ThePEG::Math Namespace Reference

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

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 ThePEG::Math::Power< N, false >

Struct for powers. More...

struct ThePEG::Math::Power< N, true >

Struct for powers. More...

struct ThePEG::Math::Power< 0, true >

Struct for powers. More...

struct ThePEG::Math::Power< 0, false >

Struct for powers. More...

Namespaces

namespace Functions

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

Functions

double gamma (double)

The gamma function.

double lngamma (double)

The log of the gamma function.

double atanh (double)

Return ${\rm atanh}(x)$ .

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 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

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 101 of file Maths.h.

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 95 of file Maths.h.

double ThePEG::Math::exp1m ( double x )

Return $1-e^x$ , with highest possible precision for $x\rightarrow 0$ .

Referenced by ThePEG::PartonBinInstance::eps(), pXGenerate(), and pXIntegrate().

double ThePEG::Math::log1m ( double )

Return $1\log(1-x)$ , with highest possible precision for $x\rightarrow 0$ .

Referenced by pXGenerate(), and pXIntegrate().

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 70 of file Maths.h.

References powi().

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 64 of file Maths.h.

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 52 of file Maths.h.

References powi().

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 47 of file Maths.h.

template<int N>

double ThePEG::Math::Pow ( double x ) [inline]

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

Definition at line 161 of file Maths.h.

double ThePEG::Math::powi	(	double	x,
		int	p
	)

Return x rased to the integer power p, using recursion.

Referenced by pGenerate(), and pIntegrate().

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 82 of file Maths.h.

References exp1m(), and log1m().

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 59 of file Maths.h.

References exp1m(), and log1m().

template<typename FloatType>

double ThePEG::Math::relativeError	(	FloatType	x,
		FloatType	y
	)			`[inline]`

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

Definition at line 89 of file Maths.h.

Referenced by ThePEG::Lorentz5Vector< QTY< 0, 1, 0 >::Type >::energyError(), ThePEG::Lorentz5Vector< QTY< 0, 1, 0 >::Type >::massError(), and ThePEG::Lorentz5Vector< QTY< 0, 1, 0 >::Type >::rhoError().

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:: if otherwise return .

Definition at line 109 of file Maths.h.


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	ThePEG::Math::Power< N, false >
	Struct for powers. More...
struct	ThePEG::Math::Power< N, true >
	Struct for powers. More...
struct	ThePEG::Math::Power< 0, true >
	Struct for powers. More...
struct	ThePEG::Math::Power< 0, false >
	Struct for powers. More...
Namespaces
namespace	Functions
	This namespace introduces some useful function classes with known primitive and inverse primitive functions.
Functions
double	gamma (double)
	The gamma function.
double	lngamma (double)
	The log of the gamma function.
double	atanh (double)
	Return ${\rm atanh}(x)$ .
double	exp1m (double x)
	Return , 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 between xl and xu.
double	pIntegrate (int p, double xl, double xu)
	Return the integral of 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 .
double	pGenerate (int p, double xl, double xu, double rnd)
	Generate an x between xl and xu distributed as .
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.