MatrixOperations.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: MatrixOperations.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: Defines the global functions needed for matrix operations.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/LinearAlgebra/ExplicitInstantiation.h>
#include <LibUtilities/LinearAlgebra/MatrixOperations.hpp>
 
namespace Nektar
{
template <typename ResultDataType, typename LhsDataType, typename LhsMatrixType>
void Multiply(NekMatrix<ResultDataType, StandardMatrixTag> &result,
              const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
              const ResultDataType &rhs)
{
    // TODO - optimize for the different matrix types.
    int n = lhs.GetRows();
    int m = lhs.GetColumns();
    for (unsigned int i = 0; i < n; ++i)
    {
        for (unsigned int j = 0; j < m; ++j)
        {
            result(i, j) = lhs(i, j) * rhs;
        }
    }
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    Multiply, NEKTAR_ALL_MATRIX_TYPES, (1, (void)), (1, (DNekMat &)),
    (1, (const NekDouble &)))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    Multiply, NEKTAR_ALL_MATRIX_TYPES_SINGLE, (1, (void)), (1, (SNekMat &)),
    (1, (const NekSingle &)))
 
template <typename DataType, typename LhsDataType, typename LhsMatrixType>
NekMatrix<typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType,
          StandardMatrixTag>
Multiply(const NekMatrix<LhsDataType, LhsMatrixType> &lhs, const DataType &rhs)
{
    typedef typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType
        ResultDataType;
    NekMatrix<ResultDataType, StandardMatrixTag> result(lhs.GetRows(),
                                                        lhs.GetColumns());
    Multiply(result, lhs, rhs);
    return result;
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    Multiply, NEKTAR_ALL_MATRIX_TYPES, (1, (DNekMat)), (0, ()),
    (1, (const NekDouble &)))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    Multiply, NEKTAR_ALL_MATRIX_TYPES_SINGLE, (1, (SNekMat)), (0, ()),
    (1, (const NekSingle &)))
 
template <typename RhsDataType, typename RhsMatrixType, typename ResultDataType>
void Multiply(NekMatrix<ResultDataType, StandardMatrixTag> &result,
              const ResultDataType &lhs,
              const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
 
{
    Multiply(result, rhs, lhs);
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    Multiply, NEKTAR_ALL_MATRIX_TYPES, (1, (void)),
    (2, (DNekMat &, const NekDouble &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    Multiply, NEKTAR_ALL_MATRIX_TYPES_SINGLE, (1, (void)),
    (2, (SNekMat &, const NekSingle &)), (0, ()))
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
NekMatrix<typename NekMatrix<RhsDataType, RhsMatrixType>::NumberType,
          StandardMatrixTag>
Multiply(const DataType &lhs, const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
 
{
    return Multiply(rhs, lhs);
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    Multiply, NEKTAR_ALL_MATRIX_TYPES, (1, (DNekMat)), (1, (const NekDouble &)),
    (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    Multiply, NEKTAR_ALL_MATRIX_TYPES_SINGLE, (1, (SNekMat)),
    (1, (const NekSingle &)), (0, ()))
 
template <typename LhsDataType>
void MultiplyEqual(
    NekMatrix<LhsDataType, StandardMatrixTag> &lhs,
    typename boost::call_traits<LhsDataType>::const_reference rhs)
{
    typedef
        typename NekMatrix<LhsDataType, StandardMatrixTag>::iterator iterator;
    for (iterator iter = lhs.begin(); iter != lhs.end(); ++iter)
    {
        *iter *= rhs;
    }
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    MultiplyEqual, (1, (DNekMat &)), (1, (void)), (0, ()),
    (1, (const NekDouble &)))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    MultiplyEqual, (1, (SNekMat &)), (1, (void)), (0, ()),
    (1, (const NekSingle &)))
 
template <typename ResultType, typename LhsDataType, typename RhsDataType,
          typename LhsMatrixType, typename RhsMatrixType>
void NekMultiplyDefaultImpl(NekMatrix<ResultType, StandardMatrixTag> &result,
                            const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
                            const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    ASSERTL1(lhs.GetColumns() == rhs.GetRows(),
             std::string("A left side matrix with column count ") +
                 std::to_string(lhs.GetColumns()) +
                 std::string(" and a right side matrix with row count ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be multiplied."));
 
    for (unsigned int i = 0; i < result.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < result.GetColumns(); ++j)
        {
            ResultType t = ResultType(0);
 
            // Set the result(i,j) element.
            for (unsigned int k = 0; k < lhs.GetColumns(); ++k)
            {
                t += lhs(i, k) * rhs(k, j);
            }
            result(i, j) = t;
        }
    }
}
 
template <typename ResultType, typename LhsDataType, typename RhsDataType,
          typename LhsMatrixType, typename RhsMatrixType>
void NekMultiplyFullMatrixFullMatrix(
    NekMatrix<ResultType, StandardMatrixTag> &result,
    const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
    const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    NekMultiplyDefaultImpl(result, lhs, rhs);
}
 
template <typename LhsDataType, typename RhsDataType, typename DataType,
          typename LhsMatrixType, typename RhsMatrixType>
void Multiply(NekMatrix<DataType, StandardMatrixTag> &result,
              const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
              const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    ASSERTL1(lhs.GetColumns() == rhs.GetRows(),
             std::string("A left side matrix with column count ") +
                 std::to_string(lhs.GetColumns()) +
                 std::string(" and a right side matrix with row count ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be multiplied."));
 
    result.SetSize(lhs.GetRows(), rhs.GetColumns());
    if (lhs.GetType() == eFULL && rhs.GetType() == eFULL)
    {
        NekMultiplyFullMatrixFullMatrix(result, lhs, rhs);
    }
    else
    {
        NekMultiplyDefaultImpl(result, lhs, rhs);
    }
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    Multiply, NEKTAR_ALL_MATRIX_TYPES, NEKTAR_ALL_MATRIX_TYPES, (1, (void)),
    (1, (DNekMat &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    Multiply, NEKTAR_ALL_MATRIX_TYPES_SINGLE, NEKTAR_ALL_MATRIX_TYPES_SINGLE,
    (1, (void)), (1, (SNekMat &)), (0, ()))
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
void AddEqual(NekMatrix<DataType, StandardMatrixTag> &result,
              const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    ASSERTL1(result.GetRows() == rhs.GetRows(),
             std::string("Matrices with different row counts  ") +
                 std::to_string(result.GetRows()) + std::string(" and ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be added."));
    ASSERTL1(result.GetColumns() == rhs.GetColumns(),
             std::string("Matrices with different column counts  ") +
                 std::to_string(result.GetColumns()) + std::string(" and ") +
                 std::to_string(rhs.GetColumns()) +
                 std::string(" can't be added."));
 
    for (unsigned int i = 0; i < rhs.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < rhs.GetColumns(); ++j)
        {
            result(i, j) += rhs(i, j);
        }
    }
}
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
void AddEqualNegatedLhs(NekMatrix<DataType, StandardMatrixTag> &result,
                        const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    ASSERTL1(result.GetRows() == rhs.GetRows(),
             std::string("Matrices with different row counts  ") +
                 std::to_string(result.GetRows()) + std::string(" and ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be added."));
    ASSERTL1(result.GetColumns() == rhs.GetColumns(),
             std::string("Matrices with different column counts  ") +
                 std::to_string(result.GetColumns()) + std::string(" and ") +
                 std::to_string(rhs.GetColumns()) +
                 std::string(" can't be added."));
 
    for (unsigned int i = 0; i < rhs.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < rhs.GetColumns(); ++j)
        {
            result(i, j) = -result(i, j) + rhs(i, j);
        }
    }
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    AddEqual, NEKTAR_ALL_MATRIX_TYPES, (1, (void)), (1, (DNekMat &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    AddEqual, NEKTAR_ALL_MATRIX_TYPES_SINGLE, (1, (void)), (1, (SNekMat &)),
    (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    AddEqualNegatedLhs, NEKTAR_ALL_MATRIX_TYPES, (1, (void)), (1, (DNekMat &)),
    (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    AddEqualNegatedLhs, NEKTAR_ALL_MATRIX_TYPES_SINGLE, (1, (void)),
    (1, (SNekMat &)), (0, ()))
 
template <typename DataType, typename LhsDataType, typename LhsMatrixType,
          typename RhsDataType, typename RhsMatrixType>
void Add(NekMatrix<DataType, StandardMatrixTag> &result,
         const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
         const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    ASSERTL1(lhs.GetRows() == rhs.GetRows(),
             std::string("Matrices with different row counts  ") +
                 std::to_string(lhs.GetRows()) + std::string(" and ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be added."));
    ASSERTL1(lhs.GetColumns() == rhs.GetColumns(),
             std::string("Matrices with different column counts  ") +
                 std::to_string(lhs.GetColumns()) + std::string(" and ") +
                 std::to_string(rhs.GetColumns()) +
                 std::string(" can't be added."));
 
    for (unsigned int i = 0; i < lhs.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < lhs.GetColumns(); ++j)
        {
            result(i, j) = lhs(i, j) + rhs(i, j);
        }
    }
}
 
template <typename DataType, typename LhsDataType, typename LhsMatrixType,
          typename RhsDataType, typename RhsMatrixType>
void AddNegatedLhs(NekMatrix<DataType, StandardMatrixTag> &result,
                   const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
                   const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    ASSERTL1(lhs.GetRows() == rhs.GetRows(),
             std::string("Matrices with different row counts  ") +
                 std::to_string(lhs.GetRows()) + std::string(" and ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be added."));
    ASSERTL1(lhs.GetColumns() == rhs.GetColumns(),
             std::string("Matrices with different column counts  ") +
                 std::to_string(lhs.GetColumns()) + std::string(" and ") +
                 std::to_string(rhs.GetColumns()) +
                 std::string(" can't be added."));
 
    for (unsigned int i = 0; i < lhs.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < lhs.GetColumns(); ++j)
        {
            result(i, j) = -lhs(i, j) + rhs(i, j);
        }
    }
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    Add, NEKTAR_ALL_MATRIX_TYPES, NEKTAR_ALL_MATRIX_TYPES, (1, (void)),
    (1, (DNekMat &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    Add, NEKTAR_ALL_MATRIX_TYPES_SINGLE, NEKTAR_ALL_MATRIX_TYPES_SINGLE,
    (1, (void)), (1, (SNekMat &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    AddNegatedLhs, NEKTAR_ALL_MATRIX_TYPES, NEKTAR_ALL_MATRIX_TYPES,
    (1, (void)), (1, (DNekMat &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    AddNegatedLhs, NEKTAR_ALL_MATRIX_TYPES_SINGLE,
    NEKTAR_ALL_MATRIX_TYPES_SINGLE, (1, (void)), (1, (SNekMat &)), (0, ()))
 
template <typename LhsDataType, typename LhsMatrixType, typename RhsDataType,
          typename RhsMatrixType>
NekMatrix<typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType,
          StandardMatrixTag>
Add(const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
    const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    typedef
        typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType NumberType;
    NekMatrix<NumberType, StandardMatrixTag> result(lhs.GetRows(),
                                                    lhs.GetColumns());
    Add(result, lhs, rhs);
    return result;
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    Add, NEKTAR_ALL_MATRIX_TYPES, NEKTAR_ALL_MATRIX_TYPES, (1, (DNekMat)),
    (0, ()), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    Add, NEKTAR_ALL_MATRIX_TYPES_SINGLE, NEKTAR_ALL_MATRIX_TYPES_SINGLE,
    (1, (SNekMat)), (0, ()), (0, ()))
 
template <typename DataType, typename LhsDataType, typename LhsMatrixType,
          typename RhsDataType, typename RhsMatrixType>
void Subtract(NekMatrix<DataType, StandardMatrixTag> &result,
              const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
              const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    ASSERTL1(lhs.GetRows() == rhs.GetRows(),
             std::string("Matrices with different row counts  ") +
                 std::to_string(lhs.GetRows()) + std::string(" and ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be subtracted."));
    ASSERTL1(lhs.GetColumns() == rhs.GetColumns(),
             std::string("Matrices with different column counts  ") +
                 std::to_string(lhs.GetColumns()) + std::string(" and ") +
                 std::to_string(rhs.GetColumns()) +
                 std::string(" can't be subtracted."));
 
    for (unsigned int i = 0; i < lhs.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < lhs.GetColumns(); ++j)
        {
            result(i, j) = lhs(i, j) - rhs(i, j);
        }
    }
}
 
template <typename DataType, typename LhsDataType, typename LhsMatrixType,
          typename RhsDataType, typename RhsMatrixType>
void SubtractNegatedLhs(NekMatrix<DataType, StandardMatrixTag> &result,
                        const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
                        const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    ASSERTL1(lhs.GetRows() == rhs.GetRows(),
             std::string("Matrices with different row counts  ") +
                 std::to_string(lhs.GetRows()) + std::string(" and ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be subtracted."));
    ASSERTL1(lhs.GetColumns() == rhs.GetColumns(),
             std::string("Matrices with different column counts  ") +
                 std::to_string(lhs.GetColumns()) + std::string(" and ") +
                 std::to_string(rhs.GetColumns()) +
                 std::string(" can't be subtracted."));
 
    for (unsigned int i = 0; i < lhs.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < lhs.GetColumns(); ++j)
        {
            result(i, j) = -lhs(i, j) - rhs(i, j);
        }
    }
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    Subtract, NEKTAR_ALL_MATRIX_TYPES, NEKTAR_ALL_MATRIX_TYPES, (1, (void)),
    (1, (DNekMat &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    Subtract, NEKTAR_ALL_MATRIX_TYPES_SINGLE, NEKTAR_ALL_MATRIX_TYPES_SINGLE,
    (1, (void)), (1, (SNekMat &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    SubtractNegatedLhs, NEKTAR_ALL_MATRIX_TYPES, NEKTAR_ALL_MATRIX_TYPES,
    (1, (void)), (1, (DNekMat &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    SubtractNegatedLhs, NEKTAR_ALL_MATRIX_TYPES_SINGLE,
    NEKTAR_ALL_MATRIX_TYPES_SINGLE, (1, (void)), (1, (SNekMat &)), (0, ()))
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
void SubtractEqual(NekMatrix<DataType, StandardMatrixTag> &result,
                   const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    ASSERTL1(result.GetRows() == rhs.GetRows(),
             std::string("Matrices with different row counts  ") +
                 std::to_string(result.GetRows()) + std::string(" and ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be subtracted."));
    ASSERTL1(result.GetColumns() == rhs.GetColumns(),
             std::string("Matrices with different column counts  ") +
                 std::to_string(result.GetColumns()) + std::string(" and ") +
                 std::to_string(rhs.GetColumns()) +
                 std::string(" can't be subtracted."));
 
    for (unsigned int i = 0; i < rhs.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < rhs.GetColumns(); ++j)
        {
            result(i, j) -= rhs(i, j);
        }
    }
}
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
void SubtractEqualNegatedLhs(NekMatrix<DataType, StandardMatrixTag> &result,
                             const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    ASSERTL1(result.GetRows() == rhs.GetRows(),
             std::string("Matrices with different row counts  ") +
                 std::to_string(result.GetRows()) + std::string(" and ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be subtracted."));
    ASSERTL1(result.GetColumns() == rhs.GetColumns(),
             std::string("Matrices with different column counts  ") +
                 std::to_string(result.GetColumns()) + std::string(" and ") +
                 std::to_string(rhs.GetColumns()) +
                 std::string(" can't be subtracted."));
 
    for (unsigned int i = 0; i < rhs.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < rhs.GetColumns(); ++j)
        {
            result(i, j) = -result(i, j) - rhs(i, j);
        }
    }
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    SubtractEqual, NEKTAR_ALL_MATRIX_TYPES, (1, (void)), (1, (DNekMat &)),
    (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    SubtractEqual, NEKTAR_ALL_MATRIX_TYPES_SINGLE, (1, (void)),
    (1, (SNekMat &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    SubtractEqualNegatedLhs, NEKTAR_ALL_MATRIX_TYPES, (1, (void)),
    (1, (DNekMat &)), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_SINGLE_MATRIX(
    SubtractEqualNegatedLhs, NEKTAR_ALL_MATRIX_TYPES_SINGLE, (1, (void)),
    (1, (SNekMat &)), (0, ()))
 
template <typename LhsDataType, typename LhsMatrixType, typename RhsDataType,
          typename RhsMatrixType>
NekMatrix<typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType,
          StandardMatrixTag>
Subtract(const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
         const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    typedef
        typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType NumberType;
    NekMatrix<NumberType, StandardMatrixTag> result(lhs.GetRows(),
                                                    lhs.GetColumns());
    Subtract(result, lhs, rhs);
    return result;
}
 
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    Subtract, NEKTAR_ALL_MATRIX_TYPES, NEKTAR_ALL_MATRIX_TYPES, (1, (DNekMat)),
    (0, ()), (0, ()))
NEKTAR_GENERATE_EXPLICIT_FUNCTION_INSTANTIATION_TWO_MATRICES(
    Subtract, NEKTAR_ALL_MATRIX_TYPES_SINGLE, NEKTAR_ALL_MATRIX_TYPES_SINGLE,
    (1, (SNekMat)), (0, ()), (0, ()))
} // namespace Nektar