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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 {
/** \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 \anchor matrix_tparam_scalar Numeric type, e.g. float, double, int or std::complex<float>.
* User defined sclar 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 \anchor matrix_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 TopicCustomizingEigen 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>
*
* \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy,
* \ref TopicStorageOrders
*/
namespace internal {
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
struct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
{
typedef _Scalar Scalar;
typedef Dense StorageKind;
typedef DenseIndex Index;
typedef MatrixXpr XprKind;
enum {
RowsAtCompileTime = _Rows,
ColsAtCompileTime = _Cols,
MaxRowsAtCompileTime = _MaxRows,
MaxColsAtCompileTime = _MaxCols,
Flags = compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
CoeffReadCost = NumTraits<Scalar>::ReadCost,
Options = _Options,
InnerStrideAtCompileTime = 1,
OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime
};
};
}
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_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_STRONG_INLINE Matrix& operator=(const MatrixBase<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_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived> &other)
{
return Base::operator=(other);
}
template<typename OtherDerived>
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_STRONG_INLINE Matrix() : Base()
{
Base::_check_template_params();
EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
}
// FIXME is it still needed
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 }
#ifdef EIGEN_HAVE_RVALUE_REFERENCES
Matrix(Matrix&& other)
: Base(std::move(other))
{
Base::_check_template_params();
if (RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic)
Base::_set_noalias(other);
}
Matrix& operator=(Matrix&& other)
{
other.swap(*this);
return *this;
}
#endif
/** \brief 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(Index dim)
: Base(dim, RowsAtCompileTime == 1 ? 1 : dim, ColsAtCompileTime == 1 ? 1 : dim)
{
Base::_check_template_params();
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Matrix)
eigen_assert(dim >= 0);
eigen_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == dim);
EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename T0, typename T1>
EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y)
{
Base::_check_template_params();
Base::template _init2<T0,T1>(x, y);
}
#else
/** \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. */
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_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_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;
}
explicit Matrix(const Scalar *data);
/** \brief Constructor copying the value of the expression \a other */
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix(const MatrixBase<OtherDerived>& other)
: Base(other.rows() * other.cols(), other.rows(), other.cols())
{
// This test resides here, to bring the error messages closer to the user. Normally, these checks
// are performed deeply within the library, thus causing long and scary error traces.
EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
Base::_check_template_params();
Base::_set_noalias(other);
}
/** \brief Copy constructor */
EIGEN_STRONG_INLINE Matrix(const Matrix& other)
: Base(other.rows() * other.cols(), other.rows(), other.cols())
{
Base::_check_template_params();
Base::_set_noalias(other);
}
/** \brief Copy constructor with in-place evaluation */
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix(const ReturnByValue<OtherDerived>& other)
{
Base::_check_template_params();
Base::resize(other.rows(), other.cols());
other.evalTo(*this);
}
/** \brief Copy constructor for generic expressions.
* \sa MatrixBase::operator=(const EigenBase<OtherDerived>&)
*/
template<typename OtherDerived>
EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived> &other)
: Base(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
{
Base::_check_template_params();
Base::_resize_to_match(other);
// FIXME/CHECK: isn't *this = other.derived() more efficient. it allows to
// go for pure _set() implementations, right?
*this = other;
}
/** \internal
* \brief Override MatrixBase::swap() since for dynamic-sized matrices
* of same type it is enough to swap the data pointers.
*/
template<typename OtherDerived>
void swap(MatrixBase<OtherDerived> const & other)
{ this->_swap(other.derived()); }
inline Index innerStride() const { return 1; }
inline Index outerStride() const { return this->innerSize(); }
/////////// Geometry module ///////////
template<typename OtherDerived>
explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
template<typename OtherDerived>
Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived>
explicit Matrix(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
template<typename OtherDerived>
Matrix& operator=(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
#endif
// 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
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