ROOT::Math::ChebyshevApprox Class Reference

Class describing a Chebyshev series which can be used to approximate a function in a defined range [a,b] using Chebyshev polynomials.

It uses the algorithm from GSL

This class does not support copying

Definition at line 71 of file ChebyshevApprox.h.

Public Member Functions
	ChebyshevApprox (const ROOT::Math::IGenFunction &f, double a, double b, size_t n)
	Construct a Chebyshev series approximation to a Function f in range [a,b]; constructor based on functions of type IGenFunction.
	ChebyshevApprox (GSLFuncPointer f, void *p, double a, double b, size_t n)
	Construct a Chebyshev series approximation to a Function f in range [a,b]; constructor based on free functions with gsl_function type signature.
virtual	~ChebyshevApprox ()
ChebyshevApprox *	Deriv ()
	Compute the derivative of the series and return a pointer to a new Chebyshev series with the derivatives coefficients.
std::pair< double, double >	EvalErr (double x) const
	Evaluate the series at a given point x estimating both the series result and its absolute error.
std::pair< double, double >	EvalErr (double x, size_t n) const
	evaluate the series at a given point x to the given order n, estimating both the series result and its absolute error.
ChebyshevApprox *	Integral ()
	Compute the integral of the series and return a pointer to a new Chebyshev series with the integral coefficients.
double	operator() (double x) const
	Evaluate the series at a given point x.
double	operator() (double x, size_t n) const
	Evaluate the series at a given point, to (at most) the given order n.

Protected Member Functions
void	Initialize (GSLFuncPointer f, void *params, double a, double b)
	Initialize series passing function and range.

Private Member Functions
	ChebyshevApprox (const ChebyshevApprox &)
	ChebyshevApprox (size_t n)
	construct a Chebyshev series or order n The series must be initialized from a function
ChebyshevApprox &	operator= (const ChebyshevApprox &)

Private Attributes
GSLFunctionWrapper *	fFunction
size_t	fOrder
GSLChebSeries *	fSeries

#include <Math/ChebyshevApprox.h>

Constructor & Destructor Documentation

ChebyshevApprox() [1/4]

ROOT::Math::ChebyshevApprox::ChebyshevApprox	(	const ROOT::Math::IGenFunction &	f,
		double	a,
		double	b,
		size_t	n
	)

Construct a Chebyshev series approximation to a Function f in range [a,b]; constructor based on functions of type IGenFunction.

Definition at line 49 of file ChebyshevApprox.cxx.

ChebyshevApprox() [2/4]

ROOT::Math::ChebyshevApprox::ChebyshevApprox	(	GSLFuncPointer	f,
		void *	p,
		double	a,
		double	b,
		size_t	n
	)

Construct a Chebyshev series approximation to a Function f in range [a,b]; constructor based on free functions with gsl_function type signature.

Definition at line 60 of file ChebyshevApprox.cxx.

~ChebyshevApprox()

ROOT::Math::ChebyshevApprox::~ChebyshevApprox ( )

virtual

Definition at line 68 of file ChebyshevApprox.cxx.

ChebyshevApprox() [3/4]

ROOT::Math::ChebyshevApprox::ChebyshevApprox ( size_t  n )

private

construct a Chebyshev series or order n The series must be initialized from a function

Definition at line 75 of file ChebyshevApprox.cxx.

ChebyshevApprox() [4/4]

ROOT::Math::ChebyshevApprox::ChebyshevApprox ( const ChebyshevApprox &  )

private

Definition at line 82 of file ChebyshevApprox.cxx.

Member Function Documentation

Deriv()

ChebyshevApprox * ROOT::Math::ChebyshevApprox::Deriv

(

)

Compute the derivative of the series and return a pointer to a new Chebyshev series with the derivatives coefficients.

The returned pointer must be managed by the user.

Definition at line 133 of file ChebyshevApprox.cxx.

EvalErr() [1/2]

std::pair< double, double > ROOT::Math::ChebyshevApprox::EvalErr

(

double

x

)

const

Evaluate the series at a given point x estimating both the series result and its absolute error.

The error estimate is made from the first neglected term in the series. A pair containing result and error is returned

Definition at line 114 of file ChebyshevApprox.cxx.

EvalErr() [2/2]

std::pair< double, double > ROOT::Math::ChebyshevApprox::EvalErr	(	double	x,
		size_t	n
	)		const

evaluate the series at a given point x to the given order n, estimating both the series result and its absolute error.

The error estimate is made from the first neglected term in the series. A pair containing result and error is returned

Definition at line 126 of file ChebyshevApprox.cxx.

Initialize()

void ROOT::Math::ChebyshevApprox::Initialize ( GSLFuncPointer  f, void *  params, double  a, double  b  )

protected

Initialize series passing function and range.

Definition at line 95 of file ChebyshevApprox.cxx.

Integral()

ChebyshevApprox * ROOT::Math::ChebyshevApprox::Integral

(

)

Compute the integral of the series and return a pointer to a new Chebyshev series with the integral coefficients.

The lower limit of the integration is the left range value a. The returned pointer must be managed by the user

Definition at line 143 of file ChebyshevApprox.cxx.

operator()() [1/2]

double ROOT::Math::ChebyshevApprox::operator()

(

double

x

)

const

Evaluate the series at a given point x.

Definition at line 109 of file ChebyshevApprox.cxx.

operator()() [2/2]

double ROOT::Math::ChebyshevApprox::operator()	(	double	x,
		size_t	n
	)		const

Evaluate the series at a given point, to (at most) the given order n.

Definition at line 121 of file ChebyshevApprox.cxx.

operator=()

ChebyshevApprox & ROOT::Math::ChebyshevApprox::operator= ( const ChebyshevApprox &  rhs )

private

Definition at line 87 of file ChebyshevApprox.cxx.

Member Data Documentation

fFunction

GSLFunctionWrapper* ROOT::Math::ChebyshevApprox::fFunction

private

Definition at line 159 of file ChebyshevApprox.h.

fOrder

size_t ROOT::Math::ChebyshevApprox::fOrder

private

Definition at line 156 of file ChebyshevApprox.h.

fSeries

GSLChebSeries* ROOT::Math::ChebyshevApprox::fSeries

private

Definition at line 158 of file ChebyshevApprox.h.

Libraries for ROOT::Math::ChebyshevApprox:

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The documentation for this class was generated from the following files:

• math/mathmore/inc/Math/ChebyshevApprox.h
• math/mathmore/src/ChebyshevApprox.cxx