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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>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef KRONECKER_TENSOR_PRODUCT_H
#define KRONECKER_TENSOR_PRODUCT_H
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)
{
const unsigned int Ar = A.rows(),
Ac = A.cols(),
Br = B.rows(),
Bc = B.cols();
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;
}
/*!
* 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)
{
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());
for (int kA=0; kA<A.outerSize(); ++kA)
{
for (int kB=0; kB<B.outerSize(); ++kB)
{
for (typename Derived_A::InnerIterator itA(A,kA); itA; ++itA)
{
for (typename Derived_B::InnerIterator itB(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();
}
}
}
}
}
} // end namespace internal
/*!
* Computes Kronecker tensor product of two dense matrices
*
* \param a Dense matrix a
* \param b Dense matrix b
* \param c Kronecker tensor product of a and b
*/
template<typename A,typename B,typename CScalar,int CRows,int CCols, int COptions, int CMaxRows, int CMaxCols>
void kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b, Matrix<CScalar,CRows,CCols,COptions,CMaxRows,CMaxCols>& c)
{
c.resize(a.rows()*b.rows(),a.cols()*b.cols());
internal::kroneckerProduct_full(a.derived(), b.derived(), c);
}
/*!
* 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
*/
template<typename A,typename B,typename C>
void kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b, MatrixBase<C> const & c_)
{
MatrixBase<C>& c = const_cast<MatrixBase<C>& >(c_);
internal::kroneckerProduct_full(a.derived(), b.derived(), c.derived());
}
/*!
* Computes Kronecker tensor product of a dense and a sparse matrix
*
* \param a Dense 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 MatrixBase<A>& a, const SparseMatrixBase<B>& b, SparseMatrixBase<C>& c)
{
internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.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)
{
internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.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)
{
internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.derived());
}
} // end namespace Eigen
#endif // KRONECKER_TENSOR_PRODUCT_H
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