/usr/include/trilinos/Stokhos_ProductLanczosGramSchmidtPCEBasis.hpp is in libtrilinos-stokhos-dev 12.10.1-3.
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#ifndef STOKHOS_PRODUCT_LANCZOS_GRAM_SCHMIDT_PCE_BASIS_HPP
#define STOKHOS_PRODUCT_LANCZOS_GRAM_SCHMIDT_PCE_BASIS_HPP
#include "Teuchos_RCP.hpp"
#include "Teuchos_Array.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_SerialDenseVector.hpp"
#include "Teuchos_ParameterList.hpp"
#include "Stokhos_ReducedPCEBasis.hpp"
#include "Stokhos_OrthogPolyApprox.hpp"
#include "Stokhos_Quadrature.hpp"
#include "Stokhos_Sparse3Tensor.hpp"
#include "Stokhos_CompletePolynomialBasis.hpp"
namespace Stokhos {
/*!
* \brief Generate a basis from a given set of PCE expansions that is
* orthogonal with respect to the product measure induced by these expansions.
*/
/*!
* Given the PCE expansions, first build a an orthogonal basis for each
* compnent, then form the multivariate basis by a total-order tensor
* product. The resulting basis is not necessarily orthogonal with respect
* to the full measure.
*/
template <typename ordinal_type, typename value_type>
class ProductLanczosGramSchmidtPCEBasis :
public ReducedPCEBasis<ordinal_type,value_type> {
public:
//! Constructor
/*!
* \param p order of the basis
* \param pce polynomial chaos expansions defining new measure
* \param Cijk sparse triple product tensor for basis defining pce
*/
ProductLanczosGramSchmidtPCEBasis(
ordinal_type p,
const Teuchos::Array< Stokhos::OrthogPolyApprox<ordinal_type, value_type> >& pce,
const Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> >& quad,
const Teuchos::RCP< const Stokhos::Sparse3Tensor<ordinal_type, value_type> >& Cijk,
const Teuchos::ParameterList& params = Teuchos::ParameterList());
//! Destructor
virtual ~ProductLanczosGramSchmidtPCEBasis();
//! \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::ReducedPCEBasis methods
//@{
//! Transform coefficients to original basis from this basis
virtual void
transformToOriginalBasis(const value_type *in,
value_type *out,
ordinal_type ncol = 1,
bool transpose = false) const;
//! Transform coefficients from original basis to this basis
virtual void
transformFromOriginalBasis(const value_type *in,
value_type *out,
ordinal_type ncol = 1,
bool transpose = false) const;
//! Get reduced quadrature object
virtual Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> >
getReducedQuadrature() const;
//@}
protected:
// Determine if a pce is linear, in that it has a total degree of at
// most 1. If the pce is nonlinear, return -2, or if it is constant,
// return -1, otherwise return the index of the variable the pce is
// linear in, ie, if return value is i, the pce = a_{i+1}*\xi_i
ordinal_type
isInvariant(const Stokhos::OrthogPolyApprox<ordinal_type, value_type>& pce) const;
private:
// Prohibit copying
ProductLanczosGramSchmidtPCEBasis(const ProductLanczosGramSchmidtPCEBasis&);
// Prohibit Assignment
ProductLanczosGramSchmidtPCEBasis& operator=(const ProductLanczosGramSchmidtPCEBasis&);
protected:
typedef Teuchos::SerialDenseVector<ordinal_type,value_type> SDV;
typedef Teuchos::SerialDenseMatrix<ordinal_type,value_type> SDM;
//! Name of basis
std::string name;
//! Algorithm parameters
Teuchos::ParameterList params;
//! Size of original pce basis
ordinal_type pce_sz;
//! Total order of basis
ordinal_type p;
//! Total dimension of basis
ordinal_type d;
//! Total size of basis
ordinal_type sz;
//! Product Lanczos basis
Teuchos::RCP< Stokhos::CompletePolynomialBasis<ordinal_type,value_type> > tensor_lanczos_basis;
//! Norms
Teuchos::Array<value_type> norms;
//! Values of transformed basis at quadrature points
SDM Q;
//! Coefficients of transformed basis in original basis
SDM Qp;
//! Reduced quadrature object
Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> > reduced_quad;
//! Temporary pce used in invariant subspace calculations
mutable Stokhos::OrthogPolyApprox<ordinal_type, value_type> tmp_pce;
}; // class ProductLanczosGramSchmidtPCEBasis
} // Namespace Stokhos
// Include template definitions
#include "Stokhos_ProductLanczosGramSchmidtPCEBasisImp.hpp"
#endif
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