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Stokhos_JacobiBasisImp.hpp
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1// $Id: Stokhos_JacobiBasisImp.hpp,v 1.1.1.1 2010/02/10 20:22:35 kevin Exp $
2// $Source: /usr/local/cvs/UQ/Ops/Stokhos_JacobiBasisImp.hpp,v $
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43
44template <typename ordinal_type, typename value_type>
46JacobiBasis(ordinal_type p,
47 value_type alphaIndex,
48 value_type betaIndex, bool normalize, Stokhos::GrowthPolicy growth) :
49 RecurrenceBasis<ordinal_type, value_type>("Jacobi", p, normalize, growth),
50 alphaIndex_(alphaIndex),
51 betaIndex_(betaIndex)
52{
53 this->setup();
54
55#ifdef HAVE_STOKHOS_DAKOTA
56 this->setSparseGridGrowthRule(webbur::level_to_order_linear_wn);
57#endif
58}
59
60template <typename ordinal_type, typename value_type>
62JacobiBasis(ordinal_type p, const JacobiBasis& basis) :
63 RecurrenceBasis<ordinal_type, value_type>(p, basis),
64 alphaIndex_(basis.alphaIndex_),
65 betaIndex_(basis.betaIndex_)
66{
67 // Compute coefficients in 3-term recurrsion
68 computeRecurrenceCoefficients(p+1, this->alpha, this->beta, this->delta,
69 this->gamma);
70
71 // Setup rest of recurrence basis
72 this->setup();
73}
74
75template <typename ordinal_type, typename value_type>
78{
79}
80
81template <typename ordinal_type, typename value_type>
82bool
85 Teuchos::Array<value_type>& alpha,
86 Teuchos::Array<value_type>& beta,
87 Teuchos::Array<value_type>& delta,
88 Teuchos::Array<value_type>& gamma) const
89{
90 value_type a = alphaIndex_;
91 value_type b = betaIndex_;
92
93 if (a==0.0 && b==0.0)
94 {
95 alpha[0] = 0.0;
96 beta[0] = 1.0;
97 delta[0] = 1.0;
98 gamma[0] = 1.0;
99 }
100 else
101 {
102 alpha[0] = getB(0)/getA(0);
103 beta[0] = 1.0;
104 delta[0] = getC(0)/getA(0);
105 gamma[0] = 1.0;
106 }
107 for (ordinal_type i=1; i<n; i++)
108 {
109 alpha[i] = getB(i)/getA(i);
110 beta[i] = getD(i)/getA(i);
111 delta[i] = getC(i)/getA(i);
112 gamma[i] = 1.0;
113 }
114
115 return false;
116}
117
118
119template <typename ordinal_type, typename value_type>
121{
122 return 2*(n+1)*(n+alphaIndex_+betaIndex_+1)*(2*n+alphaIndex_+betaIndex_);
123}
124
125template <typename ordinal_type, typename value_type>
127{
128 value_type a = alphaIndex_;
129 value_type b = betaIndex_;
130 return -(2*n+a+b+1)*(a*a-b*b);
131}
132
133template <typename ordinal_type, typename value_type>
135{
136 value_type a = alphaIndex_;
137 value_type b = betaIndex_;
138 return poch3(2*n+a+b);
139}
140
141template <typename ordinal_type, typename value_type>
143{
144 value_type a = alphaIndex_;
145 value_type b = betaIndex_;
146 return 2*(n+a)*(n+b)*(2*n + a + b + 2);
147}
148
149template <typename ordinal_type, typename value_type>
151{
152 return (m+2)*(m+1)*m;
153}
154
155template <typename ordinal_type, typename value_type>
156Teuchos::RCP<Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> >
158cloneWithOrder(ordinal_type p) const
159{
160 return
161 Teuchos::rcp(new Stokhos::JacobiBasis<ordinal_type,value_type>(p,*this));
162}
Jacobi polynomial basis.
value_type poch3(value_type x) const
virtual bool computeRecurrenceCoefficients(ordinal_type n, Teuchos::Array< value_type > &alpha, Teuchos::Array< value_type > &beta, Teuchos::Array< value_type > &delta, Teuchos::Array< value_type > &gamma) const
Compute recurrence coefficients.
value_type getC(int n) const
value_type getD(int n) const
value_type getA(int n) const
JacobiBasis(ordinal_type p, value_type alphaIndex, value_type betaIndex, bool normalize=false, GrowthPolicy growth=SLOW_GROWTH)
Constructor.
value_type getB(int n) const
virtual Teuchos::RCP< OneDOrthogPolyBasis< ordinal_type, value_type > > cloneWithOrder(ordinal_type p) const
Clone this object with the option of building a higher order basis.
Implementation of OneDOrthogPolyBasis based on the general three-term recurrence relationship:
Teuchos::Array< value_type > alpha
Recurrence coefficients.
Teuchos::Array< value_type > beta
Recurrence coefficients.
ordinal_type p
Order of basis.
Teuchos::Array< value_type > gamma
Recurrence coefficients.
Teuchos::Array< value_type > delta
Recurrence coefficients.
virtual void setSparseGridGrowthRule(LevelToOrderFnPtr ptr)
Set sparse grid rule.
virtual void setup()
Setup basis after computing recurrence coefficients.
GrowthPolicy
Enumerated type for determining Smolyak growth policies.