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Stokhos_HermiteBasisImp.hpp
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43
44template <typename ordinal_type, typename value_type>
46HermiteBasis(ordinal_type p, bool normalize, Stokhos::GrowthPolicy growth) :
47 RecurrenceBasis<ordinal_type,value_type>("Hermite", p, normalize, growth)
48{
49 this->setup();
50
51#ifdef HAVE_STOKHOS_DAKOTA
52 this->setSparseGridGrowthRule(webbur::level_to_order_linear_wn);
53#endif
54}
55
56template <typename ordinal_type, typename value_type>
58HermiteBasis(ordinal_type p, const HermiteBasis& basis) :
59 RecurrenceBasis<ordinal_type, value_type>(p, basis)
60{
61 // Compute coefficients in 3-term recurrsion
62 computeRecurrenceCoefficients(p+1, this->alpha, this->beta, this->delta,
63 this->gamma);
64
65 // Setup rest of recurrence basis
66 this->setup();
67}
68
69template <typename ordinal_type, typename value_type>
74
75template <typename ordinal_type, typename value_type>
76bool
79 Teuchos::Array<value_type>& alpha,
80 Teuchos::Array<value_type>& beta,
81 Teuchos::Array<value_type>& delta,
82 Teuchos::Array<value_type>& gamma) const
83{
84 // Hermite 3 term recurrence:
85 // He_0(x) = 1
86 // He_1(x) = x
87 // He_i(x) = x*He_{i-1}(x) - (i-1)*He_{i-2}(x), i=2,3,...
88 alpha[0] = 0.0;
89 beta[0] = 1.0;
90 delta[0] = 1.0;
91 gamma[0] = 1.0;
92 for (ordinal_type i=1; i<n; i++) {
93 alpha[i] = 0.0;
94 beta[i] = value_type(i);
95 delta[i] = 1.0;
96 gamma[i] = 1.0;
97 }
98
99 return false;
100}
101
102template <typename ordinal_type, typename value_type>
103Teuchos::RCP<Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> >
Hermite polynomial basis.
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.
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.
HermiteBasis(ordinal_type p, bool normalize=false, GrowthPolicy growth=SLOW_GROWTH)
Constructor.
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.