| // This file is part of Eigen, a lightweight C++ template library | 
 | // for linear algebra. | 
 | // | 
 | // Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com> | 
 | // Copyright (C) 2008 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_MATRIXBASE_H | 
 | #define EIGEN_MATRIXBASE_H | 
 |  | 
 | // IWYU pragma: private | 
 | #include "./InternalHeaderCheck.h" | 
 |  | 
 | namespace Eigen { | 
 |  | 
 | /** \class MatrixBase | 
 |   * \ingroup Core_Module | 
 |   * | 
 |   * \brief Base class for all dense matrices, vectors, and expressions | 
 |   * | 
 |   * This class is the base that is inherited by all matrix, vector, and related expression | 
 |   * types. Most of the Eigen API is contained in this class, and its base classes. Other important | 
 |   * classes for the Eigen API are Matrix, and VectorwiseOp. | 
 |   * | 
 |   * Note that some methods are defined in other modules such as the \ref LU_Module LU module | 
 |   * for all functions related to matrix inversions. | 
 |   * | 
 |   * \tparam Derived is the derived type, e.g. a matrix type, or an expression, etc. | 
 |   * | 
 |   * When writing a function taking Eigen objects as argument, if you want your function | 
 |   * to take as argument any matrix, vector, or expression, just let it take a | 
 |   * MatrixBase argument. As an example, here is a function printFirstRow which, given | 
 |   * a matrix, vector, or expression \a x, prints the first row of \a x. | 
 |   * | 
 |   * \code | 
 |     template<typename Derived> | 
 |     void printFirstRow(const Eigen::MatrixBase<Derived>& x) | 
 |     { | 
 |       cout << x.row(0) << endl; | 
 |     } | 
 |   * \endcode | 
 |   * | 
 |   * This class can be extended with the help of the plugin mechanism described on the page | 
 |   * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN. | 
 |   * | 
 |   * \sa \blank \ref TopicClassHierarchy | 
 |   */ | 
 | template <typename Derived> | 
 | class MatrixBase : public DenseBase<Derived> { | 
 |  public: | 
 | #ifndef EIGEN_PARSED_BY_DOXYGEN | 
 |   typedef MatrixBase StorageBaseType; | 
 |   typedef typename internal::traits<Derived>::StorageKind StorageKind; | 
 |   typedef typename internal::traits<Derived>::StorageIndex StorageIndex; | 
 |   typedef typename internal::traits<Derived>::Scalar Scalar; | 
 |   typedef typename internal::packet_traits<Scalar>::type PacketScalar; | 
 |   typedef typename NumTraits<Scalar>::Real RealScalar; | 
 |  | 
 |   typedef DenseBase<Derived> Base; | 
 |   using Base::ColsAtCompileTime; | 
 |   using Base::Flags; | 
 |   using Base::IsVectorAtCompileTime; | 
 |   using Base::MaxColsAtCompileTime; | 
 |   using Base::MaxRowsAtCompileTime; | 
 |   using Base::MaxSizeAtCompileTime; | 
 |   using Base::RowsAtCompileTime; | 
 |   using Base::SizeAtCompileTime; | 
 |  | 
 |   using Base::coeff; | 
 |   using Base::coeffRef; | 
 |   using Base::cols; | 
 |   using Base::const_cast_derived; | 
 |   using Base::derived; | 
 |   using Base::eval; | 
 |   using Base::lazyAssign; | 
 |   using Base::rows; | 
 |   using Base::size; | 
 |   using Base::operator-; | 
 |   using Base::operator+=; | 
 |   using Base::operator-=; | 
 |   using Base::operator*=; | 
 |   using Base::operator/=; | 
 |  | 
 |   typedef typename Base::CoeffReturnType CoeffReturnType; | 
 |   typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType; | 
 |   typedef typename Base::RowXpr RowXpr; | 
 |   typedef typename Base::ColXpr ColXpr; | 
 | #endif  // not EIGEN_PARSED_BY_DOXYGEN | 
 |  | 
 | #ifndef EIGEN_PARSED_BY_DOXYGEN | 
 |   /** type of the equivalent square matrix */ | 
 |   typedef Matrix<Scalar, internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime), | 
 |                  internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime)> | 
 |       SquareMatrixType; | 
 | #endif  // not EIGEN_PARSED_BY_DOXYGEN | 
 |  | 
 |   /** \returns the size of the main diagonal, which is min(rows(),cols()). | 
 |    * \sa rows(), cols(), SizeAtCompileTime. */ | 
 |   EIGEN_DEVICE_FUNC inline Index diagonalSize() const { return (numext::mini)(rows(), cols()); } | 
 |  | 
 |   typedef typename Base::PlainObject PlainObject; | 
 |  | 
 | #ifndef EIGEN_PARSED_BY_DOXYGEN | 
 |   /** \internal Represents a matrix with all coefficients equal to one another*/ | 
 |   typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> ConstantReturnType; | 
 |   /** \internal the return type of MatrixBase::adjoint() */ | 
 |   typedef std::conditional_t<NumTraits<Scalar>::IsComplex, | 
 |                              CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>, | 
 |                              ConstTransposeReturnType> | 
 |       AdjointReturnType; | 
 |   /** \internal Return type of eigenvalues() */ | 
 |   typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> | 
 |       EigenvaluesReturnType; | 
 |   /** \internal the return type of identity */ | 
 |   typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>, PlainObject> IdentityReturnType; | 
 |   /** \internal the return type of unit vectors */ | 
 |   typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>, | 
 |                 internal::traits<Derived>::RowsAtCompileTime, internal::traits<Derived>::ColsAtCompileTime> | 
 |       BasisReturnType; | 
 | #endif  // not EIGEN_PARSED_BY_DOXYGEN | 
 |  | 
 | #define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase | 
 | #define EIGEN_DOC_UNARY_ADDONS(X, Y) | 
 | #include "../plugins/CommonCwiseBinaryOps.inc" | 
 | #include "../plugins/MatrixCwiseUnaryOps.inc" | 
 | #include "../plugins/MatrixCwiseBinaryOps.inc" | 
 | #ifdef EIGEN_MATRIXBASE_PLUGIN | 
 | #include EIGEN_MATRIXBASE_PLUGIN | 
 | #endif | 
 | #undef EIGEN_CURRENT_STORAGE_BASE_CLASS | 
 | #undef EIGEN_DOC_UNARY_ADDONS | 
 |  | 
 |   /** Special case of the template operator=, in order to prevent the compiler | 
 |    * from generating a default operator= (issue hit with g++ 4.1) | 
 |    */ | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const MatrixBase& other); | 
 |  | 
 |   // We cannot inherit here via Base::operator= since it is causing | 
 |   // trouble with MSVC. | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC Derived& operator=(const EigenBase<OtherDerived>& other); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC Derived& operator=(const ReturnByValue<OtherDerived>& other); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const MatrixBase<OtherDerived>& other); | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const MatrixBase<OtherDerived>& other); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC const Product<Derived, OtherDerived> operator*(const MatrixBase<OtherDerived>& other) const; | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC const Product<Derived, OtherDerived, LazyProduct> lazyProduct( | 
 |       const MatrixBase<OtherDerived>& other) const; | 
 |  | 
 |   template <typename OtherDerived> | 
 |   Derived& operator*=(const EigenBase<OtherDerived>& other); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   void applyOnTheLeft(const EigenBase<OtherDerived>& other); | 
 |  | 
 |   template <typename OtherDerived> | 
 |   void applyOnTheRight(const EigenBase<OtherDerived>& other); | 
 |  | 
 |   template <typename DiagonalDerived> | 
 |   EIGEN_DEVICE_FUNC const Product<Derived, DiagonalDerived, LazyProduct> operator*( | 
 |       const DiagonalBase<DiagonalDerived>& diagonal) const; | 
 |  | 
 |   template <typename SkewDerived> | 
 |   EIGEN_DEVICE_FUNC const Product<Derived, SkewDerived, LazyProduct> operator*( | 
 |       const SkewSymmetricBase<SkewDerived>& skew) const; | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar, | 
 |                                                   typename internal::traits<OtherDerived>::Scalar>::ReturnType | 
 |   dot(const MatrixBase<OtherDerived>& other) const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC RealScalar squaredNorm() const; | 
 |   EIGEN_DEVICE_FUNC RealScalar norm() const; | 
 |   RealScalar stableNorm() const; | 
 |   RealScalar blueNorm() const; | 
 |   RealScalar hypotNorm() const; | 
 |   EIGEN_DEVICE_FUNC const PlainObject normalized() const; | 
 |   EIGEN_DEVICE_FUNC const PlainObject stableNormalized() const; | 
 |   EIGEN_DEVICE_FUNC void normalize(); | 
 |   EIGEN_DEVICE_FUNC void stableNormalize(); | 
 |  | 
 |   EIGEN_DEVICE_FUNC const AdjointReturnType adjoint() const; | 
 |   EIGEN_DEVICE_FUNC void adjointInPlace(); | 
 |  | 
 |   typedef Diagonal<Derived> DiagonalReturnType; | 
 |   EIGEN_DEVICE_FUNC DiagonalReturnType diagonal(); | 
 |  | 
 |   typedef Diagonal<const Derived> ConstDiagonalReturnType; | 
 |   EIGEN_DEVICE_FUNC const ConstDiagonalReturnType diagonal() const; | 
 |  | 
 |   template <int Index> | 
 |   EIGEN_DEVICE_FUNC Diagonal<Derived, Index> diagonal(); | 
 |  | 
 |   template <int Index> | 
 |   EIGEN_DEVICE_FUNC const Diagonal<const Derived, Index> diagonal() const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC Diagonal<Derived, DynamicIndex> diagonal(Index index); | 
 |   EIGEN_DEVICE_FUNC const Diagonal<const Derived, DynamicIndex> diagonal(Index index) const; | 
 |  | 
 |   template <unsigned int Mode> | 
 |   struct TriangularViewReturnType { | 
 |     typedef TriangularView<Derived, Mode> Type; | 
 |   }; | 
 |   template <unsigned int Mode> | 
 |   struct ConstTriangularViewReturnType { | 
 |     typedef const TriangularView<const Derived, Mode> Type; | 
 |   }; | 
 |  | 
 |   template <unsigned int Mode> | 
 |   EIGEN_DEVICE_FUNC typename TriangularViewReturnType<Mode>::Type triangularView(); | 
 |   template <unsigned int Mode> | 
 |   EIGEN_DEVICE_FUNC typename ConstTriangularViewReturnType<Mode>::Type triangularView() const; | 
 |  | 
 |   template <unsigned int UpLo> | 
 |   struct SelfAdjointViewReturnType { | 
 |     typedef SelfAdjointView<Derived, UpLo> Type; | 
 |   }; | 
 |   template <unsigned int UpLo> | 
 |   struct ConstSelfAdjointViewReturnType { | 
 |     typedef const SelfAdjointView<const Derived, UpLo> Type; | 
 |   }; | 
 |  | 
 |   template <unsigned int UpLo> | 
 |   EIGEN_DEVICE_FUNC typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView(); | 
 |   template <unsigned int UpLo> | 
 |   EIGEN_DEVICE_FUNC typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const; | 
 |  | 
 |   const SparseView<Derived> sparseView( | 
 |       const Scalar& m_reference = Scalar(0), | 
 |       const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const; | 
 |   EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(); | 
 |   EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(Index rows, Index cols); | 
 |   EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index size, Index i); | 
 |   EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index i); | 
 |   EIGEN_DEVICE_FUNC static const BasisReturnType UnitX(); | 
 |   EIGEN_DEVICE_FUNC static const BasisReturnType UnitY(); | 
 |   EIGEN_DEVICE_FUNC static const BasisReturnType UnitZ(); | 
 |   EIGEN_DEVICE_FUNC static const BasisReturnType UnitW(); | 
 |  | 
 |   EIGEN_DEVICE_FUNC const DiagonalWrapper<const Derived> asDiagonal() const; | 
 |   const PermutationWrapper<const Derived> asPermutation() const; | 
 |   EIGEN_DEVICE_FUNC const SkewSymmetricWrapper<const Derived> asSkewSymmetric() const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC Derived& setIdentity(); | 
 |   EIGEN_DEVICE_FUNC Derived& setIdentity(Index rows, Index cols); | 
 |   EIGEN_DEVICE_FUNC Derived& setUnit(Index i); | 
 |   EIGEN_DEVICE_FUNC Derived& setUnit(Index newSize, Index i); | 
 |  | 
 |   bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |   bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |  | 
 |   bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |   bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |  | 
 |   bool isSkewSymmetric(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |  | 
 |   template <typename OtherDerived> | 
 |   bool isOrthogonal(const MatrixBase<OtherDerived>& other, | 
 |                     const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |   bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const; | 
 |  | 
 |   /** \returns true if each coefficients of \c *this and \a other are all exactly equal. | 
 |    * \warning When using floating point scalar values you probably should rather use a | 
 |    *          fuzzy comparison such as isApprox() | 
 |    * \sa isApprox(), operator!= */ | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase<OtherDerived>& other) const { | 
 |     return cwiseEqual(other).all(); | 
 |   } | 
 |  | 
 |   /** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other. | 
 |    * \warning When using floating point scalar values you probably should rather use a | 
 |    *          fuzzy comparison such as isApprox() | 
 |    * \sa isApprox(), operator== */ | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase<OtherDerived>& other) const { | 
 |     return cwiseNotEqual(other).any(); | 
 |   } | 
 |  | 
 |   NoAlias<Derived, Eigen::MatrixBase> EIGEN_DEVICE_FUNC noalias(); | 
 |  | 
 |   // TODO forceAlignedAccess is temporarily disabled | 
 |   // Need to find a nicer workaround. | 
 |   inline const Derived& forceAlignedAccess() const { return derived(); } | 
 |   inline Derived& forceAlignedAccess() { return derived(); } | 
 |   template <bool Enable> | 
 |   inline const Derived& forceAlignedAccessIf() const { | 
 |     return derived(); | 
 |   } | 
 |   template <bool Enable> | 
 |   inline Derived& forceAlignedAccessIf() { | 
 |     return derived(); | 
 |   } | 
 |  | 
 |   EIGEN_DEVICE_FUNC Scalar trace() const; | 
 |  | 
 |   template <int p> | 
 |   EIGEN_DEVICE_FUNC RealScalar lpNorm() const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC MatrixBase<Derived>& matrix() { return *this; } | 
 |   EIGEN_DEVICE_FUNC const MatrixBase<Derived>& matrix() const { return *this; } | 
 |  | 
 |   /** \returns an \link Eigen::ArrayBase Array \endlink expression of this matrix | 
 |    * \sa ArrayBase::matrix() */ | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper<Derived> array() { return ArrayWrapper<Derived>(derived()); } | 
 |   /** \returns a const \link Eigen::ArrayBase Array \endlink expression of this matrix | 
 |    * \sa ArrayBase::matrix() */ | 
 |   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper<const Derived> array() const { | 
 |     return ArrayWrapper<const Derived>(derived()); | 
 |   } | 
 |  | 
 |   /////////// LU module /////////// | 
 |  | 
 |   template <typename PermutationIndex = DefaultPermutationIndex> | 
 |   inline const FullPivLU<PlainObject, PermutationIndex> fullPivLu() const; | 
 |   template <typename PermutationIndex = DefaultPermutationIndex> | 
 |   inline const PartialPivLU<PlainObject, PermutationIndex> partialPivLu() const; | 
 |  | 
 |   template <typename PermutationIndex = DefaultPermutationIndex> | 
 |   inline const PartialPivLU<PlainObject, PermutationIndex> lu() const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC inline const Inverse<Derived> inverse() const; | 
 |  | 
 |   template <typename ResultType> | 
 |   inline void computeInverseAndDetWithCheck( | 
 |       ResultType& inverse, typename ResultType::Scalar& determinant, bool& invertible, | 
 |       const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()) const; | 
 |  | 
 |   template <typename ResultType> | 
 |   inline void computeInverseWithCheck( | 
 |       ResultType& inverse, bool& invertible, | 
 |       const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()) const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC Scalar determinant() const; | 
 |  | 
 |   /////////// Cholesky module /////////// | 
 |  | 
 |   inline const LLT<PlainObject> llt() const; | 
 |   inline const LDLT<PlainObject> ldlt() const; | 
 |  | 
 |   /////////// QR module /////////// | 
 |  | 
 |   inline const HouseholderQR<PlainObject> householderQr() const; | 
 |   template <typename PermutationIndex = DefaultPermutationIndex> | 
 |   inline const ColPivHouseholderQR<PlainObject, PermutationIndex> colPivHouseholderQr() const; | 
 |   template <typename PermutationIndex = DefaultPermutationIndex> | 
 |   inline const FullPivHouseholderQR<PlainObject, PermutationIndex> fullPivHouseholderQr() const; | 
 |   template <typename PermutationIndex = DefaultPermutationIndex> | 
 |   inline const CompleteOrthogonalDecomposition<PlainObject, PermutationIndex> completeOrthogonalDecomposition() const; | 
 |  | 
 |   /////////// Eigenvalues module /////////// | 
 |  | 
 |   inline EigenvaluesReturnType eigenvalues() const; | 
 |   inline RealScalar operatorNorm() const; | 
 |  | 
 |   /////////// SVD module /////////// | 
 |  | 
 |   template <int Options = 0> | 
 |   inline JacobiSVD<PlainObject, Options> jacobiSvd() const; | 
 |   template <int Options = 0> | 
 |   EIGEN_DEPRECATED inline JacobiSVD<PlainObject, Options> jacobiSvd(unsigned int computationOptions) const; | 
 |  | 
 |   template <int Options = 0> | 
 |   inline BDCSVD<PlainObject, Options> bdcSvd() const; | 
 |   template <int Options = 0> | 
 |   EIGEN_DEPRECATED inline BDCSVD<PlainObject, Options> bdcSvd(unsigned int computationOptions) const; | 
 |  | 
 |   /////////// Geometry module /////////// | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC inline typename internal::cross_impl<Derived, OtherDerived>::return_type cross( | 
 |       const MatrixBase<OtherDerived>& other) const; | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC inline PlainObject unitOrthogonal(void) const; | 
 |  | 
 |   EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 1> eulerAngles(Index a0, Index a1, Index a2) const; | 
 |  | 
 |   EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 1> canonicalEulerAngles(Index a0, Index a1, Index a2) const; | 
 |  | 
 |   // put this as separate enum value to work around possible GCC 4.3 bug (?) | 
 |   enum { | 
 |     HomogeneousReturnTypeDirection = | 
 |         ColsAtCompileTime == 1 && RowsAtCompileTime == 1 | 
 |             ? ((internal::traits<Derived>::Flags & RowMajorBit) == RowMajorBit ? Horizontal : Vertical) | 
 |         : ColsAtCompileTime == 1 ? Vertical | 
 |                                  : Horizontal | 
 |   }; | 
 |   typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType; | 
 |   EIGEN_DEVICE_FUNC inline HomogeneousReturnType homogeneous() const; | 
 |  | 
 |   enum { SizeMinusOne = SizeAtCompileTime == Dynamic ? Dynamic : SizeAtCompileTime - 1 }; | 
 |   typedef Block<const Derived, internal::traits<Derived>::ColsAtCompileTime == 1 ? SizeMinusOne : 1, | 
 |                 internal::traits<Derived>::ColsAtCompileTime == 1 ? 1 : SizeMinusOne> | 
 |       ConstStartMinusOne; | 
 |   typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne, Scalar, quotient) HNormalizedReturnType; | 
 |   EIGEN_DEVICE_FUNC inline const HNormalizedReturnType hnormalized() const; | 
 |  | 
 |   ////////// Householder module /////////// | 
 |  | 
 |   EIGEN_DEVICE_FUNC void makeHouseholderInPlace(Scalar& tau, RealScalar& beta); | 
 |   template <typename EssentialPart> | 
 |   EIGEN_DEVICE_FUNC void makeHouseholder(EssentialPart& essential, Scalar& tau, RealScalar& beta) const; | 
 |   template <typename EssentialPart> | 
 |   EIGEN_DEVICE_FUNC void applyHouseholderOnTheLeft(const EssentialPart& essential, const Scalar& tau, | 
 |                                                    Scalar* workspace); | 
 |   template <typename EssentialPart> | 
 |   EIGEN_DEVICE_FUNC void applyHouseholderOnTheRight(const EssentialPart& essential, const Scalar& tau, | 
 |                                                     Scalar* workspace); | 
 |  | 
 |   ///////// Jacobi module ///////// | 
 |  | 
 |   template <typename OtherScalar> | 
 |   EIGEN_DEVICE_FUNC void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j); | 
 |   template <typename OtherScalar> | 
 |   EIGEN_DEVICE_FUNC void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j); | 
 |  | 
 |   ///////// SparseCore module ///////// | 
 |  | 
 |   template <typename OtherDerived> | 
 |   EIGEN_STRONG_INLINE const typename SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type | 
 |   cwiseProduct(const SparseMatrixBase<OtherDerived>& other) const { | 
 |     return other.cwiseProduct(derived()); | 
 |   } | 
 |  | 
 |   ///////// MatrixFunctions module ///////// | 
 |  | 
 |   typedef typename internal::stem_function<Scalar>::type StemFunction; | 
 | #define EIGEN_MATRIX_FUNCTION(ReturnType, Name, Description)                                                        \ | 
 |   /** \returns an expression of the matrix Description of \c *this. \brief This function requires the <a            \ | 
 |    * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>. To compute the \ | 
 |    * coefficient-wise Description use ArrayBase::##Name . */                                                        \ | 
 |   const ReturnType<Derived> Name() const; | 
 | #define EIGEN_MATRIX_FUNCTION_1(ReturnType, Name, Description, Argument)                                            \ | 
 |   /** \returns an expression of the matrix Description of \c *this. \brief This function requires the <a            \ | 
 |    * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>. To compute the \ | 
 |    * coefficient-wise Description use ArrayBase::##Name . */                                                        \ | 
 |   const ReturnType<Derived> Name(Argument) const; | 
 |  | 
 |   EIGEN_MATRIX_FUNCTION(MatrixExponentialReturnValue, exp, exponential) | 
 |   /** \brief Helper function for the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported | 
 |    * MatrixFunctions module</a>.*/ | 
 |   const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const; | 
 |   EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cosh, hyperbolic cosine) | 
 |   EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sinh, hyperbolic sine) | 
 |   EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, atanh, inverse hyperbolic cosine) | 
 |   EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, acosh, inverse hyperbolic cosine) | 
 |   EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, asinh, inverse hyperbolic sine) | 
 |   EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cos, cosine) | 
 |   EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sin, sine) | 
 |   EIGEN_MATRIX_FUNCTION(MatrixSquareRootReturnValue, sqrt, square root) | 
 |   EIGEN_MATRIX_FUNCTION(MatrixLogarithmReturnValue, log, logarithm) | 
 |   EIGEN_MATRIX_FUNCTION_1(MatrixPowerReturnValue, pow, power to \c p, const RealScalar& p) | 
 |   EIGEN_MATRIX_FUNCTION_1(MatrixComplexPowerReturnValue, pow, power to \c p, const std::complex<RealScalar>& p) | 
 |  | 
 |  protected: | 
 |   EIGEN_DEFAULT_COPY_CONSTRUCTOR(MatrixBase) | 
 |   EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MatrixBase) | 
 |  | 
 |  private: | 
 |   EIGEN_DEVICE_FUNC explicit MatrixBase(int); | 
 |   EIGEN_DEVICE_FUNC MatrixBase(int, int); | 
 |   template <typename OtherDerived> | 
 |   EIGEN_DEVICE_FUNC explicit MatrixBase(const MatrixBase<OtherDerived>&); | 
 |  | 
 |  protected: | 
 |   // mixing arrays and matrices is not legal | 
 |   template <typename OtherDerived> | 
 |   Derived& operator+=(const ArrayBase<OtherDerived>&) { | 
 |     EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar)) == -1, | 
 |                         YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); | 
 |     return *this; | 
 |   } | 
 |   // mixing arrays and matrices is not legal | 
 |   template <typename OtherDerived> | 
 |   Derived& operator-=(const ArrayBase<OtherDerived>&) { | 
 |     EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar)) == -1, | 
 |                         YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); | 
 |     return *this; | 
 |   } | 
 | }; | 
 |  | 
 | /*************************************************************************** | 
 |  * Implementation of matrix base methods | 
 |  ***************************************************************************/ | 
 |  | 
 | /** replaces \c *this by \c *this * \a other. | 
 |  * | 
 |  * \returns a reference to \c *this | 
 |  * | 
 |  * Example: \include MatrixBase_applyOnTheRight.cpp | 
 |  * Output: \verbinclude MatrixBase_applyOnTheRight.out | 
 |  */ | 
 | template <typename Derived> | 
 | template <typename OtherDerived> | 
 | inline Derived& MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived>& other) { | 
 |   other.derived().applyThisOnTheRight(derived()); | 
 |   return derived(); | 
 | } | 
 |  | 
 | /** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=(). | 
 |  * | 
 |  * Example: \include MatrixBase_applyOnTheRight.cpp | 
 |  * Output: \verbinclude MatrixBase_applyOnTheRight.out | 
 |  */ | 
 | template <typename Derived> | 
 | template <typename OtherDerived> | 
 | inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived>& other) { | 
 |   other.derived().applyThisOnTheRight(derived()); | 
 | } | 
 |  | 
 | /** replaces \c *this by \a other * \c *this. | 
 |  * | 
 |  * Example: \include MatrixBase_applyOnTheLeft.cpp | 
 |  * Output: \verbinclude MatrixBase_applyOnTheLeft.out | 
 |  */ | 
 | template <typename Derived> | 
 | template <typename OtherDerived> | 
 | inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived>& other) { | 
 |   other.derived().applyThisOnTheLeft(derived()); | 
 | } | 
 |  | 
 | }  // end namespace Eigen | 
 |  | 
 | #endif  // EIGEN_MATRIXBASE_H |