StandardMatrix.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: StandardMatrix.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:
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/LinearAlgebra/StandardMatrix.hpp>
 
namespace Nektar
{
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag>::NekMatrix()
    : Matrix<DataType>(0, 0, eFULL), m_data(), m_wrapperType(eCopy),
      m_numberOfSuperDiagonals(std::numeric_limits<unsigned int>::max()),
      m_numberOfSubDiagonals(std::numeric_limits<unsigned int>::max()),
      m_tempSpace()
{
    m_data = Array<OneD, DataType>(GetRequiredStorageSize());
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag>::NekMatrix(unsigned int rows,
                                                  unsigned int columns,
                                                  MatrixStorage policy,
                                                  unsigned int subDiagonals,
                                                  unsigned int superDiagonals)
    : Matrix<DataType>(rows, columns, policy), m_data(), m_wrapperType(eCopy),
      m_numberOfSuperDiagonals(superDiagonals),
      m_numberOfSubDiagonals(subDiagonals), m_tempSpace()
{
    m_data = Array<OneD, DataType>(GetRequiredStorageSize());
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag>::NekMatrix(unsigned int rows,
                                                  unsigned int columns,
                                                  MatrixStorage policy,
                                                  unsigned int subDiagonals,
                                                  unsigned int superDiagonals,
                                                  unsigned int capacity)
    : Matrix<DataType>(rows, columns, policy), m_data(), m_wrapperType(eCopy),
      m_numberOfSuperDiagonals(superDiagonals),
      m_numberOfSubDiagonals(subDiagonals), m_tempSpace()
{
    unsigned int requiredStorage = this->GetRequiredStorageSize();
    unsigned int actualSize      = std::max(requiredStorage, capacity);
    m_data                       = Array<OneD, DataType>(actualSize);
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag>::NekMatrix(
    unsigned int rows, unsigned int columns,
    typename boost::call_traits<DataType>::const_reference initValue,
    MatrixStorage policy, unsigned int subDiagonals,
    unsigned int superDiagonals)
    : Matrix<DataType>(rows, columns, policy), m_data(), m_wrapperType(eCopy),
      m_numberOfSuperDiagonals(superDiagonals),
      m_numberOfSubDiagonals(subDiagonals), m_tempSpace()
{
    m_data = Array<OneD, DataType>(GetRequiredStorageSize());
    std::fill(m_data.begin(), m_data.end(), initValue);
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag>::NekMatrix(unsigned int rows,
                                                  unsigned int columns,
                                                  const DataType *data,
                                                  MatrixStorage policy,
                                                  unsigned int subDiagonals,
                                                  unsigned int superDiagonals)
    : Matrix<DataType>(rows, columns, policy), m_data(), m_wrapperType(eCopy),
      m_numberOfSuperDiagonals(superDiagonals),
      m_numberOfSubDiagonals(subDiagonals), m_tempSpace()
{
    unsigned int size = GetRequiredStorageSize();
    m_data            = Array<OneD, DataType>(size);
    std::copy(data, data + size, m_data.begin());
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag>::NekMatrix(
    unsigned int rows, unsigned int columns,
    const Array<OneD, const DataType> &d, MatrixStorage policy,
    unsigned int subDiagonals, unsigned int superDiagonals)
    : Matrix<DataType>(rows, columns, policy), m_data(), m_wrapperType(eCopy),
      m_numberOfSuperDiagonals(superDiagonals),
      m_numberOfSubDiagonals(subDiagonals), m_tempSpace()
{
    m_data = Array<OneD, DataType>(GetRequiredStorageSize());
    CopyArrayN(d, m_data, m_data.size());
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag>::NekMatrix(
    unsigned int rows, unsigned int columns, const Array<OneD, DataType> &d,
    PointerWrapper wrapperType, MatrixStorage policy, unsigned int subDiagonals,
    unsigned int superDiagonals)
    : Matrix<DataType>(rows, columns, policy), m_data(),
      m_wrapperType(wrapperType), m_numberOfSuperDiagonals(superDiagonals),
      m_numberOfSubDiagonals(subDiagonals), m_tempSpace()
{
    if (wrapperType == eWrapper)
    {
        m_data = Array<OneD, DataType>(d);
    }
    else
    {
        m_data = Array<OneD, DataType>(GetRequiredStorageSize());
        CopyArrayN(d, m_data, m_data.size());
    }
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag>::NekMatrix(
    const NekMatrix<DataType, StandardMatrixTag> &rhs)
    : Matrix<DataType>(rhs), m_data(), m_wrapperType(rhs.m_wrapperType),
      m_numberOfSuperDiagonals(rhs.m_numberOfSuperDiagonals),
      m_numberOfSubDiagonals(rhs.m_numberOfSubDiagonals), m_tempSpace()
{
    PerformCopyConstruction(rhs);
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag> &NekMatrix<DataType, StandardMatrixTag>::
operator=(const NekMatrix<DataType, StandardMatrixTag> &rhs)
{
    if (this == &rhs)
    {
        return *this;
    }
 
    Matrix<DataType>::operator=(rhs);
    m_numberOfSubDiagonals   = rhs.m_numberOfSubDiagonals;
    m_numberOfSuperDiagonals = rhs.m_numberOfSuperDiagonals;
 
    ResizeDataArrayIfNeeded();
 
    unsigned int requiredStorageSize = GetRequiredStorageSize();
    std::copy(rhs.m_data.data(), rhs.m_data.data() + requiredStorageSize,
              m_data.data());
 
    return *this;
}
 
/// Fill matrix with scalar
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag> &NekMatrix<
    DataType, StandardMatrixTag>::operator=(const DataType &rhs)
{
    unsigned int requiredStorageSize = GetRequiredStorageSize();
 
    DataType *lhs_array = m_data.data();
 
    Vmath::Fill(requiredStorageSize, rhs, lhs_array, 1);
 
    return *this;
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::ConstGetValueType NekMatrix<
    DataType, StandardMatrixTag>::operator()(unsigned int row,
                                             unsigned int column) const
{
    ASSERTL2(row < this->GetRows(),
             std::string("Row ") + std::to_string(row) +
                 std::string(" requested in a matrix with a maximum of ") +
                 std::to_string(this->GetRows()) + std::string(" rows"));
    ASSERTL2(column < this->GetColumns(),
             std::string("Column ") + std::to_string(column) +
                 std::string(" requested in a matrix with a maximum of ") +
                 std::to_string(this->GetColumns()) + std::string(" columns"));
 
    return this->GetValue(row, column, this->GetTransposeFlag());
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::ConstGetValueType NekMatrix<
    DataType, StandardMatrixTag>::operator()(unsigned int row,
                                             unsigned int column,
                                             char transpose) const
{
    return this->GetValue(row, column, transpose);
}
 
template <typename DataType>
unsigned int NekMatrix<DataType, StandardMatrixTag>::GetRequiredStorageSize()
    const
{
    return Matrix<DataType>::GetRequiredStorageSize(
        this->GetStorageType(), this->GetRows(), this->GetColumns(),
        this->GetNumberOfSubDiagonals(), this->GetNumberOfSuperDiagonals());
}
 
template <typename DataType>
unsigned int NekMatrix<DataType, StandardMatrixTag>::CalculateIndex(
    unsigned int row, unsigned int col, const char transpose) const
{
    unsigned int numRows    = this->GetSize()[0];
    unsigned int numColumns = this->GetSize()[1];
    return Matrix<DataType>::CalculateIndex(
        this->GetStorageType(), row, col, numRows, numColumns, transpose,
        m_numberOfSubDiagonals, m_numberOfSuperDiagonals);
}
 
template <typename DataType>
typename boost::call_traits<DataType>::const_reference NekMatrix<
    DataType, StandardMatrixTag>::GetValue(unsigned int row,
                                           unsigned int column) const
{
    ASSERTL2(row < this->GetRows(),
             std::string("Row ") + std::to_string(row) +
                 std::string(" requested in a matrix with a maximum of ") +
                 std::to_string(this->GetRows()) + std::string(" rows"));
    ASSERTL2(column < this->GetColumns(),
             std::string("Column ") + std::to_string(column) +
                 std::string(" requested in a matrix with a maximum of ") +
                 std::to_string(this->GetColumns()) + std::string(" columns"));
 
    return GetValue(row, column, this->GetTransposeFlag());
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::ConstGetValueType NekMatrix<
    DataType, StandardMatrixTag>::GetValue(unsigned int row,
                                           unsigned int column,
                                           char transpose) const
{
    static DataType defaultReturnValue;
    unsigned int index = CalculateIndex(row, column, transpose);
    if (index != std::numeric_limits<unsigned int>::max())
    {
        return m_data[index];
    }
    else
    {
        return defaultReturnValue;
    }
}
 
template <typename DataType>
const Array<OneD, const DataType> &NekMatrix<DataType,
                                             StandardMatrixTag>::GetPtr() const
{
    return m_data;
}
 
template <typename DataType>
DataType NekMatrix<DataType, StandardMatrixTag>::Scale() const
{
    return DataType(1);
}
 
template <typename DataType>
const DataType *NekMatrix<DataType, StandardMatrixTag>::GetRawPtr() const
{
    return m_data.data();
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::const_iterator NekMatrix<
    DataType, StandardMatrixTag>::begin() const
{
    return begin(this->GetTransposeFlag());
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::const_iterator NekMatrix<
    DataType, StandardMatrixTag>::begin(char transpose) const
{
    if (transpose == 'N')
    {
        return const_iterator(m_data.data(), m_data.data() + m_data.size());
    }
    else
    {
        return const_iterator(this, transpose);
    }
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::const_iterator NekMatrix<
    DataType, StandardMatrixTag>::end() const
{
    return end(this->GetTransposeFlag());
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::const_iterator NekMatrix<
    DataType, StandardMatrixTag>::end(char transpose) const
{
    if (transpose == 'N')
    {
        return const_iterator(m_data.data(), m_data.data() + m_data.size(),
                              true);
    }
    else
    {
        return const_iterator(this, transpose, true);
    }
}
 
template <typename DataType>
unsigned int NekMatrix<DataType, StandardMatrixTag>::GetStorageSize() const
{
    return m_data.size();
}
 
template <typename DataType>
unsigned int NekMatrix<DataType, StandardMatrixTag>::GetNumberOfSubDiagonals()
    const
{
    if (m_numberOfSubDiagonals != std::numeric_limits<unsigned int>::max())
    {
        return m_numberOfSubDiagonals;
    }
    else if (this->GetRows() > 0)
    {
        return this->GetRows() - 1;
    }
    else
    {
        return 0;
    }
}
 
template <typename DataType>
unsigned int NekMatrix<DataType, StandardMatrixTag>::GetNumberOfSuperDiagonals()
    const
{
    if (m_numberOfSuperDiagonals != std::numeric_limits<unsigned int>::max())
    {
        return m_numberOfSuperDiagonals;
    }
    else if (this->GetRows() > 0)
    {
        return this->GetRows() - 1;
    }
    else
    {
        return 0;
    }
}
 
template <typename DataType>
unsigned int NekMatrix<DataType, StandardMatrixTag>::CalculateNumberOfRows()
    const
{
    return GetNumberOfSubDiagonals() + GetNumberOfSuperDiagonals() + 1;
}
 
template <typename DataType>
bool NekMatrix<DataType, StandardMatrixTag>::operator==(
    const NekMatrix<DataType, StandardMatrixTag> &rhs) const
{
    if (this->GetRows() != rhs.GetRows() ||
        this->GetColumns() != rhs.GetColumns())
    {
        return false;
    }
 
    if (this->GetTransposeFlag() == rhs.GetTransposeFlag())
    {
        return std::equal(begin(), end(), rhs.begin());
    }
    else
    {
        for (unsigned int i = 0; i < this->GetRows(); ++i)
        {
            for (unsigned int j = 0; j < this->GetColumns(); ++j)
            {
                if ((*this)(i, j) != rhs(i, j))
                {
                    return false;
                }
            }
        }
    }
 
    return true;
}
 
template <typename DataType>
PointerWrapper NekMatrix<DataType, StandardMatrixTag>::GetWrapperType() const
{
    return m_wrapperType;
}
 
template <typename DataType>
std::tuple<unsigned int, unsigned int> NekMatrix<
    DataType, StandardMatrixTag>::Advance(unsigned int curRow,
                                          unsigned int curColumn) const
{
    return Advance(curRow, curColumn, this->GetTransposeFlag());
}
 
template <typename DataType>
std::tuple<unsigned int, unsigned int> NekMatrix<
    DataType, StandardMatrixTag>::Advance(unsigned int curRow,
                                          unsigned int curColumn,
                                          char transpose) const
{
    unsigned int numRows    = this->GetTransposedRows(transpose);
    unsigned int numColumns = this->GetTransposedColumns(transpose);
 
    switch (this->GetStorageType())
    {
        case eFULL:
            return FullMatrixFuncs::Advance(numRows, numColumns, curRow,
                                            curColumn);
            break;
        case eDIAGONAL:
            return DiagonalMatrixFuncs::Advance(numRows, numColumns, curRow,
                                                curColumn);
            break;
        case eUPPER_TRIANGULAR:
            return UpperTriangularMatrixFuncs::Advance(numRows, numColumns,
                                                       curRow, curColumn);
            break;
 
        case eLOWER_TRIANGULAR:
            return LowerTriangularMatrixFuncs::Advance(numRows, numColumns,
                                                       curRow, curColumn);
            break;
 
        case eSYMMETRIC:
        case ePOSITIVE_DEFINITE_SYMMETRIC:
            return SymmetricMatrixFuncs::Advance(numRows, numColumns, curRow,
                                                 curColumn);
            break;
        case eBANDED:
            return BandedMatrixFuncs::Advance(numRows, numColumns, curRow,
                                              curColumn);
            break;
        case eSYMMETRIC_BANDED:
        case ePOSITIVE_DEFINITE_SYMMETRIC_BANDED:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
            break;
        case eUPPER_TRIANGULAR_BANDED:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
            break;
        case eLOWER_TRIANGULAR_BANDED:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
            break;
 
        default:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
    }
    return std::tuple<unsigned int, unsigned int>(curRow, curColumn);
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag> NekMatrix<DataType, StandardMatrixTag>::
    CreateWrapper(const NekMatrix<DataType, StandardMatrixTag> &rhs)
{
    return NekMatrix<DataType, StandardMatrixTag>(rhs, eWrapper);
}
 
template <typename DataType>
std::shared_ptr<NekMatrix<DataType, StandardMatrixTag>> NekMatrix<
    DataType, StandardMatrixTag>::
    CreateWrapper(
        const std::shared_ptr<NekMatrix<DataType, StandardMatrixTag>> &rhs)
{
    return std::shared_ptr<NekMatrix<DataType, StandardMatrixTag>>(
        new NekMatrix<DataType, StandardMatrixTag>(*rhs, eWrapper));
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag>::NekMatrix(
    const NekMatrix<DataType, StandardMatrixTag> &rhs,
    PointerWrapper wrapperType)
    : BaseType(rhs), m_data(), m_wrapperType(wrapperType),
      m_numberOfSuperDiagonals(rhs.m_numberOfSuperDiagonals),
      m_numberOfSubDiagonals(rhs.m_numberOfSubDiagonals)
{
    PerformCopyConstruction(rhs);
}
 
template <typename DataType>
Array<OneD, DataType> &NekMatrix<DataType, StandardMatrixTag>::GetData()
{
    return m_data;
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::RemoveExcessCapacity()
{
    if (m_wrapperType == eCopy)
    {
        unsigned int requiredStorageSize = GetRequiredStorageSize();
        if (m_data.size() > requiredStorageSize)
        {
            Array<OneD, DataType> newArray(requiredStorageSize);
            CopyArrayN(m_data, newArray, requiredStorageSize);
            m_data = newArray;
        }
    }
    else if (m_wrapperType == eWrapper)
    {
        ASSERTL0(true, "Can't call RemoveExcessCapacity on a wrapped matrix.");
    }
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::ResizeDataArrayIfNeeded(
    unsigned int requiredStorageSize)
{
    if (m_wrapperType == eCopy)
    {
        if (m_data.size() < requiredStorageSize)
        {
            Array<OneD, DataType> newData(requiredStorageSize);
            std::copy(m_data.data(), m_data.data() + m_data.size(),
                      newData.data());
            m_data = newData;
        }
    }
    else if (m_wrapperType == eWrapper)
    {
        // If the current matrix is wrapped, then just copy over the top,
        // but the sizes of the two matrices must be the same.
        ASSERTL0(
            m_data.size() >= requiredStorageSize,
            "Wrapped NekMatrices must have the same dimension in operator=");
    }
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::ResizeDataArrayIfNeeded()
{
    unsigned int requiredStorageSize = GetRequiredStorageSize();
    ResizeDataArrayIfNeeded(requiredStorageSize);
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::PerformCopyConstruction(
    const ThisType &rhs)
{
    if (m_wrapperType == eWrapper)
    {
        m_data = rhs.m_data;
    }
    else
    {
        m_data = Array<OneD, DataType>(GetRequiredStorageSize());
        CopyArrayN(rhs.m_data, m_data, m_data.size());
    }
}
 
template <typename DataType>
typename boost::call_traits<DataType>::value_type NekMatrix<
    DataType, StandardMatrixTag>::v_GetValue(unsigned int row,
                                             unsigned int column) const
{
    return NekMatrix<DataType, StandardMatrixTag>::operator()(row, column);
}
 
template <typename DataType>
unsigned int NekMatrix<DataType, StandardMatrixTag>::v_GetStorageSize() const
{
    return NekMatrix<DataType, StandardMatrixTag>::GetStorageSize();
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::v_SetValue(
    unsigned int row, unsigned int column,
    typename boost::call_traits<DataType>::const_reference d)
{
    return NekMatrix<DataType, StandardMatrixTag>::SetValue(row, column, d);
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::SetSize(unsigned int rows,
                                                     unsigned int cols)
{
    this->Resize(rows, cols);
 
    // Some places in Nektar++ access the matrix data array and
    // use size() to see how big it is.  When using
    // expression templates, the data array's capacity is often larger
    // than the actual number of elements, so this statement is
    // required to report the correct number of elements.
    this->GetData().ChangeSize(this->GetRequiredStorageSize());
    ASSERTL0(this->GetRequiredStorageSize() <= this->GetData().size(),
             "Can't resize matrices if there is not enough capacity.");
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::Proxy NekMatrix<
    DataType, StandardMatrixTag>::operator()(unsigned int row,
                                             unsigned int column)
{
    ASSERTL2(row < this->GetRows(),
             std::string("Row ") + std::to_string(row) +
                 std::string(" requested in a matrix with a maximum of ") +
                 std::to_string(this->GetRows()) + std::string(" rows"));
    ASSERTL2(column < this->GetColumns(),
             std::string("Column ") + std::to_string(column) +
                 std::string(" requested in a matrix with a maximum of ") +
                 std::to_string(this->GetColumns()) + std::string(" columns"));
 
    return (*this)(row, column, this->GetTransposeFlag());
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::Proxy NekMatrix<
    DataType, StandardMatrixTag>::operator()(unsigned int row,
                                             unsigned int column,
                                             char transpose)
{
    unsigned int index = this->CalculateIndex(row, column, transpose);
    if (index != std::numeric_limits<unsigned int>::max())
    {
        return Proxy(this->GetData()[index]);
    }
    else
    {
        return Proxy();
    }
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::SetValue(
    unsigned int row, unsigned int column,
    typename boost::call_traits<DataType>::const_reference d)
{
    ASSERTL2(row < this->GetRows(),
             std::string("Row ") + std::to_string(row) +
                 std::string(" requested in a matrix with a maximum of ") +
                 std::to_string(this->GetRows()) + std::string(" rows"));
    ASSERTL2(column < this->GetColumns(),
             std::string("Column ") + std::to_string(column) +
                 std::string(" requested in a matrix with a maximum of ") +
                 std::to_string(this->GetColumns()) + std::string(" columns"));
    SetValue(row, column, d, this->GetTransposeFlag());
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::SetValue(
    unsigned int row, unsigned int column,
    typename boost::call_traits<DataType>::const_reference d, char transpose)
{
    unsigned int index = this->CalculateIndex(row, column, transpose);
    if (index != std::numeric_limits<unsigned int>::max())
    {
        this->GetData()[index] = d;
    }
    else
    {
        NEKERROR(
            ErrorUtil::efatal,
            "Can't assign values into zeroed elements of a special array.");
    }
}
 
template <typename DataType>
Array<OneD, DataType> &NekMatrix<DataType, StandardMatrixTag>::GetPtr()
{
    return this->GetData();
}
 
template <typename DataType>
DataType *NekMatrix<DataType, StandardMatrixTag>::GetRawPtr()
{
    return this->GetData().data();
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::iterator NekMatrix<
    DataType, StandardMatrixTag>::begin()
{
    return begin(this->GetTransposeFlag());
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::iterator NekMatrix<
    DataType, StandardMatrixTag>::begin(char transpose)
{
    if (transpose == 'N')
    {
        return iterator(this->GetData().data(),
                        this->GetData().data() + this->GetData().size());
    }
    else
    {
        return iterator(this, transpose);
    }
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::iterator NekMatrix<
    DataType, StandardMatrixTag>::end()
{
    return end(this->GetTransposeFlag());
}
 
template <typename DataType>
typename NekMatrix<DataType, StandardMatrixTag>::iterator NekMatrix<
    DataType, StandardMatrixTag>::end(char transpose)
{
    if (transpose == 'N')
    {
        return iterator(this->GetData().data(),
                        this->GetData().data() + this->GetData().size(), true);
    }
    else
    {
        return iterator(this, transpose, true);
    }
}
 
template <typename DataType>
DataType NekMatrix<DataType, StandardMatrixTag>::AbsMaxtoMinEigenValueRatio(
    void)
{
    DataType returnval;
    int nvals = this->GetColumns();
    Array<OneD, DataType> EigValReal(nvals);
    Array<OneD, DataType> EigValImag(nvals);
    Array<OneD, DataType> Evecs;
 
    EigenSolve(EigValReal, EigValImag, Evecs);
 
    Vmath::Vmul(nvals, EigValReal, 1, EigValReal, 1, EigValReal, 1);
    Vmath::Vmul(nvals, EigValImag, 1, EigValImag, 1, EigValImag, 1);
    Vmath::Vadd(nvals, EigValReal, 1, EigValImag, 1, EigValReal, 1);
 
    returnval = sqrt(Vmath::Vmax(nvals, EigValReal, 1) /
                     Vmath::Vmin(nvals, EigValReal, 1));
 
    return returnval;
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::EigenSolve(
    Array<OneD, DataType> &EigValReal, Array<OneD, DataType> &EigValImag,
    Array<OneD, DataType> &EigVecs)
{
    ASSERTL0(this->GetRows() == this->GetColumns(),
             "Only square matrices can be called");
 
    switch (this->GetType())
    {
        case eFULL:
            FullMatrixFuncs::EigenSolve(this->GetRows(), this->GetData(),
                                        EigValReal, EigValImag, EigVecs);
            break;
        case eDIAGONAL:
            Vmath::Vcopy(this->GetRows(), &(this->GetData())[0], 1,
                         &EigValReal[0], 1);
            Vmath::Zero(this->GetRows(), &EigValImag[0], 1);
            break;
        case eUPPER_TRIANGULAR:
        case eLOWER_TRIANGULAR:
        case eSYMMETRIC:
        case eBANDED:
        case eSYMMETRIC_BANDED:
        case eUPPER_TRIANGULAR_BANDED:
        case eLOWER_TRIANGULAR_BANDED:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
            break;
 
        default:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
    }
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::Invert()
{
    ASSERTL0(this->GetRows() == this->GetColumns(),
             "Only square matrices can be inverted.");
    ASSERTL0(this->GetTransposeFlag() == 'N',
             "Only untransposed matrices may be inverted.");
 
    switch (this->GetType())
    {
        case eFULL:
            FullMatrixFuncs::Invert(this->GetRows(), this->GetColumns(),
                                    this->GetData(), this->GetTransposeFlag());
            break;
        case eDIAGONAL:
            DiagonalMatrixFuncs::Invert(this->GetRows(), this->GetColumns(),
                                        this->GetData());
            break;
        case eSYMMETRIC:
            SymmetricMatrixFuncs::Invert(this->GetRows(), this->GetColumns(),
                                         this->GetData());
            break;
        case eUPPER_TRIANGULAR:
        case eLOWER_TRIANGULAR:
        case eBANDED:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
            break;
        case eSYMMETRIC_BANDED:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
            break;
        case eUPPER_TRIANGULAR_BANDED:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
            break;
        case eLOWER_TRIANGULAR_BANDED:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
            break;
 
        default:
            NEKERROR(ErrorUtil::efatal, "Unhandled matrix type");
    }
}
 
template <typename DataType>
Array<OneD, DataType> &NekMatrix<DataType, StandardMatrixTag>::GetTempSpace()
{
    if (m_tempSpace.capacity() == 0)
    {
        m_tempSpace = Array<OneD, DataType>(this->GetData().capacity());
    }
    return m_tempSpace;
}
 
template <typename DataType>
void NekMatrix<DataType, StandardMatrixTag>::SwapTempAndDataBuffers()
{
    std::swap(m_tempSpace, this->GetData());
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag> NekMatrix<
    DataType, StandardMatrixTag>::operator-() const
{
    NekMatrix<DataType, StandardMatrixTag> result(*this);
    NegateInPlace(result);
    return result;
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag> &NekMatrix<
    DataType, StandardMatrixTag>::operator*=(const DataType &s)
{
    for (unsigned int i = 0; i < this->GetPtr().size(); ++i)
    {
        this->GetPtr()[i] *= s;
    }
    return *this;
}
 
template <typename DataType>
NekMatrix<DataType, StandardMatrixTag> Transpose(
    NekMatrix<DataType, StandardMatrixTag> &rhs)
{
    NekMatrix<DataType, StandardMatrixTag> result(
        rhs.GetRows(), rhs.GetColumns(), rhs.GetPtr(), eWrapper, rhs.GetType(),
        rhs.GetNumberOfSubDiagonals(), rhs.GetNumberOfSuperDiagonals());
    result.Transpose();
    return result;
}
 
template LIB_UTILITIES_EXPORT NekMatrix<NekDouble, StandardMatrixTag> Transpose(
    NekMatrix<NekDouble, StandardMatrixTag> &rhs);
 
template LIB_UTILITIES_EXPORT class NekMatrix<NekDouble, StandardMatrixTag>;
 
template LIB_UTILITIES_EXPORT NekMatrix<NekSingle, StandardMatrixTag> Transpose(
    NekMatrix<NekSingle, StandardMatrixTag> &rhs);
 
template LIB_UTILITIES_EXPORT class NekMatrix<NekSingle, StandardMatrixTag>;
 
template <typename DataType>
void NegateInPlace(NekMatrix<DataType, StandardMatrixTag> &m)
{
    for (unsigned int i = 0; i < m.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < m.GetColumns(); ++j)
        {
            m(i, j) *= -1.0;
        }
    }
}
 
template LIB_UTILITIES_EXPORT void NegateInPlace(
    NekMatrix<double, StandardMatrixTag> &v);
template LIB_UTILITIES_EXPORT void NegateInPlace(
    NekMatrix<NekSingle, StandardMatrixTag> &v);
 
} // namespace Nektar