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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>
-// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
-//
-// 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_DIAGONALMATRIX_H
-#define EIGEN_DIAGONALMATRIX_H
-
-namespace Eigen {
-
-#ifndef EIGEN_PARSED_BY_DOXYGEN
-template<typename Derived>
-class DiagonalBase : public EigenBase<Derived>
-{
- public:
- typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
- typedef typename DiagonalVectorType::Scalar Scalar;
- typedef typename DiagonalVectorType::RealScalar RealScalar;
- typedef typename internal::traits<Derived>::StorageKind StorageKind;
- typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
-
- enum {
- RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
- ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
- MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
- MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
- IsVectorAtCompileTime = 0,
- Flags = NoPreferredStorageOrderBit
- };
-
- typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
- typedef DenseMatrixType DenseType;
- typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;
-
- EIGEN_DEVICE_FUNC
- inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
- EIGEN_DEVICE_FUNC
- inline Derived& derived() { return *static_cast<Derived*>(this); }
-
- EIGEN_DEVICE_FUNC
- DenseMatrixType toDenseMatrix() const { return derived(); }
-
- EIGEN_DEVICE_FUNC
- inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
- EIGEN_DEVICE_FUNC
- inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
-
- EIGEN_DEVICE_FUNC
- inline Index rows() const { return diagonal().size(); }
- EIGEN_DEVICE_FUNC
- inline Index cols() const { return diagonal().size(); }
-
- template<typename MatrixDerived>
- EIGEN_DEVICE_FUNC
- const Product<Derived,MatrixDerived,LazyProduct>
- operator*(const MatrixBase<MatrixDerived> &matrix) const
- {
- return Product<Derived, MatrixDerived, LazyProduct>(derived(),matrix.derived());
- }
-
- typedef DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> > InverseReturnType;
- EIGEN_DEVICE_FUNC
- inline const InverseReturnType
- inverse() const
- {
- return InverseReturnType(diagonal().cwiseInverse());
- }
-
- EIGEN_DEVICE_FUNC
- inline const DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >
- operator*(const Scalar& scalar) const
- {
- return DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >(diagonal() * scalar);
- }
- EIGEN_DEVICE_FUNC
- friend inline const DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >
- operator*(const Scalar& scalar, const DiagonalBase& other)
- {
- return DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >(scalar * other.diagonal());
- }
-};
-
-#endif
-
-/** \class DiagonalMatrix
- * \ingroup Core_Module
- *
- * \brief Represents a diagonal matrix with its storage
- *
- * \param _Scalar the type of coefficients
- * \param SizeAtCompileTime the dimension of the matrix, or Dynamic
- * \param MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
- * to SizeAtCompileTime. Most of the time, you do not need to specify it.
- *
- * \sa class DiagonalWrapper
- */
-
-namespace internal {
-template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
-struct traits<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
- : traits<Matrix<_Scalar,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
-{
- typedef Matrix<_Scalar,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;
- typedef DiagonalShape StorageKind;
- enum {
- Flags = LvalueBit | NoPreferredStorageOrderBit
- };
-};
-}
-template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
-class DiagonalMatrix
- : public DiagonalBase<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
-{
- public:
- #ifndef EIGEN_PARSED_BY_DOXYGEN
- typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;
- typedef const DiagonalMatrix& Nested;
- typedef _Scalar Scalar;
- typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
- typedef typename internal::traits<DiagonalMatrix>::StorageIndex StorageIndex;
- #endif
-
- protected:
-
- DiagonalVectorType m_diagonal;
-
- public:
-
- /** const version of diagonal(). */
- EIGEN_DEVICE_FUNC
- inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
- /** \returns a reference to the stored vector of diagonal coefficients. */
- EIGEN_DEVICE_FUNC
- inline DiagonalVectorType& diagonal() { return m_diagonal; }
-
- /** Default constructor without initialization */
- EIGEN_DEVICE_FUNC
- inline DiagonalMatrix() {}
-
- /** Constructs a diagonal matrix with given dimension */
- EIGEN_DEVICE_FUNC
- explicit inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
-
- /** 2D constructor. */
- EIGEN_DEVICE_FUNC
- inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}
-
- /** 3D constructor. */
- EIGEN_DEVICE_FUNC
- inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}
-
- /** Copy constructor. */
- template<typename OtherDerived>
- EIGEN_DEVICE_FUNC
- inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}
-
- #ifndef EIGEN_PARSED_BY_DOXYGEN
- /** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
- inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}
- #endif
-
- /** generic constructor from expression of the diagonal coefficients */
- template<typename OtherDerived>
- EIGEN_DEVICE_FUNC
- explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
- {}
-
- /** Copy operator. */
- template<typename OtherDerived>
- EIGEN_DEVICE_FUNC
- DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)
- {
- m_diagonal = other.diagonal();
- return *this;
- }
-
- #ifndef EIGEN_PARSED_BY_DOXYGEN
- /** This is a special case of the templated operator=. Its purpose is to
- * prevent a default operator= from hiding the templated operator=.
- */
- EIGEN_DEVICE_FUNC
- DiagonalMatrix& operator=(const DiagonalMatrix& other)
- {
- m_diagonal = other.diagonal();
- return *this;
- }
- #endif
-
- /** Resizes to given size. */
- EIGEN_DEVICE_FUNC
- inline void resize(Index size) { m_diagonal.resize(size); }
- /** Sets all coefficients to zero. */
- EIGEN_DEVICE_FUNC
- inline void setZero() { m_diagonal.setZero(); }
- /** Resizes and sets all coefficients to zero. */
- EIGEN_DEVICE_FUNC
- inline void setZero(Index size) { m_diagonal.setZero(size); }
- /** Sets this matrix to be the identity matrix of the current size. */
- EIGEN_DEVICE_FUNC
- inline void setIdentity() { m_diagonal.setOnes(); }
- /** Sets this matrix to be the identity matrix of the given size. */
- EIGEN_DEVICE_FUNC
- inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
-};
-
-/** \class DiagonalWrapper
- * \ingroup Core_Module
- *
- * \brief Expression of a diagonal matrix
- *
- * \param _DiagonalVectorType the type of the vector of diagonal coefficients
- *
- * This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,
- * instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()
- * and most of the time this is the only way that it is used.
- *
- * \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()
- */
-
-namespace internal {
-template<typename _DiagonalVectorType>
-struct traits<DiagonalWrapper<_DiagonalVectorType> >
-{
- typedef _DiagonalVectorType DiagonalVectorType;
- typedef typename DiagonalVectorType::Scalar Scalar;
- typedef typename DiagonalVectorType::StorageIndex StorageIndex;
- typedef DiagonalShape StorageKind;
- typedef typename traits<DiagonalVectorType>::XprKind XprKind;
- enum {
- RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
- ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
- MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
- MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
- Flags = (traits<DiagonalVectorType>::Flags & LvalueBit) | NoPreferredStorageOrderBit
- };
-};
-}
-
-template<typename _DiagonalVectorType>
-class DiagonalWrapper
- : public DiagonalBase<DiagonalWrapper<_DiagonalVectorType> >, internal::no_assignment_operator
-{
- public:
- #ifndef EIGEN_PARSED_BY_DOXYGEN
- typedef _DiagonalVectorType DiagonalVectorType;
- typedef DiagonalWrapper Nested;
- #endif
-
- /** Constructor from expression of diagonal coefficients to wrap. */
- EIGEN_DEVICE_FUNC
- explicit inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}
-
- /** \returns a const reference to the wrapped expression of diagonal coefficients. */
- EIGEN_DEVICE_FUNC
- const DiagonalVectorType& diagonal() const { return m_diagonal; }
-
- protected:
- typename DiagonalVectorType::Nested m_diagonal;
-};
-
-/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
- *
- * \only_for_vectors
- *
- * Example: \include MatrixBase_asDiagonal.cpp
- * Output: \verbinclude MatrixBase_asDiagonal.out
- *
- * \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
- **/
-template<typename Derived>
-inline const DiagonalWrapper<const Derived>
-MatrixBase<Derived>::asDiagonal() const
-{
- return DiagonalWrapper<const Derived>(derived());
-}
-
-/** \returns true if *this is approximately equal to a diagonal matrix,
- * within the precision given by \a prec.
- *
- * Example: \include MatrixBase_isDiagonal.cpp
- * Output: \verbinclude MatrixBase_isDiagonal.out
- *
- * \sa asDiagonal()
- */
-template<typename Derived>
-bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const
-{
- if(cols() != rows()) return false;
- RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
- for(Index j = 0; j < cols(); ++j)
- {
- RealScalar absOnDiagonal = numext::abs(coeff(j,j));
- if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
- }
- for(Index j = 0; j < cols(); ++j)
- for(Index i = 0; i < j; ++i)
- {
- if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
- if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
- }
- return true;
-}
-
-namespace internal {
-
-template<> struct storage_kind_to_shape<DiagonalShape> { typedef DiagonalShape Shape; };
-
-struct Diagonal2Dense {};
-
-template<> struct AssignmentKind<DenseShape,DiagonalShape> { typedef Diagonal2Dense Kind; };
-
-// Diagonal matrix to Dense assignment
-template< typename DstXprType, typename SrcXprType, typename Functor>
-struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense>
-{
- static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
- {
- Index dstRows = src.rows();
- Index dstCols = src.cols();
- if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
- dst.resize(dstRows, dstCols);
-
- dst.setZero();
- dst.diagonal() = src.diagonal();
- }
-
- static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
- { dst.diagonal() += src.diagonal(); }
-
- static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
- { dst.diagonal() -= src.diagonal(); }
-};
-
-} // namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_DIAGONALMATRIX_H