Intrepid
Static Public Member Functions | Static Private Member Functions
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: