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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
// 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)
*/
#if defined(EIGEN_INITIALIZE_COEFFS)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix() { EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
#else
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix() = default;
#endif
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix(Matrix&&) = default;
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 constexpr Matrix(const Matrix&) = default;
/** \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`&times;`Size` matrix of type `Type`. */ \
typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
/** \brief `Size`&times;`1` vector of type `Type`. */ \
typedef Matrix<Type, Size, 1> Vector##SizeSuffix##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
/** \brief `1`&times;`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`&times;`Dynamic` matrix of type `Type`. */ \
typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
/** \brief `Dynamic`&times;`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`&times;`Size` matrix of type `Type`.*/ \
template <typename Type> \
using Matrix##SizeSuffix = Matrix<Type, Size, Size>; \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 `Size`&times;`1` vector of type `Type`.*/ \
template <typename Type> \
using Vector##SizeSuffix = Matrix<Type, Size, 1>; \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 `1`&times;`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`&times;`Dynamic` matrix of type `Type` */ \
template <typename Type> \
using Matrix##Size##X = Matrix<Type, Size, Dynamic>; \
/** \ingroup matrixtypedefs */ \
/** \brief \cpp11 `Dynamic`&times;`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`&times;`1` vector of type `Type`. */
template <typename Type, int Size>
using Vector = Matrix<Type, Size, 1>;
/** \ingroup matrixtypedefs
* \brief \cpp11 `1`&times;`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