DriverArpack.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: DriverArpack.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:  Arnoldi solver using Arpack
//
///////////////////////////////////////////////////////////////////////////////
 
#include <SolverUtils/DriverArpack.h>
 
namespace Nektar::SolverUtils
{
 
std::string DriverArpack::arpackProblemTypeLookupIds[6] = {
    LibUtilities::SessionReader::RegisterEnumValue("ArpackProblemType",
                                                   "LargestReal", 0),
    LibUtilities::SessionReader::RegisterEnumValue("ArpackProblemType",
                                                   "SmallestReal", 1),
    LibUtilities::SessionReader::RegisterEnumValue("ArpackProblemType",
                                                   "LargestImag", 2),
    LibUtilities::SessionReader::RegisterEnumValue("ArpackProblemType",
                                                   "SmallestImag", 3),
    LibUtilities::SessionReader::RegisterEnumValue("ArpackProblemType",
                                                   "LargestMag", 4),
    LibUtilities::SessionReader::RegisterEnumValue("ArpackProblemType",
                                                   "SmallestMag", 5),
};
std::string DriverArpack::arpackProblemTypeDefault =
    LibUtilities::SessionReader::RegisterDefaultSolverInfo("ArpackProblemType",
                                                           "LargestMag");
std::string DriverArpack::driverLookupId =
    LibUtilities::SessionReader::RegisterEnumValue("Driver", "Arpack", 0);
 
std::string DriverArpack::className =
    GetDriverFactory().RegisterCreatorFunction("Arpack", DriverArpack::create);
 
std::string DriverArpack::ArpackProblemTypeTrans[6] = {"LR", "SR", "LI",
                                                       "SI", "LM", "SM"};
 
/**
 *
 */
DriverArpack::DriverArpack(const LibUtilities::SessionReaderSharedPtr pSession,
                           const SpatialDomains::MeshGraphSharedPtr pGraph)
    : DriverArnoldi(pSession, pGraph)
{
}
 
/**
 *
 */
void DriverArpack::v_InitObject(std::ostream &out)
{
    DriverArnoldi::v_InitObject(out);
 
    // Initialisation of Arnoldi parameters
    m_maxn   = 1000000; // Maximum size of the problem
    m_maxnev = 200;     // maximum number of eigenvalues requested
    m_maxncv = 500;     // Largest number of basis vector used in Implicitly
                        // Restarted Arnoldi
 
    // Error alerts
    ASSERTL0(m_nvec <= m_maxnev, "NEV is greater than MAXNEV");
    ASSERTL0(m_kdim <= m_maxncv, "NEV is greater than MAXNEV");
    ASSERTL0(2 <= m_kdim - m_nvec, "NCV-NEV is less than 2");
 
    ASSERTL0(m_comm->GetSize() == 1,
             "..ARPACK is not currently set-up for parallel execution...\n");
 
    m_equ[0]->PrintSummary(out);
 
    // Print session parameters
    out << "\tArnoldi solver type    : Arpack" << std::endl;
    out << "\tArpack problem type    : ";
    out << ArpackProblemTypeTrans[m_session->GetSolverInfoAsEnum<int>(
               "ArpackProblemType")]
        << std::endl;
    DriverArnoldi::ArnoldiSummary(out);
 
    // Initialization
    for (int i = 0; i < m_nequ; ++i)
    {
        m_equ[i]->DoInitialise();
    }
 
    // FwdTrans Initial conditions to be in Coefficient Space
    m_equ[m_nequ - 1]->TransPhysToCoeff();
}
 
/**
 *
 */
void DriverArpack::v_Execute(std::ostream &out)
 
{
    Array<OneD, NekDouble> tmpworkd;
 
    int nq = m_equ[0]
                 ->UpdateFields()[0]
                 ->GetNcoeffs(); // Number of points in the mesh
    int n      = m_nfields * nq; // Number of points in eigenvalue calculation
    int lworkl = 3 * m_kdim * (m_kdim + 2); // Size of work array
    int ido;  // REVERSE COMMUNICATION parameter. At the first call must be
              // initialised at 0
    int info; // do not set initial vector (info=0 random initial vector, info=1
              // read initial vector from session file)
 
    int iparam[11];
    int ipntr[14];
 
    Array<OneD, int> ritzSelect;
    Array<OneD, NekDouble> dr;
    Array<OneD, NekDouble> di;
    Array<OneD, NekDouble> workev;
    Array<OneD, NekDouble> z;
    NekDouble sigmar, sigmai;
 
    Array<OneD, NekDouble> resid(n);
    Array<OneD, NekDouble> v(n * m_kdim);
    Array<OneD, NekDouble> workl(lworkl, 0.0);
    Array<OneD, NekDouble> workd(3 * n, 0.0);
 
    ASSERTL0(n <= m_maxn, "N is greater than   MAXN");
 
    if (m_session->DefinesFunction("InitialConditions"))
    {
        out << "\tInital vector       : input file  " << std::endl;
        info = 1;
        CopyFieldToArnoldiArray(resid);
    }
    else
    {
        out << "\tInital vector       : random  " << std::endl;
        info = 0;
    }
 
    char B;
 
    iparam[0] = 1;      // strategy for shift-invert
    iparam[1] = 0;      // (deprecated)
    iparam[2] = m_nits; // maximum number of iterations allowed/taken
    iparam[3] = 1;      // blocksize to be used for recurrence
    iparam[4] = 0;      // number of converged ritz eigenvalues
    iparam[5] = 0;      // (deprecated)
 
    // Use generalized B matrix for coupled solver.
    if (m_timeSteppingAlgorithm)
    {
        iparam[6] = 1; // computation mode 1=> matrix-vector prod
        B         = 'I';
    }
    else
    {
        iparam[6] = 3; // computation mode 1=> matrix-vector prod
        B         = 'G';
    }
#if 0
    if((fabs(m_realShift) > NekConstants::kNekZeroTol)|| // use shift if m_realShift > 1e-12
       (fabs(m_imagShift) > NekConstants::kNekZeroTol))
    {
        iparam[6] = 3; // This was 3 need to know what to set it to
        B = 'G';
    }
    else
    {
        iparam[6] = 1;      // computation mode 1=> matrix-vector prod
        B = 'I';
    }
#endif
    iparam[7]  = 0; // (for shift-invert)
    iparam[8]  = 0; // number of MV operations
    iparam[9]  = 0; // number of BV operations
    iparam[10] = 0; // number of reorthogonalisation steps
 
    int cycle = 0;
    const char *problem =
        ArpackProblemTypeTrans[m_session->GetSolverInfoAsEnum<int>(
                                   "ArpackProblemType")]
            .c_str();
 
    std::string name = m_session->GetSessionName() + ".evl";
    std::ofstream pFile(name.c_str());
 
    ido = 0; // At the first call must be initialisedat 0
 
    while (ido != 99) // ido==-1 || ido==1 || ido==0)
    {
        // Routine for eigenvalue evaluation for non-symmetric operators
        Arpack::Dnaupd(ido, &B, // B='I' for std eval problem
                       n, problem, m_nvec, m_evtol, &resid[0], m_kdim, &v[0], n,
                       iparam, ipntr, &workd[0], &workl[0], lworkl, info);
 
        // Plotting of real and imaginary part of the
        // eigenvalues from workl
        out << "\rIteration " << cycle << ", output: " << info
            << ", ido=" << ido << " " << std::flush;
 
        if (!((cycle - 1) % m_kdim) && (cycle > m_kdim) && (ido != 2))
        {
            pFile << "Krylov spectrum at iteration: " << cycle << std::endl;
 
            if (m_timeSteppingAlgorithm)
            {
                pFile << "EV  Magnitude   Angle       Growth      Frequency   "
                         "Residual"
                      << std::endl;
            }
            else
            {
                pFile << "EV  Real        Imaginary   inverse real  inverse "
                         "imag  Residual"
                      << std::endl;
            }
 
            out << std::endl;
            for (int k = 0; k < m_kdim; ++k)
            {
                // write m_kdim eigs to screen
                WriteEvs(pFile, k, workl[ipntr[5] - 1 + k],
                         workl[ipntr[6] - 1 + k]);
            }
        }
 
        if (ido == 99)
        {
            break;
        }
 
        switch (ido)
        {
            case -1:
            case 1: // Note that ido=1 we are using input x
                    // (workd[inptr[0]-1]) rather than Mx as
                    // recommended in manual since it is not
                    // possible to impose forcing directly.
                CopyArnoldiArrayToField(tmpworkd = workd + (ipntr[0] - 1));
 
                m_equ[0]->TransCoeffToPhys();
 
                m_equ[0]->DoSolve();
                if (m_EvolutionOperator == eTransientGrowth)
                {
                    // start Adjoint with latest fields of direct
                    CopyFwdToAdj();
 
                    m_equ[1]->TransCoeffToPhys();
                    m_equ[1]->DoSolve();
                }
 
                if (!(cycle % m_infosteps))
                {
                    out << std::endl;
                    m_equ[0]->Output();
                }
 
                // operated fields are copied into workd[inptr[1]-1]
                CopyFieldToArnoldiArray(tmpworkd = workd + (ipntr[1] - 1));
 
                cycle++;
                break;
            case 2: // provide y = M x (bwd trans and iproduct);
            {
                // workd[inptr[0]-1] copied into operator fields
                CopyArnoldiArrayToField(tmpworkd = workd + (ipntr[0] - 1));
 
                m_equ[0]->TransCoeffToPhys();
 
                Array<OneD, MultiRegions::ExpListSharedPtr> fields =
                    m_equ[0]->UpdateFields();
                for (int i = 0; i < fields.size(); ++i)
                {
                    fields[i]->IProductWRTBase(fields[i]->GetPhys(),
                                               fields[i]->UpdateCoeffs());
                }
 
                // operated fields are copied into workd[inptr[1]-1]
                CopyFieldToArnoldiArray(tmpworkd = workd + (ipntr[1] - 1));
                break;
            }
            default:
                ASSERTL0(false, "Unexpected reverse communication request.");
        }
    }
 
    out << std::endl
        << "Converged in " << iparam[8] << " iterations" << std::endl;
 
    ASSERTL0(info >= 0, " Error with Dnaupd");
 
    ritzSelect = Array<OneD, int>(m_kdim, 0);
    dr         = Array<OneD, NekDouble>(m_nvec + 1, 0.0);
    di         = Array<OneD, NekDouble>(m_nvec + 1, 0.0);
    workev     = Array<OneD, NekDouble>(3 * m_kdim);
    z          = Array<OneD, NekDouble>(n * (m_nvec + 1));
 
    if (m_negatedOp)
    {
        sigmar = -m_realShift;
    }
    else
    {
        sigmar = m_realShift;
    }
 
    // Do not pass imaginary shift to Arpack since we have not
    // used a Fortran complex number format and so processing
    // is mucked up. Need to do some processing afterwards.
    sigmai = 0;
 
    // Setting 'A', Ritz vectors are computed. 'S' for Shur vectors
    Arpack::Dneupd(1, "A", ritzSelect.data(), dr.data(), di.data(), z.data(), n,
                   sigmar, sigmai, workev.data(), &B, n, problem, m_nvec,
                   m_evtol, resid.data(), m_kdim, v.data(), n, iparam, ipntr,
                   workd.data(), workl.data(), lworkl, info);
 
    ASSERTL0(info == 0, " Error with Dneupd");
 
    int nconv = iparam[4];
 
    // Subtract off complex shift if it exists
    if (m_negatedOp)
    {
        Vmath::Sadd(nconv, m_imagShift, di, 1, di, 1);
    }
    else
    {
        Vmath::Sadd(nconv, -m_imagShift, di, 1, di, 1);
    }
 
    WARNINGL0(m_imagShift == 0, "Complex Shift applied. "
                                "Need to implement Ritz re-evaluation of"
                                "eigenvalue. Only one half of complex "
                                "value will be correct");
 
    Array<OneD, MultiRegions::ExpListSharedPtr> fields =
        m_equ[0]->UpdateFields();
 
    out << "Converged Eigenvalues: " << nconv << std::endl;
    pFile << "Converged Eigenvalues: " << nconv << std::endl;
 
    if (m_timeSteppingAlgorithm)
    {
        out << "         Magnitude   Angle       Growth      Frequency"
            << std::endl;
        pFile << "         Magnitude   Angle       Growth      Frequency"
              << std::endl;
        for (int i = 0; i < nconv; ++i)
        {
            WriteEvs(out, i, dr[i], di[i]);
            WriteEvs(pFile, i, dr[i], di[i]);
 
            std::string file = m_session->GetSessionName() + "_eig_" +
                               std::to_string(i) + ".fld";
            WriteFld(file, z + i * n);
        }
    }
    else
    {
        out << "         Real        Imaginary " << std::endl;
        pFile << "         Real        Imaginary " << std::endl;
        for (int i = 0; i < nconv; ++i)
        {
            WriteEvs(out, i, dr[i], di[i], NekConstants::kNekUnsetDouble,
                     false);
            WriteEvs(pFile, i, dr[i], di[i], NekConstants::kNekUnsetDouble,
                     false);
 
            std::string file = m_session->GetSessionName() + "_eig_" +
                               std::to_string(i) + ".fld";
            WriteFld(file, z + i * n);
        }
    }
 
    m_real_evl = dr;
    m_imag_evl = di;
 
    pFile.close();
 
    for (int j = 0; j < m_equ[0]->GetNvariables(); ++j)
    {
        NekDouble vL2Error   = m_equ[0]->L2Error(j, false);
        NekDouble vLinfError = m_equ[0]->LinfError(j);
        if (m_comm->GetRank() == 0)
        {
            out << "L 2 error (variable " << m_equ[0]->GetVariable(j)
                << ") : " << vL2Error << std::endl;
            out << "L inf error (variable " << m_equ[0]->GetVariable(j)
                << ") : " << vLinfError << std::endl;
        }
    }
}
 
} // namespace Nektar::SolverUtils