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Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type > Class Template Reference

Multivariate orthogonal polynomial basis generated from a Smolyak sparse grid. More...

#include <Stokhos_SmolyakBasis.hpp>

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List of all members.

Classes

struct  SmolyakPredicate
 Predicate functor for building sparse triple products. More...

Public Types

typedef MultiIndex< ordinal_type > coeff_type
typedef TensorProductBasis
< ordinal_type, value_type,
LexographicLess< coeff_type > > 
tensor_product_basis_type

Public Member Functions

template<typename index_set_type >
 SmolyakBasis (const Teuchos::Array< Teuchos::RCP< const OneDOrthogPolyBasis< ordinal_type, value_type > > > &bases, const index_set_type &index_set, const value_type &sparse_tol=1.0e-12, const coeff_compare_type &coeff_compare=coeff_compare_type())
 Constructor.
virtual ~SmolyakBasis ()
 Destructor.
ordinal_type getNumSmolyakTerms () const
 Return number of terms in Smolyak formula.
Teuchos::RCP< const
tensor_product_basis_type
getTensorProductBasis (ordinal_type i) const
 Return ith tensor product basis.
ordinal_type getSmolyakCoefficient (ordinal_type i) const
 Return ith smolyak coefficient.
template<typename index_set_type >
 SmolyakBasis (const Teuchos::Array< Teuchos::RCP< const OneDOrthogPolyBasis< ordinal_type, value_type > > > &bases_, const index_set_type &index_set, const value_type &sparse_tol_, const ordering_type &coeff_compare)
Implementation of Stokhos::OrthogPolyBasis methods
ordinal_type order () const
 Return order of basis.
ordinal_type dimension () const
 Return dimension of basis.
virtual ordinal_type size () const
 Return total size of basis.
virtual const Teuchos::Array
< value_type > & 
norm_squared () const
 Return array storing norm-squared of each basis polynomial.
virtual const value_type & norm_squared (ordinal_type i) const
 Return norm squared of basis polynomial i.
virtual Teuchos::RCP
< Stokhos::Sparse3Tensor
< ordinal_type, value_type > > 
computeTripleProductTensor (ordinal_type order) const
 Compute triple product tensor.
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 void print (std::ostream &os) const
 Print basis to stream os.
virtual const std::string & getName () const
 Return string name of basis.
Implementation of Stokhos::ProductBasis methods
virtual const MultiIndex
< ordinal_type > & 
term (ordinal_type i) const
 Get orders of each coordinate polynomial given an index i.
virtual ordinal_type index (const MultiIndex< ordinal_type > &term) const
 Get index of the multivariate polynomial given orders of each coordinate.
Teuchos::Array< Teuchos::RCP
< const OneDOrthogPolyBasis
< ordinal_type, value_type > > > 
getCoordinateBases () const
 Return coordinate bases.
virtual MultiIndex< ordinal_type > getMaxOrders () const
 Return maximum order allowable for each coordinate basis.

Protected Types

typedef std::map< coeff_type,
ordinal_type,
coeff_compare_type > 
coeff_set_type
typedef Teuchos::Array
< coeff_type
coeff_map_type
typedef MultiIndex< ordinal_type > multiindex_type

Protected Attributes

std::string name
 Name of basis.
ordinal_type p
 Total order of basis.
ordinal_type d
 Total dimension of basis.
ordinal_type sz
 Total size of basis.
Teuchos::Array< Teuchos::RCP
< const OneDOrthogPolyBasis
< ordinal_type, value_type > > > 
bases
 Array of bases.
value_type sparse_tol
 Tolerance for computing sparse Cijk.
coeff_type max_orders
 Maximum orders for each dimension.
coeff_set_type basis_set
 Basis set.
coeff_map_type basis_map
 Basis map.
Teuchos::Array< ordinal_type > smolyak_coeffs
 Smolyak coefficients.
Teuchos::Array< value_type > norms
 Norms.
Teuchos::Array< Teuchos::Array
< value_type > > 
basis_eval_tmp
 Temporary array used in basis evaluation.
Teuchos::Array< Teuchos::RCP
< tensor_product_basis_type > > 
tp_bases
 Tensor product bases comprising Smolyak set.
SmolyakPredicate
< TensorProductPredicate
< ordinal_type > > 
sm_pred
 Predicate for building sparse triple products.

Detailed Description

template<typename ordinal_type, typename value_type, typename coeff_compare_type = TotalOrderLess<MultiIndex<ordinal_type> >>
class Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >

Multivariate orthogonal polynomial basis generated from a Smolyak sparse grid.


Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type , typename coeff_compare_type = TotalOrderLess<MultiIndex<ordinal_type> >>
template<typename index_set_type >
Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >::SmolyakBasis ( const Teuchos::Array< Teuchos::RCP< const OneDOrthogPolyBasis< ordinal_type, value_type > > > &  bases,
const index_set_type &  index_set,
const value_type &  sparse_tol = 1.0e-12,
const coeff_compare_type &  coeff_compare = coeff_compare_type() 
)

Constructor.

Parameters:
basesarray of 1-D coordinate bases
sparse_toltolerance used to drop terms in sparse triple-product tensors

Member Function Documentation

template<typename ordinal_type , typename value_type , typename ordering_type >
Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::SmolyakBasis< ordinal_type, value_type, ordering_type >::computeTripleProductTensor ( ordinal_type  order) const [virtual]

Compute triple product tensor.

The $(i,j,k)$ entry of the tensor $C_{ijk}$ is given by $C_{ijk} = \langle\Psi_i\Psi_j\Psi_k\rangle$ where $\Psi_l$ represents basis polynomial $l$ and $i,j=0,\dots,P$ where $P$ is size()-1 and $k=0,\dots,p$ where $p$ is the supplied order.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type , typename ordering_type >
void Stokhos::SmolyakBasis< ordinal_type, value_type, ordering_type >::evaluateBases ( const Teuchos::ArrayView< const value_type > &  point,
Teuchos::Array< value_type > &  basis_vals 
) const [virtual]

Evaluate basis polynomials at given point point.

Size of returned array is given by size(), and coefficients are ordered from order 0 up to size size()-1.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type , typename ordering_type >
Teuchos::Array< Teuchos::RCP< const Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > > Stokhos::SmolyakBasis< ordinal_type, value_type, ordering_type >::getCoordinateBases ( ) const [virtual]

Return coordinate bases.

Array is of size dimension().

Implements Stokhos::ProductBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type , typename ordering_type >
ordinal_type Stokhos::SmolyakBasis< ordinal_type, value_type, ordering_type >::index ( const MultiIndex< ordinal_type > &  term) const [virtual]

Get index of the multivariate polynomial given orders of each coordinate.

Given the array term storing $i_1,\dots,\i_d$, returns the index $i$ such that $\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)$.

Implements Stokhos::ProductBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type , typename ordering_type >
const Teuchos::Array< value_type > & Stokhos::SmolyakBasis< ordinal_type, value_type, ordering_type >::norm_squared ( ) const [virtual]

Return array storing norm-squared of each basis polynomial.

Entry $l$ of returned array is given by $\langle\Psi_l^2\rangle$ for $l=0,\dots,P$ where $P$ is size()-1.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type , typename ordering_type >
const Stokhos::MultiIndex< ordinal_type > & Stokhos::SmolyakBasis< ordinal_type, value_type, ordering_type >::term ( ordinal_type  i) const [virtual]

Get orders of each coordinate polynomial given an index i.

The returned array is of size $d$, where $d$ is the dimension of the basis, and entry $l$ is given by $i_l$ where $\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)$.

Implements Stokhos::ProductBasis< ordinal_type, value_type >.


The documentation for this class was generated from the following files:
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