Class for evaluating the Bessel function of second kind. More...

#include <bessel.hh>

Inheritance diagram for concepts::BesselY< n >:

Collaboration diagram for concepts::BesselY< n >:

Public Types
typedef Realtype< Real >::type	G
typedef Real	value_type
Public Member Functions
	BesselY (const Real m=1.0, const Real r0=0.0)
	Constructor.
	BesselY (const Real m, const Real3d r0)
virtual BesselY< n > *	clone () const
	Virtual copy constructor.
Real	derivative (const Real3d &p)
Real	derivative (const Real p)
	Derivative of Bessel function.
Real	derivative (const Real2d &p)
virtual const Real &	dflt_value () const
	Gives default value.
virtual Real &	dflt_value ()
	Gives default value.
virtual Real	operator() (const ElementWithCell< G > &elm, const Real p, const Real t=0.0) const
virtual Real	operator() (const ElementWithCell< concepts::Realtype< Real >::type > &elm, const Real3d &p, const Real t=0.0) const =0
virtual Real	operator() (const Real2d &p, const Real t=0.0) const
	Application operator.
virtual Real	operator() (const ElementWithCell< concepts::Realtype< Real >::type > &elm, const Real2d &p, const Real t=0.0) const =0
virtual Real	operator() (const Real p, const Real t=0.0) const
	Bessel function.
virtual Real	operator() (const Real3d &p, const Real t=0.0) const
	Application operator.
virtual Real	operator() (const ElementWithCell< G > &elm, const Real3d &p, const Real t=0.0) const
virtual Real	operator() (const ElementWithCell< concepts::Realtype< Real >::type > &elm, const Real p, const Real t=0.0) const =0
	Evaluates the formula.
virtual Real	operator() (const ElementWithCell< G > &elm, const Real2d &p, const Real t=0.0) const

virtual Real	operator() (const Connector &cntr, const Real p, const Real t=0.0) const
	Convenience implementation, that by default ignores its elm param.
virtual Real	operator() (const Connector &cntr, const Real2d &p, const Real t=0.0) const
	Convenience implementation, that by default ignores its elm param.
virtual Real	operator() (const Connector &cntr, const Real3d &p, const Real t=0.0) const
	Convenience implementation, that by default ignores its elm param.
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Private Attributes
const Real	m_
	Factor.
const Real3d	r0_
	Center of the Bessel function.

Detailed Description

template<int n>
class concepts::BesselY< n >

Class for evaluating the Bessel function of second kind.

A center r0 and a shortening factor n can be given to evaluate

$Y_0(n(r-r_0))$

, where $r$ is the distance from the origin.

Author:: (C) Copr. 1988-92 Numerical Recipes Software. Abramowitz and Stegun. Handbook of Mathematical Functions.

Definition at line 135 of file bessel.hh.

Member Typedef Documentation

typedef Realtype<Real >::type concepts::Formula< Real >::G [inherited]

Reimplemented from concepts::PiecewiseFormulaBase< Real >.

Definition at line 35 of file formula.hh.

typedef Real concepts::Formula< Real >::value_type [inherited]

Reimplemented from concepts::ElementFormula< Real, concepts::Realtype< Real >::type >.

Definition at line 34 of file formula.hh.

Constructor & Destructor Documentation

template<int n>

concepts::BesselY< n >::BesselY	(	const Real	m = `1.0`,
		const Real	r0 = `0.0`
	)		`[inline]`

Constructor.

Definition at line 138 of file bessel.hh.

template<int n>

concepts::BesselY< n >::BesselY	(	const Real	m,
		const Real3d	r0
	)		`[inline]`

Definition at line 140 of file bessel.hh.

Member Function Documentation

template<int n>

virtual BesselY<n>* concepts::BesselY< n >::clone ( ) const [inline, virtual]

Virtual copy constructor.

Implements concepts::Formula< Real >.

Definition at line 151 of file bessel.hh.

template<int n>

Real concepts::BesselY< n >::derivative ( const Real2d & p )

Definition at line 185 of file bessel.hh.

Here is the call graph for this function:

template<int n>

Real concepts::BesselY< n >::derivative ( const Real p )

Derivative of Bessel function.

Definition at line 179 of file bessel.hh.

Here is the call graph for this function:

template<int n>

Real concepts::BesselY< n >::derivative ( const Real3d & p )

Definition at line 191 of file bessel.hh.

Here is the call graph for this function:

virtual const Real & concepts::PiecewiseFormulaBase< Real >::dflt_value ( ) const [inline, virtual, inherited]

Gives default value.

Definition at line 76 of file piecewiseFormula.hh.

virtual Real & concepts::PiecewiseFormulaBase< Real >::dflt_value ( ) [inline, virtual, inherited]

Gives default value.

Definition at line 78 of file piecewiseFormula.hh.

template<int n>

std::ostream & concepts::BesselY< n >::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::PiecewiseFormulaBase< Real >.

Definition at line 197 of file bessel.hh.

virtual Real concepts::PiecewiseFormulaBase< Real >::operator()	(	const ElementWithCell< G > &	elm,
		const Real2d &	p,
		const Real	t = `0.0`
	)		const `[inline, virtual, inherited]`

Definition at line 52 of file piecewiseFormula.hh.

virtual Real concepts::PiecewiseFormulaBase< Real >::operator()	(	const ElementWithCell< G > &	elm,
		const Real	p,
		const Real	t = `0.0`
	)		const `[inline, virtual, inherited]`

Definition at line 47 of file piecewiseFormula.hh.

virtual Real concepts::Formula< Real >::operator()	(	const Connector &	cntr,
		const Real3d &	p,
		const Real	t = `0.0`
	)		const `[inline, virtual, inherited]`

Convenience implementation, that by default ignores its elm param.

Implements concepts::PiecewiseFormulaBase< Real >.

Definition at line 57 of file formula.hh.

virtual Real concepts::Formula< Real >::operator()	(	const Connector &	cntr,
		const Real2d &	p,
		const Real	t = `0.0`
	)		const `[inline, virtual, inherited]`

Convenience implementation, that by default ignores its elm param.

Implements concepts::PiecewiseFormulaBase< Real >.

Definition at line 54 of file formula.hh.

virtual Real concepts::ElementFormula< Real , concepts::Realtype< Real >::type >::operator()	(	const ElementWithCell< concepts::Realtype< Real >::type > &	elm,
		const Real2d &	p,
		const Real	t = `0.0`
	)		const `[pure virtual, inherited]`

template<int n>

Real concepts::BesselY< n >::operator()	(	const Real2d &	p,
		const Real	t = `0.0`
	)		const `[virtual]`

Application operator.

Evaluates the formula.

Parameters:

p	Point in space
t	Point in time

Implements concepts::Formula< Real >.

Definition at line 169 of file bessel.hh.

Here is the call graph for this function:

virtual Real concepts::Formula< Real >::operator()	(	const Connector &	cntr,
		const Real	p,
		const Real	t = `0.0`
	)		const `[inline, virtual, inherited]`

Convenience implementation, that by default ignores its elm param.

Implements concepts::PiecewiseFormulaBase< Real >.

Definition at line 51 of file formula.hh.

template<int n>

Real concepts::BesselY< n >::operator()	(	const Real3d &	p,
		const Real	t = `0.0`
	)		const `[virtual]`

Application operator.

Evaluates the formula.

Parameters:

p	Point in space
t	Point in time

Implements concepts::Formula< Real >.

Definition at line 174 of file bessel.hh.

Here is the call graph for this function:

template<int n>

Real concepts::BesselY< n >::operator()	(	const Real	p,
		const Real	t = `0.0`
	)		const `[virtual]`

Bessel function.

Implements concepts::Formula< Real >.

Definition at line 164 of file bessel.hh.

Here is the call graph for this function:

virtual Real concepts::ElementFormula< Real , concepts::Realtype< Real >::type >::operator()	(	const ElementWithCell< concepts::Realtype< Real >::type > &	elm,
		const Real	p,
		const Real	t = `0.0`
	)		const `[pure virtual, inherited]`

Evaluates the formula.

Parameters:

elm	Element
p	Point in space in local element coordinates
t	Point in time

virtual Real concepts::ElementFormula< Real , concepts::Realtype< Real >::type >::operator()	(	const ElementWithCell< concepts::Realtype< Real >::type > &	elm,
		const Real3d &	p,
		const Real	t = `0.0`
	)		const `[pure virtual, inherited]`

virtual Real concepts::PiecewiseFormulaBase< Real >::operator()	(	const ElementWithCell< G > &	elm,
		const Real3d &	p,
		const Real	t = `0.0`
	)		const `[inline, virtual, inherited]`

Definition at line 58 of file piecewiseFormula.hh.

Member Data Documentation

template<int n>

const Real concepts::BesselY< n >::m_ [private]

Factor.

Definition at line 158 of file bessel.hh.

template<int n>

const Real3d concepts::BesselY< n >::r0_ [private]

Center of the Bessel function.

Definition at line 160 of file bessel.hh.

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

formula/bessel.hh

Public Types

Public Member Functions

Protected Member Functions

Private Attributes

Detailed Description

template<int n> class concepts::BesselY< n >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<int n>
class concepts::BesselY< n >