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Make kroneckerProduct take two arguments and return an expression, which is more straight-forward.

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This commit is contained in:
Chen-Pang He 2012-10-15 00:21:12 +08:00
parent f34db6578a
commit c4b83461d9
5 changed files with 212 additions and 120 deletions
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3
Eigen/src/Core/MatrixBase.h
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@ -165,6 +165,9 @@ template<typename Derived> class MatrixBase
template<typename ProductDerived, typename Lhs, typename Rhs>
Derived& lazyAssign(const MatrixPowerProductBase<ProductDerived, Lhs,Rhs>& other);
template<typename Lhs, typename Rhs>
Derived& lazyAssign(const KroneckerProduct<Lhs,Rhs>& other);
#endif // not EIGEN_PARSED_BY_DOXYGEN
template<typename OtherDerived>

3
Eigen/src/Core/util/ForwardDeclarations.h
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@ -282,6 +282,9 @@ struct stem_function
};
}
// KroneckerProduct module
template<typename Lhs, typename Rhs> class KroneckerProduct;
template<typename Lhs, typename Rhs> class KroneckerProductSparse;
#ifdef EIGEN2_SUPPORT
template<typename ExpressionType> class Cwise;

3
Eigen/src/SparseCore/SparseMatrixBase.h
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@ -259,6 +259,9 @@ template<typename Derived> class SparseMatrixBase : public EigenBase<Derived>
template<typename Lhs, typename Rhs>
inline Derived& operator=(const SparseSparseProduct<Lhs,Rhs>& product);
template<typename Lhs, typename Rhs>
inline Derived& operator=(const KroneckerProductSparse<Lhs,Rhs>& product);
friend std::ostream & operator << (std::ostream & s, const SparseMatrixBase& m)
{
typedef typename Derived::Nested Nested;

262
unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h
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@ -3,138 +3,230 @@
//
// 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
#define EIGEN_SIZE_PRODUCT(a,b) (!((int)a && (int)b) ? 0 \
: ((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
: (int)a * (int)b)
namespace Eigen {
namespace internal {
/*!
* Kronecker tensor product helper function for dense matrices
*
* \param A Dense matrix A
* \param B Dense matrix B
* \param AB_ Kronecker tensor product of A and B
*/
template<typename Derived_A, typename Derived_B, typename Derived_AB>
void kroneckerProduct_full(const Derived_A& A, const Derived_B& B, Derived_AB & AB)
template<typename _Lhs, typename _Rhs>
struct traits<KroneckerProduct<_Lhs,_Rhs> >
{
const unsigned int Ar = A.rows(),
Ac = A.cols(),
Br = B.rows(),
Bc = B.cols();
AB.resize(Ar*Br,Ac*Bc);
for (unsigned int i=0; i<Ar; ++i)
for (unsigned int j=0; j<Ac; ++j)
AB.block(i*Br,j*Bc,Br,Bc) = A(i,j)*B;
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 Dense StorageKind;
typedef typename promote_index_type<typename Lhs::Index, typename Rhs::Index>::type Index;
enum {
RowsAtCompileTime = EIGEN_SIZE_PRODUCT(traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime),
ColsAtCompileTime = EIGEN_SIZE_PRODUCT(traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime),
MaxRowsAtCompileTime = EIGEN_SIZE_PRODUCT(traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime),
MaxColsAtCompileTime = EIGEN_SIZE_PRODUCT(traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime),
Flags = (MaxRowsAtCompileTime==1 ? RowMajorBit : 0)
| EvalBeforeNestingBit | EvalBeforeAssigningBit | NestByRefBit,
CoeffReadCost = Lhs::CoeffReadCost + Rhs::CoeffReadCost + NumTraits<Scalar>::MulCost
};
};
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 Sparse StorageKind;
typedef typename promote_index_type<typename Lhs::Index, typename Rhs::Index>::type Index;
enum {
LhsFlags = Lhs::Flags,
RhsFlags = Rhs::Flags,
RowsAtCompileTime = EIGEN_SIZE_PRODUCT(traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime),
ColsAtCompileTime = EIGEN_SIZE_PRODUCT(traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime),
MaxRowsAtCompileTime = EIGEN_SIZE_PRODUCT(traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime),
MaxColsAtCompileTime = EIGEN_SIZE_PRODUCT(traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime),
EvalToRowMajor = (LhsFlags & RhsFlags & RowMajorBit),
RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),
Flags = ((LhsFlags | RhsFlags) & HereditaryBits & RemovedBits)
| EvalBeforeNestingBit | EvalBeforeAssigningBit,
CoeffReadCost = Dynamic
};
};
} // end namespace internal
/*!
* \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 MatrixBase<KroneckerProduct<Lhs,Rhs> >
{
public:
typedef MatrixBase<KroneckerProduct> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(KroneckerProduct)
/*! \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(); }
typename Base::CoeffReturnType coeff(Index row, Index col) const
{
return m_A.coeff(row / m_A.cols(), col / m_A.rows()) *
m_B.coeff(row % m_A.cols(), col % m_A.rows());
}
typename Base::CoeffReturnType 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());
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
struct Unusable {};
Unusable& coeffRef(Index) { return *reinterpret_cast<Unusable*>(this); }
Unusable& coeffRef(Index,Index) { return *reinterpret_cast<Unusable*>(this); }
#endif
private:
typename Lhs::Nested m_A;
typename Rhs::Nested m_B;
};
template<typename Lhs, typename Rhs>
class KroneckerProductSparse : public SparseMatrixBase<KroneckerProductSparse<Lhs,Rhs> >
{
public:
typedef SparseMatrixBase<KroneckerProductSparse> Base;
EIGEN_DENSE_PUBLIC_INTERFACE(KroneckerProductSparse)
/*! \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(); }
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;
}
/*!
* Kronecker tensor product helper function for matrices, where at least one is sparse
*
* \param A Matrix A
* \param B Matrix B
* \param AB_ Kronecker tensor product of A and B
*/
template<typename Derived_A, typename Derived_B, typename Derived_AB>
void kroneckerProduct_sparse(const Derived_A &A, const Derived_B &B, Derived_AB &AB)
template<typename Lhs, typename Rhs>
template<typename Dest>
void KroneckerProductSparse<Lhs,Rhs>::evalTo(Dest& dst) const
{
const unsigned int Ar = A.rows(),
Ac = A.cols(),
Br = B.rows(),
Bc = B.cols();
AB.resize(Ar*Br,Ac*Bc);
AB.resizeNonZeros(0);
AB.reserve(A.nonZeros()*B.nonZeros());
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 (int kA=0; kA<A.outerSize(); ++kA)
for (Index kA=0; kA < m_A.outerSize(); ++kA)
{
for (int kB=0; kB<B.outerSize(); ++kB)
for (Index kB=0; kB < m_B.outerSize(); ++kB)
{
for (typename Derived_A::InnerIterator itA(A,kA); itA; ++itA)
for (typename Lhs::InnerIterator itA(m_A,kA); itA; ++itA)
{
for (typename Derived_B::InnerIterator itB(B,kB); itB; ++itB)
for (typename Rhs::InnerIterator itB(m_B,kB); itB; ++itB)
{
const unsigned int iA = itA.row(),
jA = itA.col(),
iB = itB.row(),
jB = itB.col(),
i = iA*Br + iB,
j = jA*Bc + jB;
AB.insert(i,j) = itA.value() * itB.value();
const Index i = itA.row() * Br + itB.row(),
j = itA.col() * Bc + itB.col();
dst.insert(i,j) = itA.value() * itB.value();
}
}
}
}
}
} // end namespace internal
/*!
* Computes Kronecker tensor product of two dense matrices
*
* Remark: this function uses the const cast hack and has been
* implemented to make the function call possible, where the
* output matrix is a submatrix, e.g.
* kroneckerProduct(A,B,AB.block(2,5,6,6));
*
* \param a Dense matrix a
* \param b Dense matrix b
* \param c Kronecker tensor product of a and b
* \return Kronecker tensor product of a and b
*/
template<typename A,typename B,typename C>
void kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b, const MatrixBase<C>& c)
template<typename A, typename B>
KroneckerProduct<A,B> kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b)
{
internal::kroneckerProduct_full(a.derived(), b.derived(), c.const_cast_derived());
return KroneckerProduct<A, B>(a.derived(), b.derived());
}
/*!
* Computes Kronecker tensor product of a dense and a sparse matrix
* Computes Kronecker tensor product of two matrices, at least one of
* which is sparse.
*
* \param a Dense matrix a
* \param b Sparse matrix b
* \param c Kronecker tensor product of a and b
* \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,typename C>
void kroneckerProduct(const MatrixBase<A>& a, const SparseMatrixBase<B>& b, SparseMatrixBase<C>& c)
template<typename A, typename B>
KroneckerProductSparse<A,B> kroneckerProduct(const EigenBase<A>& a, const EigenBase<B>& b)
{
internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.derived());
return KroneckerProductSparse<A,B>(a.derived(), b.derived());
}
/*!
* Computes Kronecker tensor product of a sparse and a dense matrix
*
* \param a Sparse matrix a
* \param b Dense matrix b
* \param c Kronecker tensor product of a and b
*/
template<typename A,typename B,typename C>
void kroneckerProduct(const SparseMatrixBase<A>& a, const MatrixBase<B>& b, SparseMatrixBase<C>& c)
template<typename Derived>
template<typename Lhs, typename Rhs>
Derived& MatrixBase<Derived>::lazyAssign(const KroneckerProduct<Lhs,Rhs>& other)
{
internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.derived());
other.evalTo(derived());
return derived();
}
/*!
* Computes Kronecker tensor product of two sparse matrices
*
* \param a Sparse matrix a
* \param b Sparse matrix b
* \param c Kronecker tensor product of a and b
*/
template<typename A,typename B,typename C>
void kroneckerProduct(const SparseMatrixBase<A>& a, const SparseMatrixBase<B>& b, SparseMatrixBase<C>& c)
template<typename Derived>
template<typename Lhs, typename Rhs>
Derived& SparseMatrixBase<Derived>::operator=(const KroneckerProductSparse<Lhs,Rhs>& product)
{
internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.derived());
product.evalTo(derived());
return derived();
}
} // end namespace Eigen

61
unsupported/test/kronecker_product.cpp
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@ -3,6 +3,7 @@
//
// 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
@ -89,64 +90,55 @@ void test_kronecker_product()
MatrixXd DM_b(3,2);
SparseMatrix<double> SM_a(2,3);
SparseMatrix<double> SM_b(3,2);
SM_a.insert(0,0) = DM_a(0,0) = -0.4461540300782201;
SM_a.insert(0,1) = DM_a(0,1) = -0.8057364375283049;
SM_a.insert(0,2) = DM_a(0,2) = 0.3896572459516341;
SM_a.insert(1,0) = DM_a(1,0) = -0.9076572187376921;
SM_a.insert(1,1) = DM_a(1,1) = 0.6469156566545853;
SM_a.insert(1,2) = DM_a(1,2) = -0.3658010398782789;
SM_b.insert(0,0) = DM_b(0,0) = 0.9004440976767099;
SM_b.insert(0,1) = DM_b(0,1) = -0.2368830858139832;
SM_b.insert(1,0) = DM_b(1,0) = -0.9311078389941825;
SM_b.insert(1,1) = DM_b(1,1) = 0.5310335762980047;
SM_b.insert(2,0) = DM_b(2,0) = -0.1225112806872035;
SM_b.insert(2,1) = DM_b(2,1) = 0.5903998022741264;
SM_a.insert(0,0) = DM_a.coeffRef(0,0) = -0.4461540300782201;
SM_a.insert(0,1) = DM_a.coeffRef(0,1) = -0.8057364375283049;
SM_a.insert(0,2) = DM_a.coeffRef(0,2) = 0.3896572459516341;
SM_a.insert(1,0) = DM_a.coeffRef(1,0) = -0.9076572187376921;
SM_a.insert(1,1) = DM_a.coeffRef(1,1) = 0.6469156566545853;
SM_a.insert(1,2) = DM_a.coeffRef(1,2) = -0.3658010398782789;
SM_b.insert(0,0) = DM_b.coeffRef(0,0) = 0.9004440976767099;
SM_b.insert(0,1) = DM_b.coeffRef(0,1) = -0.2368830858139832;
SM_b.insert(1,0) = DM_b.coeffRef(1,0) = -0.9311078389941825;
SM_b.insert(1,1) = DM_b.coeffRef(1,1) = 0.5310335762980047;
SM_b.insert(2,0) = DM_b.coeffRef(2,0) = -0.1225112806872035;
SM_b.insert(2,1) = DM_b.coeffRef(2,1) = 0.5903998022741264;
SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);
// test kroneckerProduct(DM_block,DM,DM_fixedSize)
Matrix<double, 6, 6> DM_fix_ab;
DM_fix_ab(0,0)=37.0;
kroneckerProduct(DM_a.block(0,0,2,3),DM_b,DM_fix_ab);
Matrix<double, 6, 6> DM_fix_ab = kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b);
CALL_SUBTEST(check_kronecker_product(DM_fix_ab));
// test kroneckerProduct(DM,DM,DM_block)
MatrixXd DM_block_ab(10,15);
DM_block_ab(0,0)=37.0;
kroneckerProduct(DM_a,DM_b,DM_block_ab.block(2,5,6,6));
CALL_SUBTEST(check_kronecker_product(DM_block_ab.block(2,5,6,6)));
DM_block_ab.block<6,6>(2,5) = kroneckerProduct(DM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(DM_block_ab.block<6,6>(2,5)));
// test kroneckerProduct(DM,DM,DM)
MatrixXd DM_ab(1,5);
DM_ab(0,0)=37.0;
kroneckerProduct(DM_a,DM_b,DM_ab);
MatrixXd DM_ab = kroneckerProduct(DM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(DM_ab));
// test kroneckerProduct(SM,DM,SM)
SparseMatrix<double> SM_ab(1,20);
SM_ab.insert(0,0)=37.0;
kroneckerProduct(SM_a,DM_b,SM_ab);
SparseMatrix<double> SM_ab = kroneckerProduct(SM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SparseMatrix<double,RowMajor> SM_ab2(10,3);
SM_ab2.insert(0,0)=37.0;
kroneckerProduct(SM_a,DM_b,SM_ab2);
SparseMatrix<double,RowMajor> SM_ab2 = kroneckerProduct(SM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
// test kroneckerProduct(DM,SM,SM)
SM_ab.insert(0,0)=37.0;
kroneckerProduct(DM_a,SM_b,SM_ab);
SM_ab = kroneckerProduct(DM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SM_ab2.insert(0,0)=37.0;
kroneckerProduct(DM_a,SM_b,SM_ab2);
SM_ab2 = kroneckerProduct(DM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
// test kroneckerProduct(SM,SM,SM)
SM_ab.resize(2,33);
SM_ab.insert(0,0)=37.0;
kroneckerProduct(SM_a,SM_b,SM_ab);
SM_ab = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SM_ab2.resize(5,11);
SM_ab2.insert(0,0)=37.0;
kroneckerProduct(SM_a,SM_b,SM_ab2);
SM_ab2 = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
// test kroneckerProduct(SM,SM,SM) with sparse pattern
@ -163,17 +155,16 @@ void test_kronecker_product()
SM_b.finalize();
SM_ab.resize(1,1);
SM_ab.insert(0,0)=37.0;
kroneckerProduct(SM_a,SM_b,SM_ab);
SM_ab = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));
// test dimension of result of kroneckerProduct(DM,DM,DM)
MatrixXd DM_a2(2,1);
MatrixXd DM_b2(5,4);
MatrixXd DM_ab2;
kroneckerProduct(DM_a2,DM_b2,DM_ab2);
MatrixXd DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4));
DM_a2.resize(10,9);
DM_b2.resize(4,8);
kroneckerProduct(DM_a2,DM_b2,DM_ab2);
DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8));
}