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Stokhos_StieltjesBasis.hpp
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41 
42 #ifndef STOKHOS_STIELTJESBASIS_HPP
43 #define STOKHOS_STIELTJESBASIS_HPP
44 
45 #include "Teuchos_RCP.hpp"
46 #include "Teuchos_Array.hpp"
47 
49 #include "Stokhos_Quadrature.hpp"
50 
51 namespace Stokhos {
52 
57  template <typename ordinal_type, typename value_type, typename func_type>
58  class StieltjesBasis :
59  public RecurrenceBasis<ordinal_type, value_type> {
60  public:
61 
63 
74  const Teuchos::RCP<const func_type>& func,
75  const Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> >& quad,
77  bool normalize = false);
78 
81 
83 
84 
86  virtual void
87  getQuadPoints(ordinal_type quad_order,
88  Teuchos::Array<value_type>& points,
89  Teuchos::Array<value_type>& weights,
90  Teuchos::Array< Teuchos::Array<value_type> >& values) const;
91 
102  virtual Teuchos::RCP<OneDOrthogPolyBasis<ordinal_type,value_type> > cloneWithOrder(ordinal_type p) const;
103 
105 
106  protected:
107 
109 
110 
112  virtual bool
114  Teuchos::Array<value_type>& alpha,
115  Teuchos::Array<value_type>& beta,
116  Teuchos::Array<value_type>& delta,
117  Teuchos::Array<value_type>& gamma) const;
118 
120  virtual void setup();
121 
123 
125  void stieltjes(ordinal_type nstart,
126  ordinal_type nfinish,
127  const Teuchos::Array<value_type>& weights,
128  const Teuchos::Array<value_type>& points,
129  Teuchos::Array<value_type>& a,
130  Teuchos::Array<value_type>& b,
131  Teuchos::Array<value_type>& nrm,
132  Teuchos::Array< Teuchos::Array<value_type> >& phi_vals) const;
133 
139  ordinal_type k,
140  const Teuchos::Array<value_type>& a,
141  const Teuchos::Array<value_type>& b,
142  const Teuchos::Array<value_type>& weights,
143  const Teuchos::Array<value_type>& points,
144  Teuchos::Array< Teuchos::Array<value_type> >& phi_vals,
145  value_type& val1, value_type& val2) const;
146 
149  const Teuchos::Array<value_type>& a,
150  const Teuchos::Array<value_type>& b,
151  const Teuchos::Array<value_type>& points,
152  Teuchos::Array< Teuchos::Array<value_type> >& values) const;
153 
156 
157  private:
158 
159  // Prohibit copying
161 
162  // Prohibit Assignment
164 
165  protected:
166 
168  Teuchos::RCP<const func_type> func;
169 
171  Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> > quad;
172 
174  const Teuchos::Array<value_type>& pce_weights;
175 
177  const Teuchos::Array< Teuchos::Array<value_type> >& basis_values;
178 
180  mutable Teuchos::Array<value_type> func_vals;
181 
183  mutable Teuchos::Array< Teuchos::Array<value_type> > phi_vals;
184 
187 
188  }; // class StieltjesBasis
189 
190 } // Namespace Stokhos
191 
192 // Include template definitions
194 
195 #endif
Teuchos::Array< value_type > delta
Recurrence coefficients.
StieltjesBasis(ordinal_type p, const Teuchos::RCP< const func_type > &func, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad, bool use_pce_quad_points, bool normalize=false)
Constructor.
virtual void getQuadPoints(ordinal_type quad_order, Teuchos::Array< value_type > &points, Teuchos::Array< value_type > &weights, Teuchos::Array< Teuchos::Array< value_type > > &values) const
Get Gauss quadrature points, weights, and values of basis at points.
Implementation of OneDOrthogPolyBasis based on the general three-term recurrence relationship: for ...
StieltjesBasis & operator=(const StieltjesBasis &b)
const Teuchos::Array< Teuchos::Array< value_type > > & basis_values
Values of PCE basis functions at quadrature points.
Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > quad
Quadrature object.
const Teuchos::Array< value_type > & pce_weights
PCE quadrature weights.
Teuchos::RCP< const func_type > func
PC expansion.
Teuchos::Array< Teuchos::Array< value_type > > phi_vals
Values of generated polynomials at PCE quadrature points.
Teuchos::Array< value_type > beta
Recurrence coefficients.
Teuchos::Array< value_type > alpha
Recurrence coefficients.
Generates three-term recurrence using the Discretized Stieltjes procedure applied to a functional map...
virtual void setup()
Setup basis after computing recurrence coefficients.
Abstract base class for quadrature methods.
Teuchos::Array< value_type > func_vals
Values of func at quadrature points.
Top-level namespace for Stokhos classes and functions.
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.
void integrateBasisSquared(ordinal_type k, const Teuchos::Array< value_type > &a, const Teuchos::Array< value_type > &b, const Teuchos::Array< value_type > &weights, const Teuchos::Array< value_type > &points, Teuchos::Array< Teuchos::Array< value_type > > &phi_vals, value_type &val1, value_type &val2) const
Compute and .
ordinal_type p
Order of basis.
void stieltjes(ordinal_type nstart, ordinal_type nfinish, const Teuchos::Array< value_type > &weights, const Teuchos::Array< value_type > &points, Teuchos::Array< value_type > &a, Teuchos::Array< value_type > &b, Teuchos::Array< value_type > &nrm, Teuchos::Array< Teuchos::Array< value_type > > &phi_vals) const
Compute 3-term recurrence using Stieljtes procedure.
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.
Teuchos::Array< value_type > gamma
Recurrence coefficients.
void evaluateRecurrence(ordinal_type k, const Teuchos::Array< value_type > &a, const Teuchos::Array< value_type > &b, const Teuchos::Array< value_type > &points, Teuchos::Array< Teuchos::Array< value_type > > &values) const
Evaluate polynomials via 3-term recurrence.
bool use_pce_quad_points
Use underlying pce&#39;s quadrature data.