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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_MATRIX_H
#define EIGEN_MATRIX_H
/** \class Matrix
*
* \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:
* \param _Scalar Numeric type, i.e. float, double, int
* \param _Rows Number of rows, or \b Dynamic
* \param _Cols Number of columns, or \b Dynamic
*
* The remaining template parameters are optional -- in most cases you don't have to worry about them.
* \param _Options A combination of either \b RowMajor or \b ColMajor, and of either
* \b AutoAlign or \b DontAlign.
* The former controls 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.
* \param _MaxRows Maximum number of rows. Defaults to \a _Rows (\ref maxrows "note").
* \param _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>)
*
* 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
*
* <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>
*
* \see MatrixBase for the majority of the API methods for matrices
*/
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
struct ei_traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
typedef _Scalar Scalar;
enum {
RowsAtCompileTime = _Rows,
ColsAtCompileTime = _Cols,
MaxRowsAtCompileTime = _MaxRows,
MaxColsAtCompileTime = _MaxCols,
Flags = ei_compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
CoeffReadCost = NumTraits<Scalar>::ReadCost
};
};
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
class Matrix
: public MatrixBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
public:
EIGEN_GENERIC_PUBLIC_INTERFACE(Matrix)
enum { Options = _Options };
friend class Eigen::Map<Matrix, Unaligned>;
typedef class Eigen::Map<Matrix, Unaligned> UnalignedMapType;
friend class Eigen::Map<Matrix, Aligned>;
typedef class Eigen::Map<Matrix, Aligned> AlignedMapType;
protected:
ei_matrix_storage<Scalar, MaxSizeAtCompileTime, RowsAtCompileTime, ColsAtCompileTime, Options> m_storage;
public:
enum { NeedsToAlign = (Options&AutoAlign) == AutoAlign
&& SizeAtCompileTime!=Dynamic && ((sizeof(Scalar)*SizeAtCompileTime)%16)==0 };
EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
EIGEN_STRONG_INLINE int rows() const { return m_storage.rows(); }
EIGEN_STRONG_INLINE int cols() const { return m_storage.cols(); }
EIGEN_STRONG_INLINE int stride(void) const
{
if(Flags & RowMajorBit)
return m_storage.cols();
else
return m_storage.rows();
}
EIGEN_STRONG_INLINE const Scalar& coeff(int row, int col) const
{
if(Flags & RowMajorBit)
return m_storage.data()[col + row * m_storage.cols()];
else // column-major
return m_storage.data()[row + col * m_storage.rows()];
}
EIGEN_STRONG_INLINE const Scalar& coeff(int index) const
{
return m_storage.data()[index];
}
EIGEN_STRONG_INLINE Scalar& coeffRef(int row, int col)
{
if(Flags & RowMajorBit)
return m_storage.data()[col + row * m_storage.cols()];
else // column-major
return m_storage.data()[row + col * m_storage.rows()];
}
EIGEN_STRONG_INLINE Scalar& coeffRef(int index)
{
return m_storage.data()[index];
}
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(int row, int col) const
{
return ei_ploadt<Scalar, LoadMode>
(m_storage.data() + (Flags & RowMajorBit
? col + row * m_storage.cols()
: row + col * m_storage.rows()));
}
template<int LoadMode>
EIGEN_STRONG_INLINE PacketScalar packet(int index) const
{
return ei_ploadt<Scalar, LoadMode>(m_storage.data() + index);
}
template<int StoreMode>
EIGEN_STRONG_INLINE void writePacket(int row, int col, const PacketScalar& x)
{
ei_pstoret<Scalar, PacketScalar, StoreMode>
(m_storage.data() + (Flags & RowMajorBit
? col + row * m_storage.cols()
: row + col * m_storage.rows()), x);
}
template<int StoreMode>
EIGEN_STRONG_INLINE void writePacket(int index, const PacketScalar& x)
{
ei_pstoret<Scalar, PacketScalar, StoreMode>(m_storage.data() + index, x);
}
/** \returns a const pointer to the data array of this matrix */
EIGEN_STRONG_INLINE const Scalar *data() const
{ return m_storage.data(); }
/** \returns a pointer to the data array of this matrix */
EIGEN_STRONG_INLINE Scalar *data()
{ return m_storage.data(); }
/** Resizes \c *this to a \a rows x \a cols matrix.
*
* Makes sense for dynamic-size matrices only.
*
* If the current number of coefficients of \c *this exactly matches the
* product \a rows * \a cols, then no memory allocation is performed and
* the current values are left unchanged. In all other cases, including
* shrinking, the data is reallocated and all previous values are lost.
*
* \sa resize(int) for vectors.
*/
inline void resize(int rows, int cols)
{
ei_assert(rows > 0 && cols > 0 && "a matrix cannot be resized to 0 size");
ei_assert((MaxRowsAtCompileTime == Dynamic || MaxRowsAtCompileTime >= rows)
&& (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
&& (MaxColsAtCompileTime == Dynamic || MaxColsAtCompileTime >= cols)
&& (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
m_storage.resize(rows * cols, rows, cols);
}
/** Resizes \c *this to a vector of length \a size
*
* \sa resize(int,int) for the details.
*/
inline void resize(int size)
{
ei_assert(size>0 && "a vector cannot be resized to 0 length");
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Matrix)
if(RowsAtCompileTime == 1)
m_storage.resize(size, 1, size);
else
m_storage.resize(size, size, 1);
}
/** 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_STRONG_INLINE Matrix& operator=(const MatrixBase<OtherDerived>& other)
{
return _set(other);
}
/** This is a special case of the templated operator=. Its purpose is to
* prevent a default operator= from hiding the templated operator=.
*/
EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other)
{
return _set(other);
}
EIGEN_INHERIT_ASSIGNMENT_OPERATOR(Matrix, +=)
EIGEN_INHERIT_ASSIGNMENT_OPERATOR(Matrix, -=)
EIGEN_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Matrix, *=)
EIGEN_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Matrix, /=)
/** 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(int,int)
*/
EIGEN_STRONG_INLINE explicit Matrix() : m_storage()
{
_check_template_params();
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal */
Matrix(ei_constructor_without_unaligned_array_assert)
: m_storage(ei_constructor_without_unaligned_array_assert())
{}
#endif
/** Constructs a vector or row-vector with given dimension. \only_for_vectors
*
* Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
* it is redundant to pass the dimension here, so it makes more sense to use the default
* constructor Matrix() instead.
*/
EIGEN_STRONG_INLINE explicit Matrix(int dim)
: m_storage(dim, RowsAtCompileTime == 1 ? 1 : dim, ColsAtCompileTime == 1 ? 1 : dim)
{
_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Matrix)
ei_assert(dim > 0);
ei_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == dim);
}
/** This constructor has two very different behaviors, depending on the type of *this.
*
* \li When Matrix is a fixed-size vector type of size 2, this constructor constructs
* an initialized vector. The parameters \a x, \a y are copied into the first and second
* coords of the vector respectively.
* \li Otherwise, this constructor constructs an uninitialized matrix with \a x rows and
* \a y 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.
*/
EIGEN_STRONG_INLINE Matrix(int x, int y) : m_storage(x*y, x, y)
{
_check_template_params();
if((RowsAtCompileTime == 1 && ColsAtCompileTime == 2)
|| (RowsAtCompileTime == 2 && ColsAtCompileTime == 1))
{
m_storage.data()[0] = Scalar(x);
m_storage.data()[1] = Scalar(y);
}
else
{
ei_assert(x > 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == x)
&& y > 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == y));
}
}
/** constructs an initialized 2D vector with given coefficients */
EIGEN_STRONG_INLINE Matrix(const float& x, const float& y)
{
_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 2)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
}
/** constructs an initialized 2D vector with given coefficients */
EIGEN_STRONG_INLINE Matrix(const double& x, const double& y)
{
_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 2)
m_storage.data()[0] = x;
m_storage.data()[1] = y;
}
/** constructs an initialized 3D vector with given coefficients */
EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z)
{
_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;
}
/** constructs an initialized 4D vector with given coefficients */
EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
{
_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;
}
explicit Matrix(const Scalar *data);
/** Constructor copying the value of the expression \a other */
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix(const MatrixBase<OtherDerived>& other)
: m_storage(other.rows() * other.cols(), other.rows(), other.cols())
{
_check_template_params();
_set_noalias(other);
}
/** Copy constructor */
EIGEN_STRONG_INLINE Matrix(const Matrix& other)
: Base(), m_storage(other.rows() * other.cols(), other.rows(), other.cols())
{
_check_template_params();
_set_noalias(other);
}
/** Destructor */
inline ~Matrix() {}
/** Override MatrixBase::swap() since for dynamic-sized matrices of same type it is enough to swap the
* data pointers.
*/
inline void swap(Matrix& other)
{
if (Base::SizeAtCompileTime==Dynamic)
m_storage.swap(other.m_storage);
else
this->Base::swap(other);
}
/** \name Map
* These are convenience functions returning Map objects. The Map() static functions return unaligned Map objects,
* while the AlignedMap() functions return aligned Map objects and thus should be called only with 16-byte-aligned
* \a data pointers.
*
* \see class Map
*/
//@{
inline static const UnalignedMapType Map(const Scalar* data)
{ return UnalignedMapType(data); }
inline static UnalignedMapType Map(Scalar* data)
{ return UnalignedMapType(data); }
inline static const UnalignedMapType Map(const Scalar* data, int size)
{ return UnalignedMapType(data, size); }
inline static UnalignedMapType Map(Scalar* data, int size)
{ return UnalignedMapType(data, size); }
inline static const UnalignedMapType Map(const Scalar* data, int rows, int cols)
{ return UnalignedMapType(data, rows, cols); }
inline static UnalignedMapType Map(Scalar* data, int rows, int cols)
{ return UnalignedMapType(data, rows, cols); }
inline static const AlignedMapType MapAligned(const Scalar* data)
{ return AlignedMapType(data); }
inline static AlignedMapType MapAligned(Scalar* data)
{ return AlignedMapType(data); }
inline static const AlignedMapType MapAligned(const Scalar* data, int size)
{ return AlignedMapType(data, size); }
inline static AlignedMapType MapAligned(Scalar* data, int size)
{ return AlignedMapType(data, size); }
inline static const AlignedMapType MapAligned(const Scalar* data, int rows, int cols)
{ return AlignedMapType(data, rows, cols); }
inline static AlignedMapType MapAligned(Scalar* data, int rows, int cols)
{ return AlignedMapType(data, rows, cols); }
//@}
/////////// Geometry module ///////////
template<typename OtherDerived>
explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
template<typename OtherDerived>
Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
// allow to extend Matrix outside Eigen
#ifdef EIGEN_MATRIX_PLUGIN
#include EIGEN_MATRIX_PLUGIN
#endif
private:
/** \internal Resizes *this in preparation for assigning \a other to it.
* Takes care of doing all the checking that's needed.
*
* 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_STRONG_INLINE void _resize_to_match(const MatrixBase<OtherDerived>& other)
{
if(RowsAtCompileTime == 1)
{
ei_assert(other.isVector());
resize(1, other.size());
}
else if(ColsAtCompileTime == 1)
{
ei_assert(other.isVector());
resize(other.size(), 1);
}
else resize(other.rows(), other.cols());
}
/** \internal 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.
*
* \sa operator=(const MatrixBase<OtherDerived>&), _set_noalias()
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix& _set(const MatrixBase<OtherDerived>& other)
{
_resize_to_match(other);
return Base::operator=(other);
}
/** \internal Like _set() but additionally makes the assumption that no aliasing effect can happen (which
* is the case when creating a new matrix) so one can enforce lazy evaluation.
*
* \sa operator=(const MatrixBase<OtherDerived>&), _set()
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix& _set_noalias(const MatrixBase<OtherDerived>& other)
{
_resize_to_match(other);
// the 'false' below means to enforce lazy evaluation. We don't use lazyAssign() because
// it wouldn't allow to copy a row-vector into a column-vector.
return ei_assign_selector<Matrix,OtherDerived,false>::run(*this, other.derived());
}
static EIGEN_STRONG_INLINE void _check_template_params()
{
EIGEN_STATIC_ASSERT((_Rows > 0
&& _Cols > 0
&& _MaxRows <= _Rows
&& _MaxCols <= _Cols
&& (_Options & (AutoAlign|RowMajor)) == _Options),
INVALID_MATRIX_TEMPLATE_PARAMETERS)
}
};
/** \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_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_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_TYPEDEFS_LARGE
#define EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \
using Eigen::Matrix##SizeSuffix##TypeSuffix; \
using Eigen::Vector##SizeSuffix##TypeSuffix; \
using Eigen::RowVector##SizeSuffix##TypeSuffix;
#define EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(TypeSuffix) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \
#define EIGEN_USING_MATRIX_TYPEDEFS \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(i) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(f) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(d) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(cf) \
EIGEN_USING_MATRIX_TYPEDEFS_FOR_TYPE(cd)
#endif // EIGEN_MATRIX_H