ThePEG::Math Namespace Reference

The Math namespace includes the declaration of some useful mathematical functions. More...

Namespaces
namespace	Functions
	This namespace introduces some useful function classes with known primitive and inverse primitive functions.

Classes
struct	MathType
	MathType is an empty non-polymorphic base class for all mathematical function types. More...
struct	Power
	Templated class for calculating integer powers. More...
struct	Power< 0, false >
	Struct for powers. More...
struct	Power< 0, true >
	Struct for powers. More...
struct	Power< N, false >
	Struct for powers. More...
struct	Power< N, true >
	Struct for powers. More...

Functions
double	exp1m (double x)
	Return \(1-e^x\), with highest possible precision for \(x\rightarrow 0\).
double	log1m (double)
	Return \(1\log(1-x)\), with highest possible precision for \(x\rightarrow 0\).
double	powi (double x, int p)
	Return x rased to the integer power p, using recursion.
double	pIntegrate (double p, double xl, double xu)
	Return the integral of \(x^p dx\) between xl and xu.
double	pIntegrate (int p, double xl, double xu)
	Return the integral of \(x^p dx\) between xl and xu.
double	pXIntegrate (double e, double xl, double dx)
	Return the integral of \(x^{e-1} dx\) between xl and xl+dx with highest possible precision for \(dx\rightarrow 0\) and/or \(e\rightarrow 0\).
double	pGenerate (double p, double xl, double xu, double rnd)
	Generate an x between xl and xu distributed as \(x^p\).
double	pGenerate (int p, double xl, double xu, double rnd)
	Generate an x between xl and xu distributed as \(x^p\).
double	pXGenerate (double e, double xl, double dx, double rnd)
	Generate an x between xl and xl + dx distributed as \(x^{e-1}\) with highest possible precision for \(dx\rightarrow 0\) and/or * \(e\rightarrow 0\).
template<typename FloatType >
double	relativeError (FloatType x, FloatType y)
	Returns (x - y)/(|x| + |y|).
template<typename T >
T	absmin (const T &x, const T &y)
	Return x if |x|<|y|, else return y.
template<typename T >
T	absmax (const T &x, const T &y)
	Return x if |x|>|y|, else return y.
template<typename T , typename U >
T	sign (T x, U y)
	Transfer the sign of the second argument to the first.
template<int N>
double	Pow (double x)
	Templated function to calculate integer powers known at compile-time.

Detailed Description

The Math namespace includes the declaration of some useful mathematical functions.

Function Documentation

absmax()

template<typename T >

T ThePEG::Math::absmax ( const T &  x, const T &  y  )

inline

Return x if |x|>|y|, else return y.

Definition at line 92 of file Maths.h.

absmin()

template<typename T >

T ThePEG::Math::absmin ( const T &  x, const T &  y  )

inline

Return x if |x|<|y|, else return y.

Definition at line 86 of file Maths.h.

pGenerate() [1/2]

double ThePEG::Math::pGenerate ( double  p, double  xl, double  xu, double  rnd  )

inline

Generate an x between xl and xu distributed as \(x^p\).

Definition at line 55 of file Maths.h.

pGenerate() [2/2]

double ThePEG::Math::pGenerate ( int  p, double  xl, double  xu, double  rnd  )

inline

Generate an x between xl and xu distributed as \(x^p\).

Definition at line 61 of file Maths.h.

References powi().

pIntegrate() [1/2]

double ThePEG::Math::pIntegrate ( double  p, double  xl, double  xu  )

inline

Return the integral of \(x^p dx\) between xl and xu.

Definition at line 38 of file Maths.h.

pIntegrate() [2/2]

double ThePEG::Math::pIntegrate ( int  p, double  xl, double  xu  )

inline

Return the integral of \(x^p dx\) between xl and xu.

Definition at line 43 of file Maths.h.

References powi().

Pow()

template<int N>

double ThePEG::Math::Pow ( double  x )

inline

Templated function to calculate integer powers known at compile-time.

Definition at line 152 of file Maths.h.

pXGenerate()

double ThePEG::Math::pXGenerate ( double  e, double  xl, double  dx, double  rnd  )

inline

Generate an x between xl and xl + dx distributed as \(x^{e-1}\) with highest possible precision for \(dx\rightarrow 0\) and/or * \(e\rightarrow 0\).

Parameters

e	the parameter defining the power in \(x^{e-1}\).
xl	the lower bound of the generation interval.
dx	the interval.
rnd	a flat random number in the interval ]0,1[.

Definition at line 73 of file Maths.h.

References exp1m(), and log1m().

pXIntegrate()

double ThePEG::Math::pXIntegrate ( double  e, double  xl, double  dx  )

inline

Return the integral of \(x^{e-1} dx\) between xl and xl+dx with highest possible precision for \(dx\rightarrow 0\) and/or \(e\rightarrow 0\).

Definition at line 50 of file Maths.h.

References exp1m(), and log1m().

relativeError()

template<typename FloatType >

double ThePEG::Math::relativeError ( FloatType  x, FloatType  y  )

inline

Returns (x - y)/(|x| + |y|).

Definition at line 80 of file Maths.h.

Referenced by ThePEG::Lorentz5Vector< Value >::energyError(), ThePEG::Lorentz5Vector< Value >::massError(), and ThePEG::Lorentz5Vector< Value >::rhoError().

sign()

template<typename T , typename U >

T ThePEG::Math::sign ( T  x, U  y  )

inline

Transfer the sign of the second argument to the first.

Returns

\(|x|\) if \(y>0\) otherwise return \(-|x|\).

Definition at line 100 of file Maths.h.