0=0)
	Probability density function of Student's t-distribution.
double	uniform_pdf (double x, double a, double b, double x0=0)
	Probability density function of the uniform (flat) distribution.
Quantile Functions from MathCore
The implementation is provided in MathCore and for the majority of the function comes from Cephes.
double	beta_quantile (double x, double a, double b)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the beta distribution (beta_cdf_c).
double	beta_quantile_c (double x, double a, double b)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the beta distribution (beta_cdf).
double	cauchy_quantile_c (double z, double b)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the Cauchy distribution (cauchy_cdf_c) which is also called Lorentzian distribution.
double	cauchy_quantile (double z, double b)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the Cauchy distribution (cauchy_cdf) which is also called Breit-Wigner or Lorentzian distribution.
double	breitwigner_quantile_c (double z, double gamma)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the Breit-Wigner distribution (breitwigner_cdf_c) which is similar to the Cauchy distribution.
double	breitwigner_quantile (double z, double gamma)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the Breit_Wigner distribution (breitwigner_cdf) which is similar to the Cauchy distribution.
double	chisquared_quantile_c (double z, double r)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the $\chi^2$ distribution with degrees of freedom (chisquared_cdf_c).
double	chisquared_quantile (double z, double r)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the $\chi^2$ distribution with degrees of freedom (chisquared_cdf).
double	exponential_quantile_c (double z, double lambda)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the exponential distribution (exponential_cdf_c).
double	exponential_quantile (double z, double lambda)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the exponential distribution (exponential_cdf).
double	fdistribution_quantile (double z, double n, double m)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the f distribution (fdistribution_cdf).
double	fdistribution_quantile_c (double z, double n, double m)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the f distribution (fdistribution_cdf_c).
double	gamma_quantile_c (double z, double alpha, double theta)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the gamma distribution (gamma_cdf_c).
double	gamma_quantile (double z, double alpha, double theta)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the gamma distribution (gamma_cdf).
double	gaussian_quantile_c (double z, double sigma)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the normal (Gaussian) distribution (gaussian_cdf_c).
double	gaussian_quantile (double z, double sigma)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the normal (Gaussian) distribution (gaussian_cdf).
double	lognormal_quantile_c (double x, double m, double s)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the lognormal distribution (lognormal_cdf_c).
double	lognormal_quantile (double x, double m, double s)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the lognormal distribution (lognormal_cdf).
double	normal_quantile_c (double z, double sigma)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the normal (Gaussian) distribution (normal_cdf_c).
double	normal_quantile (double z, double sigma)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the normal (Gaussian) distribution (normal_cdf).
double	uniform_quantile_c (double z, double a, double b)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the uniform (flat) distribution (uniform_cdf_c).
double	uniform_quantile (double z, double a, double b)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the uniform (flat) distribution (uniform_cdf).
double	landau_quantile (double z, double xi=1)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of the Landau distribution (landau_cdf).
double	landau_quantile_c (double z, double xi=1)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of the landau distribution (landau_cdf_c).
Special Functions from MathCore
double	erf (double x)
	Error function encountered in integrating the normal distribution.
double	erfc (double x)
	Complementary error function.
double	tgamma (double x)
	The gamma function is defined to be the extension of the factorial to real numbers.
double	lgamma (double x)
	Calculates the logarithm of the gamma function.
double	inc_gamma (double a, double x)
	Calculates the normalized (regularized) lower incomplete gamma function (lower integral).
double	inc_gamma_c (double a, double x)
	Calculates the normalized (regularized) upper incomplete gamma function (upper integral).
double	beta (double x, double y)
	Calculates the beta function.
double	inc_beta (double x, double a, double b)
	Calculates the normalized (regularized) incomplete beta function.
double	sinint (double x)
	Calculates the sine integral.
double	cosint (double x)
	Calculates the real part of the cosine integral (Ci).
Quantile Functions from MathMore
The implementation used is that of GSL.
double	tdistribution_quantile_c (double z, double r)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the upper tail of Student's t-distribution (tdistribution_cdf_c).
double	tdistribution_quantile (double z, double r)
	Inverse ( $D^{-1}(z)$ ) of the cumulative distribution function of the lower tail of Student's t-distribution (tdistribution_cdf).
Special Functions from MathMore
double	assoc_laguerre (unsigned n, double m, double x)
	Computes the generalized Laguerre polynomials for $n \geq 0, m > -1$ .
double	assoc_legendre (unsigned l, unsigned m, double x)
	Computes the associated Legendre polynomials.
double	comp_ellint_1 (double k)
	Calculates the complete elliptic integral of the first kind.
double	comp_ellint_2 (double k)
	Calculates the complete elliptic integral of the second kind.
double	comp_ellint_3 (double n, double k)
	Calculates the complete elliptic integral of the third kind.
double	conf_hyperg (double a, double b, double z)
	Calculates the confluent hypergeometric functions of the first kind.
double	conf_hypergU (double a, double b, double z)
	Calculates the confluent hypergeometric functions of the second kind, known also as Kummer function of the second kind, it is related to the confluent hypergeometric functions of the first kind.
double	cyl_bessel_i (double nu, double x)
	Calculates the modified Bessel function of the first kind (also called regular modified (cylindrical) Bessel function).
double	cyl_bessel_j (double nu, double x)
	Calculates the (cylindrical) Bessel functions of the first kind (also called regular (cylindrical) Bessel functions).
double	cyl_bessel_k (double nu, double x)
	Calculates the modified Bessel functions of the second kind (also called irregular modified (cylindrical) Bessel functions).
double	cyl_neumann (double nu, double x)
	Calculates the (cylindrical) Bessel functions of the second kind (also called irregular (cylindrical) Bessel functions or (cylindrical) Neumann functions).
double	ellint_1 (double k, double phi)
	Calculates the incomplete elliptic integral of the first kind.
double	ellint_2 (double k, double phi)
	Calculates the complete elliptic integral of the second kind.
double	ellint_3 (double n, double k, double phi)
	Calculates the complete elliptic integral of the third kind.
double	expint (double x)
	Calculates the exponential integral.
double	hyperg (double a, double b, double c, double x)
	Calculates Gauss' hypergeometric function.
double	laguerre (unsigned n, double x)
	Calculates the Laguerre polynomials.
double	legendre (unsigned l, double x)
	Calculates the Legendre polynomials.
double	riemann_zeta (double x)
	Calculates the Riemann zeta function.
double	sph_bessel (unsigned n, double x)
	Calculates the spherical Bessel functions of the first kind (also called regular spherical Bessel functions).
double	sph_legendre (unsigned l, unsigned m, double theta)
	Computes the spherical (normalized) associated Legendre polynomials, or spherical harmonic without azimuthal dependence ( $e^(im\phi)$ ).
double	sph_neumann (unsigned n, double x)
	Calculates the spherical Bessel functions of the second kind (also called irregular spherical Bessel functions or spherical Neumann functions).
double	airy_Ai (double x)
	Calculates the Airy function Ai.
double	airy_Bi (double x)
	Calculates the Airy function Bi.
double	airy_Ai_deriv (double x)
	Calculates the derivative of the Airy function Ai.
double	airy_Bi_deriv (double x)
	Calculates the derivative of the Airy function Bi.
double	airy_zero_Ai (unsigned int s)
	Calculates the zeroes of the Airy function Ai.
double	airy_zero_Bi (unsigned int s)
	Calculates the zeroes of the Airy function Bi.
double	airy_zero_Ai_deriv (unsigned int s)
	Calculates the zeroes of the derivative of the Airy function Ai.
double	airy_zero_Bi_deriv (unsigned int s)
	Calculates the zeroes of the derivative of the Airy function Bi.
double	wigner_3j (int ja, int jb, int jc, int ma, int mb, int mc)
	Calculates the Wigner 3j coupling coefficients.
double	wigner_6j (int ja, int jb, int jc, int jd, int je, int jf)
	Calculates the Wigner 6j coupling coefficients.
double	wigner_9j (int ja, int jb, int jc, int jd, int je, int jf, int jg, int jh, int ji)
	Calculates the Wigner 9j coupling coefficients.
Variables
double	kPi = 3.14159265358979323846
double	kEulerGamma = 0.577215664901532860606512090082402431042

Typedef Documentation

typedef BasicFitMethodFunction<ROOT::Math::IMultiGenFunction> ROOT::Math::FitMethodFunction

Definition at line 113 of file FitMethodFunction.h.

typedef BasicFitMethodFunction<ROOT::Math::IMultiGradFunction> ROOT::Math::FitMethodGradFunction

Definition at line 114 of file FitMethodFunction.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 GSLRngRanLuxS1 ROOT::Math::GSLRngRanLux1

Definition at line 300 of file GSLRndmEngines.h.

typedef GSLRngRanLuxS2 ROOT::Math::GSLRngRanLux2

Definition at line 314 of file GSLRndmEngines.h.

typedef GSLRngRanLuxD2 ROOT::Math::GSLRngRanLux48

Definition at line 341 of file GSLRndmEngines.h.

typedef IBaseFunctionOneDim ROOT::Math::IGenFunction

Definition at line 43 of file IFunctionfwd.h.

typedef IGradientFunctionOneDim ROOT::Math::IGradFunction

Definition at line 49 of file IFunctionfwd.h.

typedef IBaseFunctionMultiDim ROOT::Math::IMultiGenFunction

Definition at line 47 of file IFunctionfwd.h.

typedef IGradientFunctionMultiDim ROOT::Math::IMultiGradFunction

Definition at line 50 of file IFunctionfwd.h.

typedef IntegratorOneDim ROOT::Math::Integrator

Definition at line 462 of file Integrator.h.

typedef IParametricFunctionOneDim ROOT::Math::IParamFunction

Definition at line 41 of file IParamFunctionfwd.h.

typedef IParametricGradFunctionOneDim ROOT::Math::IParamGradFunction

Definition at line 46 of file IParamFunctionfwd.h.

typedef IParametricFunctionMultiDim ROOT::Math::IParamMultiFunction

Definition at line 44 of file IParamFunctionfwd.h.

typedef IParametricGradFunctionMultiDim ROOT::Math::IParamMultiGradFunction

Definition at line 47 of file IParamFunctionfwd.h.

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

Definition at line 24 of file GenAlgoOptions.cxx.

typedef PositionVector2D< Polar2D<double>, DefaultCoordinateSystemTag > ROOT::Math::Polar2DPoint

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

Definition at line 47 of file Point2Dfwd.h.

typedef Polar2DPoint ROOT::Math::Polar2DPointD

Definition at line 48 of file Point2Dfwd.h.

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

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

Definition at line 53 of file Point2Dfwd.h.

typedef DisplacementVector2D< Polar2D<double>, DefaultCoordinateSystemTag > ROOT::Math::Polar2DVector

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

Definition at line 49 of file Vector2Dfwd.h.

typedef Polar2DVector ROOT::Math::Polar2DVectorD

Definition at line 50 of file Vector2Dfwd.h.

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

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

Definition at line 55 of file Vector2Dfwd.h.

typedef PositionVector3D< Polar3D<double>, DefaultCoordinateSystemTag > ROOT::Math::Polar3DPoint

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

Definition at line 59 of file Point3Dfwd.h.

typedef Polar3DPoint ROOT::Math::Polar3DPointD

Definition at line 64 of file Point3Dfwd.h.

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

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

Definition at line 63 of file Point3Dfwd.h.

typedef DisplacementVector3D< Polar3D<double>, DefaultCoordinateSystemTag > ROOT::Math::Polar3DVector

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

Definition at line 60 of file Vector3Dfwd.h.

typedef Polar3DVector ROOT::Math::Polar3DVectorD

Definition at line 65 of file Vector3Dfwd.h.

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

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

Definition at line 64 of file Vector3Dfwd.h.

typedef LorentzVector<PtEtaPhiE4D<double> > ROOT::Math::PtEtaPhiEVector

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

Definition at line 61 of file Vector4Dfwd.h.

typedef LorentzVector<PtEtaPhiM4D<double> > ROOT::Math::PtEtaPhiMVector

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

Definition at line 66 of file Vector4Dfwd.h.

typedef LorentzVector<PxPyPzE4D<double> > ROOT::Math::PxPyPzEVector

Definition at line 44 of file Vector4Dfwd.h.

typedef LorentzVector<PxPyPzM4D<double> > ROOT::Math::PxPyPzMVector

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

Definition at line 56 of file Vector4Dfwd.h.

typedef PositionVector3D< CylindricalEta3D<double>, DefaultCoordinateSystemTag > ROOT::Math::RhoEtaPhiPoint

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

Definition at line 49 of file Point3Dfwd.h.

typedef RhoEtaPhiPoint ROOT::Math::RhoEtaPhiPointD

Definition at line 54 of file Point3Dfwd.h.

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

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

Definition at line 53 of file Point3Dfwd.h.

typedef DisplacementVector3D< CylindricalEta3D<double>, DefaultCoordinateSystemTag > ROOT::Math::RhoEtaPhiVector

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

Definition at line 50 of file Vector3Dfwd.h.

typedef RhoEtaPhiVector ROOT::Math::RhoEtaPhiVectorD

Definition at line 55 of file Vector3Dfwd.h.

typedef DisplacementVector3D< CylindricalEta3D<float>, DefaultCoordinateSystemTag > ROOT::Math::RhoEtaPhiVectorF

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

Definition at line 54 of file Vector3Dfwd.h.

typedef PositionVector3D< Cylindrical3D<double>, DefaultCoordinateSystemTag > ROOT::Math::RhoZPhiPoint

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

Definition at line 69 of file Point3Dfwd.h.

typedef RhoZPhiPoint ROOT::Math::RhoZPhiPointD

Definition at line 74 of file Point3Dfwd.h.

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

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

Definition at line 73 of file Point3Dfwd.h.

typedef DisplacementVector3D< Cylindrical3D<double>, DefaultCoordinateSystemTag > ROOT::Math::RhoZPhiVector

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

Definition at line 70 of file Vector3Dfwd.h.

typedef RhoZPhiVector ROOT::Math::RhoZPhiVectorD

Definition at line 75 of file Vector3Dfwd.h.

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

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

Definition at line 74 of file Vector3Dfwd.h.

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

Definition at line 29 of file Plane3D.cxx.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

typedef PositionVector2D< Cartesian2D<double>, DefaultCoordinateSystemTag > ROOT::Math::XYPoint

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

Definition at line 30 of file Point2Dfwd.h.

typedef XYPoint ROOT::Math::XYPointD

Definition at line 36 of file Point2Dfwd.h.

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

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

Definition at line 41 of file Point2Dfwd.h.

typedef DisplacementVector2D< Cartesian2D<double>, DefaultCoordinateSystemTag > ROOT::Math::XYVector

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

Definition at line 31 of file Vector2Dfwd.h.

typedef XYVector ROOT::Math::XYVectorD

Definition at line 38 of file Vector2Dfwd.h.

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

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

Definition at line 43 of file Vector2Dfwd.h.

typedef PositionVector3D< Cartesian3D< double > > ROOT::Math::XYZPoint

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

Definition at line 33 of file Point3Dfwd.h.

typedef XYZPoint ROOT::Math::XYZPointD

Definition at line 44 of file Point3Dfwd.h.

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

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

Definition at line 43 of file Point3Dfwd.h.

typedef LorentzVector<PxPyPzE4D<double> > ROOT::Math::XYZTVector

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

Definition at line 33 of file Vector4Dfwd.h.

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

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

Definition at line 50 of file Vector4Dfwd.h.

typedef Translation3D::Vector ROOT::Math::XYZVector

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

Definition at line 34 of file Vector3Dfwd.h.

typedef XYZVector ROOT::Math::XYZVectorD

Definition at line 45 of file Vector3Dfwd.h.

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

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

Definition at line 44 of file Vector3Dfwd.h.

Enumeration Type Documentation

enum ROOT::Math::EMinimVariableType

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

Enumerator:

kDefault
kFix
kBounds
kLowBound
kUpBound

Definition at line 30 of file MinimizerVariable.h.

enum ROOT::Math::ERotation3DMatrixIndex

Enumerator:

kXX
kXY
kXZ
kYX
kYY
kYZ
kZX
kZY
kZZ

Definition at line 64 of file AxisAngle.cxx.

Function Documentation

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.

References ROOT::Math::VecExpr< ExprType, T, D >::apply().

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.

References ROOT::Math::VecExpr< ExprType, T, D >::apply(), and ROOT::Math::SVector< T, D >::apply().

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.

References ROOT::Math::SVector< T, D >::apply(), and ROOT::Math::VecExpr< ExprType, T, D >::apply().

template<class Matrix , unsigned int n, unsigned int idim>

bool ROOT::Math::Dfactir	(	Matrix &	rhs,
		typename Matrix::value_type &	det,
		unsigned int *	ir
	)			`[inline]`

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
	)			`[inline]`

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.

References m.

template<class R >

RotationZYX::Scalar ROOT::Math::Distance	(	const RotationZYX &	r1,
		const R &	r2
	)			`[inline]`

Distance between two rotations.

Definition at line 337 of file GenVector/RotationZYX.h.

References ROOT::Math::gv_detail::dist().

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 GenVector/RotationZ.h.

References ROOT::Math::gv_detail::dist().

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 GenVector/RotationY.h.

References ROOT::Math::gv_detail::dist().

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 GenVector/RotationX.h.

References ROOT::Math::gv_detail::dist().

template<class R >

Rotation3D::Scalar ROOT::Math::Distance	(	const Rotation3D &	r1,
		const R &	r2
	)			`[inline]`

Distance between two rotations.

Definition at line 488 of file GenVector/Rotation3D.h.

References ROOT::Math::gv_detail::dist().

template<class R >

Quaternion::Scalar ROOT::Math::Distance	(	const Quaternion &	r1,
		const R &	r2
	)			`[inline]`

Distance between two rotations.

Definition at line 326 of file GenVector/Quaternion.h.

References ROOT::Math::gv_detail::dist().

template<class R >

EulerAngles::Scalar ROOT::Math::Distance	(	const EulerAngles &	r1,
		const R &	r2
	)			`[inline]`

Distance between two rotations.

Definition at line 354 of file GenVector/EulerAngles.h.

References ROOT::Math::gv_detail::dist().

template<class R >

AxisAngle::Scalar ROOT::Math::Distance	(	const AxisAngle &	r1,
		const R &	r2
	)			`[inline]`

Distance between two rotations.

Definition at line 318 of file GenVector/AxisAngle.h.

References ROOT::Math::gv_detail::dist().

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 932 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 920 of file BinaryOperators.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 908 of file BinaryOperators.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.

References ROOT::Math::meta_dot< I >::f().

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.

References ROOT::Math::meta_dot< I >::f().

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.

References ROOT::Math::meta_dot< I >::f().

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.

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.

References log().

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

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

Definition at line 74 of file Math.h.

References exp().

Referenced by exponential_cdf().

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 158 of file UnaryOperators.h.

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 129 of file UnaryOperators.h.

double ROOT::Math::gaussian_cdf	(	double	x,
		double	sigma = `1`,
		double	x0 = `0`
	)			`[inline]`

Alternative name for same function.

Definition at line 453 of file ProbFuncMathCore.h.

References normal_cdf().

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

Alternative name for same function.

Definition at line 431 of file ProbFuncMathCore.h.

References normal_cdf_c().

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 204 of file GenVectorIO.h.

References ROOT::Math::detail::bitforbit, and ROOT::Math::detail::ios_data().

template<class A , class T >

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

Definition at line 309 of file Functions.h.

References Lmag2(), and sqrt().

template<class A , class T >

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

Definition at line 285 of file Functions.h.

References ROOT::Math::VecExpr< ExprType, T, D >::apply(), and Square().

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 63 of file Math.h.

References log().

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 215 of file GenVectorIO.h.

References ROOT::Math::detail::bitforbit, and ROOT::Math::detail::ios_data().

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.

References Mag2(), and sqrt().

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.

References ROOT::Math::meta_mag< I >::f().

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 398 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 387 of file MatrixFunctions.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 376 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 260 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 250 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 240 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 230 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 220 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 210 of file MatrixFunctions.h.

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 200 of file MatrixFunctions.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 750 of file BinaryOperators.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 738 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 634 of file BinaryOperators.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 623 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 611 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 600 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 589 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 578 of file BinaryOperators.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 567 of file BinaryOperators.h.

XYZTVector ROOT::Math::operator*	(	double	a,
		XYZTVector	v
	)

Definition at line 46 of file VectorUtil_Cint.h.

XYZPoint ROOT::Math::operator*	(	double	a,
		XYZPoint	p
	)

Definition at line 42 of file VectorUtil_Cint.h.

XYZVector ROOT::Math::operator*	(	double	a,
		XYZVector	v
	)

Definition at line 37 of file VectorUtil_Cint.h.

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

Definition at line 843 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), ROOT::Math::Transform3D::Translation(), and ROOT::Math::Translation3D::Vect().

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

Definition at line 839 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), ROOT::Math::Transform3D::Translation(), and ROOT::Math::Translation3D::Vect().

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

Definition at line 835 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), ROOT::Math::Transform3D::Translation(), and ROOT::Math::Translation3D::Vect().

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

Definition at line 831 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), ROOT::Math::Transform3D::Translation(), and ROOT::Math::Translation3D::Vect().

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

Definition at line 827 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), ROOT::Math::Transform3D::Translation(), and ROOT::Math::Translation3D::Vect().

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

Definition at line 823 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), ROOT::Math::Transform3D::Translation(), and ROOT::Math::Translation3D::Vect().

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

Definition at line 819 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), ROOT::Math::Transform3D::Translation(), and ROOT::Math::Translation3D::Vect().

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 816 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), ROOT::Math::Transform3D::Translation(), and ROOT::Math::Translation3D::Vect().

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

Definition at line 806 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), and ROOT::Math::Transform3D::Translation().

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

Definition at line 803 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), and ROOT::Math::Transform3D::Translation().

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

Definition at line 800 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), and ROOT::Math::Transform3D::Translation().

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

Definition at line 797 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), and ROOT::Math::Transform3D::Translation().

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

Definition at line 794 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), and ROOT::Math::Transform3D::Translation().

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

Definition at line 791 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), and ROOT::Math::Transform3D::Translation().

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

Definition at line 788 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), and ROOT::Math::Transform3D::Translation().

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 785 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), and ROOT::Math::Transform3D::Translation().

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 774 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), ROOT::Math::Transform3D::Translation(), and ROOT::Math::Translation3D::Vect().

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 765 of file GenVector/Transform3D.h.

References ROOT::Math::Transform3D::Rotation(), ROOT::Math::Transform3D::Translation(), and ROOT::Math::Translation3D::Vect().

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

Definition at line 755 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 752 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 749 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 746 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 743 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 740 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 737 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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 734 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 723 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 719 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 715 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 711 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 707 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 703 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 699 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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 696 of file GenVector/Transform3D.h.

References ROOT::Math::Translation3D::Vect().

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

Definition at line 105 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*	(	RotationX const &	r1,
		RotationZYX const &	r2
	)

Multiplication of an axial rotation by an AxisAngle.

Definition at line 96 of file RotationZYX.cxx.

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

Definition at line 132 of file Rotation3DxAxial.cxx.

References ROOT::Math::RotationZ::CosAngle(), ROOT::Math::RotationY::CosAngle(), ROOT::Math::RotationZ::SinAngle(), and ROOT::Math::RotationY::SinAngle().

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

Definition at line 120 of file Rotation3DxAxial.cxx.

References ROOT::Math::RotationZ::CosAngle(), ROOT::Math::RotationX::CosAngle(), ROOT::Math::RotationZ::SinAngle(), and ROOT::Math::RotationX::SinAngle().

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

Definition at line 108 of file Rotation3DxAxial.cxx.

References ROOT::Math::RotationZ::CosAngle(), ROOT::Math::RotationY::CosAngle(), ROOT::Math::RotationZ::SinAngle(), and ROOT::Math::RotationY::SinAngle().

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

Definition at line 96 of file Rotation3DxAxial.cxx.

References ROOT::Math::RotationY::CosAngle(), ROOT::Math::RotationX::CosAngle(), ROOT::Math::RotationY::SinAngle(), and ROOT::Math::RotationX::SinAngle().

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

Definition at line 84 of file Rotation3DxAxial.cxx.

References ROOT::Math::RotationZ::CosAngle(), ROOT::Math::RotationX::CosAngle(), ROOT::Math::RotationZ::SinAngle(), and ROOT::Math::RotationX::SinAngle().

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.

References ROOT::Math::RotationY::CosAngle(), ROOT::Math::RotationX::CosAngle(), ROOT::Math::RotationY::SinAngle(), and ROOT::Math::RotationX::SinAngle().

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

Definition at line 63 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*	(	RotationX const &	r1,
		Rotation3D const &	r2
	)

Multiplication of an axial rotation by a Rotation3D.

Definition at line 51 of file Rotation3DxAxial.cxx.

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

Definition at line 73 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*	(	RotationX const &	r1,
		Quaternion const &	r2
	)

Multiplication of an axial rotation by an AxisAngle.

Definition at line 63 of file QuaternionXaxial.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 513 of file GenVector/PositionVector3D.h.

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 385 of file GenVector/PositionVector2D.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:

	a	scalar quantity of typpe a
	v	mathcore::LorentzVector based on any coordinate system

Returns:: a new mathcoreLorentzVector q = v * a same type as v

Definition at line 676 of file GenVector/LorentzVector.h.

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

Definition at line 122 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*	(	RotationX const &	r1,
		EulerAngles const &	r2
	)

Multiplication of an axial rotation by an AxisAngle.

Definition at line 113 of file EulerAngles.cxx.

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 607 of file GenVector/DisplacementVector3D.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 474 of file GenVector/DisplacementVector2D.h.

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

Definition at line 190 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*	(	RotationX const &	r1,
		AxisAngle const &	r2
	)

Multiplication of an axial rotation by an AxisAngle.

Definition at line 182 of file AxisAngleXother.cxx.

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 271 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 259 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 211 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 199 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 187 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 157 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 146 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 99 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 87 of file BinaryOperators.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 75 of file BinaryOperators.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 558 of file GenVector/PositionVector3D.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 545 of file GenVector/PositionVector3D.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 430 of file GenVector/PositionVector2D.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 417 of file GenVector/PositionVector2D.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 581 of file GenVector/DisplacementVector3D.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 446 of file GenVector/DisplacementVector2D.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 83 of file UnaryOperators.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 54 of file UnaryOperators.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 513 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 502 of file BinaryOperators.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 455 of file BinaryOperators.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 443 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 431 of file BinaryOperators.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 401 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 390 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 343 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 331 of file BinaryOperators.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 319 of file BinaryOperators.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 571 of file GenVector/PositionVector3D.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 530 of file GenVector/PositionVector3D.h.

References ROOT::Math::PositionVector3D< CoordSystem, Tag >::X(), ROOT::Math::PositionVector3D< CoordSystem, Tag >::Y(), and ROOT::Math::PositionVector3D< CoordSystem, Tag >::Z().

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 443 of file GenVector/PositionVector2D.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 402 of file GenVector/PositionVector2D.h.

References ROOT::Math::PositionVector2D< CoordSystem, Tag >::X(), and ROOT::Math::PositionVector2D< CoordSystem, Tag >::Y().

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 594 of file GenVector/DisplacementVector3D.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 459 of file GenVector/DisplacementVector2D.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 993 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 981 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 878 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 867 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 820 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 808 of file BinaryOperators.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 797 of file BinaryOperators.h.

template<class T , unsigned int D>

std::ostream& ROOT::Math::operator<<	(	std::ostream &	os,
		const ROOT::Math::SVector< T, D > &	rhs
	)			`[inline]`

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 716 of file SMatrix.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 206 of file Expression.h.

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 201 of file Expression.h.

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

Definition at line 50 of file Translation3D.cxx.

References ROOT::Math::Translation3D::GetComponents(), and m.

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.

References ROOT::Math::Transform3D::GetComponents(), and m.

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

Stream Output and Input.

Definition at line 151 of file RotationZYX.cxx.

References ROOT::Math::RotationZYX::Phi(), ROOT::Math::RotationZYX::Psi(), and ROOT::Math::RotationZYX::Theta().

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

Stream Output and Input.

Definition at line 243 of file GenVector/RotationZ.h.

References ROOT::Math::RotationZ::Angle().

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

Stream Output and Input.

Definition at line 243 of file GenVector/RotationY.h.

References ROOT::Math::RotationY::Angle().

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

Stream Output and Input.

Definition at line 243 of file GenVector/RotationX.h.

References ROOT::Math::RotationX::Angle().

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

Stream Output and Input.

Definition at line 137 of file Rotation3D.cxx.

References ROOT::Math::Rotation3D::GetComponents(), and m.

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

Stream Output and Input.

Definition at line 101 of file Quaternion.cxx.

References ROOT::Math::Quaternion::I(), ROOT::Math::Quaternion::J(), ROOT::Math::Quaternion::K(), and ROOT::Math::Quaternion::U().

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 583 of file GenVector/PositionVector3D.h.

References ROOT::Math::detail::bitforbit, ROOT::Math::detail::close, ROOT::Math::detail::get_manip(), ROOT::Math::detail::open, ROOT::Math::detail::sep, ROOT::Math::detail::set_manip(), and v.

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 455 of file GenVector/PositionVector2D.h.

References ROOT::Math::detail::bitforbit, ROOT::Math::detail::close, ROOT::Math::detail::get_manip(), ROOT::Math::detail::open, ROOT::Math::detail::sep, ROOT::Math::detail::set_manip(), and v.

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

Stream Output and Input.

Definition at line 94 of file Plane3D.cxx.

References ROOT::Math::Plane3D::HesseDistance(), and ROOT::Math::Plane3D::Normal().

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 688 of file GenVector/LorentzVector.h.

References ROOT::Math::detail::bitforbit, ROOT::Math::detail::close, ROOT::Math::detail::get_manip(), ROOT::Math::detail::open, ROOT::Math::detail::sep, and ROOT::Math::detail::set_manip().

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

Stream Output and Input.

Definition at line 219 of file LorentzRotation.cxx.

References ROOT::Math::LorentzRotation::GetComponents(), and m.

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

Stream Output and Input.

Definition at line 128 of file EulerAngles.cxx.

References ROOT::Math::EulerAngles::Phi(), ROOT::Math::EulerAngles::Psi(), and ROOT::Math::EulerAngles::Theta().

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 625 of file GenVector/DisplacementVector3D.h.

References ROOT::Math::detail::bitforbit, ROOT::Math::detail::close, ROOT::Math::detail::get_manip(), ROOT::Math::detail::open, ROOT::Math::detail::sep, ROOT::Math::detail::set_manip(), and v.

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 492 of file GenVector/DisplacementVector2D.h.

References ROOT::Math::detail::bitforbit, ROOT::Math::detail::close, ROOT::Math::detail::get_manip(), ROOT::Math::detail::open, ROOT::Math::detail::sep, ROOT::Math::detail::set_manip(), and v.

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

Stream Output and Input.

Definition at line 108 of file BoostZ.cxx.

References ROOT::Math::BoostZ::Beta(), and ROOT::Math::BoostZ::Gamma().

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

Stream Output and Input.

Definition at line 107 of file BoostY.cxx.

References ROOT::Math::BoostY::Beta(), and ROOT::Math::BoostY::Gamma().

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

Stream Output and Input.

Definition at line 108 of file BoostX.cxx.

References ROOT::Math::BoostX::Beta(), and ROOT::Math::BoostX::Gamma().

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

Stream Output and Input.

Definition at line 173 of file Boost.cxx.

References ROOT::Math::Boost::GetLorentzRotation(), and m.

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

Stream Output and Input.

Definition at line 91 of file AxisAngle.cxx.

References ROOT::Math::AxisAngle::Angle(), and ROOT::Math::AxisAngle::Axis().

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 614 of file GenVector/PositionVector3D.h.

References ROOT::Math::detail::bitforbit, ROOT::Math::detail::close, ROOT::Math::detail::get_manip(), ROOT::Math::detail::open, ROOT::Math::detail::require_delim(), ROOT::Math::detail::sep, ROOT::Math::detail::set_manip(), and ROOT::Math::PositionVector3D< CoordSystem, Tag >::SetCoordinates().

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 484 of file GenVector/PositionVector2D.h.

References ROOT::Math::detail::bitforbit, ROOT::Math::detail::close, ROOT::Math::detail::get_manip(), ROOT::Math::detail::open, ROOT::Math::detail::require_delim(), ROOT::Math::detail::sep, ROOT::Math::detail::set_manip(), and ROOT::Math::PositionVector2D< CoordSystem, Tag >::SetCoordinates().

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 717 of file GenVector/LorentzVector.h.

References ROOT::Math::detail::bitforbit, ROOT::Math::detail::close, ROOT::Math::detail::get_manip(), ROOT::Math::detail::open, ROOT::Math::detail::require_delim(), ROOT::Math::detail::sep, ROOT::Math::detail::set_manip(), and ROOT::Math::LorentzVector< CoordSystem >::SetCoordinates().

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 656 of file GenVector/DisplacementVector3D.h.

References ROOT::Math::detail::bitforbit, ROOT::Math::detail::close, ROOT::Math::detail::get_manip(), ROOT::Math::detail::open, ROOT::Math::detail::require_delim(), ROOT::Math::detail::sep, ROOT::Math::detail::set_manip(), and ROOT::Math::DisplacementVector3D< CoordSystem, Tag >::SetCoordinates().

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 521 of file GenVector/DisplacementVector2D.h.

References ROOT::Math::detail::bitforbit, ROOT::Math::detail::close, ROOT::Math::detail::get_manip(), ROOT::Math::detail::open, ROOT::Math::detail::require_delim(), ROOT::Math::detail::sep, ROOT::Math::detail::set_manip(), and ROOT::Math::DisplacementVector2D< CoordSystem, Tag >::SetCoordinates().

double ROOT::Math::Pi ( ) [inline]

Mathematical constants.

Definition at line 56 of file Math.h.

References M_PI.

Referenced by ROOT::Math::Cephes::gamma(), ROOT::Math::Cephes::lgam(), TRandom::Poisson(), and TRandom::PoissonD().

double ROOT::Math::Polynomial1eval	(	double	x,
		double *	a,
		unsigned int	N
	)

Definition at line 967 of file SpecFuncCephes.cxx.

Referenced by ROOT::Math::Cephes::erf(), ROOT::Math::Cephes::erfc(), ROOT::Math::Cephes::lgam(), and ROOT::Math::Cephes::ndtri().

double ROOT::Math::Polynomialeval	(	double	x,
		double *	a,
		unsigned int	N
	)

Definition at line 951 of file SpecFuncCephes.cxx.

Referenced by ROOT::Math::Cephes::erf(), ROOT::Math::Cephes::erfc(), ROOT::Math::Cephes::gamma(), ROOT::Math::Cephes::lgam(), and ROOT::Math::Cephes::ndtri().

void ROOT::Math::PrintAllDefault ( std::ostream & os )

Definition at line 68 of file GenAlgoOptions.cxx.

References ROOT::Math::IntegOptionsUtil::Print().

template<class char_t >

detail::manipulator<char_t> ROOT::Math::set_close ( char_t ch ) [inline]

Definition at line 194 of file GenVectorIO.h.

References ROOT::Math::detail::close.

template<class char_t >

detail::manipulator<char_t> ROOT::Math::set_open ( char_t ch ) [inline]

Definition at line 174 of file GenVectorIO.h.

References ROOT::Math::detail::open.

template<class char_t >

detail::manipulator<char_t> ROOT::Math::set_separator ( char_t ch ) [inline]

Definition at line 184 of file GenVectorIO.h.

References ROOT::Math::detail::sep.

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 729 of file MatrixFunctions.h.

References ROOT::Math::AssignSym::Evaluate(), and Transpose().

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 698 of file MatrixFunctions.h.

References Dot().

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 690 of file MatrixFunctions.h.

References Dot().

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 682 of file MatrixFunctions.h.

References Dot().

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 674 of file MatrixFunctions.h.

References Dot().

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 666 of file MatrixFunctions.h.

References Dot().

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 658 of file MatrixFunctions.h.

References Dot().

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 650 of file MatrixFunctions.h.

References Dot().

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 779 of file MatrixFunctions.h.

References ROOT::Math::AssignSym::Evaluate(), and Transpose().

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
	)			`[inline]`

same function as before but not overwriting the matrix and returning a copy of the vector (this is the slow version)

Definition at line 970 of file MatrixFunctions.h.

References SolveChol().

template<class T , unsigned int D>

bool ROOT::Math::SolveChol	(	SMatrix< T, D, D, MatRepSym< T, D > > &	mat,
		SVector< T, D > &	vec
	)			`[inline]`

Definition at line 962 of file MatrixFunctions.h.

References ROOT::Math::CholeskyDecomp< F, N >::Solve().

Referenced by SolveChol().

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 233 of file UnaryOperators.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 204 of file UnaryOperators.h.

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 308 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]

Definition at line 279 of file UnaryOperators.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 893 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 882 of file MatrixFunctions.h.

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 872 of file MatrixFunctions.h.

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

throw explicity GenVector exceptions

Definition at line 21 of file GenVector_exception.cxx.

Referenced by ROOT::Math::LorentzVector< CoordSystem >::Beta(), ROOT::Math::VectorUtil::boost(), ROOT::Math::VectorUtil::boostX(), ROOT::Math::VectorUtil::boostY(), ROOT::Math::VectorUtil::boostZ(), ROOT::Math::LorentzVector< CoordSystem >::Gamma(), ROOT::Math::PxPyPzE4D< ScalarType >::M(), ROOT::Math::PtEtaPhiE4D< ScalarType >::M(), ROOT::Math::PxPyPzM4D< ScalarType >::Mt(), ROOT::Math::PxPyPzE4D< ScalarType >::Mt(), ROOT::Math::PtEtaPhiM4D< ScalarType >::Mt(), ROOT::Math::PtEtaPhiE4D< ScalarType >::Mt(), ROOT::Math::PxPyPzM4D< ScalarType >::Negate(), ROOT::Math::PtEtaPhiM4D< ScalarType >::Negate(), ROOT::Math::LorentzRotation::Rectify(), ROOT::Math::BoostZ::Rectify(), ROOT::Math::BoostY::Rectify(), ROOT::Math::BoostX::Rectify(), ROOT::Math::Boost::Rectify(), ROOT::Math::BoostZ::SetComponents(), ROOT::Math::BoostY::SetComponents(), ROOT::Math::BoostX::SetComponents(), and ROOT::Math::Boost::SetComponents().

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 689 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 677 of file BinaryOperators.h.

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 665 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 528 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.

References Unit().

Variable Documentation

double ROOT::Math::kEulerGamma = 0.577215664901532860606512090082402431042

Definition at line 34 of file KelvinFunctions.cxx.

Referenced by ROOT::Math::KelvinFunctions::DKei(), ROOT::Math::KelvinFunctions::DKer(), ROOT::Math::KelvinFunctions::Kei(), and ROOT::Math::KelvinFunctions::Ker().

double ROOT::Math::kPi = 3.14159265358979323846

Definition at line 33 of file KelvinFunctions.cxx.

ROOT::Math Namespace Reference

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Typedef Documentation

Enumeration Type Documentation

Function Documentation

Variable Documentation