Intrepid
Intrepid::OrthogonalBases Class Reference

List of all members.

## 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.

## Member Function Documentation

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().

template<class Scalar , class ScalarArray1 , class ScalarArray2 >
 void Intrepid::OrthogonalBases::tabulateTriangle ( 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,2) n [in] - the maximum polynomial degree tabulated poly_val [out] - 2d array poly_val((n+1)(n+2)/2,np)
• The ScalarArray types must support (i,j) indexing and a dimension(i) operation.

Definition at line 65 of file Intrepid_OrthogonalBasesDef.hpp.

References idxtri(), and jrc().

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