508 lines
18 KiB
C
508 lines
18 KiB
C
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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) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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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 http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_SPARSE_SELFADJOINTVIEW_H
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#define EIGEN_SPARSE_SELFADJOINTVIEW_H
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namespace Eigen {
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/** \ingroup SparseCore_Module
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* \class SparseSelfAdjointView
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*
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* \brief Pseudo expression to manipulate a triangular sparse matrix as a selfadjoint matrix.
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*
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* \param MatrixType the type of the dense matrix storing the coefficients
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* \param UpLo can be either \c #Lower or \c #Upper
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*
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* This class is an expression of a sefladjoint matrix from a triangular part of a matrix
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* with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
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* and most of the time this is the only way that it is used.
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*
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* \sa SparseMatrixBase::selfadjointView()
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*/
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template<typename Lhs, typename Rhs, int UpLo>
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class SparseSelfAdjointTimeDenseProduct;
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template<typename Lhs, typename Rhs, int UpLo>
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class DenseTimeSparseSelfAdjointProduct;
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namespace internal {
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template<typename MatrixType, unsigned int UpLo>
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struct traits<SparseSelfAdjointView<MatrixType,UpLo> > : traits<MatrixType> {
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};
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template<int SrcUpLo,int DstUpLo,typename MatrixType,int DestOrder>
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void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm = 0);
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template<int UpLo,typename MatrixType,int DestOrder>
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void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm = 0);
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}
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template<typename MatrixType, unsigned int UpLo> class SparseSelfAdjointView
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: public EigenBase<SparseSelfAdjointView<MatrixType,UpLo> >
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{
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public:
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::Index Index;
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typedef Matrix<Index,Dynamic,1> VectorI;
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typedef typename MatrixType::Nested MatrixTypeNested;
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typedef typename internal::remove_all<MatrixTypeNested>::type _MatrixTypeNested;
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inline SparseSelfAdjointView(const MatrixType& matrix) : m_matrix(matrix)
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{
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eigen_assert(rows()==cols() && "SelfAdjointView is only for squared matrices");
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}
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inline Index rows() const { return m_matrix.rows(); }
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inline Index cols() const { return m_matrix.cols(); }
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/** \internal \returns a reference to the nested matrix */
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const _MatrixTypeNested& matrix() const { return m_matrix; }
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_MatrixTypeNested& matrix() { return m_matrix.const_cast_derived(); }
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/** \returns an expression of the matrix product between a sparse self-adjoint matrix \c *this and a sparse matrix \a rhs.
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*
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* Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
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* Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
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*/
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template<typename OtherDerived>
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SparseSparseProduct<typename OtherDerived::PlainObject, OtherDerived>
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operator*(const SparseMatrixBase<OtherDerived>& rhs) const
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{
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return SparseSparseProduct<typename OtherDerived::PlainObject, OtherDerived>(*this, rhs.derived());
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}
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/** \returns an expression of the matrix product between a sparse matrix \a lhs and a sparse self-adjoint matrix \a rhs.
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*
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* Note that there is no algorithmic advantage of performing such a product compared to a general sparse-sparse matrix product.
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* Indeed, the SparseSelfadjointView operand is first copied into a temporary SparseMatrix before computing the product.
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*/
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template<typename OtherDerived> friend
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SparseSparseProduct<OtherDerived, typename OtherDerived::PlainObject >
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operator*(const SparseMatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
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{
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return SparseSparseProduct<OtherDerived, typename OtherDerived::PlainObject>(lhs.derived(), rhs);
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}
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/** Efficient sparse self-adjoint matrix times dense vector/matrix product */
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template<typename OtherDerived>
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SparseSelfAdjointTimeDenseProduct<MatrixType,OtherDerived,UpLo>
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operator*(const MatrixBase<OtherDerived>& rhs) const
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{
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return SparseSelfAdjointTimeDenseProduct<MatrixType,OtherDerived,UpLo>(m_matrix, rhs.derived());
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}
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/** Efficient dense vector/matrix times sparse self-adjoint matrix product */
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template<typename OtherDerived> friend
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DenseTimeSparseSelfAdjointProduct<OtherDerived,MatrixType,UpLo>
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operator*(const MatrixBase<OtherDerived>& lhs, const SparseSelfAdjointView& rhs)
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{
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return DenseTimeSparseSelfAdjointProduct<OtherDerived,_MatrixTypeNested,UpLo>(lhs.derived(), rhs.m_matrix);
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}
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/** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
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* \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
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*
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* \returns a reference to \c *this
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*
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* To perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
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* call this function with u.adjoint().
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*/
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template<typename DerivedU>
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SparseSelfAdjointView& rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));
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/** \internal triggered by sparse_matrix = SparseSelfadjointView; */
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template<typename DestScalar,int StorageOrder> void evalTo(SparseMatrix<DestScalar,StorageOrder,Index>& _dest) const
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{
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internal::permute_symm_to_fullsymm<UpLo>(m_matrix, _dest);
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}
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template<typename DestScalar> void evalTo(DynamicSparseMatrix<DestScalar,ColMajor,Index>& _dest) const
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{
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// TODO directly evaluate into _dest;
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SparseMatrix<DestScalar,ColMajor,Index> tmp(_dest.rows(),_dest.cols());
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internal::permute_symm_to_fullsymm<UpLo>(m_matrix, tmp);
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_dest = tmp;
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}
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/** \returns an expression of P H P^-1 */
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SparseSymmetricPermutationProduct<_MatrixTypeNested,UpLo> twistedBy(const PermutationMatrix<Dynamic,Dynamic,Index>& perm) const
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{
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return SparseSymmetricPermutationProduct<_MatrixTypeNested,UpLo>(m_matrix, perm);
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}
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template<typename SrcMatrixType,int SrcUpLo>
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SparseSelfAdjointView& operator=(const SparseSymmetricPermutationProduct<SrcMatrixType,SrcUpLo>& permutedMatrix)
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{
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permutedMatrix.evalTo(*this);
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return *this;
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}
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SparseSelfAdjointView& operator=(const SparseSelfAdjointView& src)
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{
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PermutationMatrix<Dynamic> pnull;
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return *this = src.twistedBy(pnull);
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}
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template<typename SrcMatrixType,unsigned int SrcUpLo>
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SparseSelfAdjointView& operator=(const SparseSelfAdjointView<SrcMatrixType,SrcUpLo>& src)
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{
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PermutationMatrix<Dynamic> pnull;
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return *this = src.twistedBy(pnull);
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}
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// const SparseLLT<PlainObject, UpLo> llt() const;
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// const SparseLDLT<PlainObject, UpLo> ldlt() const;
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protected:
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typename MatrixType::Nested m_matrix;
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mutable VectorI m_countPerRow;
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mutable VectorI m_countPerCol;
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};
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/***************************************************************************
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* Implementation of SparseMatrixBase methods
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***************************************************************************/
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template<typename Derived>
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template<unsigned int UpLo>
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const SparseSelfAdjointView<Derived, UpLo> SparseMatrixBase<Derived>::selfadjointView() const
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{
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return derived();
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}
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template<typename Derived>
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template<unsigned int UpLo>
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SparseSelfAdjointView<Derived, UpLo> SparseMatrixBase<Derived>::selfadjointView()
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{
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return derived();
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}
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/***************************************************************************
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* Implementation of SparseSelfAdjointView methods
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***************************************************************************/
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template<typename MatrixType, unsigned int UpLo>
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template<typename DerivedU>
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SparseSelfAdjointView<MatrixType,UpLo>&
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SparseSelfAdjointView<MatrixType,UpLo>::rankUpdate(const SparseMatrixBase<DerivedU>& u, const Scalar& alpha)
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{
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SparseMatrix<Scalar,MatrixType::Flags&RowMajorBit?RowMajor:ColMajor> tmp = u * u.adjoint();
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if(alpha==Scalar(0))
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m_matrix.const_cast_derived() = tmp.template triangularView<UpLo>();
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else
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m_matrix.const_cast_derived() += alpha * tmp.template triangularView<UpLo>();
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return *this;
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}
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/***************************************************************************
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* Implementation of sparse self-adjoint time dense matrix
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***************************************************************************/
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namespace internal {
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template<typename Lhs, typename Rhs, int UpLo>
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struct traits<SparseSelfAdjointTimeDenseProduct<Lhs,Rhs,UpLo> >
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: traits<ProductBase<SparseSelfAdjointTimeDenseProduct<Lhs,Rhs,UpLo>, Lhs, Rhs> >
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{
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typedef Dense StorageKind;
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};
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}
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template<typename Lhs, typename Rhs, int UpLo>
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class SparseSelfAdjointTimeDenseProduct
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: public ProductBase<SparseSelfAdjointTimeDenseProduct<Lhs,Rhs,UpLo>, Lhs, Rhs>
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{
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public:
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EIGEN_PRODUCT_PUBLIC_INTERFACE(SparseSelfAdjointTimeDenseProduct)
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SparseSelfAdjointTimeDenseProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
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{}
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template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
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{
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EIGEN_ONLY_USED_FOR_DEBUG(alpha);
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// TODO use alpha
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eigen_assert(alpha==Scalar(1) && "alpha != 1 is not implemented yet, sorry");
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typedef typename internal::remove_all<Lhs>::type _Lhs;
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typedef typename _Lhs::InnerIterator LhsInnerIterator;
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enum {
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LhsIsRowMajor = (_Lhs::Flags&RowMajorBit)==RowMajorBit,
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ProcessFirstHalf =
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((UpLo&(Upper|Lower))==(Upper|Lower))
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|| ( (UpLo&Upper) && !LhsIsRowMajor)
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|| ( (UpLo&Lower) && LhsIsRowMajor),
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ProcessSecondHalf = !ProcessFirstHalf
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};
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for (Index j=0; j<m_lhs.outerSize(); ++j)
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{
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LhsInnerIterator i(m_lhs,j);
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if (ProcessSecondHalf)
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{
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while (i && i.index()<j) ++i;
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if(i && i.index()==j)
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{
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dest.row(j) += i.value() * m_rhs.row(j);
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++i;
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}
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}
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for(; (ProcessFirstHalf ? i && i.index() < j : i) ; ++i)
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{
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Index a = LhsIsRowMajor ? j : i.index();
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Index b = LhsIsRowMajor ? i.index() : j;
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typename Lhs::Scalar v = i.value();
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dest.row(a) += (v) * m_rhs.row(b);
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dest.row(b) += numext::conj(v) * m_rhs.row(a);
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}
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if (ProcessFirstHalf && i && (i.index()==j))
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dest.row(j) += i.value() * m_rhs.row(j);
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}
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}
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private:
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SparseSelfAdjointTimeDenseProduct& operator=(const SparseSelfAdjointTimeDenseProduct&);
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};
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namespace internal {
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template<typename Lhs, typename Rhs, int UpLo>
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struct traits<DenseTimeSparseSelfAdjointProduct<Lhs,Rhs,UpLo> >
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: traits<ProductBase<DenseTimeSparseSelfAdjointProduct<Lhs,Rhs,UpLo>, Lhs, Rhs> >
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{};
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}
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template<typename Lhs, typename Rhs, int UpLo>
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class DenseTimeSparseSelfAdjointProduct
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: public ProductBase<DenseTimeSparseSelfAdjointProduct<Lhs,Rhs,UpLo>, Lhs, Rhs>
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{
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public:
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EIGEN_PRODUCT_PUBLIC_INTERFACE(DenseTimeSparseSelfAdjointProduct)
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DenseTimeSparseSelfAdjointProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
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{}
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template<typename Dest> void scaleAndAddTo(Dest& /*dest*/, const Scalar& /*alpha*/) const
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{
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// TODO
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}
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private:
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DenseTimeSparseSelfAdjointProduct& operator=(const DenseTimeSparseSelfAdjointProduct&);
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};
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/***************************************************************************
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* Implementation of symmetric copies and permutations
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***************************************************************************/
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namespace internal {
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template<typename MatrixType, int UpLo>
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struct traits<SparseSymmetricPermutationProduct<MatrixType,UpLo> > : traits<MatrixType> {
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};
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template<int UpLo,typename MatrixType,int DestOrder>
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void permute_symm_to_fullsymm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DestOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm)
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{
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typedef typename MatrixType::Index Index;
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typedef typename MatrixType::Scalar Scalar;
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typedef SparseMatrix<Scalar,DestOrder,Index> Dest;
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typedef Matrix<Index,Dynamic,1> VectorI;
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Dest& dest(_dest.derived());
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enum {
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StorageOrderMatch = int(Dest::IsRowMajor) == int(MatrixType::IsRowMajor)
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};
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Index size = mat.rows();
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VectorI count;
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count.resize(size);
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count.setZero();
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dest.resize(size,size);
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for(Index j = 0; j<size; ++j)
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{
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Index jp = perm ? perm[j] : j;
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for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
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{
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Index i = it.index();
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Index r = it.row();
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Index c = it.col();
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Index ip = perm ? perm[i] : i;
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if(UpLo==(Upper|Lower))
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count[StorageOrderMatch ? jp : ip]++;
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else if(r==c)
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count[ip]++;
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else if(( UpLo==Lower && r>c) || ( UpLo==Upper && r<c))
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{
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count[ip]++;
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count[jp]++;
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}
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}
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}
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Index nnz = count.sum();
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|
||
|
|
// reserve space
|
||
|
|
dest.resizeNonZeros(nnz);
|
||
|
|
dest.outerIndexPtr()[0] = 0;
|
||
|
|
for(Index j=0; j<size; ++j)
|
||
|
|
dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];
|
||
|
|
for(Index j=0; j<size; ++j)
|
||
|
|
count[j] = dest.outerIndexPtr()[j];
|
||
|
|
|
||
|
|
// copy data
|
||
|
|
for(Index j = 0; j<size; ++j)
|
||
|
|
{
|
||
|
|
for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
|
||
|
|
{
|
||
|
|
Index i = it.index();
|
||
|
|
Index r = it.row();
|
||
|
|
Index c = it.col();
|
||
|
|
|
||
|
|
Index jp = perm ? perm[j] : j;
|
||
|
|
Index ip = perm ? perm[i] : i;
|
||
|
|
|
||
|
|
if(UpLo==(Upper|Lower))
|
||
|
|
{
|
||
|
|
Index k = count[StorageOrderMatch ? jp : ip]++;
|
||
|
|
dest.innerIndexPtr()[k] = StorageOrderMatch ? ip : jp;
|
||
|
|
dest.valuePtr()[k] = it.value();
|
||
|
|
}
|
||
|
|
else if(r==c)
|
||
|
|
{
|
||
|
|
Index k = count[ip]++;
|
||
|
|
dest.innerIndexPtr()[k] = ip;
|
||
|
|
dest.valuePtr()[k] = it.value();
|
||
|
|
}
|
||
|
|
else if(( (UpLo&Lower)==Lower && r>c) || ( (UpLo&Upper)==Upper && r<c))
|
||
|
|
{
|
||
|
|
if(!StorageOrderMatch)
|
||
|
|
std::swap(ip,jp);
|
||
|
|
Index k = count[jp]++;
|
||
|
|
dest.innerIndexPtr()[k] = ip;
|
||
|
|
dest.valuePtr()[k] = it.value();
|
||
|
|
k = count[ip]++;
|
||
|
|
dest.innerIndexPtr()[k] = jp;
|
||
|
|
dest.valuePtr()[k] = numext::conj(it.value());
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
template<int _SrcUpLo,int _DstUpLo,typename MatrixType,int DstOrder>
|
||
|
|
void permute_symm_to_symm(const MatrixType& mat, SparseMatrix<typename MatrixType::Scalar,DstOrder,typename MatrixType::Index>& _dest, const typename MatrixType::Index* perm)
|
||
|
|
{
|
||
|
|
typedef typename MatrixType::Index Index;
|
||
|
|
typedef typename MatrixType::Scalar Scalar;
|
||
|
|
SparseMatrix<Scalar,DstOrder,Index>& dest(_dest.derived());
|
||
|
|
typedef Matrix<Index,Dynamic,1> VectorI;
|
||
|
|
enum {
|
||
|
|
SrcOrder = MatrixType::IsRowMajor ? RowMajor : ColMajor,
|
||
|
|
StorageOrderMatch = int(SrcOrder) == int(DstOrder),
|
||
|
|
DstUpLo = DstOrder==RowMajor ? (_DstUpLo==Upper ? Lower : Upper) : _DstUpLo,
|
||
|
|
SrcUpLo = SrcOrder==RowMajor ? (_SrcUpLo==Upper ? Lower : Upper) : _SrcUpLo
|
||
|
|
};
|
||
|
|
|
||
|
|
Index size = mat.rows();
|
||
|
|
VectorI count(size);
|
||
|
|
count.setZero();
|
||
|
|
dest.resize(size,size);
|
||
|
|
for(Index j = 0; j<size; ++j)
|
||
|
|
{
|
||
|
|
Index jp = perm ? perm[j] : j;
|
||
|
|
for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
|
||
|
|
{
|
||
|
|
Index i = it.index();
|
||
|
|
if((int(SrcUpLo)==int(Lower) && i<j) || (int(SrcUpLo)==int(Upper) && i>j))
|
||
|
|
continue;
|
||
|
|
|
||
|
|
Index ip = perm ? perm[i] : i;
|
||
|
|
count[int(DstUpLo)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
dest.outerIndexPtr()[0] = 0;
|
||
|
|
for(Index j=0; j<size; ++j)
|
||
|
|
dest.outerIndexPtr()[j+1] = dest.outerIndexPtr()[j] + count[j];
|
||
|
|
dest.resizeNonZeros(dest.outerIndexPtr()[size]);
|
||
|
|
for(Index j=0; j<size; ++j)
|
||
|
|
count[j] = dest.outerIndexPtr()[j];
|
||
|
|
|
||
|
|
for(Index j = 0; j<size; ++j)
|
||
|
|
{
|
||
|
|
|
||
|
|
for(typename MatrixType::InnerIterator it(mat,j); it; ++it)
|
||
|
|
{
|
||
|
|
Index i = it.index();
|
||
|
|
if((int(SrcUpLo)==int(Lower) && i<j) || (int(SrcUpLo)==int(Upper) && i>j))
|
||
|
|
continue;
|
||
|
|
|
||
|
|
Index jp = perm ? perm[j] : j;
|
||
|
|
Index ip = perm? perm[i] : i;
|
||
|
|
|
||
|
|
Index k = count[int(DstUpLo)==int(Lower) ? (std::min)(ip,jp) : (std::max)(ip,jp)]++;
|
||
|
|
dest.innerIndexPtr()[k] = int(DstUpLo)==int(Lower) ? (std::max)(ip,jp) : (std::min)(ip,jp);
|
||
|
|
|
||
|
|
if(!StorageOrderMatch) std::swap(ip,jp);
|
||
|
|
if( ((int(DstUpLo)==int(Lower) && ip<jp) || (int(DstUpLo)==int(Upper) && ip>jp)))
|
||
|
|
dest.valuePtr()[k] = numext::conj(it.value());
|
||
|
|
else
|
||
|
|
dest.valuePtr()[k] = it.value();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename MatrixType,int UpLo>
|
||
|
|
class SparseSymmetricPermutationProduct
|
||
|
|
: public EigenBase<SparseSymmetricPermutationProduct<MatrixType,UpLo> >
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef typename MatrixType::Scalar Scalar;
|
||
|
|
typedef typename MatrixType::Index Index;
|
||
|
|
protected:
|
||
|
|
typedef PermutationMatrix<Dynamic,Dynamic,Index> Perm;
|
||
|
|
public:
|
||
|
|
typedef Matrix<Index,Dynamic,1> VectorI;
|
||
|
|
typedef typename MatrixType::Nested MatrixTypeNested;
|
||
|
|
typedef typename internal::remove_all<MatrixTypeNested>::type _MatrixTypeNested;
|
||
|
|
|
||
|
|
SparseSymmetricPermutationProduct(const MatrixType& mat, const Perm& perm)
|
||
|
|
: m_matrix(mat), m_perm(perm)
|
||
|
|
{}
|
||
|
|
|
||
|
|
inline Index rows() const { return m_matrix.rows(); }
|
||
|
|
inline Index cols() const { return m_matrix.cols(); }
|
||
|
|
|
||
|
|
template<typename DestScalar, int Options, typename DstIndex>
|
||
|
|
void evalTo(SparseMatrix<DestScalar,Options,DstIndex>& _dest) const
|
||
|
|
{
|
||
|
|
// internal::permute_symm_to_fullsymm<UpLo>(m_matrix,_dest,m_perm.indices().data());
|
||
|
|
SparseMatrix<DestScalar,(Options&RowMajor)==RowMajor ? ColMajor : RowMajor, DstIndex> tmp;
|
||
|
|
internal::permute_symm_to_fullsymm<UpLo>(m_matrix,tmp,m_perm.indices().data());
|
||
|
|
_dest = tmp;
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename DestType,unsigned int DestUpLo> void evalTo(SparseSelfAdjointView<DestType,DestUpLo>& dest) const
|
||
|
|
{
|
||
|
|
internal::permute_symm_to_symm<UpLo,DestUpLo>(m_matrix,dest.matrix(),m_perm.indices().data());
|
||
|
|
}
|
||
|
|
|
||
|
|
protected:
|
||
|
|
MatrixTypeNested m_matrix;
|
||
|
|
const Perm& m_perm;
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
} // end namespace Eigen
|
||
|
|
|
||
|
|
#endif // EIGEN_SPARSE_SELFADJOINTVIEW_H
|