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

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#ifndef STOKHOS_PECOS_ONED_ORTHOG_POLY_BASIS_HPP
#define STOKHOS_PECOS_ONED_ORTHOG_POLY_BASIS_HPP

#include "Stokhos_ConfigDefs.h"
#ifdef HAVE_STOKHOS_DAKOTA

#include "Stokhos_OneDOrthogPolyBasis.hpp"
#include "TriKota_ConfigDefs.hpp"
#include "OrthogonalPolynomial.hpp"

namespace Stokhos {

  /*! 
   * \brief Implementation of OneDOrthogPolyBasis via Pecos.
   */
  template <typename ordinal_type, typename value_type>
  class PecosOneDOrthogPolyBasis : 
    public OneDOrthogPolyBasis<ordinal_type, value_type> {
  public:

    //! Constructor
    /*!
     * \c name is the name for the basis that will be displayed when
     * printing the basis and \c p is the order of the basis.
     */
    PecosOneDOrthogPolyBasis(
      const Teuchos::RCP<Pecos::OrthogonalPolynomial>& pecosPoly, 
      const std::string& name, ordinal_type p);

    //! Destructor
    virtual ~PecosOneDOrthogPolyBasis();

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

    //! Return order of basis (largest monomial degree \f$P\f$).
    virtual ordinal_type order() const;

    //! Return total size of basis (given by order() + 1).
    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 given by order().
     */
    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$i,j=0,\dots,P\f$ where
     * \f$P\f$ is size()-1 and \f$k=0,\dots,p\f$ where \f$p\f$
     * is the supplied \c order.
     *
     * This method is implemented by computing \f$C_{ijk}\f$ using Gaussian
     * quadrature.
     */
    virtual Teuchos::RCP< Stokhos::Dense3Tensor<ordinal_type, value_type> > 
    computeTripleProductTensor() const;

     virtual 
    Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> > 
    computeSparseTripleProductTensor(ordinal_type order) const;

    //! Compute derivative double product tensor
    /*!
     * The \f$(i,j)\f$ entry of the tensor \f$B_{ij}\f$ is given by
     * \f$B_{ij} = \langle\psi_i'\psi_j\rangle\f$ where \f$\psi_l\f$
     * represents basis polynomial \f$l\f$ and \f$i,j=0,\dots,P\f$ where
     * \f$P\f$ is the order of the basis.
     *
     * This method is implemented by computing \f$B_{ij}\f$ using Gaussian
     * quadrature.
     */
    virtual Teuchos::RCP< Teuchos::SerialDenseMatrix<ordinal_type, value_type> > computeDerivDoubleProductTensor() const;

    //! Evaluate each basis polynomial at given point \c point
    /*!
     * Size of returned array is given by size(), and coefficients are
     * ordered from order 0 up to order order().
     */
    virtual void evaluateBases(const value_type& point,
                               Teuchos::Array<value_type>& basis_pts) const;

    /*! 
     * \brief Evaluate basis polynomial given by order \c order at given 
     * point \c point.
     */
    virtual value_type evaluate(const value_type& point, 
				ordinal_type order) 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;

    /*! 
     * \brief Compute quadrature points, weights, and values of 
     * basis polynomials at given set of points \c points.
     */
    /*!
     * \c quad_order specifies the order to which the quadrature should be
     * accurate, not the number of quadrature points.  The number of points
     * is given by (\c quad_order + 1) / 2.   Note however the passed arrays
     * do NOT need to be sized correctly on input as they will be resized
     * appropriately.
     *
     * The quadrature points and weights are computed from the three-term
     * recurrence by solving a tri-diagional symmetric eigenvalue problem
     * (see Gene H. Golub and John H. Welsch, "Calculation of Gauss Quadrature 
     * Rules", Mathematics of Computation, Vol. 23, No. 106 (Apr., 1969), 
     * pp. 221-230).
     */
    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;

    /*!
     * Return polynomial degree of exactness for a given number of quadrature
     * points.
     */
    virtual ordinal_type quadDegreeOfExactness(ordinal_type n) const;

    //! Evaluate coefficient growth rule for Smolyak-type bases
    virtual ordinal_type coefficientGrowth(ordinal_type n) const;

    //! Evaluate point growth rule for Smolyak-type bases
    virtual ordinal_type pointGrowth(ordinal_type n) const;

    //! Function pointer needed for level_to_order mappings
    typedef typename OneDOrthogPolyBasis<ordinal_type,value_type>::LevelToOrderFnPtr LevelToOrderFnPtr;

    //! Get sparse grid level_to_order mapping function
    /*!
     * Predefined functions are:
     *  webbur::level_to_order_linear_wn Symmetric Gaussian linear growth
     *  webbur::level_to_order_linear_nn Asymmetric Gaussian linear growth
     *  webbur::level_to_order_exp_cc    Clenshaw-Curtis exponential growth
     *  webbur::level_to_order_exp_gp    Gauss-Patterson exponential growth
     *  webbur::level_to_order_exp_hgk   Genz-Keister exponential growth
     *  webbur::level_to_order_exp_f2    Fejer-2 exponential growth
     */
    virtual LevelToOrderFnPtr getSparseGridGrowthRule() const {
      return sparse_grid_growth_rule; }

    //! Set sparse grid rule
    virtual void setSparseGridGrowthRule(LevelToOrderFnPtr ptr) {
      sparse_grid_growth_rule = ptr; }

    /*! 
     * \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;

    //@}

    //! Evaluate basis polynomials and their derivatives at given point \c point
    virtual void evaluateBasesAndDerivatives(const value_type& point,
					     Teuchos::Array<value_type>& vals,
					     Teuchos::Array<value_type>& derivs) const;

  protected:

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

  private:

    // Prohibit copying
    PecosOneDOrthogPolyBasis(const PecosOneDOrthogPolyBasis&);

    // Prohibit Assignment
    PecosOneDOrthogPolyBasis& operator=(const PecosOneDOrthogPolyBasis& b);
    
  protected:

    //! Pointer to Pecos orthgonal polynomial object
    Teuchos::RCP<Pecos::OrthogonalPolynomial> pecosPoly;

    //! Name of basis
    std::string name;

    //! Order of basis
    ordinal_type p;

    //! Sparse grid growth rule (as determined by Pecos)
    LevelToOrderFnPtr sparse_grid_growth_rule;

    //! Norms
    Teuchos::Array<value_type> norms;

  }; // class PecosOneDOrthogPolyBasis

} // Namespace Stokhos

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

#endif // HAVE_STOKHOS_DAKOTA

#endif // STOKHOS_PECOS_ONED_ORTHOG_POLY_BASIS_HPP