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Stokhos_TotalOrderBasis.hpp
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41
42#ifndef STOKHOS_TOTAL_ORDER_BASIS_HPP
43#define STOKHOS_TOTAL_ORDER_BASIS_HPP
44
45#include "Teuchos_RCP.hpp"
46
50
51namespace Stokhos {
52
65 template <typename ordinal_type, typename value_type,
66 typename coeff_compare_type =
67 TotalOrderLess<MultiIndex<ordinal_type> > >
69 public ProductBasis<ordinal_type,value_type> {
70 public:
71
73
79 const Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type,
80 value_type> > >& bases,
81 const value_type& sparse_tol = 1.0e-12,
82 const coeff_compare_type& coeff_compare = coeff_compare_type());
83
85 virtual ~TotalOrderBasis();
86
88
89
91 ordinal_type order() const;
92
94 ordinal_type dimension() const;
95
97 virtual ordinal_type size() const;
98
100
104 virtual const Teuchos::Array<value_type>& norm_squared() const;
105
107 virtual const value_type& norm_squared(ordinal_type i) const;
108
110
116 virtual
117 Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> >
119
121 virtual
122 Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> >
124
126 virtual value_type evaluateZero(ordinal_type i) const;
127
129
133 virtual void evaluateBases(
134 const Teuchos::ArrayView<const value_type>& point,
135 Teuchos::Array<value_type>& basis_vals) const;
136
138 virtual void print(std::ostream& os) const;
139
141 virtual const std::string& getName() const;
142
144
146
147
149
154 virtual const MultiIndex<ordinal_type>& term(ordinal_type i) const;
155
157
161 virtual ordinal_type index(const MultiIndex<ordinal_type>& term) const;
162
164
167 Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type,
168 value_type> > >
169 getCoordinateBases() const;
170
173
175
176 private:
177
178 // Prohibit copying
180
181 // Prohibit Assignment
183
184 protected:
185
187 typedef std::map<coeff_type,ordinal_type,coeff_compare_type> coeff_set_type;
188 typedef Teuchos::Array<coeff_type> coeff_map_type;
189
191 std::string name;
192
194 ordinal_type p;
195
197 ordinal_type d;
198
200 ordinal_type sz;
201
203 Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type, value_type> > > bases;
204
206 value_type sparse_tol;
207
210
213
216
218 Teuchos::Array<value_type> norms;
219
221 mutable Teuchos::Array< Teuchos::Array<value_type> > basis_eval_tmp;
222
223 }; // class TotalOrderBasis
224
225 // An approach for building a sparse 3-tensor only for lexicographically
226 // ordered total order basis
227 // To-do:
228 // * Remove the n_choose_k() calls
229 // * Remove the loops in the Cijk_1D_Iterator::increment() functions
230 // * Store the 1-D Cijk tensors in a compressed format and eliminate
231 // the implicit searches with getValue()
232 // * Instead of looping over (i,j,k) multi-indices we could just store
233 // the 1-D Cijk tensors as an array of (i,j,k,c) tuples.
234 template <typename ordinal_type,
235 typename value_type>
236 Teuchos::RCP< Sparse3Tensor<ordinal_type, value_type> >
238 const TotalOrderBasis<ordinal_type, value_type,LexographicLess<MultiIndex<ordinal_type> > >& product_basis,
239 bool symmetric = false) {
240#ifdef STOKHOS_TEUCHOS_TIME_MONITOR
241 TEUCHOS_FUNC_TIME_MONITOR("Stokhos: Total Triple-Product Tensor Time");
242#endif
243 using Teuchos::RCP;
244 using Teuchos::rcp;
245 using Teuchos::Array;
246
247 typedef MultiIndex<ordinal_type> coeff_type;
248 const Array< RCP<const OneDOrthogPolyBasis<ordinal_type, value_type> > >& bases = product_basis.getCoordinateBases();
249 ordinal_type d = bases.size();
250 //ordinal_type p = product_basis.order();
251 Array<ordinal_type> basis_orders(d);
252 for (int i=0; i<d; ++i)
253 basis_orders[i] = bases[i]->order();
254
255 // Create 1-D triple products
256 Array< RCP<Sparse3Tensor<ordinal_type,value_type> > > Cijk_1d(d);
257 for (ordinal_type i=0; i<d; i++) {
258 Cijk_1d[i] =
259 bases[i]->computeSparseTripleProductTensor(bases[i]->order()+1);
260 }
261
262 RCP< Sparse3Tensor<ordinal_type, value_type> > Cijk =
264
265 // Create i, j, k iterators for each dimension
267 Array<Cijk_Iterator> Cijk_1d_iterators(d);
268 coeff_type terms_i(d,0), terms_j(d,0), terms_k(d,0);
269 Array<ordinal_type> sum_i(d,0), sum_j(d,0), sum_k(d,0);
270 for (ordinal_type dim=0; dim<d; dim++) {
271 Cijk_1d_iterators[dim] = Cijk_Iterator(bases[dim]->order(), symmetric);
272 }
273
274 ordinal_type I = 0;
275 ordinal_type J = 0;
276 ordinal_type K = 0;
277 ordinal_type cnt = 0;
278 bool stop = false;
279 while (!stop) {
280
281 // Fill out terms from 1-D iterators
282 for (ordinal_type dim=0; dim<d; ++dim) {
283 terms_i[dim] = Cijk_1d_iterators[dim].i;
284 terms_j[dim] = Cijk_1d_iterators[dim].j;
285 terms_k[dim] = Cijk_1d_iterators[dim].k;
286 }
287
288 // Compute global I,J,K
289 /*
290 ordinal_type II = lexicographicMapping(terms_i, p);
291 ordinal_type JJ = lexicographicMapping(terms_j, p);
292 ordinal_type KK = lexicographicMapping(terms_k, p);
293 if (I != II || J != JJ || K != KK) {
294 std::cout << "DIFF!!!" << std::endl;
295 std::cout << terms_i << ": I = " << I << ", II = " << II << std::endl;
296 std::cout << terms_j << ": J = " << J << ", JJ = " << JJ << std::endl;
297 std::cout << terms_k << ": K = " << K << ", KK = " << KK << std::endl;
298 }
299 */
300
301 // Compute triple-product value
302 value_type c = value_type(1.0);
303 for (ordinal_type dim=0; dim<d; dim++) {
304 c *= Cijk_1d[dim]->getValue(Cijk_1d_iterators[dim].i,
305 Cijk_1d_iterators[dim].j,
306 Cijk_1d_iterators[dim].k);
307 }
308
309 TEUCHOS_TEST_FOR_EXCEPTION(
310 std::abs(c) <= 1.0e-12,
311 std::logic_error,
312 "Got 0 triple product value " << c
313 << ", I = " << I << " = " << terms_i
314 << ", J = " << J << " = " << terms_j
315 << ", K = " << K << " = " << terms_k
316 << std::endl);
317
318 // Add term to global Cijk
319 Cijk->add_term(I,J,K,c);
320 // Cijk->add_term(I,K,J,c);
321 // Cijk->add_term(J,I,K,c);
322 // Cijk->add_term(J,K,I,c);
323 // Cijk->add_term(K,I,J,c);
324 // Cijk->add_term(K,J,I,c);
325
326 // Increment iterators to the next valid term
327 ordinal_type cdim = d-1;
328 bool inc = true;
329 while (inc && cdim >= 0) {
330 ordinal_type delta_i, delta_j, delta_k;
331 bool more =
332 Cijk_1d_iterators[cdim].increment(delta_i, delta_j, delta_k);
333
334 // Update number of terms used for computing global index
335 if (cdim == d-1) {
336 I += delta_i;
337 J += delta_j;
338 K += delta_k;
339 }
340 else {
341 if (delta_i > 0) {
342 for (ordinal_type ii=0; ii<delta_i; ++ii)
343 I +=
345 basis_orders[cdim+1]-sum_i[cdim] -
346 (Cijk_1d_iterators[cdim].i-ii)+d-cdim,
347 d-cdim-1);
348 }
349 else {
350 for (ordinal_type ii=0; ii<-delta_i; ++ii)
351 I -=
353 basis_orders[cdim+1]-sum_i[cdim] -
354 (Cijk_1d_iterators[cdim].i+ii)+d-cdim-1,
355 d-cdim-1);
356 }
357
358 if (delta_j > 0) {
359 for (ordinal_type jj=0; jj<delta_j; ++jj)
360 J +=
362 basis_orders[cdim+1]-sum_j[cdim] -
363 (Cijk_1d_iterators[cdim].j-jj)+d-cdim,
364 d-cdim-1);
365 }
366 else {
367 for (ordinal_type jj=0; jj<-delta_j; ++jj)
368 J -=
370 basis_orders[cdim+1]-sum_j[cdim] -
371 (Cijk_1d_iterators[cdim].j+jj)+d-cdim-1,
372 d-cdim-1);
373 }
374
375 if (delta_k > 0) {
376 for (ordinal_type kk=0; kk<delta_k; ++kk)
377 K +=
379 basis_orders[cdim+1]-sum_k[cdim] -
380 (Cijk_1d_iterators[cdim].k-kk)+d-cdim,
381 d-cdim-1);
382 }
383 else {
384 for (ordinal_type kk=0; kk<-delta_k; ++kk)
385 K -=
387 basis_orders[cdim+1]-sum_k[cdim] -
388 (Cijk_1d_iterators[cdim].k+kk)+d-cdim-1,
389 d-cdim-1);
390 }
391 }
392
393 if (!more) {
394 // If no more terms in this dimension, go to previous one
395 --cdim;
396 }
397 else {
398 // cdim has more terms, so reset iterators for all dimensions > cdim
399 // adjusting max order based on sum of i,j,k for previous dims
400 inc = false;
401
402 for (ordinal_type dim=cdim+1; dim<d; ++dim) {
403
404 // Update sums of orders for previous dimension
405 sum_i[dim] = sum_i[dim-1] + Cijk_1d_iterators[dim-1].i;
406 sum_j[dim] = sum_j[dim-1] + Cijk_1d_iterators[dim-1].j;
407 sum_k[dim] = sum_k[dim-1] + Cijk_1d_iterators[dim-1].k;
408
409 // Reset iterator for this dimension
410 Cijk_1d_iterators[dim] =
411 Cijk_Iterator(basis_orders[dim]-sum_i[dim],
412 basis_orders[dim]-sum_j[dim],
413 basis_orders[dim]-sum_k[dim],
414 symmetric);
415 }
416 }
417 }
418
419 if (cdim < 0)
420 stop = true;
421
422 cnt++;
423 }
424
425 Cijk->fillComplete();
426
427 return Cijk;
428 }
429
430} // Namespace Stokhos
431
432// Include template definitions
434
435#endif
A comparison functor implementing a strict weak ordering based lexographic ordering.
A multidimensional index.
Abstract base class for 1-D orthogonal polynomials.
Abstract base class for multivariate orthogonal polynomials generated from tensor products of univari...
Data structure storing a sparse 3-tensor C(i,j,k) in a a compressed format.
Multivariate orthogonal polynomial basis generated from a total order tensor product of univariate po...
ordinal_type sz
Total size of basis.
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 d
Total dimension of basis.
ordinal_type dimension() const
Return dimension of basis.
Teuchos::Array< Teuchos::RCP< const OneDOrthogPolyBasis< ordinal_type, value_type > > > getCoordinateBases() const
Return coordinate bases.
value_type sparse_tol
Tolerance for computing sparse Cijk.
virtual const MultiIndex< ordinal_type > & term(ordinal_type i) const
Get orders of each coordinate polynomial given an index i.
MultiIndex< ordinal_type > coeff_type
ordinal_type p
Total order of basis.
virtual value_type evaluateZero(ordinal_type i) const
Evaluate basis polynomial i at zero.
Teuchos::Array< Teuchos::RCP< const OneDOrthogPolyBasis< ordinal_type, value_type > > > bases
Array of bases.
Teuchos::Array< value_type > norms
Norms.
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 & operator=(const TotalOrderBasis &b)
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.
coeff_set_type basis_set
Basis set.
TotalOrderBasis(const TotalOrderBasis &)
std::map< coeff_type, ordinal_type, coeff_compare_type > coeff_set_type
coeff_map_type basis_map
Basis map.
coeff_type max_orders
Maximum orders for each dimension.
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.
std::string name
Name of basis.
Teuchos::Array< coeff_type > coeff_map_type
virtual const std::string & getName() const
Return string name of basis.
Teuchos::Array< Teuchos::Array< value_type > > basis_eval_tmp
Temporary array used in basis evaluation.
virtual ordinal_type size() const
Return total size of basis.
Top-level namespace for Stokhos classes and functions.
Teuchos::RCP< Sparse3Tensor< ordinal_type, value_type > > computeTripleProductTensorLTO(const TotalOrderBasis< ordinal_type, value_type, LexographicLess< MultiIndex< ordinal_type > > > &product_basis, bool symmetric=false)
ordinal_type n_choose_k(const ordinal_type &n, const ordinal_type &k)
Compute bionomial coefficient (n ; k) = n!/( k! (n-k)! )