|  | // This file is part of Eigen, a lightweight C++ template library | 
|  | // for linear algebra. | 
|  | // | 
|  | // Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com> | 
|  | // Copyright (C) 2008-2009 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_MATRIX_H | 
|  | #define EIGEN_MATRIX_H | 
|  |  | 
|  | // IWYU pragma: private | 
|  | #include "./InternalHeaderCheck.h" | 
|  |  | 
|  | namespace Eigen { | 
|  |  | 
|  | namespace internal { | 
|  | template <typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_> | 
|  | struct traits<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>> { | 
|  | private: | 
|  | constexpr static int size = internal::size_at_compile_time(Rows_, Cols_); | 
|  | typedef typename find_best_packet<Scalar_, size>::type PacketScalar; | 
|  | enum { | 
|  | row_major_bit = Options_ & RowMajor ? RowMajorBit : 0, | 
|  | is_dynamic_size_storage = MaxRows_ == Dynamic || MaxCols_ == Dynamic, | 
|  | max_size = is_dynamic_size_storage ? Dynamic : MaxRows_ * MaxCols_, | 
|  | default_alignment = compute_default_alignment<Scalar_, max_size>::value, | 
|  | actual_alignment = ((Options_ & DontAlign) == 0) ? default_alignment : 0, | 
|  | required_alignment = unpacket_traits<PacketScalar>::alignment, | 
|  | packet_access_bit = (packet_traits<Scalar_>::Vectorizable && | 
|  | (EIGEN_UNALIGNED_VECTORIZE || (int(actual_alignment) >= int(required_alignment)))) | 
|  | ? PacketAccessBit | 
|  | : 0 | 
|  | }; | 
|  |  | 
|  | public: | 
|  | typedef Scalar_ Scalar; | 
|  | typedef Dense StorageKind; | 
|  | typedef Eigen::Index StorageIndex; | 
|  | typedef MatrixXpr XprKind; | 
|  | enum { | 
|  | RowsAtCompileTime = Rows_, | 
|  | ColsAtCompileTime = Cols_, | 
|  | MaxRowsAtCompileTime = MaxRows_, | 
|  | MaxColsAtCompileTime = MaxCols_, | 
|  | Flags = compute_matrix_flags(Options_), | 
|  | Options = Options_, | 
|  | InnerStrideAtCompileTime = 1, | 
|  | OuterStrideAtCompileTime = (int(Options) & int(RowMajor)) ? ColsAtCompileTime : RowsAtCompileTime, | 
|  |  | 
|  | // FIXME, the following flag in only used to define NeedsToAlign in PlainObjectBase | 
|  | EvaluatorFlags = LinearAccessBit | DirectAccessBit | packet_access_bit | row_major_bit, | 
|  | Alignment = actual_alignment | 
|  | }; | 
|  | }; | 
|  | }  // namespace internal | 
|  |  | 
|  | /** \class Matrix | 
|  | * \ingroup Core_Module | 
|  | * | 
|  | * \brief The matrix class, also used for vectors and row-vectors | 
|  | * | 
|  | * The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen. | 
|  | * Vectors are matrices with one column, and row-vectors are matrices with one row. | 
|  | * | 
|  | * The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note"). | 
|  | * | 
|  | * The first three template parameters are required: | 
|  | * \tparam Scalar_ Numeric type, e.g. float, double, int or std::complex<float>. | 
|  | *                 User defined scalar types are supported as well (see \ref user_defined_scalars "here"). | 
|  | * \tparam Rows_ Number of rows, or \b Dynamic | 
|  | * \tparam Cols_ Number of columns, or \b Dynamic | 
|  | * | 
|  | * The remaining template parameters are optional -- in most cases you don't have to worry about them. | 
|  | * \tparam Options_ A combination of either \b #RowMajor or \b #ColMajor, and of either | 
|  | *                 \b #AutoAlign or \b #DontAlign. | 
|  | *                 The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter | 
|  | * controls alignment, which is required for vectorization. It defaults to aligning matrices except for fixed sizes that | 
|  | * aren't a multiple of the packet size. \tparam MaxRows_ Maximum number of rows. Defaults to \a Rows_ (\ref maxrows | 
|  | * "note"). \tparam MaxCols_ Maximum number of columns. Defaults to \a Cols_ (\ref maxrows "note"). | 
|  | * | 
|  | * Eigen provides a number of typedefs covering the usual cases. Here are some examples: | 
|  | * | 
|  | * \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix<double, 2, 2>) | 
|  | * \li \c Vector4f is a vector of 4 floats (\c Matrix<float, 4, 1>) | 
|  | * \li \c RowVector3i is a row-vector of 3 ints (\c Matrix<int, 1, 3>) | 
|  | * | 
|  | * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>) | 
|  | * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>) | 
|  | * | 
|  | * \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>) | 
|  | * \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>) | 
|  | * | 
|  | * See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs. | 
|  | * | 
|  | * You can access elements of vectors and matrices using normal subscripting: | 
|  | * | 
|  | * \code | 
|  | * Eigen::VectorXd v(10); | 
|  | * v[0] = 0.1; | 
|  | * v[1] = 0.2; | 
|  | * v(0) = 0.3; | 
|  | * v(1) = 0.4; | 
|  | * | 
|  | * Eigen::MatrixXi m(10, 10); | 
|  | * m(0, 1) = 1; | 
|  | * m(0, 2) = 2; | 
|  | * m(0, 3) = 3; | 
|  | * \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_MATRIX_PLUGIN. | 
|  | * | 
|  | * <i><b>Some notes:</b></i> | 
|  | * | 
|  | * <dl> | 
|  | * <dt><b>\anchor dense Dense versus sparse:</b></dt> | 
|  | * <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the | 
|  | * Sparse module. | 
|  | * | 
|  | * Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary | 
|  | * contiguous array. This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero | 
|  | * coefficients.</dd> | 
|  | * | 
|  | * <dt><b>\anchor fixedsize Fixed-size versus dynamic-size:</b></dt> | 
|  | * <dd>Fixed-size means that the numbers of rows and columns are known at compile-time. In this case, Eigen allocates | 
|  | * the array of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, | 
|  | * typically up to 4x4, sometimes up to 16x16. Larger matrices should be declared as dynamic-size even if one happens to | 
|  | * know their size at compile-time. | 
|  | * | 
|  | * Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they | 
|  | * are runtime variables, and the array of coefficients is allocated dynamically on the heap. | 
|  | * | 
|  | * Note that \em dense matrices, be they Fixed-size or Dynamic-size, <em>do not</em> expand dynamically in the sense of | 
|  | * a std::map. If you want this behavior, see the Sparse module.</dd> | 
|  | * | 
|  | * <dt><b>\anchor maxrows MaxRows_ and MaxCols_:</b></dt> | 
|  | * <dd>In most cases, one just leaves these parameters to the default values. | 
|  | * These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases | 
|  | * when the exact numbers of rows and columns are not known at compile-time, but it is known at compile-time that they | 
|  | * cannot exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case | 
|  | * MaxRows_ and MaxCols_ are the dimensions of the original matrix, while Rows_ and Cols_ are Dynamic.</dd> | 
|  | * </dl> | 
|  | * | 
|  | * <i><b>ABI and storage layout</b></i> | 
|  | * | 
|  | * The table below summarizes the ABI of some possible Matrix instances which is fixed thorough the lifetime of Eigen 3. | 
|  | * <table  class="manual"> | 
|  | * <tr><th>Matrix type</th><th>Equivalent C structure</th></tr> | 
|  | * <tr><td>\code Matrix<T,Dynamic,Dynamic> \endcode</td><td>\code | 
|  | * struct { | 
|  | *   T *data;                  // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0 | 
|  | *   Eigen::Index rows, cols; | 
|  | *  }; | 
|  | * \endcode</td></tr> | 
|  | * <tr class="alt"><td>\code | 
|  | * Matrix<T,Dynamic,1> | 
|  | * Matrix<T,1,Dynamic> \endcode</td><td>\code | 
|  | * struct { | 
|  | *   T *data;                  // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0 | 
|  | *   Eigen::Index size; | 
|  | *  }; | 
|  | * \endcode</td></tr> | 
|  | * <tr><td>\code Matrix<T,Rows,Cols> \endcode</td><td>\code | 
|  | * struct { | 
|  | *   T data[Rows*Cols];        // with (size_t(data)%A(Rows*Cols*sizeof(T)))==0 | 
|  | *  }; | 
|  | * \endcode</td></tr> | 
|  | * <tr class="alt"><td>\code Matrix<T,Dynamic,Dynamic,0,MaxRows,MaxCols> \endcode</td><td>\code | 
|  | * struct { | 
|  | *   T data[MaxRows*MaxCols];  // with (size_t(data)%A(MaxRows*MaxCols*sizeof(T)))==0 | 
|  | *   Eigen::Index rows, cols; | 
|  | *  }; | 
|  | * \endcode</td></tr> | 
|  | * </table> | 
|  | * Note that in this table Rows, Cols, MaxRows and MaxCols are all positive integers. A(S) is defined to the largest | 
|  | * possible power-of-two smaller to EIGEN_MAX_STATIC_ALIGN_BYTES. | 
|  | * | 
|  | * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy, | 
|  | * \ref TopicStorageOrders | 
|  | */ | 
|  |  | 
|  | template <typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_> | 
|  | class Matrix : public PlainObjectBase<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>> { | 
|  | public: | 
|  | /** \brief Base class typedef. | 
|  | * \sa PlainObjectBase | 
|  | */ | 
|  | typedef PlainObjectBase<Matrix> Base; | 
|  |  | 
|  | enum { Options = Options_ }; | 
|  |  | 
|  | EIGEN_DENSE_PUBLIC_INTERFACE(Matrix) | 
|  |  | 
|  | typedef typename Base::PlainObject PlainObject; | 
|  |  | 
|  | using Base::base; | 
|  | using Base::coeffRef; | 
|  |  | 
|  | /** | 
|  | * \brief Assigns matrices to each other. | 
|  | * | 
|  | * \note This is a special case of the templated operator=. Its purpose is | 
|  | * to prevent a default operator= from hiding the templated operator=. | 
|  | * | 
|  | * \callgraph | 
|  | */ | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix& operator=(const Matrix& other) { return Base::_set(other); } | 
|  |  | 
|  | /** \internal | 
|  | * \brief Copies the value of the expression \a other into \c *this with automatic resizing. | 
|  | * | 
|  | * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized), | 
|  | * it will be initialized. | 
|  | * | 
|  | * Note that copying a row-vector into a vector (and conversely) is allowed. | 
|  | * The resizing, if any, is then done in the appropriate way so that row-vectors | 
|  | * remain row-vectors and vectors remain vectors. | 
|  | */ | 
|  | template <typename OtherDerived> | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix& operator=(const DenseBase<OtherDerived>& other) { | 
|  | return Base::_set(other); | 
|  | } | 
|  |  | 
|  | /* Here, doxygen failed to copy the brief information when using \copydoc */ | 
|  |  | 
|  | /** | 
|  | * \brief Copies the generic expression \a other into *this. | 
|  | * \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other) | 
|  | */ | 
|  | template <typename OtherDerived> | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived>& other) { | 
|  | return Base::operator=(other); | 
|  | } | 
|  |  | 
|  | template <typename OtherDerived> | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived>& func) { | 
|  | return Base::operator=(func); | 
|  | } | 
|  |  | 
|  | /** \brief Default constructor. | 
|  | * | 
|  | * For fixed-size matrices, does nothing. | 
|  | * | 
|  | * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix | 
|  | * is called a null matrix. This constructor is the unique way to create null matrices: resizing | 
|  | * a matrix to 0 is not supported. | 
|  | * | 
|  | * \sa resize(Index,Index) | 
|  | */ | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix() | 
|  | : Base(){EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED} | 
|  |  | 
|  | // FIXME is it still needed | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr explicit Matrix( | 
|  | internal::constructor_without_unaligned_array_assert) | 
|  | : Base(internal::constructor_without_unaligned_array_assert()){EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED} | 
|  |  | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix(Matrix && other) | 
|  | EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value) | 
|  | : Base(std::move(other)) {} | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix& operator=(Matrix&& other) | 
|  | EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value) { | 
|  | Base::operator=(std::move(other)); | 
|  | return *this; | 
|  | } | 
|  |  | 
|  | /** \copydoc PlainObjectBase(const Scalar&, const Scalar&, const Scalar&,  const Scalar&, const ArgTypes&... args) | 
|  | * | 
|  | * Example: \include Matrix_variadic_ctor_cxx11.cpp | 
|  | * Output: \verbinclude Matrix_variadic_ctor_cxx11.out | 
|  | * | 
|  | * \sa Matrix(const std::initializer_list<std::initializer_list<Scalar>>&) | 
|  | */ | 
|  | template <typename... ArgTypes> | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, | 
|  | const ArgTypes&... args) | 
|  | : Base(a0, a1, a2, a3, args...) {} | 
|  |  | 
|  | /** \brief Constructs a Matrix and initializes it from the coefficients given as initializer-lists grouped by row. | 
|  | * \cpp11 | 
|  | * | 
|  | * In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients: | 
|  | * | 
|  | * Example: \include Matrix_initializer_list_23_cxx11.cpp | 
|  | * Output: \verbinclude Matrix_initializer_list_23_cxx11.out | 
|  | * | 
|  | * Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is | 
|  | * triggered. | 
|  | * | 
|  | * In the case of a compile-time column vector, implicit transposition from a single row is allowed. | 
|  | * Therefore <code>VectorXd{{1,2,3,4,5}}</code> is legal and the more verbose syntax | 
|  | * <code>RowVectorXd{{1},{2},{3},{4},{5}}</code> can be avoided: | 
|  | * | 
|  | * Example: \include Matrix_initializer_list_vector_cxx11.cpp | 
|  | * Output: \verbinclude Matrix_initializer_list_vector_cxx11.out | 
|  | * | 
|  | * In the case of fixed-sized matrices, the initializer list sizes must exactly match the matrix sizes, | 
|  | * and implicit transposition is allowed for compile-time vectors only. | 
|  | * | 
|  | * \sa Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2,  const Scalar& a3, const ArgTypes&... args) | 
|  | */ | 
|  | EIGEN_DEVICE_FUNC explicit constexpr EIGEN_STRONG_INLINE Matrix( | 
|  | const std::initializer_list<std::initializer_list<Scalar>>& list) | 
|  | : Base(list) {} | 
|  |  | 
|  | #ifndef EIGEN_PARSED_BY_DOXYGEN | 
|  |  | 
|  | // This constructor is for both 1x1 matrices and dynamic vectors | 
|  | template <typename T> | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Matrix(const T& x) { | 
|  | Base::template _init1<T>(x); | 
|  | } | 
|  |  | 
|  | template <typename T0, typename T1> | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y) { | 
|  | Base::template _init2<T0, T1>(x, y); | 
|  | } | 
|  |  | 
|  | #else | 
|  | /** \brief Constructs a fixed-sized matrix initialized with coefficients starting at \a data */ | 
|  | EIGEN_DEVICE_FUNC explicit Matrix(const Scalar* data); | 
|  |  | 
|  | /** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors | 
|  | * | 
|  | * This is useful for dynamic-size vectors. For fixed-size vectors, | 
|  | * it is redundant to pass these parameters, so one should use the default constructor | 
|  | * Matrix() instead. | 
|  | * | 
|  | * \warning This constructor is disabled for fixed-size \c 1x1 matrices. For instance, | 
|  | * calling Matrix<double,1,1>(1) will call the initialization constructor: Matrix(const Scalar&). | 
|  | * For fixed-size \c 1x1 matrices it is therefore recommended to use the default | 
|  | * constructor Matrix() instead, especially when using one of the non standard | 
|  | * \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives). | 
|  | */ | 
|  | EIGEN_STRONG_INLINE explicit Matrix(Index dim); | 
|  | /** \brief Constructs an initialized 1x1 matrix with the given coefficient | 
|  | * \sa Matrix(const Scalar&, const Scalar&, const Scalar&,  const Scalar&, const ArgTypes&...) */ | 
|  | Matrix(const Scalar& x); | 
|  | /** \brief Constructs an uninitialized matrix with \a rows rows and \a cols columns. | 
|  | * | 
|  | * This is useful for dynamic-size matrices. For fixed-size matrices, | 
|  | * it is redundant to pass these parameters, so one should use the default constructor | 
|  | * Matrix() instead. | 
|  | * | 
|  | * \warning This constructor is disabled for fixed-size \c 1x2 and \c 2x1 vectors. For instance, | 
|  | * calling Matrix2f(2,1) will call the initialization constructor: Matrix(const Scalar& x, const Scalar& y). | 
|  | * For fixed-size \c 1x2 or \c 2x1 vectors it is therefore recommended to use the default | 
|  | * constructor Matrix() instead, especially when using one of the non standard | 
|  | * \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives). | 
|  | */ | 
|  | EIGEN_DEVICE_FUNC Matrix(Index rows, Index cols); | 
|  |  | 
|  | /** \brief Constructs an initialized 2D vector with given coefficients | 
|  | * \sa Matrix(const Scalar&, const Scalar&, const Scalar&,  const Scalar&, const ArgTypes&...) */ | 
|  | Matrix(const Scalar& x, const Scalar& y); | 
|  | #endif  // end EIGEN_PARSED_BY_DOXYGEN | 
|  |  | 
|  | /** \brief Constructs an initialized 3D vector with given coefficients | 
|  | * \sa Matrix(const Scalar&, const Scalar&, const Scalar&,  const Scalar&, const ArgTypes&...) | 
|  | */ | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z) { | 
|  | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3) | 
|  | m_storage.data()[0] = x; | 
|  | m_storage.data()[1] = y; | 
|  | m_storage.data()[2] = z; | 
|  | } | 
|  | /** \brief Constructs an initialized 4D vector with given coefficients | 
|  | * \sa Matrix(const Scalar&, const Scalar&, const Scalar&,  const Scalar&, const ArgTypes&...) | 
|  | */ | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w) { | 
|  | EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4) | 
|  | m_storage.data()[0] = x; | 
|  | m_storage.data()[1] = y; | 
|  | m_storage.data()[2] = z; | 
|  | m_storage.data()[3] = w; | 
|  | } | 
|  |  | 
|  | /** \brief Copy constructor */ | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const Matrix& other) : Base(other) {} | 
|  |  | 
|  | /** \brief Copy constructor for generic expressions. | 
|  | * \sa MatrixBase::operator=(const EigenBase<OtherDerived>&) | 
|  | */ | 
|  | template <typename OtherDerived> | 
|  | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived>& other) : Base(other.derived()) {} | 
|  |  | 
|  | EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT { return 1; } | 
|  | EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT { return this->innerSize(); } | 
|  |  | 
|  | /////////// Geometry module /////////// | 
|  |  | 
|  | template <typename OtherDerived> | 
|  | EIGEN_DEVICE_FUNC explicit Matrix(const RotationBase<OtherDerived, ColsAtCompileTime>& r); | 
|  | template <typename OtherDerived> | 
|  | EIGEN_DEVICE_FUNC Matrix& operator=(const RotationBase<OtherDerived, ColsAtCompileTime>& r); | 
|  |  | 
|  | // allow to extend Matrix outside Eigen | 
|  | #ifdef EIGEN_MATRIX_PLUGIN | 
|  | #include EIGEN_MATRIX_PLUGIN | 
|  | #endif | 
|  |  | 
|  | protected: | 
|  | template <typename Derived, typename OtherDerived, bool IsVector> | 
|  | friend struct internal::conservative_resize_like_impl; | 
|  |  | 
|  | using Base::m_storage; | 
|  | }; | 
|  |  | 
|  | /** \defgroup matrixtypedefs Global matrix typedefs | 
|  | * | 
|  | * \ingroup Core_Module | 
|  | * | 
|  | * %Eigen defines several typedef shortcuts for most common matrix and vector types. | 
|  | * | 
|  | * The general patterns are the following: | 
|  | * | 
|  | * \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size, | 
|  | * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd | 
|  | * for complex double. | 
|  | * | 
|  | * For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of | 
|  | * floats. | 
|  | * | 
|  | * There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is | 
|  | * a fixed-size vector of 4 complex floats. | 
|  | * | 
|  | * With \cpp11, template alias are also defined for common sizes. | 
|  | * They follow the same pattern as above except that the scalar type suffix is replaced by a | 
|  | * template parameter, i.e.: | 
|  | *   - `MatrixSize<Type>` where `Size` can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size. | 
|  | *   - `MatrixXSize<Type>` and `MatrixSizeX<Type>` where `Size` can be \c 2,\c 3,\c 4 for hybrid dynamic/fixed matrices. | 
|  | *   - `VectorSize<Type>` and `RowVectorSize<Type>` for column and row vectors. | 
|  | * | 
|  | * With \cpp11, you can also use fully generic column and row vector types: `Vector<Type,Size>` and | 
|  | * `RowVector<Type,Size>`. | 
|  | * | 
|  | * \sa class Matrix | 
|  | */ | 
|  |  | 
|  | #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)    \ | 
|  | /** \ingroup matrixtypedefs */                                   \ | 
|  | /** \brief `Size`×`Size` matrix of type `Type`. */         \ | 
|  | typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix; \ | 
|  | /** \ingroup matrixtypedefs */                                   \ | 
|  | /** \brief `Size`×`1` vector of type `Type`. */            \ | 
|  | typedef Matrix<Type, Size, 1> Vector##SizeSuffix##TypeSuffix;    \ | 
|  | /** \ingroup matrixtypedefs */                                   \ | 
|  | /** \brief `1`×`Size` vector of type `Type`. */            \ | 
|  | typedef Matrix<Type, 1, Size> RowVector##SizeSuffix##TypeSuffix; | 
|  |  | 
|  | #define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size)          \ | 
|  | /** \ingroup matrixtypedefs */                                   \ | 
|  | /** \brief `Size`×`Dynamic` matrix of type `Type`. */      \ | 
|  | typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix; \ | 
|  | /** \ingroup matrixtypedefs */                                   \ | 
|  | /** \brief `Dynamic`×`Size` matrix of type `Type`. */      \ | 
|  | typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix; | 
|  |  | 
|  | #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \ | 
|  | EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2)           \ | 
|  | EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3)           \ | 
|  | EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4)           \ | 
|  | EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)     \ | 
|  | EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2)        \ | 
|  | EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3)        \ | 
|  | EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4) | 
|  |  | 
|  | EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i) | 
|  | EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f) | 
|  | EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d) | 
|  | EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>, cf) | 
|  | EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd) | 
|  |  | 
|  | #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES | 
|  | #undef EIGEN_MAKE_TYPEDEFS | 
|  | #undef EIGEN_MAKE_FIXED_TYPEDEFS | 
|  |  | 
|  | #define EIGEN_MAKE_TYPEDEFS(Size, SizeSuffix)                    \ | 
|  | /** \ingroup matrixtypedefs */                                 \ | 
|  | /** \brief \cpp11 `Size`×`Size` matrix of type `Type`.*/ \ | 
|  | template <typename Type>                                       \ | 
|  | using Matrix##SizeSuffix = Matrix<Type, Size, Size>;           \ | 
|  | /** \ingroup matrixtypedefs */                                 \ | 
|  | /** \brief \cpp11 `Size`×`1` vector of type `Type`.*/    \ | 
|  | template <typename Type>                                       \ | 
|  | using Vector##SizeSuffix = Matrix<Type, Size, 1>;              \ | 
|  | /** \ingroup matrixtypedefs */                                 \ | 
|  | /** \brief \cpp11 `1`×`Size` vector of type `Type`.*/    \ | 
|  | template <typename Type>                                       \ | 
|  | using RowVector##SizeSuffix = Matrix<Type, 1, Size>; | 
|  |  | 
|  | #define EIGEN_MAKE_FIXED_TYPEDEFS(Size)                              \ | 
|  | /** \ingroup matrixtypedefs */                                     \ | 
|  | /** \brief \cpp11 `Size`×`Dynamic` matrix of type `Type` */  \ | 
|  | template <typename Type>                                           \ | 
|  | using Matrix##Size##X = Matrix<Type, Size, Dynamic>;               \ | 
|  | /** \ingroup matrixtypedefs */                                     \ | 
|  | /** \brief \cpp11 `Dynamic`×`Size` matrix of type `Type`. */ \ | 
|  | template <typename Type>                                           \ | 
|  | using Matrix##X##Size = Matrix<Type, Dynamic, Size>; | 
|  |  | 
|  | EIGEN_MAKE_TYPEDEFS(2, 2) | 
|  | EIGEN_MAKE_TYPEDEFS(3, 3) | 
|  | EIGEN_MAKE_TYPEDEFS(4, 4) | 
|  | EIGEN_MAKE_TYPEDEFS(Dynamic, X) | 
|  | EIGEN_MAKE_FIXED_TYPEDEFS(2) | 
|  | EIGEN_MAKE_FIXED_TYPEDEFS(3) | 
|  | EIGEN_MAKE_FIXED_TYPEDEFS(4) | 
|  |  | 
|  | /** \ingroup matrixtypedefs | 
|  | * \brief \cpp11 `Size`×`1` vector of type `Type`. */ | 
|  | template <typename Type, int Size> | 
|  | using Vector = Matrix<Type, Size, 1>; | 
|  |  | 
|  | /** \ingroup matrixtypedefs | 
|  | * \brief \cpp11 `1`×`Size` vector of type `Type`. */ | 
|  | template <typename Type, int Size> | 
|  | using RowVector = Matrix<Type, 1, Size>; | 
|  |  | 
|  | #undef EIGEN_MAKE_TYPEDEFS | 
|  | #undef EIGEN_MAKE_FIXED_TYPEDEFS | 
|  |  | 
|  | }  // end namespace Eigen | 
|  |  | 
|  | #endif  // EIGEN_MATRIX_H |