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- // 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
- 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 = EIGEN_SIZE_MIN_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((Options&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 = (Options&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
- ? EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime, RowsAtCompileTime + ActualIndex)
- : EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime - ActualIndex))
- };
- typedef Block<CoefficientsType,1, DiagonalSize> BuildType;
- typedef typename internal::conditional<Conjugate,
- CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,BuildType >,
- BuildType>::type 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,Options&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 Index rows() const { return m_rows.value(); }
- /** \returns the number of rows */
- inline Index cols() const { return m_coeffs.cols(); }
- /** \returns the number of super diagonals */
- inline Index supers() const { return m_supers.value(); }
- /** \returns the number of sub diagonals */
- inline 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);
- //internal::assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows());
- }
- /** \returns the number of columns */
- inline Index rows() const { return m_rows.value(); }
- /** \returns the number of rows */
- inline Index cols() const { return m_coeffs.cols(); }
- /** \returns the number of super diagonals */
- inline Index supers() const { return m_supers.value(); }
- /** \returns the number of sub diagonals */
- inline 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
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