Polynomials1D is a container class. Its aim is to call the apropriate 1D polynomials class according to the given polynomial type. The following polynomial bases are implemented: Lagrange, Truncated Lagrange and Jacobi. Only one object of the available 1D polynomial basis is created for each instance of this class. More...

#include <Polynomials1D.h>

Collaboration diagram for Polynomials1D:

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List of all members.

Public Member Functions
	Polynomials1D ()
	Default constructor.
	Polynomials1D (PolynomialType_E PolynomialType, unsigned long Alpha, unsigned long Beta)
	Constructor with parameters.
	Polynomials1D (Polynomials1D &Instance)
	Copy-initializer constructor.
	~Polynomials1D ()
	Class destructor.
Polynomials1D &	operator= (Polynomials1D &Instance)
	Copies the contents of instance to the object.
void	SetPolynomials1DAttributes (PolynomialType_E PolynomialType, unsigned long Alpha, unsigned long Beta)
	Sets the attributes for Polynomial1D.
void	GetPolynomialValue (unsigned long PolyOrder, QuadCollocType_E QuadratureType, unsigned long Alpha, unsigned long Beta, double const CollocCoordinates, double const Coordinates, unsigned long NumCoordinates, double *Phi)
	Return the polynomial values on Coordinates.
void	Get1stDerivative (unsigned long PolyOrder, QuadCollocType_E QuadratureType, unsigned long Alpha, unsigned long Beta, double const CollocCoordinates, double const Coordinates, unsigned long NumCoordinates, double *dPhi)
	Return the polynomial first derivatives values on Coordinates.
void	Get2ndDerivative (unsigned long PolyOrder, QuadCollocType_E QuadratureType, unsigned long Alpha, unsigned long Beta, double const CollocCoordinates, double const Coordinates, unsigned long NumCoordinates, double *d2Phi)
	Return the polynomial second derivatives values on Coordinates.
Protected Attributes
PolynomialType_E	PolyType
	Polynomial type.
unsigned long	Alpha
	Orthogonal polynomial weight alpha.
unsigned long	Beta
	Orthogonal polynomial weight beta.
LagrangeJacobi1D	LagJacPoly
	Variable of the type LagrangeJacobi1D class.
Jacobi1D	JacPoly
	Variable of the type Jacobi1D class.
Hermite1D	HermPoly
	Variable of the type Hermite1D class.
StandardLagrange1D	StLagPoly
	Variable of the type StandardLagrange1D class.
TruncatedLagrange1D	TrLagPoly
	Variable of the type TruncatedLagrange1D class.
Lobatto1D	LobattoPoly
	Variable of the type Lobatto1D class.

Detailed Description

Polynomials1D is a container class. Its aim is to call the apropriate 1D polynomials class according to the given polynomial type. The following polynomial bases are implemented: Lagrange, Truncated Lagrange and Jacobi. Only one object of the available 1D polynomial basis is created for each instance of this class.

Author:: Fabiano Fernandes Bargos/Marco Lcio Bittencourt

Date:: March/17/2011

Constructor & Destructor Documentation

Polynomials1D::Polynomials1D	(	PolynomialType_E	PolynomialType,
		unsigned long	Alpha,
		unsigned long	Beta
	)

Constructor with parameters.

Parameters:

[in]	PolynomialType	- type of the 1D polynomial basis
[in]	Alpha,Beta,:	weights of the orthogonal polynomials.

Polynomials1D::Polynomials1D ( Polynomials1D & Instance )

Copy-initializer constructor.

Parameters:

[in] Instance - instance of the Polynomials1D class.

Member Function Documentation

void Polynomials1D::Get1stDerivative	(	unsigned long	PolyOrder,
		QuadCollocType_E	QuadratureType,
		unsigned long	Alpha,
		unsigned long	Beta,
		double *const	CollocCoordinates,
		double *const	Coordinates,
		unsigned long	NumCoordinates,
		double *	dPhi
	)

Return the polynomial first derivatives values on Coordinates.

Parameters:

[in]	PolyOrder	- polynomial order.
[in]	CollocationType	- Type of collocation quadrature. The following opitons are avaialble: 'GAUSS_JACOBI', 'GAUSS_LEGENDRE', 'GAUSS_RADAU_JACOBI', 'GAUSS_RADAU_LEGENDRE', 'GAUSS_LOBATTO_JACOBI', 'GAUSS_LOBATTO_LEGENDRE' and 'EQUALLY_SPACED'.
[in]	Alpha,Beta	- Weights of the Jacobi polynomials (integers and greater than -1).
[in]	CollocCoordinates	: Collocation points coordinates for nodal basis.
[in]	Coordinates	- Coordinates on which the polynomial first derivative values are calculated.
[in]	NumCoordinates	- number of coordinates where the polynomials are calculated for the Collocation points.
[out]	dPhi	: array with the polynomial first derivatives values for all coordinates.

void Polynomials1D::Get2ndDerivative	(	unsigned long	PolyOrder,
		QuadCollocType_E	QuadratureType,
		unsigned long	Alpha,
		unsigned long	Beta,
		double *const	CollocCoordinates,
		double *const	Coordinates,
		unsigned long	NumCoordinates,
		double *	d2Phi
	)

Return the polynomial second derivatives values on Coordinates.

Parameters:

[in]	PolyOrder	- polynomial order.
[in]	CollocationType	- Type of collocation quadrature. The following opitons are avaialble: 'GAUSS_JACOBI', 'GAUSS_LEGENDRE', 'GAUSS_RADAU_JACOBI', 'GAUSS_RADAU_LEGENDRE', 'GAUSS_LOBATTO_JACOBI', 'GAUSS_LOBATTO_LEGENDRE' and 'EQUALLY_SPACED'.
[in]	Alpha,Beta	- Weights of the Jacobi polynomials (integers and greater than -1).
[in]	CollocCoordinates	: Collocation points coordinates for nodal basis.
[in]	Coordinates	- Coordinates on which the polynomial second derivatives values are calculated.
[in]	NumCollocCoordinates	- number of coordinates where the polynomials are calculated..
[out]	d2Phi	: array with the polynomial second derivatives values for all coordinates.

void Polynomials1D::GetPolynomialValue	(	unsigned long	PolyOrder,
		QuadCollocType_E	QuadratureType,
		unsigned long	Alpha,
		unsigned long	Beta,
		double *const	CollocCoordinates,
		double *const	Coordinates,
		unsigned long	NumCoordinates,
		double *	Phi
	)

Return the polynomial values on Coordinates.

Parameters:

[in]	PolyOrder	- polynomial order.
[in]	CollocationType	- Type of collocation quadrature. The following opitons are avaialble: 'GAUSS_JACOBI', 'GAUSS_LEGENDRE', 'GAUSS_RADAU_JACOBI', 'GAUSS_RADAU_LEGENDRE', 'GAUSS_LOBATTO_JACOBI', 'GAUSS_LOBATTO_LEGENDRE' and 'EQUALLY_SPACED'.
[in]	Alpha,Beta	- Weights of the Jacobi polynomials (integers and greater than -1).
[in]	CollocCoordinates	: Collocation points coordinates for nodal basis.
[in]	Coordinates	- Coordinates on which the polynomial values are calculated.
[in]	NumCoordinates	- number of coordinates where the polynomials are calculated.
[out]	Phi	: array with the polynomial values for all coordinates.

Polynomials1D & Polynomials1D::operator= ( Polynomials1D & Instance )

Copies the contents of instance to the object.

Parameters:

[in] Instance - instance of the Polynomials1D class

Returns:: Instance of the Polynomials1D class

void Polynomials1D::SetPolynomials1DAttributes	(	PolynomialType_E	PolynomialType,
		unsigned long	Alpha,
		unsigned long	Beta
	)

Sets the attributes for Polynomial1D.

Parameters:

[in]	PolynomialType	- type of the 1D polynomial basis
[in]	Alpha,Beta,:	weights of the orthogonal polynomials.

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

include/interpolation/polynomials1d/Polynomials1D.h
src/interpolation/polynomials1d/Polynomials1D.cpp

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation