| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> |
| // |
| // 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 EIGEN_BANDMATRIX_H |
| #define EIGEN_BANDMATRIX_H |
| |
| // IWYU pragma: private |
| #include "./InternalHeaderCheck.h" |
| |
| namespace Eigen { |
| |
| namespace internal { |
| |
| template<typename Derived> |
| class BandMatrixBase : public EigenBase<Derived> |
| { |
| public: |
| |
| enum { |
| Flags = internal::traits<Derived>::Flags, |
| CoeffReadCost = internal::traits<Derived>::CoeffReadCost, |
| RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime, |
| ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime, |
| MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime, |
| MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime, |
| Supers = internal::traits<Derived>::Supers, |
| Subs = internal::traits<Derived>::Subs, |
| Options = internal::traits<Derived>::Options |
| }; |
| typedef typename internal::traits<Derived>::Scalar Scalar; |
| typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> DenseMatrixType; |
| typedef typename DenseMatrixType::StorageIndex StorageIndex; |
| typedef typename internal::traits<Derived>::CoefficientsType CoefficientsType; |
| typedef EigenBase<Derived> Base; |
| |
| protected: |
| enum { |
| DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) |
| ? 1 + Supers + Subs |
| : Dynamic, |
| SizeAtCompileTime = min_size_prefer_dynamic(RowsAtCompileTime,ColsAtCompileTime) |
| }; |
| |
| public: |
| |
| using Base::derived; |
| using Base::rows; |
| using Base::cols; |
| |
| /** \returns the number of super diagonals */ |
| inline Index supers() const { return derived().supers(); } |
| |
| /** \returns the number of sub diagonals */ |
| inline Index subs() const { return derived().subs(); } |
| |
| /** \returns an expression of the underlying coefficient matrix */ |
| inline const CoefficientsType& coeffs() const { return derived().coeffs(); } |
| |
| /** \returns an expression of the underlying coefficient matrix */ |
| inline CoefficientsType& coeffs() { return derived().coeffs(); } |
| |
| /** \returns a vector expression of the \a i -th column, |
| * only the meaningful part is returned. |
| * \warning the internal storage must be column major. */ |
| inline Block<CoefficientsType,Dynamic,1> col(Index i) |
| { |
| EIGEN_STATIC_ASSERT((int(Options) & int(RowMajor)) == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES); |
| Index start = 0; |
| Index len = coeffs().rows(); |
| if (i<=supers()) |
| { |
| start = supers()-i; |
| len = (std::min)(rows(),std::max<Index>(0,coeffs().rows() - (supers()-i))); |
| } |
| else if (i>=rows()-subs()) |
| len = std::max<Index>(0,coeffs().rows() - (i + 1 - rows() + subs())); |
| return Block<CoefficientsType,Dynamic,1>(coeffs(), start, i, len, 1); |
| } |
| |
| /** \returns a vector expression of the main diagonal */ |
| inline Block<CoefficientsType,1,SizeAtCompileTime> diagonal() |
| { return Block<CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); } |
| |
| /** \returns a vector expression of the main diagonal (const version) */ |
| inline const Block<const CoefficientsType,1,SizeAtCompileTime> diagonal() const |
| { return Block<const CoefficientsType,1,SizeAtCompileTime>(coeffs(),supers(),0,1,(std::min)(rows(),cols())); } |
| |
| template<int Index> struct DiagonalIntReturnType { |
| enum { |
| ReturnOpposite = (int(Options) & int(SelfAdjoint)) && (((Index) > 0 && Supers == 0) || ((Index) < 0 && Subs == 0)), |
| Conjugate = ReturnOpposite && NumTraits<Scalar>::IsComplex, |
| ActualIndex = ReturnOpposite ? -Index : Index, |
| DiagonalSize = (RowsAtCompileTime==Dynamic || ColsAtCompileTime==Dynamic) |
| ? Dynamic |
| : (ActualIndex<0 |
| ? min_size_prefer_dynamic(ColsAtCompileTime, RowsAtCompileTime + ActualIndex) |
| : min_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime - ActualIndex)) |
| }; |
| typedef Block<CoefficientsType,1, DiagonalSize> BuildType; |
| typedef std::conditional_t<Conjugate, |
| CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,BuildType >, |
| BuildType> Type; |
| }; |
| |
| /** \returns a vector expression of the \a N -th sub or super diagonal */ |
| template<int N> inline typename DiagonalIntReturnType<N>::Type diagonal() |
| { |
| return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N)); |
| } |
| |
| /** \returns a vector expression of the \a N -th sub or super diagonal */ |
| template<int N> inline const typename DiagonalIntReturnType<N>::Type diagonal() const |
| { |
| return typename DiagonalIntReturnType<N>::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N)); |
| } |
| |
| /** \returns a vector expression of the \a i -th sub or super diagonal */ |
| inline Block<CoefficientsType,1,Dynamic> diagonal(Index i) |
| { |
| eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers())); |
| return Block<CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i)); |
| } |
| |
| /** \returns a vector expression of the \a i -th sub or super diagonal */ |
| inline const Block<const CoefficientsType,1,Dynamic> diagonal(Index i) const |
| { |
| eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers())); |
| return Block<const CoefficientsType,1,Dynamic>(coeffs(), supers()-i, std::max<Index>(0,i), 1, diagonalLength(i)); |
| } |
| |
| template<typename Dest> inline void evalTo(Dest& dst) const |
| { |
| dst.resize(rows(),cols()); |
| dst.setZero(); |
| dst.diagonal() = diagonal(); |
| for (Index i=1; i<=supers();++i) |
| dst.diagonal(i) = diagonal(i); |
| for (Index i=1; i<=subs();++i) |
| dst.diagonal(-i) = diagonal(-i); |
| } |
| |
| DenseMatrixType toDenseMatrix() const |
| { |
| DenseMatrixType res(rows(),cols()); |
| evalTo(res); |
| return res; |
| } |
| |
| protected: |
| |
| inline Index diagonalLength(Index i) const |
| { return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); } |
| }; |
| |
| /** |
| * \class BandMatrix |
| * \ingroup Core_Module |
| * |
| * \brief Represents a rectangular matrix with a banded storage |
| * |
| * \tparam Scalar_ Numeric type, i.e. float, double, int |
| * \tparam Rows_ Number of rows, or \b Dynamic |
| * \tparam Cols_ Number of columns, or \b Dynamic |
| * \tparam Supers_ Number of super diagonal |
| * \tparam Subs_ Number of sub diagonal |
| * \tparam Options_ A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint |
| * The former controls \ref TopicStorageOrders "storage order", and defaults to |
| * column-major. The latter controls whether the matrix represents a selfadjoint |
| * matrix in which case either Supers of Subs have to be null. |
| * |
| * \sa class TridiagonalMatrix |
| */ |
| |
| template<typename Scalar_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_> |
| struct traits<BandMatrix<Scalar_,Rows_,Cols_,Supers_,Subs_,Options_> > |
| { |
| typedef Scalar_ Scalar; |
| typedef Dense StorageKind; |
| typedef Eigen::Index StorageIndex; |
| enum { |
| CoeffReadCost = NumTraits<Scalar>::ReadCost, |
| RowsAtCompileTime = Rows_, |
| ColsAtCompileTime = Cols_, |
| MaxRowsAtCompileTime = Rows_, |
| MaxColsAtCompileTime = Cols_, |
| Flags = LvalueBit, |
| Supers = Supers_, |
| Subs = Subs_, |
| Options = Options_, |
| DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic |
| }; |
| typedef Matrix<Scalar, DataRowsAtCompileTime, ColsAtCompileTime, int(Options) & int(RowMajor) ? RowMajor : ColMajor> CoefficientsType; |
| }; |
| |
| template<typename Scalar_, int Rows, int Cols, int Supers, int Subs, int Options> |
| class BandMatrix : public BandMatrixBase<BandMatrix<Scalar_,Rows,Cols,Supers,Subs,Options> > |
| { |
| public: |
| |
| typedef typename internal::traits<BandMatrix>::Scalar Scalar; |
| typedef typename internal::traits<BandMatrix>::StorageIndex StorageIndex; |
| typedef typename internal::traits<BandMatrix>::CoefficientsType CoefficientsType; |
| |
| explicit inline BandMatrix(Index rows=Rows, Index cols=Cols, Index supers=Supers, Index subs=Subs) |
| : m_coeffs(1+supers+subs,cols), |
| m_rows(rows), m_supers(supers), m_subs(subs) |
| { |
| } |
| |
| /** \returns the number of columns */ |
| inline EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); } |
| |
| /** \returns the number of rows */ |
| inline EIGEN_CONSTEXPR Index cols() const { return m_coeffs.cols(); } |
| |
| /** \returns the number of super diagonals */ |
| inline EIGEN_CONSTEXPR Index supers() const { return m_supers.value(); } |
| |
| /** \returns the number of sub diagonals */ |
| inline EIGEN_CONSTEXPR Index subs() const { return m_subs.value(); } |
| |
| inline const CoefficientsType& coeffs() const { return m_coeffs; } |
| inline CoefficientsType& coeffs() { return m_coeffs; } |
| |
| protected: |
| |
| CoefficientsType m_coeffs; |
| internal::variable_if_dynamic<Index, Rows> m_rows; |
| internal::variable_if_dynamic<Index, Supers> m_supers; |
| internal::variable_if_dynamic<Index, Subs> m_subs; |
| }; |
| |
| template<typename CoefficientsType_,int Rows_, int Cols_, int Supers_, int Subs_,int Options_> |
| class BandMatrixWrapper; |
| |
| template<typename CoefficientsType_,int Rows_, int Cols_, int Supers_, int Subs_,int Options_> |
| struct traits<BandMatrixWrapper<CoefficientsType_,Rows_,Cols_,Supers_,Subs_,Options_> > |
| { |
| typedef typename CoefficientsType_::Scalar Scalar; |
| typedef typename CoefficientsType_::StorageKind StorageKind; |
| typedef typename CoefficientsType_::StorageIndex StorageIndex; |
| enum { |
| CoeffReadCost = internal::traits<CoefficientsType_>::CoeffReadCost, |
| RowsAtCompileTime = Rows_, |
| ColsAtCompileTime = Cols_, |
| MaxRowsAtCompileTime = Rows_, |
| MaxColsAtCompileTime = Cols_, |
| Flags = LvalueBit, |
| Supers = Supers_, |
| Subs = Subs_, |
| Options = Options_, |
| DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic |
| }; |
| typedef CoefficientsType_ CoefficientsType; |
| }; |
| |
| template<typename CoefficientsType_,int Rows_, int Cols_, int Supers_, int Subs_,int Options_> |
| class BandMatrixWrapper : public BandMatrixBase<BandMatrixWrapper<CoefficientsType_,Rows_,Cols_,Supers_,Subs_,Options_> > |
| { |
| public: |
| |
| typedef typename internal::traits<BandMatrixWrapper>::Scalar Scalar; |
| typedef typename internal::traits<BandMatrixWrapper>::CoefficientsType CoefficientsType; |
| typedef typename internal::traits<BandMatrixWrapper>::StorageIndex StorageIndex; |
| |
| explicit inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows=Rows_, Index cols=Cols_, Index supers=Supers_, Index subs=Subs_) |
| : m_coeffs(coeffs), |
| m_rows(rows), m_supers(supers), m_subs(subs) |
| { |
| EIGEN_UNUSED_VARIABLE(cols); |
| // eigen_assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows()); |
| } |
| |
| /** \returns the number of columns */ |
| inline EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); } |
| |
| /** \returns the number of rows */ |
| inline EIGEN_CONSTEXPR Index cols() const { return m_coeffs.cols(); } |
| |
| /** \returns the number of super diagonals */ |
| inline EIGEN_CONSTEXPR Index supers() const { return m_supers.value(); } |
| |
| /** \returns the number of sub diagonals */ |
| inline EIGEN_CONSTEXPR Index subs() const { return m_subs.value(); } |
| |
| inline const CoefficientsType& coeffs() const { return m_coeffs; } |
| |
| protected: |
| |
| const CoefficientsType& m_coeffs; |
| internal::variable_if_dynamic<Index, Rows_> m_rows; |
| internal::variable_if_dynamic<Index, Supers_> m_supers; |
| internal::variable_if_dynamic<Index, Subs_> m_subs; |
| }; |
| |
| /** |
| * \class TridiagonalMatrix |
| * \ingroup Core_Module |
| * |
| * \brief Represents a tridiagonal matrix with a compact banded storage |
| * |
| * \tparam Scalar Numeric type, i.e. float, double, int |
| * \tparam Size Number of rows and cols, or \b Dynamic |
| * \tparam Options Can be 0 or \b SelfAdjoint |
| * |
| * \sa class BandMatrix |
| */ |
| template<typename Scalar, int Size, int Options> |
| class TridiagonalMatrix : public BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor> |
| { |
| typedef BandMatrix<Scalar,Size,Size,Options&SelfAdjoint?0:1,1,Options|RowMajor> Base; |
| typedef typename Base::StorageIndex StorageIndex; |
| public: |
| explicit TridiagonalMatrix(Index size = Size) : Base(size,size,Options&SelfAdjoint?0:1,1) {} |
| |
| inline typename Base::template DiagonalIntReturnType<1>::Type super() |
| { return Base::template diagonal<1>(); } |
| inline const typename Base::template DiagonalIntReturnType<1>::Type super() const |
| { return Base::template diagonal<1>(); } |
| inline typename Base::template DiagonalIntReturnType<-1>::Type sub() |
| { return Base::template diagonal<-1>(); } |
| inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const |
| { return Base::template diagonal<-1>(); } |
| protected: |
| }; |
| |
| |
| struct BandShape {}; |
| |
| template<typename Scalar_, int Rows_, int Cols_, int Supers_, int Subs_, int Options_> |
| struct evaluator_traits<BandMatrix<Scalar_,Rows_,Cols_,Supers_,Subs_,Options_> > |
| : public evaluator_traits_base<BandMatrix<Scalar_,Rows_,Cols_,Supers_,Subs_,Options_> > |
| { |
| typedef BandShape Shape; |
| }; |
| |
| template<typename CoefficientsType_,int Rows_, int Cols_, int Supers_, int Subs_,int Options_> |
| struct evaluator_traits<BandMatrixWrapper<CoefficientsType_,Rows_,Cols_,Supers_,Subs_,Options_> > |
| : public evaluator_traits_base<BandMatrixWrapper<CoefficientsType_,Rows_,Cols_,Supers_,Subs_,Options_> > |
| { |
| typedef BandShape Shape; |
| }; |
| |
| template<> struct AssignmentKind<DenseShape,BandShape> { typedef EigenBase2EigenBase Kind; }; |
| |
| } // end namespace internal |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_BANDMATRIX_H |