Eigen入门之密集矩阵 3 - Array操作

简介

在Eigen内，有Matrix，vector进行线性代数的相关运算，但也需要执行对矩阵内的系数的相关操作时，这是正常的功能需求。Eigen中的Array类就是满足此需求的。

Array 定义

和前面介绍的Matrix和Vector类似，Array类也是一个模板类

/** \class Array
  * \ingroup Core_Module
  *
  * \brief General-purpose arrays with easy API for coefficient-wise operations
  *
  * The %Array class is very similar to the Matrix class. It provides
  * general-purpose one- and two-dimensional arrays. The difference between the
  * %Array and the %Matrix class is primarily in the API: the API for the
  * %Array class provides easy access to coefficient-wise operations, while the
  * API for the %Matrix class provides easy access to linear-algebra
  * operations.
  *
  * See documentation of class Matrix for detailed information on the template parameters
  * storage layout.
  *
  * 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_ARRAY_PLUGIN.
  *
  * \sa \blank \ref TutorialArrayClass, \ref TopicClassHierarchy
  */
template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
class Array
  : public PlainObjectBase<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >

同样，Eigen也使用macro为Array定义了一些快捷简单Array类型。如下：

/** \defgroup arraytypedefs Global array typedefs
  * \ingroup Core_Module
  *
  * Eigen defines several typedef shortcuts for most common 1D and 2D array types.
  *
  * The general patterns are the following:
  *
  * \c ArrayRowsColsType where \c Rows and \c Cols 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 Array33d is a fixed-size 3x3 array type of doubles, and \c ArrayXXf is a dynamic-size matrix of floats.
  *
  * There are also \c ArraySizeType which are self-explanatory. For example, \c Array4cf is
  * a fixed-size 1D array of 4 complex floats.
  *
  * \sa class Array
  */

#define EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)   \
/** \ingroup arraytypedefs */                                    \
typedef Array<Type, Size, Size> Array##SizeSuffix##SizeSuffix##TypeSuffix;  \
/** \ingroup arraytypedefs */                                    \
typedef Array<Type, Size, 1>    Array##SizeSuffix##TypeSuffix;

#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, Size)         \
/** \ingroup arraytypedefs */                                    \
typedef Array<Type, Size, Dynamic> Array##Size##X##TypeSuffix;  \
/** \ingroup arraytypedefs */                                    \
typedef Array<Type, Dynamic, Size> Array##X##Size##TypeSuffix;

#define EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 2, 2) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 3, 3) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 4, 4) \
EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 4)

EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(int,                  i)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(float,                f)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(double,               d)
EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES