Basis.h

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///////////////////////////////////////////////////////////////////////////////
//
// File: Basis.h
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// DEALINGS IN THE SOFTWARE.
//
// Description: Header file of Basis definition
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_LIB_UTILIITIES_FOUNDATIONS_BASIS_H
#define NEKTAR_LIB_UTILIITIES_FOUNDATIONS_BASIS_H
 
#include <LibUtilities/Foundations/Points.h>
#include <LibUtilities/LinearAlgebra/NekMatrix.hpp>
 
namespace Nektar::LibUtilities
{
/// Describes the specification for a Basis.
class BasisKey
{
public:
    // Use for looking up the creator. The creator for number of points
    // can generate for any number, so we want the same creator called
    // for all number.
    struct opLess
    {
        LIB_UTILITIES_EXPORT bool operator()(const BasisKey &lhs,
                                             const BasisKey &rhs) const;
    };
 
    /// Constructor
    BasisKey(const BasisType btype, const size_t nummodes, const PointsKey pkey)
        : m_nummodes(nummodes), m_basistype(btype), m_pointsKey(pkey)
    {
    }
 
    /// Copy constructor
    BasisKey(const BasisKey &B) = default;
 
    /// Destructor
    ~BasisKey()
    {
    }
 
    /// Assignment operator
    BasisKey &operator=(const BasisKey &) = default;
 
    /// Returns the order of the basis.
    inline int GetNumModes() const
    {
        return m_nummodes;
    }
 
    /// \todo Generalise to arbitrary polynomials
    inline int GetTotNumModes() const
    {
        size_t value = 0;
 
        switch (m_basistype)
        {
            case eOrtho_B:
            case eModified_B:
                value = m_nummodes * (m_nummodes + 1) / 2;
                break;
            case eModified_C:
            case eOrtho_C:
                value = m_nummodes * (m_nummodes + 1) * (m_nummodes + 2) / 6;
                break;
            case eModifiedPyr_C:
            case eOrthoPyr_C:
                value =
                    m_nummodes * (m_nummodes + 1) * (2 * m_nummodes + 1) / 6;
                break;
            case eOrtho_A:
            case eModified_A:
            case eFourier:
            case eGLL_Lagrange:
            case eGauss_Lagrange:
            case eLegendre:
            case eChebyshev:
            case eMonomial:
            case eFourierSingleMode:
            case eFourierHalfModeRe:
            case eFourierHalfModeIm:
                value = m_nummodes;
                break;
 
            default:
                NEKERROR(ErrorUtil::efatal, "Unknown basis being used");
        }
        return value;
    }
 
    /// Return points order at which  basis is defined
    inline int GetNumPoints() const
    {
        return m_pointsKey.GetNumPoints();
    }
 
    inline int GetTotNumPoints() const
    {
        return m_pointsKey.GetTotNumPoints();
    }
 
    /// Return type of expansion basis.
    inline BasisType GetBasisType() const
    {
        return m_basistype;
    }
 
    /// Return distribution of points.
    inline PointsKey GetPointsKey() const
    {
        return m_pointsKey;
    }
 
    /// Return type of quadrature.
    inline PointsType GetPointsType() const
    {
        return m_pointsKey.GetPointsType();
    }
 
    /// Determine if quadrature of expansion \a x matches this.
    inline bool SamePoints(const BasisKey &x) const
    {
        return (x.m_pointsKey == m_pointsKey);
    }
 
    /// Determine if basis expansion \a x matches this.
    inline bool SameExp(const BasisKey &x) const
    {
        return ((x.m_nummodes == m_nummodes) && (x.m_basistype == m_basistype));
    }
 
    /// Determine if basis has exact integration for inner product.
    LIB_UTILITIES_EXPORT bool ExactIprodInt() const;
 
    /// Determine if basis has collocation properties.
    LIB_UTILITIES_EXPORT bool Collocation() const;
 
    /// Overloaded Operators
    LIB_UTILITIES_EXPORT friend bool operator==(const BasisKey &x,
                                                const BasisKey &y);
    LIB_UTILITIES_EXPORT friend bool operator==(const BasisKey *x,
                                                const BasisKey &y);
    LIB_UTILITIES_EXPORT friend bool operator==(const BasisKey &x,
                                                const BasisKey *y);
    LIB_UTILITIES_EXPORT friend bool operator!=(const BasisKey &x,
                                                const BasisKey &y);
    LIB_UTILITIES_EXPORT friend bool operator!=(const BasisKey *x,
                                                const BasisKey &y);
    LIB_UTILITIES_EXPORT friend bool operator!=(const BasisKey &x,
                                                const BasisKey *y);
    LIB_UTILITIES_EXPORT friend bool operator<(const BasisKey &lhs,
                                               const BasisKey &rhs);
    LIB_UTILITIES_EXPORT friend bool opLess::operator()(
        const BasisKey &lhs, const BasisKey &rhs) const;
 
protected:
    size_t m_nummodes;     ///< Expansion order.
    BasisType m_basistype; ///< Expansion type.
    PointsKey m_pointsKey; ///< Points specification.
 
private:
    BasisKey() = delete;
};
 
/// Defines a null basis with no type or points.
static const BasisKey NullBasisKey(eNoBasisType, 0, NullPointsKey);
 
/// Represents a basis of a given type.
class Basis
{
public:
    /// Returns a new instance of a Basis with given BasisKey.
    static std::shared_ptr<Basis> Create(const BasisKey &bkey);
 
    /// Destructor.
    virtual ~Basis(){};
 
    /// Return order of basis from the basis specification.
    inline int GetNumModes() const
    {
        return m_basisKey.GetNumModes();
    }
 
    /// Return total number of modes from the basis specification.
    inline int GetTotNumModes() const
    {
        return m_basisKey.GetTotNumModes();
    }
 
    /// Return the number of points from the basis specification.
    inline int GetNumPoints() const
    {
        return m_basisKey.GetNumPoints();
    }
 
    /// Return total number of points from the basis specification.
    inline int GetTotNumPoints() const
    {
        return m_basisKey.GetTotNumPoints();
    }
 
    /// Return the type of expansion basis.
    inline BasisType GetBasisType() const
    {
        return m_basisKey.GetBasisType();
    }
 
    /// Return the points specification for the basis.
    inline PointsKey GetPointsKey() const
    {
        return m_basisKey.GetPointsKey();
    }
 
    /// Return the type of quadrature.
    inline PointsType GetPointsType() const
    {
        return m_basisKey.GetPointsType();
    }
 
    inline const Array<OneD, const NekDouble> &GetZ() const
    {
        return m_points->GetZ();
    }
 
    inline const Array<OneD, const NekDouble> &GetW() const
    {
        return m_points->GetW();
    }
 
    inline void GetZW(Array<OneD, const NekDouble> &z,
                      Array<OneD, const NekDouble> &w) const
    {
        m_points->GetZW(z, w);
    }
 
    inline const Array<OneD, const NekDouble> &GetBaryWeights() const
    {
        return m_points->GetBaryWeights();
    }
 
    inline const std::shared_ptr<NekMatrix<NekDouble>> &GetD(
        Direction dir = xDir) const
    {
        return m_points->GetD(dir);
    }
 
    const std::shared_ptr<NekMatrix<NekDouble>> GetI(
        const Array<OneD, const NekDouble> &x)
    {
        return m_points->GetI(x);
    }
 
    const std::shared_ptr<NekMatrix<NekDouble>> GetI(const BasisKey &bkey)
    {
        ASSERTL0(bkey.GetPointsKey().GetPointsDim() == 1,
                 "Interpolation only to other 1d basis");
        return m_InterpManager[bkey];
    }
 
    /// Determine if basis has exact integration for inner product.
    inline bool ExactIprodInt() const
    {
        return m_basisKey.ExactIprodInt();
    }
 
    /// Determine if basis has collocation properties.
    inline bool Collocation() const
    {
        return m_basisKey.Collocation();
    }
 
    /// Return basis definition array m_bdata.
    inline const Array<OneD, const NekDouble> &GetBdata() const
    {
        return m_bdata;
    }
 
    /// Return basis definition array m_dbdata.
    inline const Array<OneD, const NekDouble> &GetDbdata() const
    {
        return m_dbdata;
    }
 
    /// Returns the specification for the Basis.
    inline const BasisKey GetBasisKey() const
    {
        return m_basisKey;
    }
 
    LIB_UTILITIES_EXPORT void Initialize();
 
protected:
    BasisKey m_basisKey;             ///< Basis specification.
    PointsSharedPtr m_points;        ///< Set of points.
    Array<OneD, NekDouble> m_bdata;  ///< Basis definition.
    Array<OneD, NekDouble> m_dbdata; ///< Derivative Basis definition.
    NekManager<BasisKey, NekMatrix<NekDouble>, BasisKey::opLess>
        m_InterpManager;
 
private:
    static bool initBasisManager;
 
    /// Private constructor with BasisKey.
    Basis(const BasisKey &bkey);
 
    /// Private default constructor.
    Basis() = delete;
 
    std::shared_ptr<NekMatrix<NekDouble>> CalculateInterpMatrix(
        const BasisKey &tbasis0);
 
    /// Generate appropriate basis and their derivatives.
    void GenBasis();
};
 
LIB_UTILITIES_EXPORT bool operator<(const BasisKey &lhs, const BasisKey &rhs);
LIB_UTILITIES_EXPORT bool operator>(const BasisKey &lhs, const BasisKey &rhs);
 
LIB_UTILITIES_EXPORT std::ostream &operator<<(std::ostream &os,
                                              const BasisKey &rhs);
 
static BasisSharedPtr NullBasisSharedPtr;
static Array<OneD, BasisSharedPtr> NullBasisSharedPtr1DArray;
 
} // namespace Nektar::LibUtilities
 
#endif // NEKTAR_LIB_UTILIITIES_FOUNDATIONS_BASIS_H