This class provides method to work with Jacobi Polynomials relatively to an order of constraint q = myWorkDegree-2*(myNivConstr+1) Jk(t) for k=0,q compose the Jacobi Polynomial base relatively to the weight W(t) iorder is the integer value for the constraints: iorder = 0 <=> ConstraintOrder = GeomAbs_C0 iorder = 1 <=> ConstraintOrder = GeomAbs_C1 iorder = 2 <=> ConstraintOrder = GeomAbs_C2 P(t) = R(t) + W(t) * Q(t) Where W(t) = (1-t**2)**(2*iordre+2) the coefficients JacCoeff represents P(t) JacCoeff are stored as follow: More...

#include <PLib_JacobiPolynomial.hxx>

Public Member Functions
	PLib_JacobiPolynomial (const int theWorkDegree, const GeomAbs_Shape theConstraintOrder)
	Initialize the polynomial class Degree has to be <= 30 ConstraintOrder has to be GeomAbs_C0 GeomAbs_C1 GeomAbs_C2.

void	Points (const int theNbGaussPoints, NCollection_Array1< double > &theTabPoints) const
	returns the Jacobi Points for Gauss integration ie the positive values of the Legendre roots by increasing values NbGaussPoints is the number of points chosen for the integral computation. TabPoints (0,NbGaussPoints/2) TabPoints (0) is loaded only for the odd values of NbGaussPoints The possible values for NbGaussPoints are : 8, 10, 15, 20, 25, 30, 35, 40, 50, 61 NbGaussPoints must be greater than Degree

void	Weights (const int theNbGaussPoints, NCollection_Array2< double > &theTabWeights) const
	returns the Jacobi weights for Gauss integration only for the positive values of the Legendre roots in the order they are given by the method Points NbGaussPoints is the number of points chosen for the integral computation. TabWeights (0,NbGaussPoints/2,0,Degree) TabWeights (0,.) are only loaded for the odd values of NbGaussPoints The possible values for NbGaussPoints are: 8, 10, 15, 20, 25, 30, 35, 40, 50, 61 NbGaussPoints must be greater than Degree

void	MaxValue (NCollection_Array1< double > &theTabMax) const
	this method loads for k=0,q the maximum value of abs ( W(t)Jk(t) ) for t bellonging to [-1,1] This values are loaded is the array TabMax(0,myWorkDegree-2(myNivConst+1)) MaxValue ( me ; TabMaxPointer : in out Real );

double	MaxError (const int theDimension, double &theJacCoeff, const int theNewDegree) const
	This method computes the maximum error on the polynomial W(t) Q(t) obtained by missing the coefficients of JacCoeff from NewDegree +1 to Degree.

void	ReduceDegree (const int theDimension, const int theMaxDegree, const double theTol, double &theJacCoeff, int &theNewDegree, double &theMaxError) const
	Compute NewDegree <= MaxDegree so that MaxError is lower than Tol. MaxError can be greater than Tol if it is not possible to find a NewDegree <= MaxDegree. In this case NewDegree = MaxDegree.

double	AverageError (const int theDimension, double &theJacCoeff, const int theNewDegree) const

void	ToCoefficients (const int theDimension, const int theDegree, const NCollection_Array1< double > &theJacCoeff, NCollection_Array1< double > &theCoefficients) const
	Convert the polynomial P(t) = R(t) + W(t) Q(t) in the canonical base.

void	D0 (const double theU, NCollection_Array1< double > &theBasisValue) const
	Compute the values of the basis functions in u.

void	D1 (const double theU, NCollection_Array1< double > &theBasisValue, NCollection_Array1< double > &theBasisD1) const
	Compute the values and the derivatives values of the basis functions in u.

void	D2 (const double theU, NCollection_Array1< double > &theBasisValue, NCollection_Array1< double > &theBasisD1, NCollection_Array1< double > &theBasisD2) const
	Compute the values and the derivatives values of the basis functions in u.

void	D3 (const double theU, NCollection_Array1< double > &theBasisValue, NCollection_Array1< double > &theBasisD1, NCollection_Array1< double > &theBasisD2, NCollection_Array1< double > &theBasisD3) const
	Compute the values and the derivatives values of the basis functions in u.

int	WorkDegree () const noexcept
	returns WorkDegree

int	NivConstr () const noexcept
	returns NivConstr

Protected Member Functions
void	D0123 (const int theNDeriv, const double theU, NCollection_Array1< double > &theBasisValue, NCollection_Array1< double > &theBasisD1, NCollection_Array1< double > &theBasisD2, NCollection_Array1< double > &theBasisD3) const
	Compute the values and the derivatives values of the basis functions in u.

Detailed Description

This class provides method to work with Jacobi Polynomials relatively to an order of constraint q = myWorkDegree-2*(myNivConstr+1) Jk(t) for k=0,q compose the Jacobi Polynomial base relatively to the weight W(t) iorder is the integer value for the constraints: iorder = 0 <=> ConstraintOrder = GeomAbs_C0 iorder = 1 <=> ConstraintOrder = GeomAbs_C1 iorder = 2 <=> ConstraintOrder = GeomAbs_C2 P(t) = R(t) + W(t) * Q(t) Where W(t) = (1-t**2)**(2*iordre+2) the coefficients JacCoeff represents P(t) JacCoeff are stored as follow:

c0(1) c0(2) .... c0(Dimension) c1(1) c1(2) .... c1(Dimension)

cDegree(1) cDegree(2) .... cDegree(Dimension)

The coefficients c0(1) c0(2) .... c0(Dimension) c2*ordre+1(1) ... c2*ordre+1(dimension)

represents the part of the polynomial in the canonical base: R(t) R(t) = c0 + c1 t + ...+ c2*iordre+1 t**2*iordre+1 The following coefficients represents the part of the polynomial in the Jacobi base ie Q(t) Q(t) = c2*iordre+2 J0(t) + ...+ cDegree JDegree-2*iordre-2

Constructor & Destructor Documentation

◆ PLib_JacobiPolynomial()

PLib_JacobiPolynomial::PLib_JacobiPolynomial	(	const int	theWorkDegree,
		const GeomAbs_Shape	theConstraintOrder )

Initialize the polynomial class Degree has to be <= 30 ConstraintOrder has to be GeomAbs_C0 GeomAbs_C1 GeomAbs_C2.

Member Function Documentation

◆ AverageError()

double PLib_JacobiPolynomial::AverageError	(	const int	theDimension,
		double &	theJacCoeff,
		const int	theNewDegree ) const

◆ D0()

void PLib_JacobiPolynomial::D0	(	const double	theU,
		NCollection_Array1< double > &	theBasisValue ) const

Compute the values of the basis functions in u.

◆ D0123()

void PLib_JacobiPolynomial::D0123	(	const int	theNDeriv,
		const double	theU,
		NCollection_Array1< double > &	theBasisValue,
		NCollection_Array1< double > &	theBasisD1,
		NCollection_Array1< double > &	theBasisD2,
		NCollection_Array1< double > &	theBasisD3 ) const

protected

Compute the values and the derivatives values of the basis functions in u.

◆ D1()

void PLib_JacobiPolynomial::D1	(	const double	theU,
		NCollection_Array1< double > &	theBasisValue,
		NCollection_Array1< double > &	theBasisD1 ) const

Compute the values and the derivatives values of the basis functions in u.

◆ D2()

void PLib_JacobiPolynomial::D2	(	const double	theU,
		NCollection_Array1< double > &	theBasisValue,
		NCollection_Array1< double > &	theBasisD1,
		NCollection_Array1< double > &	theBasisD2 ) const

Compute the values and the derivatives values of the basis functions in u.

◆ D3()

void PLib_JacobiPolynomial::D3	(	const double	theU,
		NCollection_Array1< double > &	theBasisValue,
		NCollection_Array1< double > &	theBasisD1,
		NCollection_Array1< double > &	theBasisD2,
		NCollection_Array1< double > &	theBasisD3 ) const

Compute the values and the derivatives values of the basis functions in u.

◆ MaxError()

double PLib_JacobiPolynomial::MaxError	(	const int	theDimension,
		double &	theJacCoeff,
		const int	theNewDegree ) const

This method computes the maximum error on the polynomial W(t) Q(t) obtained by missing the coefficients of JacCoeff from NewDegree +1 to Degree.

◆ MaxValue()

void PLib_JacobiPolynomial::MaxValue ( NCollection_Array1< double > & theTabMax ) const

this method loads for k=0,q the maximum value of abs ( W(t)*Jk(t) ) for t bellonging to [-1,1] This values are loaded is the array TabMax(0,myWorkDegree-2*(myNivConst+1)) MaxValue ( me ; TabMaxPointer : in out Real );

◆ NivConstr()

int PLib_JacobiPolynomial::NivConstr ( ) const

inlinenoexcept

returns NivConstr

◆ Points()

void PLib_JacobiPolynomial::Points	(	const int	theNbGaussPoints,
		NCollection_Array1< double > &	theTabPoints ) const

returns the Jacobi Points for Gauss integration ie the positive values of the Legendre roots by increasing values NbGaussPoints is the number of points chosen for the integral computation. TabPoints (0,NbGaussPoints/2) TabPoints (0) is loaded only for the odd values of NbGaussPoints The possible values for NbGaussPoints are : 8, 10, 15, 20, 25, 30, 35, 40, 50, 61 NbGaussPoints must be greater than Degree

◆ ReduceDegree()

void PLib_JacobiPolynomial::ReduceDegree	(	const int	theDimension,
		const int	theMaxDegree,
		const double	theTol,
		double &	theJacCoeff,
		int &	theNewDegree,
		double &	theMaxError ) const

Compute NewDegree <= MaxDegree so that MaxError is lower than Tol. MaxError can be greater than Tol if it is not possible to find a NewDegree <= MaxDegree. In this case NewDegree = MaxDegree.

◆ ToCoefficients()

void PLib_JacobiPolynomial::ToCoefficients	(	const int	theDimension,
		const int	theDegree,
		const NCollection_Array1< double > &	theJacCoeff,
		NCollection_Array1< double > &	theCoefficients ) const

Convert the polynomial P(t) = R(t) + W(t) Q(t) in the canonical base.

◆ Weights()

void PLib_JacobiPolynomial::Weights	(	const int	theNbGaussPoints,
		NCollection_Array2< double > &	theTabWeights ) const

returns the Jacobi weights for Gauss integration only for the positive values of the Legendre roots in the order they are given by the method Points NbGaussPoints is the number of points chosen for the integral computation. TabWeights (0,NbGaussPoints/2,0,Degree) TabWeights (0,.) are only loaded for the odd values of NbGaussPoints The possible values for NbGaussPoints are: 8, 10, 15, 20, 25, 30, 35, 40, 50, 61 NbGaussPoints must be greater than Degree

◆ WorkDegree()

int PLib_JacobiPolynomial::WorkDegree ( ) const

inlinenoexcept

returns WorkDegree

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

PLib_JacobiPolynomial.hxx

Public Member Functions

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ PLib_JacobiPolynomial()

Member Function Documentation

◆ AverageError()

◆ D0()

◆ D0123()

◆ D1()

◆ D2()

◆ D3()

◆ MaxError()

◆ MaxValue()

◆ NivConstr()

◆ Points()

◆ ReduceDegree()

◆ ToCoefficients()

◆ Weights()

◆ WorkDegree()