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-// 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
-
-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:
- 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<PacketScalar>::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<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 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, <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 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.</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 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 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<Scalar>::value)
- : Base(std::move(other))
- {
- Base::_check_template_params();
- if (RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic)
- Base::_set_noalias(other);
- }
- EIGEN_DEVICE_FUNC
- Matrix& operator=(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
- {
- other.swap(*this);
- return *this;
- }
-#endif
-
- #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::_check_template_params();
- Base::template _init1<T>(x);
- }
-
- template<typename T0, typename T1>
- EIGEN_DEVICE_FUNC
- EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y)
- {
- Base::_check_template_params();
- 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 */
- 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<OtherDerived>&)
- */
- template<typename OtherDerived>
- EIGEN_DEVICE_FUNC
- EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived> &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<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.
- *
- * \sa class Matrix
- */
-
-#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
-/** \ingroup matrixtypedefs */ \
-typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix; \
-/** \ingroup matrixtypedefs */ \
-typedef Matrix<Type, Size, 1> Vector##SizeSuffix##TypeSuffix; \
-/** \ingroup matrixtypedefs */ \
-typedef Matrix<Type, 1, Size> RowVector##SizeSuffix##TypeSuffix;
-
-#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
-/** \ingroup matrixtypedefs */ \
-typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix; \
-/** \ingroup matrixtypedefs */ \
-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
-
-} // end namespace Eigen
-
-#endif // EIGEN_MATRIX_H