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basis.cpp
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41 
42 #include "Stokhos.hpp"
43 #include "Teuchos_CommandLineProcessor.hpp"
44 
45 // basis
46 //
47 // usage:
48 // basis [options]
49 //
50 // output:
51 // prints the dimensionality and corresponding sparse-grid size for
52 // various multi-variate basis choices.
53 
54 // Basis types
56 const int num_basis_types = 6;
59 const char *basis_type_names[] = {
60  "hermite", "legendre", "clenshaw-curtis", "gauss-patterson", "rys", "jacobi" };
61 
62 // Growth policies
63 const int num_growth_types = 2;
66 const char *growth_type_names[] = { "slow", "moderate" };
67 
68 // Product Basis types
70 const int num_prod_basis_types = 4;
73 const char *prod_basis_type_names[] = {
74  "complete", "tensor", "total", "smolyak" };
75 
76 // Ordering types
78 const int num_ordering_types = 3;
81 const char *ordering_type_names[] = {
82  "total", "lexicographic", "morton-z" };
83 
84 int main(int argc, char **argv)
85 {
86  try {
87 
88  // Setup command line options
89  Teuchos::CommandLineProcessor CLP;
90  CLP.setDocString(
91  "This example prints out the dimensionality of various basis choices.\n");
92  int d = 3;
93  CLP.setOption("dimension", &d, "Stochastic dimension");
94  int p = 5;
95  CLP.setOption("order", &p, "Polynomial order");
96  double drop = 1.0e-12;
97  CLP.setOption("drop", &drop, "Drop tolerance");
99  CLP.setOption("basis", &basis_type,
101  "Basis type");
103  CLP.setOption("growth", &growth_type,
105  "Growth type");
106  ProductBasisType prod_basis_type = COMPLETE;
107  CLP.setOption("product_basis", &prod_basis_type,
110  "Product basis type");
111  OrderingType ordering_type = TOTAL_ORDERING;
112  CLP.setOption("ordering", &ordering_type,
115  "Product basis ordering");
116  double alpha = 1.0;
117  CLP.setOption("alpha", &alpha, "Jacobi alpha index");
118  double beta = 1.0;
119  CLP.setOption("beta", &beta, "Jacobi beta index");
120 
121  // Parse arguments
122  CLP.parse( argc, argv );
123 
124  // Basis
125  Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > bases(d);
126  for (int i=0; i<d; i++) {
127  if (basis_type == HERMITE)
128  bases[i] = Teuchos::rcp(new Stokhos::HermiteBasis<int,double>(
129  p, true, growth_type));
130  else if (basis_type == LEGENDRE)
131  bases[i] = Teuchos::rcp(new Stokhos::LegendreBasis<int,double>(
132  p, true, growth_type));
133  else if (basis_type == CC_LEGENDRE)
134  bases[i] =
136  p, true));
137  else if (basis_type == GP_LEGENDRE)
138  bases[i] =
140  p, true));
141  else if (basis_type == RYS)
142  bases[i] = Teuchos::rcp(new Stokhos::RysBasis<int,double>(
143  p, 1.0, true, growth_type));
144  else if (basis_type == JACOBI)
145  bases[i] = Teuchos::rcp(new Stokhos::JacobiBasis<int,double>(
146  p, alpha, beta, true, growth_type));
147  }
148  Teuchos::RCP<const Stokhos::ProductBasis<int,double> > basis;
152  if (prod_basis_type == COMPLETE)
153  basis =
155  bases, drop));
156  else if (prod_basis_type == TENSOR) {
157  if (ordering_type == TOTAL_ORDERING)
158  basis =
160  bases, drop));
161  else if (ordering_type == LEXICOGRAPHIC_ORDERING)
162  basis =
164  bases, drop));
165  else if (ordering_type == MORTON_Z_ORDERING)
166  basis =
168  bases, drop));
169  }
170  else if (prod_basis_type == TOTAL) {
171  if (ordering_type == TOTAL_ORDERING)
172  basis =
174  bases, drop));
175  else if (ordering_type == LEXICOGRAPHIC_ORDERING)
176  basis =
178  bases, drop));
179  else if (ordering_type == MORTON_Z_ORDERING)
180  basis =
182  bases, drop));
183  }
184  else if (prod_basis_type == SMOLYAK) {
185  Stokhos::TotalOrderIndexSet<int> index_set(d, p);
186  if (ordering_type == TOTAL_ORDERING)
187  basis =
189  bases, index_set, drop));
190  else if (ordering_type == LEXICOGRAPHIC_ORDERING)
191  basis =
193  bases, index_set, drop));
194  else if (ordering_type == MORTON_Z_ORDERING)
195  basis =
197  bases, index_set, drop));
198  }
199 
200  Stokhos::TotalOrderIndexSet<int> index_set(d, p);
201  Teuchos::RCP<const Stokhos::Quadrature<int,double> > quad =
202  Teuchos::rcp(new Stokhos::SmolyakSparseGridQuadrature<int,double>(basis, index_set));
203 
204  std::cout << "order = " << p << " dim = " << d
205  << " basis size = " << basis->size()
206  << " sparse grid size = " << quad->size()
207  << std::endl;
208  }
209  catch (std::exception& e) {
210  std::cout << e.what() << std::endl;
211  }
212 
213  return 0;
214 }
Hermite polynomial basis.
Multivariate orthogonal polynomial basis generated from a total order tensor product of univariate po...
const int num_ordering_types
Definition: basis.cpp:78
GrowthPolicy
Enumerated type for determining Smolyak growth policies.
const ProductBasisType prod_basis_type_values[]
Definition: basis.cpp:71
Defines quadrature for a tensor product basis by Smolyak sparse grids.
A comparison functor implementing a strict weak ordering based total-order ordering, recursive on the dimension.
Definition: basis.cpp:69
OrderingType
const char * prod_basis_type_names[]
Definition: basis.cpp:73
Legendre polynomial basis using Gauss-Patterson quadrature points.
ProductBasisType
Definition: basis.cpp:55
Rys polynomial basis.
const char * ordering_type_names[]
Definition: basis.cpp:81
const int num_growth_types
Definition: basis.cpp:63
Jacobi polynomial basis.
BasisType
Multivariate orthogonal polynomial basis generated from a total-order complete-polynomial tensor prod...
const BasisType basis_type_values[]
Definition: basis.cpp:57
Multivariate orthogonal polynomial basis generated from a Smolyak sparse grid.
Multivariate orthogonal polynomial basis generated from a tensor product of univariate polynomials...
Legendre polynomial basis.
const char * basis_type_names[]
Definition: basis.cpp:59
An isotropic total order index set.
A comparison functor implementing a strict weak ordering based Morton Z-ordering. ...
Legendre polynomial basis using Clenshaw-Curtis quadrature points.
A comparison functor implementing a strict weak ordering based lexographic ordering.
Definition: basis.cpp:55
const Stokhos::GrowthPolicy growth_type_values[]
Definition: basis.cpp:64
const OrderingType ordering_type_values[]
Definition: basis.cpp:79
const int num_prod_basis_types
Definition: basis.cpp:70
const char * growth_type_names[]
Definition: basis.cpp:66
const int num_basis_types
Definition: basis.cpp:56
Definition: basis.cpp:69
int main(int argc, char **argv)
Definition: basis.cpp:84