Intrepid
Intrepid_OrthogonalBases.hpp
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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 
61 namespace Intrepid {
62 
81  public:
82  OrthogonalBases() {;}
83  ~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 
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}.
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...
Contains definitions of custom data types in Intrepid.
Intrepid utilities.
static int idxtri(int p, int q)
Given indices p,q, computes the linear index of the Dubiner polynomial D^{p,q}.
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,beta}_{n+1}(x) = (an x + bn) P^{alpha,beta}_n(x) - cn P^{alpha,beta}_{n-1}(x)