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Stokhos_SmolyakPseudoSpectralOperatorUnitTest.cpp
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43 
44 #include "Teuchos_UnitTestHarness.hpp"
45 #include "Teuchos_TestingHelpers.hpp"
46 #include "Teuchos_UnitTestRepository.hpp"
47 #include "Teuchos_GlobalMPISession.hpp"
48 #include "Teuchos_ArrayView.hpp"
49 
50 #include "Stokhos.hpp"
51 #include "Stokhos_UnitTestHelpers.hpp"
52 
53 namespace SmolyakBasisUtilsUnitTest {
54 
55  // Common setup for unit tests
56  template <typename ordinal_type, typename value_type>
57  struct UnitTestSetup {
58  value_type rtol, atol;
59  value_type apply_rtol, apply_atol;
60  ordinal_type p,d;
61 
62  UnitTestSetup() {
63  rtol = 1e-12;
64  atol = 1e-12;
65  apply_rtol = 1e-2;
66  apply_atol = 1e-3;
67  p = 4;
68  d = 2;
69  }
70 
71  };
72 
73  typedef int ordinal_type;
74  typedef double value_type;
75  typedef UnitTestSetup<ordinal_type,value_type> setup_type;
76  setup_type setup;
77 
78  // Function for testing quadratures
79  value_type quad_func1(const Teuchos::ArrayView<const value_type>& x) {
80  value_type val = 0.0;
81  for (int i=0; i<x.size(); i++)
82  val += x[i];
83  return std::exp(val);
84  }
85 
86  // Function for testing quadratures
87  value_type quad_func2(const Teuchos::ArrayView<const value_type>& x) {
88  value_type val = 0.0;
89  for (int i=0; i<x.size(); i++)
90  val += x[i];
91  return std::sin(val);
92  }
93 
94  TEUCHOS_UNIT_TEST( Direct, Linear ) {
95  // Build isotropic Smolyak basis of dimension d and order p with
96  // linear growth
97  Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> > > bases(setup.d);
98  for (ordinal_type i=0; i<setup.d; i++)
99  bases[i] = Teuchos::rcp(new Stokhos::LegendreBasis<ordinal_type,value_type>(setup.p, true));
100  Stokhos::TotalOrderIndexSet<ordinal_type> coeff_index_set(setup.d, setup.p);
101  Teuchos::RCP< Stokhos::SmolyakBasis<ordinal_type,value_type> > smolyak_basis = Teuchos::rcp(new Stokhos::SmolyakBasis<ordinal_type,value_type>(bases, coeff_index_set));
102 
103  // Build corresponding pseudospectral operator
104  Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type> sm_op(
105  *smolyak_basis, false);
106 
107  // Generate sparse grids using original approach
108  Stokhos::SparseGridQuadrature<ordinal_type,value_type> quad(
109  smolyak_basis, setup.p, 1e-12, Pecos::SLOW_RESTRICTED_GROWTH);
110  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> quad_op(
111  *smolyak_basis, quad);
112 
113  // Test grid
114  success = Stokhos::testPseudoSpectralPoints(
115  sm_op, quad_op, setup.rtol, setup.atol, out);
116 
117  // Test apply
118  success = success &&
119  Stokhos::testPseudoSpectralApply(
120  sm_op, quad_op, quad_func1, quad_func2, setup.rtol, setup.atol, out);
121 
122  // Test transpose apply
123  success = success &&
124  Stokhos::testPseudoSpectralApplyTrans(
125  sm_op, quad_op, quad_func1, quad_func2, setup.rtol, setup.atol, out);
126 
127  // Test discrete orthogonality
128  success = success &&
129  Stokhos::testPseudoSpectralDiscreteOrthogonality(
130  *smolyak_basis, sm_op, setup.rtol, setup.atol, out);
131  }
132 
133  TEUCHOS_UNIT_TEST( Direct, ModerateLinear ) {
134  // Build isotropic Smolyak basis of dimension d and order p with
135  // moderate linear growth
136  Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> > > bases(setup.d);
137  for (ordinal_type i=0; i<setup.d; i++)
138  bases[i] = Teuchos::rcp(new Stokhos::LegendreBasis<ordinal_type,value_type>(setup.p, true, Stokhos::MODERATE_GROWTH));
139  Stokhos::TotalOrderIndexSet<ordinal_type> coeff_index_set(setup.d, setup.p);
140  Teuchos::RCP< Stokhos::SmolyakBasis<ordinal_type,value_type> > smolyak_basis = Teuchos::rcp(new Stokhos::SmolyakBasis<ordinal_type,value_type>(bases, coeff_index_set));
141 
142  // Build corresponding pseudospectral operator
143  Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type> sm_op(
144  *smolyak_basis, false);
145 
146  // Generate sparse grids using original approach
147  Stokhos::SparseGridQuadrature<ordinal_type,value_type> quad(
148  smolyak_basis, setup.p, 1e-12, Pecos::MODERATE_RESTRICTED_GROWTH);
149  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> quad_op(
150  *smolyak_basis, quad);
151 
152  // Test grid
153  success = Stokhos::testPseudoSpectralPoints(
154  sm_op, quad_op, setup.rtol, setup.atol, out);
155 
156  // Test apply
157  success = success &&
158  Stokhos::testPseudoSpectralApply(
159  sm_op, quad_op, quad_func1, quad_func2, setup.rtol, setup.atol, out);
160 
161  // Test transpose apply
162  success = success &&
163  Stokhos::testPseudoSpectralApplyTrans(
164  sm_op, quad_op, quad_func1, quad_func2, setup.rtol, setup.atol, out);
165 
166  // Direct apply will not satisfy discrete orthogonality
167  }
168 
169  TEUCHOS_UNIT_TEST( Smolyak, Linear ) {
170  // Build isotropic Smolyak basis of dimension d and order p with
171  // linear growth
172  Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> > > bases(setup.d);
173  for (ordinal_type i=0; i<setup.d; i++)
174  bases[i] = Teuchos::rcp(new Stokhos::LegendreBasis<ordinal_type,value_type>(setup.p, true));
175  Stokhos::TotalOrderIndexSet<ordinal_type> coeff_index_set(setup.d, setup.p);
176  Teuchos::RCP< Stokhos::SmolyakBasis<ordinal_type,value_type> > smolyak_basis = Teuchos::rcp(new Stokhos::SmolyakBasis<ordinal_type,value_type>(bases, coeff_index_set));
177 
178  // Build corresponding pseudospectral operator
179  Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type> sm_op(
180  *smolyak_basis, true);
181 
182  // Generate sparse grids using original approach
183  Stokhos::SparseGridQuadrature<ordinal_type,value_type> quad(
184  smolyak_basis, setup.p, 1e-12, Pecos::SLOW_RESTRICTED_GROWTH);
185  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> quad_op(
186  *smolyak_basis, quad);
187 
188  Stokhos::TensorProductQuadrature<ordinal_type,value_type> tp_quad(
189  smolyak_basis);
190  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> tp_quad_op(*smolyak_basis, tp_quad);
191 
192  // Test grid
193  success = Stokhos::testPseudoSpectralPoints(
194  sm_op, quad_op, setup.rtol, setup.atol, out);
195 
196  // Test apply
197  success = success &&
198  Stokhos::testPseudoSpectralApply(
199  sm_op, tp_quad_op, quad_func1, quad_func2, setup.apply_rtol, setup.apply_atol, out);
200 
201  // Test transpose apply
202  success = success &&
203  Stokhos::testPseudoSpectralApplyTrans(
204  sm_op, tp_quad_op, quad_func1, quad_func2, setup.apply_rtol, setup.apply_atol, out);
205 
206  // Test discrete orthogonality
207  success = success &&
208  Stokhos::testPseudoSpectralDiscreteOrthogonality(
209  *smolyak_basis, sm_op, setup.rtol, setup.atol, out);
210  }
211 
212  TEUCHOS_UNIT_TEST( Smolyak, ModerateLinear ) {
213  // Build isotropic Smolyak basis of dimension d and order p with
214  // moderate linear growth
215  Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> > > bases(setup.d);
216  for (ordinal_type i=0; i<setup.d; i++)
217  bases[i] = Teuchos::rcp(new Stokhos::LegendreBasis<ordinal_type,value_type>(setup.p, true, Stokhos::MODERATE_GROWTH));
218  Stokhos::TotalOrderIndexSet<ordinal_type> coeff_index_set(setup.d, setup.p);
219  Teuchos::RCP< Stokhos::SmolyakBasis<ordinal_type,value_type> > smolyak_basis = Teuchos::rcp(new Stokhos::SmolyakBasis<ordinal_type,value_type>(bases, coeff_index_set));
220 
221  // Build corresponding pseudospectral operator
222  Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type> sm_op(
223  *smolyak_basis, true);
224 
225  // Generate sparse grids using original approach
226  Stokhos::SparseGridQuadrature<ordinal_type,value_type> quad(
227  smolyak_basis, setup.p, 1e-12, Pecos::MODERATE_RESTRICTED_GROWTH);
228  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> quad_op(
229  *smolyak_basis, quad);
230 
231  Stokhos::TensorProductQuadrature<ordinal_type,value_type> tp_quad(
232  smolyak_basis);
233  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> tp_quad_op(*smolyak_basis, tp_quad);
234 
235  // Test grid
236  success = Stokhos::testPseudoSpectralPoints(
237  sm_op, quad_op, setup.rtol, setup.atol, out);
238 
239  // Test apply
240  success = success &&
241  Stokhos::testPseudoSpectralApply(
242  sm_op, tp_quad_op, quad_func1, quad_func2, setup.apply_rtol, setup.apply_atol, out);
243 
244  // Test transpose apply
245  success = success &&
246  Stokhos::testPseudoSpectralApplyTrans(
247  sm_op, tp_quad_op, quad_func1, quad_func2, setup.apply_rtol, setup.apply_atol, out);
248 
249  // Test discrete orthogonality
250  success = success &&
251  Stokhos::testPseudoSpectralDiscreteOrthogonality(
252  *smolyak_basis, sm_op, setup.rtol, setup.atol, out);
253  }
254 
255 #ifdef HAVE_STOKHOS_DAKOTA
256 
257  TEUCHOS_UNIT_TEST( Direct, ClenshawCurtis ) {
258  // Build isotropic Smolyak basis of dimension d and order p with
259  // exponential growth
260  Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> > > bases(setup.d);
261  for (ordinal_type i=0; i<setup.d; i++)
262  bases[i] = Teuchos::rcp(new Stokhos::ClenshawCurtisLegendreBasis<ordinal_type,value_type>(setup.p, true));
263  Stokhos::TotalOrderIndexSet<ordinal_type> coeff_index_set(setup.d, setup.p);
264  Teuchos::RCP< Stokhos::SmolyakBasis<ordinal_type,value_type> > smolyak_basis = Teuchos::rcp(new Stokhos::SmolyakBasis<ordinal_type,value_type>(bases, coeff_index_set));
265 
266  // Build corresponding pseudospectral operator
267  Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type> sm_op(
268  *smolyak_basis, false);
269 
270  // Generate sparse grids using original approach
271  Stokhos::SparseGridQuadrature<ordinal_type,value_type> quad(
272  smolyak_basis, setup.p, 1e-12, Pecos::UNRESTRICTED_GROWTH);
273  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> quad_op(
274  *smolyak_basis, quad);
275 
276  // Test grid
277  success = Stokhos::testPseudoSpectralPoints(
278  sm_op, quad_op, setup.rtol, setup.atol, out);
279 
280  // Test apply
281  success = success &&
282  Stokhos::testPseudoSpectralApply(
283  sm_op, quad_op, quad_func1, quad_func2, setup.rtol, setup.atol, out);
284 
285  // Test transpose apply
286  success = success &&
287  Stokhos::testPseudoSpectralApplyTrans(
288  sm_op, quad_op, quad_func1, quad_func2, setup.rtol, setup.atol, out);
289 
290  // Direct apply will not satisfy discrete orthogonality
291  }
292 
293  TEUCHOS_UNIT_TEST( Direct, GaussPatterson ) {
294  // Build isotropic Smolyak basis of dimension d and order p with
295  // exponential Gauss-Patterson growth
296  Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> > > bases(setup.d);
297  for (ordinal_type i=0; i<setup.d; i++)
298  bases[i] = Teuchos::rcp(new Stokhos::GaussPattersonLegendreBasis<ordinal_type,value_type>(setup.p, true));
299  Stokhos::TotalOrderIndexSet<ordinal_type> coeff_index_set(setup.d, setup.p);
300  Teuchos::RCP< Stokhos::SmolyakBasis<ordinal_type,value_type> > smolyak_basis = Teuchos::rcp(new Stokhos::SmolyakBasis<ordinal_type,value_type>(bases, coeff_index_set));
301 
302  // Build corresponding pseudospectral operator
303  Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type> sm_op(
304  *smolyak_basis, false);
305 
306  // Generate sparse grids using original approach
307  Stokhos::SparseGridQuadrature<ordinal_type,value_type> quad(
308  smolyak_basis, setup.p, 1e-12, Pecos::UNRESTRICTED_GROWTH);
309  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> quad_op(
310  *smolyak_basis, quad);
311 
312  // Test grid
313  success = Stokhos::testPseudoSpectralPoints(
314  sm_op, quad_op, setup.rtol, setup.atol, out);
315 
316  // Test apply
317  success = success &&
318  Stokhos::testPseudoSpectralApply(
319  sm_op, quad_op, quad_func1, quad_func2, setup.rtol, setup.atol, out);
320 
321  // Test transpose apply
322  success = success &&
323  Stokhos::testPseudoSpectralApplyTrans(
324  sm_op, quad_op, quad_func1, quad_func2, setup.rtol, setup.atol, out);
325 
326  // Direct apply will not satisfy discrete orthogonality
327  }
328 
329  TEUCHOS_UNIT_TEST( Smolyak, ClenshawCurtis ) {
330  // Build isotropic Smolyak basis of dimension d and order p with
331  // exponential growth
332  Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> > > bases(setup.d);
333  for (ordinal_type i=0; i<setup.d; i++)
334  bases[i] = Teuchos::rcp(new Stokhos::ClenshawCurtisLegendreBasis<ordinal_type,value_type>(setup.p, true));
335  Stokhos::TotalOrderIndexSet<ordinal_type> coeff_index_set(setup.d, setup.p);
336  Teuchos::RCP< Stokhos::SmolyakBasis<ordinal_type,value_type> > smolyak_basis = Teuchos::rcp(new Stokhos::SmolyakBasis<ordinal_type,value_type>(bases, coeff_index_set));
337 
338  // Build corresponding pseudospectral operator
339  Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type> sm_op(
340  *smolyak_basis, true);
341 
342  // Generate sparse grids using original approach
343  Stokhos::SparseGridQuadrature<ordinal_type,value_type> quad(
344  smolyak_basis, setup.p, 1e-12, Pecos::UNRESTRICTED_GROWTH);
345  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> quad_op(
346  *smolyak_basis, quad);
347 
348  Stokhos::TensorProductQuadrature<ordinal_type,value_type> tp_quad(
349  smolyak_basis);
350  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> tp_quad_op(*smolyak_basis, tp_quad);
351 
352  // Test grid
353  success = Stokhos::testPseudoSpectralPoints(
354  sm_op, quad_op, setup.rtol, setup.atol, out);
355 
356  // Test apply
357  success = success &&
358  Stokhos::testPseudoSpectralApply(
359  sm_op, tp_quad_op, quad_func1, quad_func2, setup.apply_rtol, setup.apply_atol, out);
360 
361  // Test transpose apply
362  success = success &&
363  Stokhos::testPseudoSpectralApplyTrans(
364  sm_op, tp_quad_op, quad_func1, quad_func2, setup.apply_rtol, setup.apply_atol, out);
365 
366  // Test discrete orthogonality
367  success = success &&
368  Stokhos::testPseudoSpectralDiscreteOrthogonality(
369  *smolyak_basis, sm_op, setup.rtol, setup.atol, out);
370  }
371 
372  TEUCHOS_UNIT_TEST( Smolyak, GaussPatterson ) {
373  // Build isotropic Smolyak basis of dimension d and order p with
374  // exponential Gauss-Patterson growth
375  Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<ordinal_type,value_type> > > bases(setup.d);
376  for (ordinal_type i=0; i<setup.d; i++)
377  bases[i] = Teuchos::rcp(new Stokhos::GaussPattersonLegendreBasis<ordinal_type,value_type>(setup.p, true));
378  Stokhos::TotalOrderIndexSet<ordinal_type> coeff_index_set(setup.d, setup.p);
379  Teuchos::RCP< Stokhos::SmolyakBasis<ordinal_type,value_type> > smolyak_basis = Teuchos::rcp(new Stokhos::SmolyakBasis<ordinal_type,value_type>(bases, coeff_index_set));
380 
381  // Build corresponding pseudospectral operator
382  Stokhos::SmolyakPseudoSpectralOperator<ordinal_type,value_type> sm_op(
383  *smolyak_basis, true);
384 
385  // Generate sparse grids using original approach
386  Stokhos::SparseGridQuadrature<ordinal_type,value_type> quad(
387  smolyak_basis, setup.p, 1e-12, Pecos::UNRESTRICTED_GROWTH);
388  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> quad_op(
389  *smolyak_basis, quad);
390 
391  Stokhos::TensorProductQuadrature<ordinal_type,value_type> tp_quad(
392  smolyak_basis);
393  Stokhos::QuadraturePseudoSpectralOperator<ordinal_type,value_type> tp_quad_op(*smolyak_basis, tp_quad);
394 
395  // Test grid
396  success = Stokhos::testPseudoSpectralPoints(
397  sm_op, quad_op, setup.rtol, setup.atol, out);
398 
399  // Test apply
400  success = success &&
401  Stokhos::testPseudoSpectralApply(
402  sm_op, tp_quad_op, quad_func1, quad_func2, setup.apply_rtol, setup.apply_atol, out);
403 
404  // Test transpose apply
405  success = success &&
406  Stokhos::testPseudoSpectralApplyTrans(
407  sm_op, tp_quad_op, quad_func1, quad_func2, setup.apply_rtol, setup.apply_atol, out);
408 
409  // Test discrete orthogonality
410  success = success &&
411  Stokhos::testPseudoSpectralDiscreteOrthogonality(
412  *smolyak_basis, sm_op, setup.rtol, setup.atol, out);
413  }
414 
415 #endif
416 
417 }
418 
419 int main( int argc, char* argv[] ) {
420  Teuchos::GlobalMPISession mpiSession(&argc, &argv);
421  return Teuchos::UnitTestRepository::runUnitTestsFromMain(argc, argv);
422 }
argv
char * argv[]
Definition: Stokhos_HouseTriDiagUnitTest.cpp:286
Teuchos_ArrayView.hpp
Teuchos::ArrayView::size
size_type size() const
SmolyakBasisUtilsUnitTest::TEUCHOS_UNIT_TEST
TEUCHOS_UNIT_TEST(Coefficients, IsotropicLinear)
Definition: Stokhos_SmolyakBasisUnitTest.cpp:104
Teuchos_UnitTestRepository.hpp
Stokhos::GaussPattersonLegendreBasis
Legendre polynomial basis using Gauss-Patterson quadrature points.
Definition: Stokhos_GaussPattersonLegendreBasis.hpp:57
Teuchos::UnitTestRepository::runUnitTestsFromMain
static int runUnitTestsFromMain(int argc, char *argv[])
Teuchos::rcp
TEUCHOS_DEPRECATED RCP< T > rcp(T *p, Dealloc_T dealloc, bool owns_mem)
Teuchos_UnitTestHarness.hpp
Stokhos::SmolyakPseudoSpectralOperator
An operator for building pseudo-spectral coefficients using a sparse Smolyak construction.
Definition: Stokhos_SmolyakPseudoSpectralOperator.hpp:61
SmolyakBasisUtilsUnitTest::quad_func2
value_type quad_func2(const Teuchos::ArrayView< const value_type > &x)
Definition: Stokhos_SmolyakPseudoSpectralOperatorUnitTest.cpp:87
Stokhos_UnitTestHelpers.hpp
Stokhos::SmolyakBasis
Multivariate orthogonal polynomial basis generated from a Smolyak sparse grid.
Definition: Stokhos_SmolyakBasis.hpp:62
Sacado::UQ::exp
KOKKOS_INLINE_FUNCTION PCE< Storage > exp(const PCE< Storage > &a)
Definition: Sacado_UQ_PCE_Imp.hpp:827
Stokhos::LegendreBasis
Legendre polynomial basis.
Definition: Stokhos_LegendreBasis.hpp:67
main
int main(int argc, char **argv)
Definition: cijk_ltb_partition.cpp:57
Teuchos_TestingHelpers.hpp
val
expr val()
Stokhos::TotalOrderIndexSet
An isotropic total order index set.
Definition: Stokhos_ProductBasisUtils.hpp:215
SmolyakBasisUtilsUnitTest::setup_type
UnitTestSetup< ordinal_type, value_type > setup_type
Definition: Stokhos_SmolyakBasisUnitTest.cpp:72
Stokhos::testPseudoSpectralDiscreteOrthogonality
bool testPseudoSpectralDiscreteOrthogonality(const basis_type &basis, const operator_type &op, const scalar_type &rel_tol, const scalar_type &abs_tol, Teuchos::FancyOStream &out)
Definition: Stokhos_UnitTestHelpers.hpp:524
Teuchos_GlobalMPISession.hpp
Stokhos::ClenshawCurtisLegendreBasis
Legendre polynomial basis using Clenshaw-Curtis quadrature points.
Definition: Stokhos_ClenshawCurtisLegendreBasis.hpp:57
Sacado::UQ::sin
KOKKOS_INLINE_FUNCTION PCE< Storage > sin(const PCE< Storage > &a)
Definition: Sacado_UQ_PCE_Imp.hpp:965
Stokhos::QuadraturePseudoSpectralOperator
An operator for building pseudo-spectral coefficients using an arbitrary quadrature rule...
Definition: Stokhos_QuadraturePseudoSpectralOperator.hpp:60
Stokhos::testPseudoSpectralPoints
bool testPseudoSpectralPoints(const operator_type1 &op1, const operator_type2 &op2, const scalar_type &rel_tol, const scalar_type &abs_tol, Teuchos::FancyOStream &out)
Definition: Stokhos_UnitTestHelpers.hpp:362
Stokhos::testPseudoSpectralApply
bool testPseudoSpectralApply(const operator_type1 &op1, const operator_type2 &op2, const func_type1 &func1, const func_type2 &func2, const scalar_type &rel_tol, const scalar_type &abs_tol, Teuchos::FancyOStream &out)
Definition: Stokhos_UnitTestHelpers.hpp:404
Stokhos::TensorProductQuadrature
Defines quadrature for a tensor product basis by tensor products of 1-D quadrature rules...
Definition: Stokhos_TensorProductQuadrature.hpp:58
Stokhos::testPseudoSpectralApplyTrans
bool testPseudoSpectralApplyTrans(const operator_type1 &op1, const operator_type2 &op2, const func_type1 &func1, const func_type2 &func2, const scalar_type &rel_tol, const scalar_type &abs_tol, Teuchos::FancyOStream &out)
Definition: Stokhos_UnitTestHelpers.hpp:465
SmolyakBasisUtilsUnitTest::quad_func1
value_type quad_func1(const Teuchos::ArrayView< const value_type > &x)
Definition: Stokhos_SmolyakPseudoSpectralOperatorUnitTest.cpp:79
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