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Stokhos_TotalOrderBasisImp.hpp
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41#include "Teuchos_TimeMonitor.hpp"
42#include "Teuchos_TestForException.hpp"
43
44template <typename ordinal_type, typename value_type, typename ordering_type>
47 const Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type, value_type> > >& bases_,
48 const value_type& sparse_tol_,
49 const ordering_type& coeff_compare) :
50 p(0),
51 d(bases_.size()),
52 sz(0),
53 bases(bases_),
54 sparse_tol(sparse_tol_),
55 max_orders(d),
56 basis_set(coeff_compare),
57 norms()
58{
59
60 // Compute largest order
61 for (ordinal_type i=0; i<d; i++) {
62 max_orders[i] = bases[i]->order();
63 if (max_orders[i] > p)
64 p = max_orders[i];
65 }
66
67 // Compute basis terms
68 MultiIndex<ordinal_type> orders(d);
69 for (ordinal_type i=0; i<d; ++i)
70 orders[i] = bases[i]->order();
71 AnisotropicTotalOrderIndexSet<ordinal_type> index_set(p, orders);
72 ProductBasisUtils::buildProductBasis(index_set, basis_set, basis_map);
73 sz = basis_map.size();
74
75 // Compute norms
76 norms.resize(sz);
77 value_type nrm;
78 for (ordinal_type k=0; k<sz; k++) {
79 nrm = value_type(1.0);
80 for (ordinal_type i=0; i<d; i++)
81 nrm = nrm * bases[i]->norm_squared(basis_map[k][i]);
82 norms[k] = nrm;
83 }
84
85 // Create name
86 name = "Tensor product basis (";
87 for (ordinal_type i=0; i<d-1; i++)
88 name += bases[i]->getName() + ", ";
89 name += bases[d-1]->getName() + ")";
90
91 // Allocate array for basis evaluation
92 basis_eval_tmp.resize(d);
93 for (ordinal_type j=0; j<d; j++)
94 basis_eval_tmp[j].resize(max_orders[j]+1);
95}
96
97template <typename ordinal_type, typename value_type, typename ordering_type>
100{
101}
102
103template <typename ordinal_type, typename value_type, typename ordering_type>
104ordinal_type
106order() const
107{
108 return p;
109}
110
111template <typename ordinal_type, typename value_type, typename ordering_type>
112ordinal_type
114dimension() const
115{
116 return d;
117}
118
119template <typename ordinal_type, typename value_type, typename ordering_type>
120ordinal_type
122size() const
123{
124 return sz;
125}
126
127template <typename ordinal_type, typename value_type, typename ordering_type>
128const Teuchos::Array<value_type>&
130norm_squared() const
131{
132 return norms;
133}
134
135template <typename ordinal_type, typename value_type, typename ordering_type>
136const value_type&
138norm_squared(ordinal_type i) const
139{
140 return norms[i];
141}
142
143template <typename ordinal_type, typename value_type, typename ordering_type>
144Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> >
147{
148#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
149 TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total Triple-Product Tensor Fill Time");
150#endif
151
152 TotalOrderPredicate<ordinal_type> predicate(p, max_orders);
153
154 return ProductBasisUtils::computeTripleProductTensor(
155 bases, basis_set, basis_map, predicate, predicate, sparse_tol);
156}
157
158template <typename ordinal_type, typename value_type, typename ordering_type>
159Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> >
162{
163#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
164 TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total Triple-Product Tensor Fill Time");
165#endif
166
167 TotalOrderPredicate<ordinal_type> predicate(p, max_orders);
168 TotalOrderPredicate<ordinal_type> k_predicate(1, max_orders);
169
170 return ProductBasisUtils::computeTripleProductTensor(
171 bases, basis_set, basis_map, predicate, k_predicate, sparse_tol);
172}
173
174template <typename ordinal_type, typename value_type, typename ordering_type>
175value_type
177evaluateZero(ordinal_type i) const
178{
179 // z = psi_{i_1}(0) * ... * psi_{i_d}(0) where i_1,...,i_d are the basis
180 // terms for coefficient i
181 value_type z = value_type(1.0);
182 for (ordinal_type j=0; j<d; j++)
183 z = z * bases[j]->evaluate(value_type(0.0), basis_map[i][j]);
184
185 return z;
186}
187
188template <typename ordinal_type, typename value_type, typename ordering_type>
189void
191evaluateBases(const Teuchos::ArrayView<const value_type>& point,
192 Teuchos::Array<value_type>& basis_vals) const
193{
194 for (ordinal_type j=0; j<d; j++)
195 bases[j]->evaluateBases(point[j], basis_eval_tmp[j]);
196
197 // Only evaluate basis upto number of terms included in basis_pts
198 for (ordinal_type i=0; i<sz; i++) {
199 value_type t = value_type(1.0);
200 for (ordinal_type j=0; j<d; j++)
201 t *= basis_eval_tmp[j][basis_map[i][j]];
202 basis_vals[i] = t;
203 }
204}
205
206template <typename ordinal_type, typename value_type, typename ordering_type>
207void
209print(std::ostream& os) const
210{
211 os << "Tensor product basis of order " << p << ", dimension " << d
212 << ", and size " << sz << ". Component bases:\n";
213 for (ordinal_type i=0; i<d; i++)
214 os << *bases[i];
215 os << "Basis vector norms (squared):\n\t";
216 for (ordinal_type i=0; i<static_cast<ordinal_type>(norms.size()); i++)
217 os << norms[i] << " ";
218 os << "\n";
219}
220
221template <typename ordinal_type, typename value_type, typename ordering_type>
224term(ordinal_type i) const
225{
226 return basis_map[i];
227}
228
229template <typename ordinal_type, typename value_type, typename ordering_type>
230ordinal_type
232index(const MultiIndex<ordinal_type>& term) const
233{
234 typename coeff_set_type::const_iterator it = basis_set.find(term);
235 TEUCHOS_TEST_FOR_EXCEPTION(it == basis_set.end(), std::logic_error,
236 "Invalid term " << term);
237 return it->second;
238}
239
240template <typename ordinal_type, typename value_type, typename ordering_type>
241const std::string&
243getName() const
244{
245 return name;
246}
247
248template <typename ordinal_type, typename value_type, typename ordering_type>
249Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<ordinal_type, value_type> > >
251getCoordinateBases() const
252{
253 return bases;
254}
255
256template <typename ordinal_type, typename value_type, typename ordering_type>
259getMaxOrders() const
260{
261 return max_orders;
262}
A multidimensional index.
virtual ordinal_type index(const MultiIndex< ordinal_type > &term) const
Get index of the multivariate polynomial given orders of each coordinate.
virtual const Teuchos::Array< value_type > & norm_squared() const
Return array storing norm-squared of each basis polynomial.
ordinal_type dimension() const
Return dimension of basis.
Teuchos::Array< Teuchos::RCP< const OneDOrthogPolyBasis< ordinal_type, value_type > > > getCoordinateBases() const
Return coordinate bases.
virtual const MultiIndex< ordinal_type > & term(ordinal_type i) const
Get orders of each coordinate polynomial given an index i.
virtual value_type evaluateZero(ordinal_type i) const
Evaluate basis polynomial i at zero.
virtual void evaluateBases(const Teuchos::ArrayView< const value_type > &point, Teuchos::Array< value_type > &basis_vals) const
Evaluate basis polynomials at given point point.
virtual MultiIndex< ordinal_type > getMaxOrders() const
Return maximum order allowable for each coordinate basis.
TotalOrderBasis(const Teuchos::Array< Teuchos::RCP< const OneDOrthogPolyBasis< ordinal_type, value_type > > > &bases, const value_type &sparse_tol=1.0e-12, const coeff_compare_type &coeff_compare=coeff_compare_type())
Constructor.
virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > computeLinearTripleProductTensor() const
Compute linear triple product tensor where k = 0,1,..,d.
virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > computeTripleProductTensor() const
Compute triple product tensor.
virtual void print(std::ostream &os) const
Print basis to stream os.
ordinal_type order() const
Return order of basis.
virtual const std::string & getName() const
Return string name of basis.
virtual ordinal_type size() const
Return total size of basis.
Predicate functor for building sparse triple products based on total order.