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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef KRONECKER_TENSOR_PRODUCT_H
#define KRONECKER_TENSOR_PRODUCT_H
namespace Eigen {
template<typename Scalar, int Options, typename Index> class SparseMatrix;
/*!
* \brief Kronecker tensor product helper class for dense matrices
*
* This class is the return value of kroneckerProduct(MatrixBase,
* MatrixBase). Use the function rather than construct this class
* directly to avoid specifying template prarameters.
*
* \tparam Lhs Type of the left-hand side, a matrix expression.
* \tparam Rhs Type of the rignt-hand side, a matrix expression.
*/
template<typename Lhs, typename Rhs>
class KroneckerProduct : public ReturnByValue<KroneckerProduct<Lhs,Rhs> >
{
private:
typedef ReturnByValue<KroneckerProduct> Base;
typedef typename Base::Scalar Scalar;
typedef typename Base::Index Index;
public:
/*! \brief Constructor. */
KroneckerProduct(const Lhs& A, const Rhs& B)
: m_A(A), m_B(B)
{}
/*! \brief Evaluate the Kronecker tensor product. */
template<typename Dest> void evalTo(Dest& dst) const;
inline Index rows() const { return m_A.rows() * m_B.rows(); }
inline Index cols() const { return m_A.cols() * m_B.cols(); }
Scalar coeff(Index row, Index col) const
{
return m_A.coeff(row / m_B.rows(), col / m_B.cols()) *
m_B.coeff(row % m_B.rows(), col % m_B.cols());
}
Scalar coeff(Index i) const
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(KroneckerProduct);
return m_A.coeff(i / m_A.size()) * m_B.coeff(i % m_A.size());
}
private:
typename Lhs::Nested m_A;
typename Rhs::Nested m_B;
};
/*!
* \brief Kronecker tensor product helper class for sparse matrices
*
* If at least one of the operands is a sparse matrix expression,
* then this class is returned and evaluates into a sparse matrix.
*
* This class is the return value of kroneckerProduct(EigenBase,
* EigenBase). Use the function rather than construct this class
* directly to avoid specifying template prarameters.
*
* \tparam Lhs Type of the left-hand side, a matrix expression.
* \tparam Rhs Type of the rignt-hand side, a matrix expression.
*/
template<typename Lhs, typename Rhs>
class KroneckerProductSparse : public EigenBase<KroneckerProductSparse<Lhs,Rhs> >
{
private:
typedef typename internal::traits<KroneckerProductSparse>::Index Index;
public:
/*! \brief Constructor. */
KroneckerProductSparse(const Lhs& A, const Rhs& B)
: m_A(A), m_B(B)
{}
/*! \brief Evaluate the Kronecker tensor product. */
template<typename Dest> void evalTo(Dest& dst) const;
inline Index rows() const { return m_A.rows() * m_B.rows(); }
inline Index cols() const { return m_A.cols() * m_B.cols(); }
template<typename Scalar, int Options, typename Index>
operator SparseMatrix<Scalar, Options, Index>()
{
SparseMatrix<Scalar, Options, Index> result;
evalTo(result.derived());
return result;
}
private:
typename Lhs::Nested m_A;
typename Rhs::Nested m_B;
};
template<typename Lhs, typename Rhs>
template<typename Dest>
void KroneckerProduct<Lhs,Rhs>::evalTo(Dest& dst) const
{
const int BlockRows = Rhs::RowsAtCompileTime,
BlockCols = Rhs::ColsAtCompileTime;
const Index Br = m_B.rows(),
Bc = m_B.cols();
for (Index i=0; i < m_A.rows(); ++i)
for (Index j=0; j < m_A.cols(); ++j)
Block<Dest,BlockRows,BlockCols>(dst,i*Br,j*Bc,Br,Bc) = m_A.coeff(i,j) * m_B;
}
template<typename Lhs, typename Rhs>
template<typename Dest>
void KroneckerProductSparse<Lhs,Rhs>::evalTo(Dest& dst) const
{
const Index Br = m_B.rows(),
Bc = m_B.cols();
dst.resize(rows(),cols());
dst.resizeNonZeros(0);
dst.reserve(m_A.nonZeros() * m_B.nonZeros());
for (Index kA=0; kA < m_A.outerSize(); ++kA)
{
for (Index kB=0; kB < m_B.outerSize(); ++kB)
{
for (typename Lhs::InnerIterator itA(m_A,kA); itA; ++itA)
{
for (typename Rhs::InnerIterator itB(m_B,kB); itB; ++itB)
{
const Index i = itA.row() * Br + itB.row(),
j = itA.col() * Bc + itB.col();
dst.insert(i,j) = itA.value() * itB.value();
}
}
}
}
}
namespace internal {
template<typename _Lhs, typename _Rhs>
struct traits<KroneckerProduct<_Lhs,_Rhs> >
{
typedef typename remove_all<_Lhs>::type Lhs;
typedef typename remove_all<_Rhs>::type Rhs;
typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
enum {
Rows = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,
Cols = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,
MaxRows = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,
MaxCols = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret,
CoeffReadCost = Lhs::CoeffReadCost + Rhs::CoeffReadCost + NumTraits<Scalar>::MulCost
};
typedef Matrix<Scalar,Rows,Cols> ReturnType;
};
template<typename _Lhs, typename _Rhs>
struct traits<KroneckerProductSparse<_Lhs,_Rhs> >
{
typedef MatrixXpr XprKind;
typedef typename remove_all<_Lhs>::type Lhs;
typedef typename remove_all<_Rhs>::type Rhs;
typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
typedef typename promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind>::ret StorageKind;
typedef typename promote_index_type<typename Lhs::Index, typename Rhs::Index>::type Index;
enum {
LhsFlags = Lhs::Flags,
RhsFlags = Rhs::Flags,
RowsAtCompileTime = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,
ColsAtCompileTime = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,
MaxRowsAtCompileTime = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,
MaxColsAtCompileTime = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret,
EvalToRowMajor = (LhsFlags & RhsFlags & RowMajorBit),
RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),
Flags = ((LhsFlags | RhsFlags) & HereditaryBits & RemovedBits)
| EvalBeforeNestingBit | EvalBeforeAssigningBit,
CoeffReadCost = Dynamic
};
};
} // end namespace internal
/*!
* \ingroup KroneckerProduct_Module
*
* Computes Kronecker tensor product of two dense matrices
*
* \warning If you want to replace a matrix by its Kronecker product
* with some matrix, do \b NOT do this:
* \code
* A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
* \endcode
* instead, use eval() to work around this:
* \code
* A = kroneckerProduct(A,B).eval();
* \endcode
*
* \param a Dense matrix a
* \param b Dense matrix b
* \return Kronecker tensor product of a and b
*/
template<typename A, typename B>
KroneckerProduct<A,B> kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b)
{
return KroneckerProduct<A, B>(a.derived(), b.derived());
}
/*!
* \ingroup KroneckerProduct_Module
*
* Computes Kronecker tensor product of two matrices, at least one of
* which is sparse
*
* \param a Dense/sparse matrix a
* \param b Dense/sparse matrix b
* \return Kronecker tensor product of a and b, stored in a sparse
* matrix
*/
template<typename A, typename B>
KroneckerProductSparse<A,B> kroneckerProduct(const EigenBase<A>& a, const EigenBase<B>& b)
{
return KroneckerProductSparse<A,B>(a.derived(), b.derived());
}
} // end namespace Eigen
#endif // KRONECKER_TENSOR_PRODUCT_H
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