// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2006-2010 Benoit Jacob // Copyright (C) 2008-2009 Gael Guennebaud // // 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 namespace Eigen { namespace internal { template struct traits > { private: enum { size = internal::size_at_compile_time<_Rows,_Cols>::ret }; 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::alignment, packet_access_bit = (packet_traits<_Scalar>::Vectorizable && (EIGEN_UNALIGNED_VECTORIZE || (actual_alignment>=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<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret, Options = _Options, InnerStrideAtCompileTime = 1, OuterStrideAtCompileTime = (Options&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 }; }; } /** \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. * 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) * \li \c Vector4f is a vector of 4 floats (\c Matrix) * \li \c RowVector3i is a row-vector of 3 ints (\c Matrix) * * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix) * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix) * * \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix) * \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix) * * 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. * * Some notes: * *
*
\anchor dense Dense versus sparse:
*
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.
* *
\anchor fixedsize Fixed-size versus dynamic-size:
*
Fixed-size means that the numbers of rows and columns are known are 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, do not expand dynamically in the sense of a std::map. * If you want this behavior, see the Sparse module.
* *
\anchor maxrows _MaxRows and _MaxCols:
*
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 are 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.
*
* * ABI and storage layout * * The table below summarizes the ABI of some possible Matrix instances which is fixed thorough the lifetime of Eigen 3. * * * * * * *
Matrix typeEquivalent C structure
\code Matrix \endcode\code * struct { * T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0 * Eigen::Index rows, cols; * }; * \endcode
\code * Matrix * Matrix \endcode\code * struct { * T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0 * Eigen::Index size; * }; * \endcode
\code Matrix \endcode\code * struct { * T data[Rows*Cols]; // with (size_t(data)%A(Rows*Cols*sizeof(T)))==0 * }; * \endcode
\code Matrix \endcode\code * struct { * T data[MaxRows*MaxCols]; // with (size_t(data)%A(MaxRows*MaxCols*sizeof(T)))==0 * Eigen::Index rows, cols; * }; * \endcode
* 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 class Matrix : public PlainObjectBase > { public: /** \brief Base class typedef. * \sa PlainObjectBase */ typedef PlainObjectBase 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 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 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix& operator=(const DenseBase& 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 &other) */ template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase &other) { return Base::operator=(other); } template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue& 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 Matrix() : Base() { Base::_check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED } // FIXME is it still needed EIGEN_DEVICE_FUNC explicit Matrix(internal::constructor_without_unaligned_array_assert) : Base(internal::constructor_without_unaligned_array_assert()) { Base::_check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED } #if EIGEN_HAS_RVALUE_REFERENCES EIGEN_DEVICE_FUNC Matrix(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible::value) : Base(std::move(other)) { Base::_check_template_params(); } EIGEN_DEVICE_FUNC Matrix& operator=(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable::value) { other.swap(*this); return *this; } #endif #ifndef EIGEN_PARSED_BY_DOXYGEN // This constructor is for both 1x1 matrices and dynamic vectors template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit Matrix(const T& x) { Base::_check_template_params(); Base::template _init1(x); } template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y) { Base::_check_template_params(); Base::template _init2(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(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 */ 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 */ Matrix(const Scalar& x, const Scalar& y); #endif /** \brief Constructs an initialized 3D vector with given coefficients */ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z) { Base::_check_template_params(); 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 */ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w) { Base::_check_template_params(); 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&) */ template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const EigenBase &other) : Base(other.derived()) { } EIGEN_DEVICE_FUNC inline Index innerStride() const { return 1; } EIGEN_DEVICE_FUNC inline Index outerStride() const { return this->innerSize(); } /////////// Geometry module /////////// template EIGEN_DEVICE_FUNC explicit Matrix(const RotationBase& r); template EIGEN_DEVICE_FUNC Matrix& operator=(const RotationBase& r); // allow to extend Matrix outside Eigen #ifdef EIGEN_MATRIX_PLUGIN #include EIGEN_MATRIX_PLUGIN #endif protected: template 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. * * \sa class Matrix */ #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \ /** \ingroup matrixtypedefs */ \ typedef Matrix Matrix##SizeSuffix##TypeSuffix; \ /** \ingroup matrixtypedefs */ \ typedef Matrix Vector##SizeSuffix##TypeSuffix; \ /** \ingroup matrixtypedefs */ \ typedef Matrix RowVector##SizeSuffix##TypeSuffix; #define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \ /** \ingroup matrixtypedefs */ \ typedef Matrix Matrix##Size##X##TypeSuffix; \ /** \ingroup matrixtypedefs */ \ typedef Matrix 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, cf) EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex, cd) #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES #undef EIGEN_MAKE_TYPEDEFS #undef EIGEN_MAKE_FIXED_TYPEDEFS } // end namespace Eigen #endif // EIGEN_MATRIX_H