Intrepid_Polylib.hpp

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//
// File: Intrepid_Polylib.hpp
//
// 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).
//
// License for the specific language governing rights and limitations under
// 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:
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// The above copyright notice and this permission notice shall be included
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// Description:
// This file is redistributed with the Intrepid package. It should be used
// in accordance with the above MIT license, at the request of the authors.
// This file is NOT covered by the usual Intrepid/Trilinos LGPL license.
//
// Origin: Nektar++ library, http://www.nektar.info, downloaded on
//         March 10, 2009.
//


#ifndef INTREPID_POLYLIB_HPP
#define INTREPID_POLYLIB_HPP

#include "Intrepid_ConfigDefs.hpp"
#include "Intrepid_Types.hpp"
#include "Teuchos_Assert.hpp"

namespace Intrepid {

  enum EIntrepidPLPoly {
    PL_GAUSS=0,
    PL_GAUSS_RADAU_LEFT,
    PL_GAUSS_RADAU_RIGHT,
    PL_GAUSS_LOBATTO,
    PL_MAX
  };

  inline EIntrepidPLPoly & operator++(EIntrepidPLPoly &type) {
    return type = static_cast<EIntrepidPLPoly>(type+1);
  }

  inline EIntrepidPLPoly operator++(EIntrepidPLPoly &type, int) {
    EIntrepidPLPoly oldval = type;
    ++type;
    return oldval;
  }


  class IntrepidPolylib {

    public:

    /* Points and weights */

    template<class Scalar>
    static void   zwgj   (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void   zwgrjm (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void   zwgrjp (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void   zwglj  (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);



    /* Derivative operators */

    template<class Scalar>
    static void   Dgj    (Scalar *D,  const Scalar *z, const int np, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void   Dgrjm  (Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void   Dgrjp  (Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void   Dglj   (Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta);



    /* Lagrangian interpolants */

    template<class Scalar>
    static Scalar hgj     (const int i, const Scalar z, const Scalar *zgj,
                           const int np, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static Scalar hgrjm   (const int i, const Scalar z, const Scalar *zgrj,
                           const int np, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static Scalar hgrjp   (const int i, const Scalar z, const Scalar *zgrj,
                           const int np, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static Scalar hglj    (const int i, const Scalar z, const Scalar *zglj,
                           const int np, const Scalar alpha, const Scalar beta);



    /* Interpolation operators */

    template<class Scalar>
    static void  Imgj  (Scalar *im, const Scalar *zgj, const Scalar *zm, const int nz,
                        const int mz, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void  Imgrjm(Scalar *im, const Scalar *zgrj, const Scalar *zm, const int nz,
                        const int mz, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void  Imgrjp(Scalar *im, const Scalar *zgrj, const Scalar *zm, const int nz,
                        const int mz, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void  Imglj (Scalar *im, const Scalar *zglj, const Scalar *zm, const int nz,
                        const int mz, const Scalar alpha, const Scalar beta);


    /* Polynomial functions */

    template<class Scalar>
    static void jacobfd (const int np, const Scalar *z, Scalar *poly_in, Scalar *polyd,
                         const int n, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void jacobd  (const int np, const Scalar *z, Scalar *polyd, const int n,
                         const Scalar alpha, const Scalar beta);



    /* Helper functions. */

    template<class Scalar>
    static void   Jacobz (const int n, Scalar *z, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void   JacZeros (const int n, Scalar *a, const Scalar alpha, const Scalar beta);


    template<class Scalar>
    static void   TriQL    (const int n, Scalar *d, Scalar *e);


    template<class Scalar>
    static Scalar gammaF (const Scalar x);


  }; // class IntrepidPolylib

} // end of Intrepid namespace

// include templated definitions
#include <Intrepid_PolylibDef.hpp>

#endif