/usr/include/trilinos/Stokhos_TensorProductBasis.hpp is in libtrilinos-stokhos-dev 12.10.1-3.
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#ifndef STOKHOS_TENSOR_PRODUCT_BASIS_HPP
#define STOKHOS_TENSOR_PRODUCT_BASIS_HPP
#include "Teuchos_RCP.hpp"
#include "Stokhos_ProductBasis.hpp"
#include "Stokhos_OneDOrthogPolyBasis.hpp"
#include "Stokhos_ProductBasisUtils.hpp"
namespace Stokhos {
/*!
* \brief Multivariate orthogonal polynomial basis generated from a
* tensor product of univariate polynomials.
*/
/*!
* The multivariate polynomials are given by
* \f[
* \Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)
* \f]
* where \f$d\f$ is the dimension of the basis and \f$i_j\leq p_j\f$,
* where \f$p_j\f$ is the order of the $j$th basis. The size of the basis
* is given by \f$(p_1+1)\dots(p_d+1)\f$.
*/
template <typename ordinal_type, typename value_type,
typename coeff_compare_type =
TotalOrderLess<MultiIndex<ordinal_type> > >
class TensorProductBasis :
public ProductBasis<ordinal_type,value_type> {
public:
//! Constructor
/*!
* \param bases array of 1-D coordinate bases
* \param sparse_tol tolerance used to drop terms in sparse triple-product
* tensors
*/
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());
//! Destructor
virtual ~TensorProductBasis();
//! \name Implementation of Stokhos::OrthogPolyBasis methods
//@{
//! Return order of basis
ordinal_type order() const;
//! Return dimension of basis
ordinal_type dimension() const;
//! Return total size of basis
virtual ordinal_type size() const;
//! Return array storing norm-squared of each basis polynomial
/*!
* Entry \f$l\f$ of returned array is given by \f$\langle\Psi_l^2\rangle\f$
* for \f$l=0,\dots,P\f$ where \f$P\f$ is size()-1.
*/
virtual const Teuchos::Array<value_type>& norm_squared() const;
//! Return norm squared of basis polynomial \c i.
virtual const value_type& norm_squared(ordinal_type i) const;
//! Compute triple product tensor
/*!
* The \f$(i,j,k)\f$ entry of the tensor \f$C_{ijk}\f$ is given by
* \f$C_{ijk} = \langle\Psi_i\Psi_j\Psi_k\rangle\f$ where \f$\Psi_l\f$
* represents basis polynomial \f$l\f$ and \f$i,j,k=0,\dots,P\f$ where
* \f$P\f$ is size()-1.
*/
virtual
Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> >
computeTripleProductTensor() const;
//! Compute linear triple product tensor where k = 0,1,..,d
virtual
Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> >
computeLinearTripleProductTensor() const;
//! Evaluate basis polynomial \c i at zero
virtual value_type evaluateZero(ordinal_type i) const;
//! Evaluate basis polynomials at given point \c point
/*!
* Size of returned array is given by size(), and coefficients are
* ordered from order 0 up to size size()-1.
*/
virtual void evaluateBases(
const Teuchos::ArrayView<const value_type>& point,
Teuchos::Array<value_type>& basis_vals) const;
//! Print basis to stream \c os
virtual void print(std::ostream& os) const;
//! Return string name of basis
virtual const std::string& getName() const;
//@}
//! \name Implementation of Stokhos::ProductBasis methods
//@{
//! Get orders of each coordinate polynomial given an index \c i
/*!
* The returned array is of size \f$d\f$, where \f$d\f$ is the dimension of
* the basis, and entry \f$l\f$ is given by \f$i_l\f$ where
* \f$\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)\f$.
*/
virtual const MultiIndex<ordinal_type>& term(ordinal_type i) const;
//! Get index of the multivariate polynomial given orders of each coordinate
/*!
* Given the array \c term storing \f$i_1,\dots,\i_d\f$, returns the index
* \f$i\f$ such that \f$\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)\f$.
*/
virtual ordinal_type index(const MultiIndex<ordinal_type>& term) const;
//! Return coordinate bases
/*!
* Array is of size dimension().
*/
Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type,
value_type> > >
getCoordinateBases() const;
//! Return maximum order allowable for each coordinate basis
virtual MultiIndex<ordinal_type> getMaxOrders() const;
//@}
private:
// Prohibit copying
TensorProductBasis(const TensorProductBasis&);
// Prohibit Assignment
TensorProductBasis& operator=(const TensorProductBasis& b);
protected:
typedef MultiIndex<ordinal_type> coeff_type;
typedef std::map<coeff_type,ordinal_type,coeff_compare_type> coeff_set_type;
typedef Teuchos::Array<coeff_type> coeff_map_type;
//! Name of basis
std::string name;
//! Total order of basis
ordinal_type p;
//! Total dimension of basis
ordinal_type d;
//! Total size of basis
ordinal_type sz;
//! Array of bases
Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type, value_type> > > bases;
//! Tolerance for computing sparse Cijk
value_type sparse_tol;
//! Maximum orders for each dimension
coeff_type max_orders;
//! Basis set
coeff_set_type basis_set;
//! Basis map
coeff_map_type basis_map;
//! Norms
Teuchos::Array<value_type> norms;
//! Temporary array used in basis evaluation
mutable Teuchos::Array< Teuchos::Array<value_type> > basis_eval_tmp;
}; // class TensorProductBasis
} // Namespace Stokhos
// Include template definitions
#include "Stokhos_TensorProductBasisImp.hpp"
#endif
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