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Stokhos_TensorProductBasisImp.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_,
50 const ordering_type& coeff_compare) :
51 p(0),
52 d(bases_.size()),
53 sz(0),
54 bases(bases_),
55 sparse_tol(sparse_tol_),
56 max_orders(d),
57 basis_set(coeff_compare),
58 norms()
59{
60 // Resize bases for given index if necessary
61 if (index.dimension() > 0) {
62 for (ordinal_type i=0; i<d; i++) {
63 if (index[i] != bases[i]->order())
64 bases[i] = bases[i]->cloneWithOrder(index[i]);
65 }
66 }
67
68 // Compute largest order
69 for (ordinal_type i=0; i<d; i++) {
70 max_orders[i] = bases[i]->order();
71 if (max_orders[i] > p)
72 p = max_orders[i];
73 }
74
75 // Compute basis terms
76 MultiIndex<ordinal_type> orders(d);
77 for (ordinal_type i=0; i<d; ++i)
78 orders[i] = bases[i]->order();
79 TensorProductIndexSet<ordinal_type> index_set(orders);
80 ProductBasisUtils::buildProductBasis(index_set, basis_set, basis_map);
81 sz = basis_map.size();
82
83 // Compute norms
84 norms.resize(sz);
85 value_type nrm;
86 for (ordinal_type k=0; k<sz; k++) {
87 nrm = value_type(1.0);
88 for (ordinal_type i=0; i<d; i++)
89 nrm = nrm * bases[i]->norm_squared(basis_map[k][i]);
90 norms[k] = nrm;
91 }
92
93 // Create name
94 name = "Tensor product basis (";
95 for (ordinal_type i=0; i<d-1; i++)
96 name += bases[i]->getName() + ", ";
97 name += bases[d-1]->getName() + ")";
98
99 // Allocate array for basis evaluation
100 basis_eval_tmp.resize(d);
101 for (ordinal_type j=0; j<d; j++)
102 basis_eval_tmp[j].resize(max_orders[j]+1);
103}
104
105template <typename ordinal_type, typename value_type, typename ordering_type>
110
111template <typename ordinal_type, typename value_type, typename ordering_type>
112ordinal_type
118
119template <typename ordinal_type, typename value_type, typename ordering_type>
120ordinal_type
126
127template <typename ordinal_type, typename value_type, typename ordering_type>
128ordinal_type
134
135template <typename ordinal_type, typename value_type, typename ordering_type>
136const Teuchos::Array<value_type>&
142
143template <typename ordinal_type, typename value_type, typename ordering_type>
144const value_type&
146norm_squared(ordinal_type i) const
147{
148 return norms[i];
149}
150
151template <typename ordinal_type, typename value_type, typename ordering_type>
152Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> >
155{
156#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
157 TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total Triple-Product Tensor Fill Time");
158#endif
159
160 TensorProductPredicate<ordinal_type> predicate(max_orders);
161
162 return ProductBasisUtils::computeTripleProductTensor(
163 bases, basis_set, basis_map, predicate, predicate, sparse_tol);
164}
165
166template <typename ordinal_type, typename value_type, typename ordering_type>
167Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> >
170{
171#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
172 TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total Triple-Product Tensor Fill Time");
173#endif
174
175 TensorProductPredicate<ordinal_type> predicate(max_orders);
176 TotalOrderPredicate<ordinal_type> k_predicate(1, max_orders);
177
178 return ProductBasisUtils::computeTripleProductTensor(
179 bases, basis_set, basis_map, predicate, k_predicate, sparse_tol);
180}
181
182template <typename ordinal_type, typename value_type, typename ordering_type>
183value_type
185evaluateZero(ordinal_type i) const
186{
187 // z = psi_{i_1}(0) * ... * psi_{i_d}(0) where i_1,...,i_d are the basis
188 // terms for coefficient i
189 value_type z = value_type(1.0);
190 for (ordinal_type j=0; j<d; j++)
191 z = z * bases[j]->evaluate(value_type(0.0), basis_map[i][j]);
192
193 return z;
194}
195
196template <typename ordinal_type, typename value_type, typename ordering_type>
197void
199evaluateBases(const Teuchos::ArrayView<const value_type>& point,
200 Teuchos::Array<value_type>& basis_vals) const
201{
202 for (ordinal_type j=0; j<d; j++)
203 bases[j]->evaluateBases(point[j], basis_eval_tmp[j]);
204
205 // Only evaluate basis upto number of terms included in basis_pts
206 for (ordinal_type i=0; i<sz; i++) {
207 value_type t = value_type(1.0);
208 for (ordinal_type j=0; j<d; j++)
209 t *= basis_eval_tmp[j][basis_map[i][j]];
210 basis_vals[i] = t;
211 }
212}
213
214template <typename ordinal_type, typename value_type, typename ordering_type>
215void
217print(std::ostream& os) const
218{
219 os << "Tensor product basis of order " << p << ", dimension " << d
220 << ", and size " << sz << ". Component bases:\n";
221 for (ordinal_type i=0; i<d; i++)
222 os << *bases[i];
223 os << "Basis vector norms (squared):\n\t";
224 for (ordinal_type i=0; i<static_cast<ordinal_type>(norms.size()); i++)
225 os << norms[i] << " ";
226 os << "\n";
227}
228
229template <typename ordinal_type, typename value_type, typename ordering_type>
232term(ordinal_type i) const
233{
234 return basis_map[i];
235}
236
237template <typename ordinal_type, typename value_type, typename ordering_type>
238ordinal_type
240index(const MultiIndex<ordinal_type>& term) const
241{
242 typename coeff_set_type::const_iterator it = basis_set.find(term);
243 TEUCHOS_TEST_FOR_EXCEPTION(it == basis_set.end(), std::logic_error,
244 "Invalid term " << term);
245 return it->second;
246}
247
248template <typename ordinal_type, typename value_type, typename ordering_type>
249const std::string&
255
256template <typename ordinal_type, typename value_type, typename ordering_type>
257Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<ordinal_type, value_type> > >
263
264template <typename ordinal_type, typename value_type, typename ordering_type>
A multidimensional index.
ordinal_type dimension() const
Dimension.
virtual const std::string & getName() const
Return string name of basis.
virtual const MultiIndex< ordinal_type > & term(ordinal_type i) const
Get orders of each coordinate polynomial given an index i.
virtual ordinal_type size() const
Return total size of basis.
virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > computeLinearTripleProductTensor() const
Compute linear triple product tensor where k = 0,1,..,d.
virtual void evaluateBases(const Teuchos::ArrayView< const value_type > &point, Teuchos::Array< value_type > &basis_vals) const
Evaluate basis polynomials at given point point.
TensorProductBasis(const Teuchos::Array< Teuchos::RCP< const OneDOrthogPolyBasis< ordinal_type, value_type > > > &bases, const value_type &sparse_tol=1.0e-12, const MultiIndex< ordinal_type > &index=MultiIndex< ordinal_type >(), const coeff_compare_type &coeff_compare=coeff_compare_type())
Constructor.
virtual const Teuchos::Array< value_type > & norm_squared() const
Return array storing norm-squared of each basis polynomial.
virtual ordinal_type index(const MultiIndex< ordinal_type > &term) const
Get index of the multivariate polynomial given orders of each coordinate.
virtual value_type evaluateZero(ordinal_type i) const
Evaluate basis polynomial i at zero.
Teuchos::Array< Teuchos::RCP< const OneDOrthogPolyBasis< ordinal_type, value_type > > > getCoordinateBases() const
Return coordinate bases.
virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > computeTripleProductTensor() const
Compute triple product tensor.
ordinal_type order() const
Return order of basis.
ordinal_type dimension() const
Return dimension of basis.
virtual MultiIndex< ordinal_type > getMaxOrders() const
Return maximum order allowable for each coordinate basis.
virtual void print(std::ostream &os) const
Print basis to stream os.