MatrixOperations.hpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: MatrixOperations.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).
//
// 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.
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_LIB_UTILITIES_LINEAR_ALGEBRA_MATRIX_OPERATIONS_DECLARATIONS_HPP
#define NEKTAR_LIB_UTILITIES_LINEAR_ALGEBRA_MATRIX_OPERATIONS_DECLARATIONS_HPP
 
#include <boost/core/ignore_unused.hpp>
 
// Since this file defines all of the operations for all combination of matrix
// types, we have to include all matrix specializations first.
 
#include <LibUtilities/BasicUtils/RawType.hpp>
#include <LibUtilities/LinearAlgebra/Blas.hpp>
#include <LibUtilities/LinearAlgebra/BlockMatrix.hpp>
#include <LibUtilities/LinearAlgebra/CanGetRawPtr.hpp>
#include <LibUtilities/LinearAlgebra/NekVectorFwd.hpp>
#include <LibUtilities/LinearAlgebra/ScaledMatrix.hpp>
#include <LibUtilities/LinearAlgebra/StandardMatrix.hpp>
 
#include <string>
#include <type_traits>
 
namespace Nektar
{
////////////////////////////////////////////////////////////////////////////////
// Matrix-Vector Multiplication
////////////////////////////////////////////////////////////////////////////////
template <typename DataType, typename LhsDataType, typename MatrixType>
NekVector<DataType> Multiply(const NekMatrix<LhsDataType, MatrixType> &lhs,
                             const NekVector<DataType> &rhs);
 
template <typename DataType, typename LhsDataType, typename MatrixType>
void Multiply(NekVector<DataType> &result,
              const NekMatrix<LhsDataType, MatrixType> &lhs,
              const NekVector<DataType> &rhs);
 
template <typename DataType, typename LhsInnerMatrixType>
void Multiply(NekVector<DataType> &result,
              const NekMatrix<LhsInnerMatrixType, BlockMatrixTag> &lhs,
              const NekVector<DataType> &rhs);
 
template <typename DataType, typename LhsDataType, typename MatrixType>
NekVector<DataType> operator*(const NekMatrix<LhsDataType, MatrixType> &lhs,
                              const NekVector<DataType> &rhs)
{
    return Multiply(lhs, rhs);
}
 
LIB_UTILITIES_EXPORT void DiagonalBlockFullScalMatrixMultiply(
    NekVector<double> &result,
    const NekMatrix<
        NekMatrix<NekMatrix<NekDouble, StandardMatrixTag>, ScaledMatrixTag>,
        BlockMatrixTag> &lhs,
    const NekVector<double> &rhs);
 
LIB_UTILITIES_EXPORT void DiagonalBlockFullScalMatrixMultiply(
    NekVector<NekSingle> &result,
    const NekMatrix<
        NekMatrix<NekMatrix<NekSingle, StandardMatrixTag>, ScaledMatrixTag>,
        BlockMatrixTag> &lhs,
    const NekVector<NekSingle> &rhs);
 
////////////////////////////////////////////////////////////////////////////////
// Matrix-Constant Multiplication
////////////////////////////////////////////////////////////////////////////////
template <typename ResultDataType, typename LhsDataType, typename LhsMatrixType>
void Multiply(NekMatrix<ResultDataType, StandardMatrixTag> &result,
              const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
              const ResultDataType &rhs);
 
template <typename DataType, typename LhsDataType, typename LhsMatrixType>
NekMatrix<typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType,
          StandardMatrixTag>
Multiply(const NekMatrix<LhsDataType, LhsMatrixType> &lhs, const DataType &rhs);
 
template <typename RhsDataType, typename RhsMatrixType, typename ResultDataType>
void Multiply(NekMatrix<ResultDataType, StandardMatrixTag> &result,
              const ResultDataType &lhs,
              const NekMatrix<RhsDataType, RhsMatrixType> &rhs);
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
NekMatrix<typename NekMatrix<RhsDataType, RhsMatrixType>::NumberType,
          StandardMatrixTag>
Multiply(const DataType &lhs, const NekMatrix<RhsDataType, RhsMatrixType> &rhs);
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
NekMatrix<typename NekMatrix<RhsDataType, RhsMatrixType>::NumberType,
          StandardMatrixTag>
operator*(const DataType &lhs, const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    return Multiply(lhs, rhs);
}
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
NekMatrix<typename NekMatrix<RhsDataType, RhsMatrixType>::NumberType,
          StandardMatrixTag>
operator*(const NekMatrix<RhsDataType, RhsMatrixType> &lhs, const DataType &rhs)
{
    return Multiply(lhs, rhs);
}
 
template <typename LhsDataType>
void MultiplyEqual(
    NekMatrix<LhsDataType, StandardMatrixTag> &lhs,
    typename boost::call_traits<LhsDataType>::const_reference rhs);
 
///////////////////////////////////////////////////////////////////
// Matrix-Matrix Multipliation
//////////////////////////////////////////////////////////////////
 
template <typename LhsDataType, typename RhsDataType, typename LhsMatrixType,
          typename RhsMatrixType>
void NekMultiplyFullMatrixFullMatrix(
    NekMatrix<LhsDataType, StandardMatrixTag> &result,
    const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
    const NekMatrix<RhsDataType, RhsMatrixType> &rhs,
    typename std::enable_if<
        CanGetRawPtr<NekMatrix<LhsDataType, LhsMatrixType>>::value &&
        CanGetRawPtr<NekMatrix<RhsDataType, RhsMatrixType>>::value>::type *p =
        0)
{
    boost::ignore_unused(p);
 
    ASSERTL1(lhs.GetType() == eFULL && rhs.GetType() == eFULL,
             "Only full matrices are supported.");
 
    unsigned int M = lhs.GetRows();
    unsigned int N = rhs.GetColumns();
    unsigned int K = lhs.GetColumns();
 
    unsigned int LDA = M;
    if (lhs.GetTransposeFlag() == 'T')
    {
        LDA = K;
    }
 
    unsigned int LDB = K;
    if (rhs.GetTransposeFlag() == 'T')
    {
        LDB = N;
    }
 
    Blas::Gemm(lhs.GetTransposeFlag(), rhs.GetTransposeFlag(), M, N, K,
               lhs.Scale() * rhs.Scale(), lhs.GetRawPtr(), LDA, rhs.GetRawPtr(),
               LDB, 0.0, result.GetRawPtr(), result.GetRows());
}
 
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);
 
template <typename RhsInnerType, typename RhsMatrixType>
void MultiplyEqual(
    NekMatrix<RhsInnerType, StandardMatrixTag> &result,
    const NekMatrix<RhsInnerType, RhsMatrixType> &rhs,
    typename std::enable_if<
        std::is_same<RawType_t<typename NekMatrix<RhsInnerType,
                                                  RhsMatrixType>::NumberType>,
                     RhsInnerType>::value &&
        CanGetRawPtr<NekMatrix<RhsInnerType, RhsMatrixType>>::value>::type *t =
        0)
{
    boost::ignore_unused(t);
    ASSERTL0(result.GetType() == eFULL && rhs.GetType() == eFULL,
             "Only full matrices supported.");
    unsigned int M = result.GetRows();
    unsigned int N = rhs.GetColumns();
    unsigned int K = result.GetColumns();
 
    unsigned int LDA = M;
    if (result.GetTransposeFlag() == 'T')
    {
        LDA = K;
    }
 
    unsigned int LDB = K;
    if (rhs.GetTransposeFlag() == 'T')
    {
        LDB = N;
    }
    RhsInnerType scale             = rhs.Scale();
    Array<OneD, RhsInnerType> &buf = result.GetTempSpace();
    Blas::Gemm(result.GetTransposeFlag(), rhs.GetTransposeFlag(), M, N, K,
               scale, result.GetRawPtr(), LDA, rhs.GetRawPtr(), LDB, 0.0,
               buf.data(), result.GetRows());
    result.SetSize(result.GetRows(), rhs.GetColumns());
    result.SwapTempAndDataBuffers();
}
 
template <typename DataType, typename RhsInnerType, typename RhsMatrixType>
void MultiplyEqual(
    NekMatrix<DataType, StandardMatrixTag> &result,
    const NekMatrix<RhsInnerType, RhsMatrixType> &rhs,
    typename std::enable_if<
        !std::is_same<RawType_t<typename NekMatrix<RhsInnerType,
                                                   RhsMatrixType>::NumberType>,
                      DataType>::value ||
        !CanGetRawPtr<NekMatrix<RhsInnerType, RhsMatrixType>>::value>::type *t =
        0)
{
    boost::ignore_unused(t);
    ASSERTL1(result.GetColumns() == rhs.GetRows(),
             std::string("A left side matrix with column count ") +
                 std::to_string(result.GetColumns()) +
                 std::string(" and a right side matrix with row count ") +
                 std::to_string(rhs.GetRows()) +
                 std::string(" can't be multiplied."));
    NekMatrix<DataType, StandardMatrixTag> temp(result.GetRows(),
                                                result.GetColumns());
 
    for (unsigned int i = 0; i < result.GetRows(); ++i)
    {
        for (unsigned int j = 0; j < result.GetColumns(); ++j)
        {
            DataType t = DataType(0);
 
            // Set the result(i,j) element.
            for (unsigned int k = 0; k < result.GetColumns(); ++k)
            {
                t += result(i, k) * rhs(k, j);
            }
            temp(i, j) = t;
        }
    }
 
    result = temp;
}
 
template <typename LhsDataType, typename RhsDataType, typename LhsMatrixType,
          typename RhsMatrixType>
NekMatrix<typename std::remove_const<
              typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType>::type,
          StandardMatrixTag>
Multiply(const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
         const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    typedef typename std::remove_const<
        typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType>::type
        NumberType;
    NekMatrix<NumberType, StandardMatrixTag> result(lhs.GetRows(),
                                                    rhs.GetColumns());
    Multiply(result, lhs, rhs);
    return result;
}
 
template <typename LhsDataType, typename RhsDataType, typename LhsMatrixType,
          typename RhsMatrixType>
NekMatrix<typename std::remove_const<
              typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType>::type,
          StandardMatrixTag>
operator*(const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
          const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    return Multiply(lhs, rhs);
}
 
///////////////////////////////////////////////////////////////////
// Addition
///////////////////////////////////////////////////////////////////
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
void AddEqual(NekMatrix<DataType, StandardMatrixTag> &result,
              const NekMatrix<RhsDataType, RhsMatrixType> &rhs);
 
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);
 
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);
 
template <typename LhsDataType, typename LhsMatrixType, typename RhsDataType,
          typename RhsMatrixType>
NekMatrix<typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType,
          StandardMatrixTag>
operator+(const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
          const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    return Add(lhs, rhs);
}
 
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);
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
void AddEqualNegatedLhs(NekMatrix<DataType, StandardMatrixTag> &result,
                        const NekMatrix<RhsDataType, RhsMatrixType> &rhs);
 
////////////////////////////////////////////////////////////////////////////////
// Subtraction
////////////////////////////////////////////////////////////////////////////////
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);
 
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);
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
void SubtractEqual(NekMatrix<DataType, StandardMatrixTag> &result,
                   const NekMatrix<RhsDataType, RhsMatrixType> &rhs);
 
template <typename DataType, typename RhsDataType, typename RhsMatrixType>
void SubtractEqualNegatedLhs(NekMatrix<DataType, StandardMatrixTag> &result,
                             const NekMatrix<RhsDataType, RhsMatrixType> &rhs);
 
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);
 
template <typename LhsDataType, typename LhsMatrixType, typename RhsDataType,
          typename RhsMatrixType>
NekMatrix<typename NekMatrix<LhsDataType, LhsMatrixType>::NumberType,
          StandardMatrixTag>
operator-(const NekMatrix<LhsDataType, LhsMatrixType> &lhs,
          const NekMatrix<RhsDataType, RhsMatrixType> &rhs)
{
    return Subtract(lhs, rhs);
}
 
} // namespace Nektar
 
#endif