add vcglib
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
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// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
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// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at the mozilla.org home page
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#ifndef KRONECKER_TENSOR_PRODUCT_H
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#define KRONECKER_TENSOR_PRODUCT_H
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namespace Eigen {
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/*!
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* \ingroup KroneckerProduct_Module
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*
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* \brief The base class of dense and sparse Kronecker product.
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*
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* \tparam Derived is the derived type.
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*/
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template<typename Derived>
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class KroneckerProductBase : public ReturnByValue<Derived>
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{
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private:
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typedef typename internal::traits<Derived> Traits;
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typedef typename Traits::Scalar Scalar;
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protected:
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typedef typename Traits::Lhs Lhs;
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typedef typename Traits::Rhs Rhs;
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public:
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/*! \brief Constructor. */
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KroneckerProductBase(const Lhs& A, const Rhs& B)
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: m_A(A), m_B(B)
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{}
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inline Index rows() const { return m_A.rows() * m_B.rows(); }
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inline Index cols() const { return m_A.cols() * m_B.cols(); }
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/*!
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* This overrides ReturnByValue::coeff because this function is
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* efficient enough.
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*/
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Scalar coeff(Index row, Index col) const
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{
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return m_A.coeff(row / m_B.rows(), col / m_B.cols()) *
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m_B.coeff(row % m_B.rows(), col % m_B.cols());
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}
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/*!
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* This overrides ReturnByValue::coeff because this function is
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* efficient enough.
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*/
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Scalar coeff(Index i) const
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{
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
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return m_A.coeff(i / m_A.size()) * m_B.coeff(i % m_A.size());
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}
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protected:
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typename Lhs::Nested m_A;
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typename Rhs::Nested m_B;
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};
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/*!
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* \ingroup KroneckerProduct_Module
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*
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* \brief Kronecker tensor product helper class for dense matrices
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*
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* This class is the return value of kroneckerProduct(MatrixBase,
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* MatrixBase). Use the function rather than construct this class
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* directly to avoid specifying template prarameters.
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*
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* \tparam Lhs Type of the left-hand side, a matrix expression.
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* \tparam Rhs Type of the rignt-hand side, a matrix expression.
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*/
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template<typename Lhs, typename Rhs>
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class KroneckerProduct : public KroneckerProductBase<KroneckerProduct<Lhs,Rhs> >
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{
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private:
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typedef KroneckerProductBase<KroneckerProduct> Base;
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using Base::m_A;
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using Base::m_B;
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public:
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/*! \brief Constructor. */
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KroneckerProduct(const Lhs& A, const Rhs& B)
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: Base(A, B)
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{}
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/*! \brief Evaluate the Kronecker tensor product. */
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template<typename Dest> void evalTo(Dest& dst) const;
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};
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/*!
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* \ingroup KroneckerProduct_Module
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*
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* \brief Kronecker tensor product helper class for sparse matrices
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*
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* If at least one of the operands is a sparse matrix expression,
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* then this class is returned and evaluates into a sparse matrix.
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*
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* This class is the return value of kroneckerProduct(EigenBase,
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* EigenBase). Use the function rather than construct this class
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* directly to avoid specifying template prarameters.
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*
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* \tparam Lhs Type of the left-hand side, a matrix expression.
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* \tparam Rhs Type of the rignt-hand side, a matrix expression.
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*/
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template<typename Lhs, typename Rhs>
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class KroneckerProductSparse : public KroneckerProductBase<KroneckerProductSparse<Lhs,Rhs> >
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{
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private:
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typedef KroneckerProductBase<KroneckerProductSparse> Base;
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using Base::m_A;
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using Base::m_B;
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public:
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/*! \brief Constructor. */
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KroneckerProductSparse(const Lhs& A, const Rhs& B)
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: Base(A, B)
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{}
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/*! \brief Evaluate the Kronecker tensor product. */
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template<typename Dest> void evalTo(Dest& dst) const;
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};
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template<typename Lhs, typename Rhs>
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template<typename Dest>
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void KroneckerProduct<Lhs,Rhs>::evalTo(Dest& dst) const
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{
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const int BlockRows = Rhs::RowsAtCompileTime,
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BlockCols = Rhs::ColsAtCompileTime;
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const Index Br = m_B.rows(),
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Bc = m_B.cols();
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for (Index i=0; i < m_A.rows(); ++i)
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for (Index j=0; j < m_A.cols(); ++j)
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Block<Dest,BlockRows,BlockCols>(dst,i*Br,j*Bc,Br,Bc) = m_A.coeff(i,j) * m_B;
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}
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template<typename Lhs, typename Rhs>
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template<typename Dest>
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void KroneckerProductSparse<Lhs,Rhs>::evalTo(Dest& dst) const
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{
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Index Br = m_B.rows(), Bc = m_B.cols();
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dst.resize(this->rows(), this->cols());
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dst.resizeNonZeros(0);
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// 1 - evaluate the operands if needed:
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typedef typename internal::nested_eval<Lhs,Dynamic>::type Lhs1;
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typedef typename internal::remove_all<Lhs1>::type Lhs1Cleaned;
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const Lhs1 lhs1(m_A);
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typedef typename internal::nested_eval<Rhs,Dynamic>::type Rhs1;
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typedef typename internal::remove_all<Rhs1>::type Rhs1Cleaned;
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const Rhs1 rhs1(m_B);
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// 2 - construct respective iterators
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typedef Eigen::InnerIterator<Lhs1Cleaned> LhsInnerIterator;
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typedef Eigen::InnerIterator<Rhs1Cleaned> RhsInnerIterator;
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// compute number of non-zeros per innervectors of dst
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{
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// TODO VectorXi is not necessarily big enough!
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VectorXi nnzA = VectorXi::Zero(Dest::IsRowMajor ? m_A.rows() : m_A.cols());
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for (Index kA=0; kA < m_A.outerSize(); ++kA)
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for (LhsInnerIterator itA(lhs1,kA); itA; ++itA)
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nnzA(Dest::IsRowMajor ? itA.row() : itA.col())++;
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VectorXi nnzB = VectorXi::Zero(Dest::IsRowMajor ? m_B.rows() : m_B.cols());
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for (Index kB=0; kB < m_B.outerSize(); ++kB)
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for (RhsInnerIterator itB(rhs1,kB); itB; ++itB)
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nnzB(Dest::IsRowMajor ? itB.row() : itB.col())++;
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Matrix<int,Dynamic,Dynamic,ColMajor> nnzAB = nnzB * nnzA.transpose();
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dst.reserve(VectorXi::Map(nnzAB.data(), nnzAB.size()));
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}
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for (Index kA=0; kA < m_A.outerSize(); ++kA)
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{
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for (Index kB=0; kB < m_B.outerSize(); ++kB)
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{
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for (LhsInnerIterator itA(lhs1,kA); itA; ++itA)
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{
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for (RhsInnerIterator itB(rhs1,kB); itB; ++itB)
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{
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Index i = itA.row() * Br + itB.row(),
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j = itA.col() * Bc + itB.col();
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dst.insert(i,j) = itA.value() * itB.value();
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}
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}
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}
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}
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}
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namespace internal {
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template<typename _Lhs, typename _Rhs>
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struct traits<KroneckerProduct<_Lhs,_Rhs> >
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{
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typedef typename remove_all<_Lhs>::type Lhs;
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typedef typename remove_all<_Rhs>::type Rhs;
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typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
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typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;
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enum {
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Rows = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,
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Cols = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,
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MaxRows = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,
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MaxCols = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret
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};
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typedef Matrix<Scalar,Rows,Cols> ReturnType;
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};
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template<typename _Lhs, typename _Rhs>
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struct traits<KroneckerProductSparse<_Lhs,_Rhs> >
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{
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typedef MatrixXpr XprKind;
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typedef typename remove_all<_Lhs>::type Lhs;
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typedef typename remove_all<_Rhs>::type Rhs;
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typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
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typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind, scalar_product_op<typename Lhs::Scalar, typename Rhs::Scalar> >::ret StorageKind;
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typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;
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enum {
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LhsFlags = Lhs::Flags,
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RhsFlags = Rhs::Flags,
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RowsAtCompileTime = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,
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ColsAtCompileTime = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,
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MaxRowsAtCompileTime = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,
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MaxColsAtCompileTime = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret,
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EvalToRowMajor = (int(LhsFlags) & int(RhsFlags) & RowMajorBit),
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RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),
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Flags = ((int(LhsFlags) | int(RhsFlags)) & HereditaryBits & RemovedBits)
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| EvalBeforeNestingBit,
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CoeffReadCost = HugeCost
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};
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typedef SparseMatrix<Scalar, 0, StorageIndex> ReturnType;
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};
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} // end namespace internal
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/*!
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* \ingroup KroneckerProduct_Module
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*
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* Computes Kronecker tensor product of two dense matrices
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*
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* \warning If you want to replace a matrix by its Kronecker product
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* with some matrix, do \b NOT do this:
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* \code
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* A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
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* \endcode
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* instead, use eval() to work around this:
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* \code
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* A = kroneckerProduct(A,B).eval();
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* \endcode
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*
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* \param a Dense matrix a
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* \param b Dense matrix b
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* \return Kronecker tensor product of a and b
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*/
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template<typename A, typename B>
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KroneckerProduct<A,B> kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b)
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{
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return KroneckerProduct<A, B>(a.derived(), b.derived());
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}
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/*!
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* \ingroup KroneckerProduct_Module
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*
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* Computes Kronecker tensor product of two matrices, at least one of
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* which is sparse
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*
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* \warning If you want to replace a matrix by its Kronecker product
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* with some matrix, do \b NOT do this:
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* \code
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* A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
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* \endcode
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* instead, use eval() to work around this:
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* \code
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* A = kroneckerProduct(A,B).eval();
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* \endcode
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*
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* \param a Dense/sparse matrix a
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* \param b Dense/sparse matrix b
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* \return Kronecker tensor product of a and b, stored in a sparse
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* matrix
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*/
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template<typename A, typename B>
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KroneckerProductSparse<A,B> kroneckerProduct(const EigenBase<A>& a, const EigenBase<B>& b)
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{
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return KroneckerProductSparse<A,B>(a.derived(), b.derived());
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}
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} // end namespace Eigen
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#endif // KRONECKER_TENSOR_PRODUCT_H
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