// 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