// 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 // // 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 . #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) * \li \c Vector4f is a vector of 4 floats (\c Matrix) * \li \c RowVector3i is a row-vector of 3 ints (\c Matrix) * * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix) * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix) * * 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 * * Some notes: * *
*
\anchor dense Dense versus sparse:
*
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.
* *
\anchor fixedsize Fixed-size versus dynamic-size:
*
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, do not expand dynamically in the sense of a std::map. * If you want this behavior, see the Sparse module.
* *
\anchor maxrows _MaxRows and _MaxCols:
*
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.
*
* * \see MatrixBase for the majority of the API methods for matrices */ template struct ei_traits > { 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::ReadCost }; }; template class Matrix : public MatrixBase > { public: EIGEN_GENERIC_PUBLIC_INTERFACE(Matrix) enum { Options = _Options }; friend class Eigen::Map; typedef class Eigen::Map UnalignedMapType; friend class Eigen::Map; typedef class Eigen::Map AlignedMapType; protected: ei_matrix_storage m_storage; public: enum { NeedsToAlign = (Options&AutoAlign) == AutoAlign && SizeAtCompileTime!=Dynamic && ((sizeof(Scalar)*SizeAtCompileTime)%16)==0 }; EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign) Base& base() { return *static_cast(this); } const Base& base() const { return *static_cast(this); } 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 EIGEN_STRONG_INLINE PacketScalar packet(int row, int col) const { return ei_ploadt (m_storage.data() + (Flags & RowMajorBit ? col + row * m_storage.cols() : row + col * m_storage.rows())); } template EIGEN_STRONG_INLINE PacketScalar packet(int index) const { return ei_ploadt(m_storage.data() + index); } template EIGEN_STRONG_INLINE void writePacket(int row, int col, const PacketScalar& x) { ei_pstoret (m_storage.data() + (Flags & RowMajorBit ? col + row * m_storage.cols() : row + col * m_storage.rows()), x); } template EIGEN_STRONG_INLINE void writePacket(int index, const PacketScalar& x) { ei_pstoret(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((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) { 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 EIGEN_STRONG_INLINE Matrix& operator=(const MatrixBase& 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 EIGEN_STRONG_INLINE Matrix(const MatrixBase& 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. */ template void swap(const MatrixBase& 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); } //@} using Base::setConstant; Matrix& setConstant(int size, const Scalar& value); Matrix& setConstant(int rows, int cols, const Scalar& value); using Base::setZero; Matrix& setZero(int size); Matrix& setZero(int rows, int cols); using Base::setOnes; Matrix& setOnes(int size); Matrix& setOnes(int rows, int cols); using Base::setRandom; Matrix& setRandom(int size); Matrix& setRandom(int rows, int cols); using Base::setIdentity; Matrix& setIdentity(int rows, int cols); /////////// Geometry module /////////// template explicit Matrix(const RotationBase& r); template Matrix& operator=(const RotationBase& 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 EIGEN_STRONG_INLINE void _resize_to_match(const MatrixBase& 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&), _set_noalias() */ template EIGEN_STRONG_INLINE Matrix& _set(const MatrixBase& other) { // this enum introduced to fix compilation with gcc 3.3 enum { cond = int(OtherDerived::Flags) & EvalBeforeAssigningBit }; _set_selector(other.derived(), typename ei_meta_if::ret()); return *this; } template EIGEN_STRONG_INLINE void _set_selector(const OtherDerived& other, const ei_meta_true&) { _set_noalias(other.eval()); } template EIGEN_STRONG_INLINE void _set_selector(const OtherDerived& other, const ei_meta_false&) { _set_noalias(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&), _set() */ template EIGEN_STRONG_INLINE Matrix& _set_noalias(const MatrixBase& 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::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) } template friend struct ei_matrix_swap_impl; }; template::ret, bool IsDynamicSize = MatrixType::SizeAtCompileTime==Dynamic> struct ei_matrix_swap_impl { static inline void run(MatrixType& matrix, MatrixBase& other) { matrix.base().swap(other); } }; template struct ei_matrix_swap_impl { static inline void run(MatrixType& matrix, MatrixBase& other) { matrix.m_storage.swap(other.derived().m_storage); } }; template template inline void Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::swap(const MatrixBase& other) { ei_matrix_swap_impl::run(*this, *const_cast*>(&other)); } /** \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 Matrix##SizeSuffix##TypeSuffix; \ /** \ingroup matrixtypedefs */ \ typedef Matrix Vector##SizeSuffix##TypeSuffix; \ /** \ingroup matrixtypedefs */ \ typedef Matrix 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, cf) EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex, 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