Intrepid
Intrepid_OrthogonalBases.hpp
Go to the documentation of this file.
1// @HEADER
2// ************************************************************************
3//
4// Intrepid Package
5// Copyright (2007) Sandia Corporation
6//
7// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
8// license for use of this work by or on behalf of the U.S. Government.
9//
10// Redistribution and use in source and binary forms, with or without
11// modification, are permitted provided that the following conditions are
12// met:
13//
14// 1. Redistributions of source code must retain the above copyright
15// notice, this list of conditions and the following disclaimer.
16//
17// 2. Redistributions in binary form must reproduce the above copyright
18// notice, this list of conditions and the following disclaimer in the
19// documentation and/or other materials provided with the distribution.
20//
21// 3. Neither the name of the Corporation nor the names of the
22// contributors may be used to endorse or promote products derived from
23// this software without specific prior written permission.
24//
25// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
26// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
28// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
29// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
30// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
31// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
32// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
33// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
34// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
35// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
36//
37// Questions? Contact Pavel Bochev (pbboche@sandia.gov)
38// Denis Ridzal (dridzal@sandia.gov), or
39// Kara Peterson (kjpeter@sandia.gov)
40//
41// ************************************************************************
42// @HEADER
43
49#ifndef INTREPID_ORTHOGONALBASES_HPP
50#define INTREPID_ORTHGONALBASES_HPP
51
52#include "Intrepid_ConfigDefs.hpp"
53#include "Intrepid_Types.hpp"
54#include "Intrepid_Utils.hpp"
55#include "Teuchos_Array.hpp"
56#include "Teuchos_RCP.hpp"
57#include "Teuchos_BLAS.hpp"
58#include "Teuchos_oblackholestream.hpp"
59#include "Teuchos_Assert.hpp"
60
61namespace Intrepid {
62
81 public:
82 OrthogonalBases() {;}
84
97 template<class Scalar, class ScalarArray1, class ScalarArray2>
98 static void tabulateTriangle( const ScalarArray1& z ,
99 const int n ,
100 ScalarArray2 & poly_val );
101
114 template<class Scalar, class ScalarArray1, class ScalarArray2>
115 static void tabulateTetrahedron( const ScalarArray1& z ,
116 const int n ,
117 ScalarArray2 & poly_val );
118
119 private:
126 template<class Scalar>
127 static void jrc( const Scalar &alpha , const Scalar &beta , const int &n ,
128 Scalar &an , Scalar &bn, Scalar &cn );
129
132 static inline int idxtri(int p, int q)
133 {
134 return (p+q)*(p+q+1)/2+q;
135 }
136
139 static inline int idxtet(int p, int q, int r)
140 {
141 return (p+q+r)*(p+q+r+1)*(p+q+r+2)/6+(q+r)*(q+r+1)/2+r;
142 }
143
144
145 }; // class OrthogonalBases
146} // namespace Intrepid
147
148#include "Intrepid_OrthogonalBasesDef.hpp"
149
150#endif
151
152
153
154
155
156
Contains definitions of custom data types in Intrepid.
Intrepid utilities.
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.
static int idxtet(int p, int q, int r)
Given indices p,q,r, computes the linear index of the tetrahedral polynomial D^{p,...
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 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,...
static int idxtri(int p, int q)
Given indices p,q, computes the linear index of the Dubiner polynomial D^{p,q}.