PolyEPoints.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: PolyEPoints.cpp
//
// 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
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: 1D Evenly-Spaced Points
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/BasicUtils/ErrorUtil.hpp>
#include <LibUtilities/Foundations/Foundations.hpp>
#include <LibUtilities/Foundations/ManagerAccess.h>
#include <LibUtilities/Foundations/PolyEPoints.h>
#include <LibUtilities/LinearAlgebra/NekMatrix.hpp>
 
namespace Nektar
{
namespace LibUtilities
{
bool PolyEPoints::initPointsManager[] = {PointsManager().RegisterCreator(
    PointsKey(0, ePolyEvenlySpaced), PolyEPoints::Create)};
 
void PolyEPoints::v_CalculatePoints()
{
    // Allocate the storage for points
    PointsBaseType::v_CalculatePoints();
 
    unsigned int npts = m_pointsKey.GetNumPoints();
    if (npts == 1)
    {
        m_points[0][0] = 0.0;
    }
    else
    {
        NekDouble dx = 2.0 / (NekDouble)(npts - 1);
        for (unsigned int i = 0; i < npts; ++i)
        {
            m_points[0][i] = -1.0 + i * dx;
        }
    }
}
 
void PolyEPoints::v_CalculateWeights()
{
    // Allocate the storage for points
    PointsBaseType::v_CalculateWeights();
 
    unsigned int npts = m_pointsKey.GetNumPoints();
    if (npts == 1)
    {
        m_weights[0] = 2.0; // midpoint rule
    }
    else
    {
        PointsKey gaussKey(npts, eGaussLobattoLegendre);
        std::shared_ptr<PointsBaseType> ptr = PointsManager()[gaussKey];
        Array<OneD, const NekDouble> z;
        Array<OneD, const NekDouble> w;
 
        ptr->GetZW(z, w);
        for (unsigned int i = 0; i < npts; ++i)
        {
            m_weights[i] = 0.0;
            for (unsigned j = 0; j < npts; ++j)
            {
                m_weights[i] += w[j] * LagrangePoly(z[j], i, npts, m_points[0]);
            }
        }
    }
}
 
void PolyEPoints::v_CalculateDerivMatrix()
{
    // Allocate the derivative matrix.
    PointsBaseType::v_CalculateDerivMatrix();
 
    for (unsigned int i = 0; i < m_pointsKey.GetNumPoints(); ++i)
    {
        for (unsigned int j = 0; j < m_pointsKey.GetNumPoints(); ++j)
        {
            (*m_derivmatrix[0])(i, j) = LagrangePolyDeriv(
                m_points[0][i], j, m_pointsKey.GetNumPoints(), m_points[0]);
        }
    }
}
 
void PolyEPoints::CalculateInterpMatrix(
    unsigned int npts, const Array<OneD, const NekDouble> &xpoints,
    Array<OneD, NekDouble> &interp)
{
    for (unsigned int i = 0; i < npts; ++i)
    {
        for (unsigned int j = 0; j < m_pointsKey.GetNumPoints(); ++j)
        {
            interp[i + j * npts] = LagrangePoly(
                xpoints[i], j, m_pointsKey.GetNumPoints(), m_points[0]);
        }
    }
}
 
std::shared_ptr<PolyEPoints::PointsBaseType> PolyEPoints::Create(
    const PointsKey &key)
{
    std::shared_ptr<PointsBaseType> returnval(
        MemoryManager<PolyEPoints>::AllocateSharedPtr(key));
 
    returnval->Initialize();
 
    return returnval;
}
 
const std::shared_ptr<NekMatrix<NekDouble>> PolyEPoints::v_GetI(
    const PointsKey &pkey)
{
    ASSERTL0(pkey.GetPointsDim() == 1,
             "Gauss Points can only interp to other 1d point distributions");
 
    int numpoints = pkey.GetNumPoints();
    Array<OneD, const NekDouble> xpoints;
 
    PointsManager()[pkey]->GetPoints(xpoints);
 
    return GetI(numpoints, xpoints);
}
 
const std::shared_ptr<NekMatrix<NekDouble>> PolyEPoints::v_GetI(
    const Array<OneD, const NekDouble> &x)
{
    int numpoints = 1;
 
    /// Delegate to function below.
    return GetI(numpoints, x);
}
 
const std::shared_ptr<NekMatrix<NekDouble>> PolyEPoints::v_GetI(
    unsigned int numpoints, const Array<OneD, const NekDouble> &x)
{
    Array<OneD, NekDouble> interp(GetNumPoints() * numpoints);
 
    CalculateInterpMatrix(numpoints, x, interp);
 
    unsigned int np = GetTotNumPoints();
    NekDouble *d    = interp.data();
    std::shared_ptr<NekMatrix<NekDouble>> returnval(
        MemoryManager<NekMatrix<NekDouble>>::AllocateSharedPtr(numpoints, np,
                                                               d));
 
    return returnval;
}
 
NekDouble PolyEPoints::LagrangeInterpolant(
    NekDouble x, int npts, const Array<OneD, const NekDouble> &xpts,
    const Array<OneD, const NekDouble> &funcvals)
{
    NekDouble sum = 0.0;
 
    for (int i = 0; i < npts; ++i)
    {
        sum += funcvals[i] * LagrangePoly(x, i, npts, xpts);
    }
    return sum;
}
 
NekDouble PolyEPoints::LagrangePoly(NekDouble x, int pt, int npts,
                                    const Array<OneD, const NekDouble> &xpts)
{
    NekDouble h = 1.0;
 
    for (int i = 0; i < pt; ++i)
    {
        h = h * (x - xpts[i]) / (xpts[pt] - xpts[i]);
    }
 
    for (int i = pt + 1; i < npts; ++i)
    {
        h = h * (x - xpts[i]) / (xpts[pt] - xpts[i]);
    }
 
    return h;
}
 
NekDouble PolyEPoints::LagrangePolyDeriv(
    NekDouble x, int pt, int npts, const Array<OneD, const NekDouble> &xpts)
{
    NekDouble h;
    NekDouble y = 0.0;
 
    for (int j = 0; j < npts; ++j)
    {
        if (j != pt)
        {
            h = 1.0;
            for (int i = 0; i < npts; ++i)
            {
                if (i != pt)
                {
                    if (i != j)
                    {
                        h = h * (x - xpts[i]);
                    }
                    h = h / (xpts[pt] - xpts[i]);
                }
            }
            y = y + h;
        }
    }
    return y;
}
} // end of namespace LibUtilities
} // end of namespace Nektar