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Stokhos_LegendreBasisImp.hpp
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43
44template <typename ordinal_type, typename value_type>
46LegendreBasis(ordinal_type p, bool normalize, Stokhos::GrowthPolicy growth) :
47 RecurrenceBasis<ordinal_type, value_type>("Legendre", 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>
58LegendreBasis(ordinal_type p, const LegendreBasis& 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>& theAlpha,
80 Teuchos::Array<value_type>& theBeta,
81 Teuchos::Array<value_type>& theDelta,
82 Teuchos::Array<value_type>& theGamma) const
83{
84 // Legendre 3 term recurrence:
85 // P_0(x) = 1
86 // P_1(x) = x
87 // P_i(x) = (2*i-1)/i*x*P_{i-1}(x) - (i-1)/i*P_{i-2}(x), i=2,3,...
88 theAlpha[0] = 0.0;
89 theBeta[0] = 1.0;
90 theDelta[0] = 1.0;
91 theGamma[0] = 1.0;
92 for (ordinal_type i=1; i<n; i++) {
93 theAlpha[i] = 0.0;
94 //theBeta[i] = value_type(i*i) / value_type((2*i-1)*(2*i+1));
95 theBeta[i] = value_type(i) / value_type(i+1);
96 theDelta[i] = value_type(2*i+1) / value_type(i+1);
97 theGamma[i] = 1.0;
98 }
99
100 return false;
101}
102
103template <typename ordinal_type, typename value_type>
104Teuchos::RCP<Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> >
106cloneWithOrder(ordinal_type pp) const
107{
108 return
109 Teuchos::rcp(new Stokhos::LegendreBasis<ordinal_type,value_type>(pp,*this));
110}
Legendre polynomial basis.
LegendreBasis(ordinal_type p, bool normalize=false, GrowthPolicy growth=SLOW_GROWTH)
Constructor.
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.
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.