Static Public Member Functions
template<class Scalar, class ScalarArray1, class ScalarArray2>
static void	tabulateTriangle (const ScalarArray1 &z, const int n, ScalarArray2 &poly_val)
	Calculates triangular orthogonal expansions (e.g. Dubiner basis) at a range of input points.
template<class Scalar, class ScalarArray1, class ScalarArray2>
static void	tabulateTetrahedron (const ScalarArray1 &z, const int n, ScalarArray2 &poly_val)
	Calculates triangular orthogonal expansions (e.g. Dubiner basis) at a range of input points.

Static Private Member Functions
template<class Scalar>
static void	jrc (const Scalar &alpha, const Scalar &beta, const int &n, Scalar &an, Scalar &bn, Scalar &cn)
	computes Jacobi recurrence coefficients of order n with weights a,b so that P^{alpha,beta}_{n+1}(x) = (an x + bn) P^{alpha,beta}_n(x) - cn P^{alpha,beta}_{n-1}(x)
static int	idxtri (int p, int q)
	Given indices p,q, computes the linear index of the Dubiner polynomial D^{p,q}.
static int	idxtet (int p, int q, int r)
	Given indices p,q,r, computes the linear index of the tetrahedral polynomial D^{p,q,r}.

Detailed Description

Definition at line 80 of file Intrepid_OrthogonalBases.hpp.

Constructor & Destructor Documentation

◆ OrthogonalBases()

Intrepid::OrthogonalBases::OrthogonalBases ( )

inline

Definition at line 82 of file Intrepid_OrthogonalBases.hpp.

◆ ~OrthogonalBases()

Intrepid::OrthogonalBases::~OrthogonalBases ( )

inline

Definition at line 83 of file Intrepid_OrthogonalBases.hpp.

Member Function Documentation

◆ idxtet()

int Intrepid::OrthogonalBases::idxtet	(	int	p,
		int	q,
		int	r )

inlinestaticprivate

Given indices p,q,r, computes the linear index of the tetrahedral polynomial D^{p,q,r}.

Definition at line 139 of file Intrepid_OrthogonalBases.hpp.

Referenced by tabulateTetrahedron().

◆ idxtri()

int Intrepid::OrthogonalBases::idxtri	(	int	p,
		int	q )

inlinestaticprivate

Given indices p,q, computes the linear index of the Dubiner polynomial D^{p,q}.

Definition at line 132 of file Intrepid_OrthogonalBases.hpp.

Referenced by tabulateTriangle().

◆ jrc()

template<class Scalar>

void Intrepid::OrthogonalBases::jrc	(	const Scalar &	alpha,
		const Scalar &	beta,
		const int &	n,
		Scalar &	an,
		Scalar &	bn,
		Scalar &	cn )

staticprivate

computes Jacobi recurrence coefficients of order n with weights a,b so that P^{alpha,beta}_{n+1}(x) = (an x + bn) P^{alpha,beta}_n(x) - cn P^{alpha,beta}_{n-1}(x)

Definition at line 49 of file Intrepid_OrthogonalBasesDef.hpp.

Referenced by tabulateTetrahedron(), and tabulateTriangle().

◆ tabulateTetrahedron()

template<class Scalar, class ScalarArray1, class ScalarArray2>

void Intrepid::OrthogonalBases::tabulateTetrahedron	(	const ScalarArray1 &	z,
		const int	n,
		ScalarArray2 &	poly_val )

static

Calculates triangular orthogonal expansions (e.g. Dubiner basis) at a range of input points.

Parameters

np	[in] - number of input points
z	[in] - 2d array of points z(pt,3)
n	[in] - the maximum polynomial degree tabulated
poly_val	[out] - 2d array poly_val((n+1)(n+2)(n+3)/6,np)

The ScalarArray types must support (i,j) indexing and a dimension(i) operation.

Definition at line 142 of file Intrepid_OrthogonalBasesDef.hpp.

References idxtet(), and jrc().

Referenced by main().

◆ tabulateTriangle()