Matrix.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
00005 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
00006 //
00007 // This Source Code Form is subject to the terms of the Mozilla
00008 // Public License v. 2.0. If a copy of the MPL was not distributed
00009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00010 
00011 #ifndef EIGEN_MATRIX_H
00012 #define EIGEN_MATRIX_H
00013 
00014 namespace Eigen {
00015 
00016 /** \class Matrix
00017   * \ingroup Core_Module
00018   *
00019   * \brief The matrix class, also used for vectors and row-vectors
00020   *
00021   * The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen.
00022   * Vectors are matrices with one column, and row-vectors are matrices with one row.
00023   *
00024   * The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note").
00025   *
00026   * The first three template parameters are required:
00027   * \tparam _Scalar \anchor matrix_tparam_scalar Numeric type, e.g. float, double, int or std::complex<float>.
00028   *                 User defined sclar types are supported as well (see \ref user_defined_scalars "here").
00029   * \tparam _Rows Number of rows, or \b Dynamic
00030   * \tparam _Cols Number of columns, or \b Dynamic
00031   *
00032   * The remaining template parameters are optional -- in most cases you don't have to worry about them.
00033   * \tparam _Options \anchor matrix_tparam_options A combination of either \b #RowMajor or \b #ColMajor, and of either
00034   *                 \b #AutoAlign or \b #DontAlign.
00035   *                 The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required
00036   *                 for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.
00037   * \tparam _MaxRows Maximum number of rows. Defaults to \a _Rows (\ref maxrows "note").
00038   * \tparam _MaxCols Maximum number of columns. Defaults to \a _Cols (\ref maxrows "note").
00039   *
00040   * Eigen provides a number of typedefs covering the usual cases. Here are some examples:
00041   *
00042   * \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix<double, 2, 2>)
00043   * \li \c Vector4f is a vector of 4 floats (\c Matrix<float, 4, 1>)
00044   * \li \c RowVector3i is a row-vector of 3 ints (\c Matrix<int, 1, 3>)
00045   *
00046   * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
00047   * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
00048   *
00049   * \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>)
00050   * \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>)
00051   *
00052   * See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
00053   *
00054   * You can access elements of vectors and matrices using normal subscripting:
00055   *
00056   * \code
00057   * Eigen::VectorXd v(10);
00058   * v[0] = 0.1;
00059   * v[1] = 0.2;
00060   * v(0) = 0.3;
00061   * v(1) = 0.4;
00062   *
00063   * Eigen::MatrixXi m(10, 10);
00064   * m(0, 1) = 1;
00065   * m(0, 2) = 2;
00066   * m(0, 3) = 3;
00067   * \endcode
00068   *
00069   * This class can be extended with the help of the plugin mechanism described on the page
00070   * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_MATRIX_PLUGIN.
00071   *
00072   * <i><b>Some notes:</b></i>
00073   *
00074   * <dl>
00075   * <dt><b>\anchor dense Dense versus sparse:</b></dt>
00076   * <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module.
00077   *
00078   * Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array.
00079   * This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.</dd>
00080   *
00081   * <dt><b>\anchor fixedsize Fixed-size versus dynamic-size:</b></dt>
00082   * <dd>Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array
00083   * of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up
00084   * to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time.
00085   *
00086   * Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime
00087   * variables, and the array of coefficients is allocated dynamically on the heap.
00088   *
00089   * 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.
00090   * If you want this behavior, see the Sparse module.</dd>
00091   *
00092   * <dt><b>\anchor maxrows _MaxRows and _MaxCols:</b></dt>
00093   * <dd>In most cases, one just leaves these parameters to the default values.
00094   * These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases
00095   * when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot
00096   * exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case _MaxRows and _MaxCols
00097   * are the dimensions of the original matrix, while _Rows and _Cols are Dynamic.</dd>
00098   * </dl>
00099   *
00100   * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy, 
00101   * \ref TopicStorageOrders 
00102   */
00103 
00104 namespace internal {
00105 template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
00106 struct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
00107 {
00108   typedef _Scalar Scalar;
00109   typedef Dense StorageKind;
00110   typedef DenseIndex Index;
00111   typedef MatrixXpr XprKind;
00112   enum {
00113     RowsAtCompileTime = _Rows,
00114     ColsAtCompileTime = _Cols,
00115     MaxRowsAtCompileTime = _MaxRows,
00116     MaxColsAtCompileTime = _MaxCols,
00117     Flags = compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
00118     CoeffReadCost = NumTraits<Scalar>::ReadCost,
00119     Options = _Options,
00120     InnerStrideAtCompileTime = 1,
00121     OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime
00122   };
00123 };
00124 }
00125 
00126 template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
00127 class Matrix
00128   : public PlainObjectBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
00129 {
00130   public:
00131 
00132     /** \brief Base class typedef.
00133       * \sa PlainObjectBase
00134       */
00135     typedef PlainObjectBase<Matrix> Base;
00136 
00137     enum { Options = _Options };
00138 
00139     EIGEN_DENSE_PUBLIC_INTERFACE(Matrix)
00140 
00141     typedef typename Base::PlainObject PlainObject;
00142 
00143     using Base::base;
00144     using Base::coeffRef;
00145 
00146     /**
00147       * \brief Assigns matrices to each other.
00148       *
00149       * \note This is a special case of the templated operator=. Its purpose is
00150       * to prevent a default operator= from hiding the templated operator=.
00151       *
00152       * \callgraph
00153       */
00154     EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other)
00155     {
00156       return Base::_set(other);
00157     }
00158 
00159     /** \internal
00160       * \brief Copies the value of the expression \a other into \c *this with automatic resizing.
00161       *
00162       * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
00163       * it will be initialized.
00164       *
00165       * Note that copying a row-vector into a vector (and conversely) is allowed.
00166       * The resizing, if any, is then done in the appropriate way so that row-vectors
00167       * remain row-vectors and vectors remain vectors.
00168       */
00169     template<typename OtherDerived>
00170     EIGEN_STRONG_INLINE Matrix& operator=(const MatrixBase<OtherDerived>& other)
00171     {
00172       return Base::_set(other);
00173     }
00174 
00175     /* Here, doxygen failed to copy the brief information when using \copydoc */
00176 
00177     /**
00178       * \brief Copies the generic expression \a other into *this.
00179       * \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)
00180       */
00181     template<typename OtherDerived>
00182     EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived> &other)
00183     {
00184       return Base::operator=(other);
00185     }
00186 
00187     template<typename OtherDerived>
00188     EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived>& func)
00189     {
00190       return Base::operator=(func);
00191     }
00192 
00193     /** \brief Default constructor.
00194       *
00195       * For fixed-size matrices, does nothing.
00196       *
00197       * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
00198       * is called a null matrix. This constructor is the unique way to create null matrices: resizing
00199       * a matrix to 0 is not supported.
00200       *
00201       * \sa resize(Index,Index)
00202       */
00203     EIGEN_STRONG_INLINE Matrix() : Base()
00204     {
00205       Base::_check_template_params();
00206       EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
00207     }
00208 
00209     // FIXME is it still needed
00210     Matrix(internal::constructor_without_unaligned_array_assert)
00211       : Base(internal::constructor_without_unaligned_array_assert())
00212     { Base::_check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
00213 
00214 #ifdef EIGEN_HAVE_RVALUE_REFERENCES
00215     Matrix(Matrix&& other)
00216       : Base(std::move(other))
00217     {
00218       Base::_check_template_params();
00219       if (RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic)
00220         Base::_set_noalias(other);
00221     }
00222     Matrix& operator=(Matrix&& other)
00223     {
00224       other.swap(*this);
00225       return *this;
00226     }
00227 #endif
00228 
00229     /** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors
00230       *
00231       * Note that this is only useful for dynamic-size vectors. For fixed-size vectors,
00232       * it is redundant to pass the dimension here, so it makes more sense to use the default
00233       * constructor Matrix() instead.
00234       */
00235     EIGEN_STRONG_INLINE explicit Matrix(Index dim)
00236       : Base(dim, RowsAtCompileTime == 1 ? 1 : dim, ColsAtCompileTime == 1 ? 1 : dim)
00237     {
00238       Base::_check_template_params();
00239       EIGEN_STATIC_ASSERT_VECTOR_ONLY(Matrix)
00240       eigen_assert(dim >= 0);
00241       eigen_assert(SizeAtCompileTime == Dynamic || SizeAtCompileTime == dim);
00242       EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
00243     }
00244 
00245     #ifndef EIGEN_PARSED_BY_DOXYGEN
00246     template<typename T0, typename T1>
00247     EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y)
00248     {
00249       Base::_check_template_params();
00250       Base::template _init2<T0,T1>(x, y);
00251     }
00252     #else
00253     /** \brief Constructs an uninitialized matrix with \a rows rows and \a cols columns.
00254       *
00255       * This is useful for dynamic-size matrices. For fixed-size matrices,
00256       * it is redundant to pass these parameters, so one should use the default constructor
00257       * Matrix() instead. */
00258     Matrix(Index rows, Index cols);
00259     /** \brief Constructs an initialized 2D vector with given coefficients */
00260     Matrix(const Scalar& x, const Scalar& y);
00261     #endif
00262 
00263     /** \brief Constructs an initialized 3D vector with given coefficients */
00264     EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z)
00265     {
00266       Base::_check_template_params();
00267       EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3)
00268       m_storage.data()[0] = x;
00269       m_storage.data()[1] = y;
00270       m_storage.data()[2] = z;
00271     }
00272     /** \brief Constructs an initialized 4D vector with given coefficients */
00273     EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
00274     {
00275       Base::_check_template_params();
00276       EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4)
00277       m_storage.data()[0] = x;
00278       m_storage.data()[1] = y;
00279       m_storage.data()[2] = z;
00280       m_storage.data()[3] = w;
00281     }
00282 
00283     explicit Matrix(const Scalar *data);
00284 
00285     /** \brief Constructor copying the value of the expression \a other */
00286     template<typename OtherDerived>
00287     EIGEN_STRONG_INLINE Matrix(const MatrixBase<OtherDerived>& other)
00288              : Base(other.rows() * other.cols(), other.rows(), other.cols())
00289     {
00290       // This test resides here, to bring the error messages closer to the user. Normally, these checks
00291       // are performed deeply within the library, thus causing long and scary error traces.
00292       EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
00293         YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
00294 
00295       Base::_check_template_params();
00296       Base::_set_noalias(other);
00297     }
00298     /** \brief Copy constructor */
00299     EIGEN_STRONG_INLINE Matrix(const Matrix& other)
00300             : Base(other.rows() * other.cols(), other.rows(), other.cols())
00301     {
00302       Base::_check_template_params();
00303       Base::_set_noalias(other);
00304     }
00305     /** \brief Copy constructor with in-place evaluation */
00306     template<typename OtherDerived>
00307     EIGEN_STRONG_INLINE Matrix(const ReturnByValue<OtherDerived>& other)
00308     {
00309       Base::_check_template_params();
00310       Base::resize(other.rows(), other.cols());
00311       other.evalTo(*this);
00312     }
00313 
00314     /** \brief Copy constructor for generic expressions.
00315       * \sa MatrixBase::operator=(const EigenBase<OtherDerived>&)
00316       */
00317     template<typename OtherDerived>
00318     EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived> &other)
00319       : Base(other.derived().rows() * other.derived().cols(), other.derived().rows(), other.derived().cols())
00320     {
00321       Base::_check_template_params();
00322       Base::_resize_to_match(other);
00323       // FIXME/CHECK: isn't *this = other.derived() more efficient. it allows to
00324       //              go for pure _set() implementations, right?
00325       *this = other;
00326     }
00327 
00328     /** \internal
00329       * \brief Override MatrixBase::swap() since for dynamic-sized matrices
00330       * of same type it is enough to swap the data pointers.
00331       */
00332     template<typename OtherDerived>
00333     void swap(MatrixBase<OtherDerived> const & other)
00334     { this->_swap(other.derived()); }
00335 
00336     inline Index innerStride() const { return 1; }
00337     inline Index outerStride() const { return this->innerSize(); }
00338 
00339     /////////// Geometry module ///////////
00340 
00341     template<typename OtherDerived>
00342     explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
00343     template<typename OtherDerived>
00344     Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
00345 
00346     #ifdef EIGEN2_SUPPORT
00347     template<typename OtherDerived>
00348     explicit Matrix(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
00349     template<typename OtherDerived>
00350     Matrix& operator=(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
00351     #endif
00352 
00353     // allow to extend Matrix outside Eigen
00354     #ifdef EIGEN_MATRIX_PLUGIN
00355     #include EIGEN_MATRIX_PLUGIN
00356     #endif
00357 
00358   protected:
00359     template <typename Derived, typename OtherDerived, bool IsVector>
00360     friend struct internal::conservative_resize_like_impl;
00361 
00362     using Base::m_storage;
00363 };
00364 
00365 /** \defgroup matrixtypedefs Global matrix typedefs
00366   *
00367   * \ingroup Core_Module
00368   *
00369   * Eigen defines several typedef shortcuts for most common matrix and vector types.
00370   *
00371   * The general patterns are the following:
00372   *
00373   * \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
00374   * 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
00375   * for complex double.
00376   *
00377   * For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of floats.
00378   *
00379   * There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is
00380   * a fixed-size vector of 4 complex floats.
00381   *
00382   * \sa class Matrix
00383   */
00384 
00385 #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)   \
00386 /** \ingroup matrixtypedefs */                                    \
00387 typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix;  \
00388 /** \ingroup matrixtypedefs */                                    \
00389 typedef Matrix<Type, Size, 1>    Vector##SizeSuffix##TypeSuffix;  \
00390 /** \ingroup matrixtypedefs */                                    \
00391 typedef Matrix<Type, 1, Size>    RowVector##SizeSuffix##TypeSuffix;
00392 
00393 #define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size)         \
00394 /** \ingroup matrixtypedefs */                                    \
00395 typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix;  \
00396 /** \ingroup matrixtypedefs */                                    \
00397 typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;
00398 
00399 #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
00400 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
00401 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
00402 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
00403 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
00404 EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
00405 EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
00406 EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
00407 
00408 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int,                  i)
00409 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float,                f)
00410 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double,               d)
00411 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>,  cf)
00412 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
00413 
00414 #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
00415 #undef EIGEN_MAKE_TYPEDEFS
00416 #undef EIGEN_MAKE_FIXED_TYPEDEFS
00417 
00418 } // end namespace Eigen
00419 
00420 #endif // EIGEN_MATRIX_H