libtrilinos-stokhos-dev 12.4.2-2 / usr / include / trilinos / Stokhos_LanczosProjPCEBasis.hpp

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#ifndef STOKHOS_LANCZOSPROJPCEBASIS_HPP
#define STOKHOS_LANCZOSPROJPCEBASIS_HPP

#include "Teuchos_RCP.hpp"
#include "Teuchos_Array.hpp"
#include "Teuchos_SerialDenseVector.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"

#include "Stokhos_RecurrenceBasis.hpp"
#include "Stokhos_OrthogPolyApprox.hpp"
#include "Stokhos_Sparse3Tensor.hpp"
#include "Stokhos_Lanczos.hpp"

namespace Stokhos {

  template <typename ord_type, typename val_type>
  class DenseOperator {
  public:
    typedef ord_type ordinal_type;
    typedef val_type value_type;
    typedef Teuchos::SerialDenseMatrix<ordinal_type, value_type> matrix_type;
    typedef Teuchos::SerialDenseVector<ordinal_type, value_type> vector_type;

    DenseOperator(const matrix_type& A_): A(A_) {}
    
    void 
    apply(const vector_type& u, vector_type& v) const {
      v.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, value_type(1), 
                A, u, value_type(0));
    }

  protected:

    const matrix_type& A;

  };

  /*! 
   * \brief Generates three-term recurrence using the Lanczos 
   * procedure applied to a polynomial chaos expansion in another basis.
   */
  template <typename ordinal_type, typename value_type>
  class LanczosProjPCEBasis : 
    public RecurrenceBasis<ordinal_type, value_type> {
  public:

    //! Constructor
    /*!
     * \param p order of the basis
     * \param pce polynomial chaos expansion defining new density function
     * \param quad quadrature data for basis of PC expansion
     */
    LanczosProjPCEBasis(
      ordinal_type p,
      const Teuchos::RCP< const Stokhos::OrthogPolyApprox<ordinal_type, value_type> >& pce,
      const Teuchos::RCP< const Stokhos::Sparse3Tensor<ordinal_type, value_type> >& Cijk,
      bool normalize,
      bool limit_integration_order = false);

    //! Destructor
    ~LanczosProjPCEBasis();

    //! \name Implementation of Stokhos::OneDOrthogPolyBasis methods
    //@{

    //! Get Gauss quadrature points, weights, and values of basis at points
    virtual void 
    getQuadPoints(ordinal_type quad_order,
		  Teuchos::Array<value_type>& points,
		  Teuchos::Array<value_type>& weights,
		  Teuchos::Array< Teuchos::Array<value_type> >& values) const;

    /*! 
     * \brief Clone this object with the option of building a higher order
     * basis.
     */
    /*!
     * This method is following the Prototype pattern (see Design Pattern's textbook).
     * The slight variation is that it allows the order of the polynomial to be modified,
     * otherwise an exact copy is formed. The use case for this is creating basis functions
     * for column indices in a spatially varying adaptive refinement context.
     */
    virtual Teuchos::RCP<OneDOrthogPolyBasis<ordinal_type,value_type> > cloneWithOrder(ordinal_type p) const;

    //@}

    //! Get new coefficients in this new basis
    value_type getNewCoeffs(ordinal_type i) const;

    //! Map expansion coefficients from this basis to original
    void transformCoeffsFromLanczos(const value_type *in, 
				      value_type *out) const;

  protected:

    //! \name Implementation of Stokhos::RecurrenceBasis methods
    //@{ 

    //! Compute recurrence coefficients
    virtual bool
    computeRecurrenceCoefficients(ordinal_type n,
				  Teuchos::Array<value_type>& alpha,
				  Teuchos::Array<value_type>& beta,
				  Teuchos::Array<value_type>& delta,
				  Teuchos::Array<value_type>& gamma) const;

    //! Setup basis after computing recurrence coefficients
    virtual void setup();

    //@}

    //! Copy constructor with specified order
    LanczosProjPCEBasis(ordinal_type p, const LanczosProjPCEBasis& basis);

  private:

    // Prohibit copying
    LanczosProjPCEBasis(const LanczosProjPCEBasis&);

    // Prohibit Assignment
    LanczosProjPCEBasis& operator=(const LanczosProjPCEBasis& b);

  protected:

    typedef WeightedVectorSpace<ordinal_type,value_type> vectorspace_type;
    typedef DenseOperator<ordinal_type,value_type> operator_type;
    typedef Stokhos::Lanczos<vectorspace_type, operator_type> lanczos_type;
    typedef typename lanczos_type::matrix_type matrix_type;
    typedef typename lanczos_type::vector_type vector_type;

    //! PCE Lanczos procedure is based on
    Teuchos::RCP< const Stokhos::OrthogPolyApprox<ordinal_type, value_type> > pce;

    //! Flag indicating whether to limit the integration order
    bool limit_integration_order;

    //! Size of PC expansion
    ordinal_type pce_sz;

    //! Basis norms
    Teuchos::Array<value_type> pce_norms;

    //! Triple-product matrix used in generating lanczos vectors
    matrix_type Cijk_matrix;

    //! Weighting vector used in inner-products
    vector_type weights;

    //! Initial Lanczos vector
    vector_type u0;

    //! Lanczos vectors
    mutable matrix_type lanczos_vecs;

    //! Projection of pce in new basis
    vector_type new_pce;

  }; // class LanczosProjPCEBasis

} // Namespace Stokhos

// Include template definitions
#include "Stokhos_LanczosProjPCEBasisImp.hpp"

#endif