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      1 namespace Eigen {
      2 
      3 /** \page TopicClassHierarchy The class hierarchy
      4 
      5 This page explains the design of the core classes in Eigen's class hierarchy and how they fit together. Casual
      6 users probably need not concern themselves with these details, but it may be useful for both advanced users
      7 and Eigen developers.
      8 
      9 \eigenAutoToc
     10 
     11 
     12 \section TopicClassHierarchyPrinciples Principles
     13 
     14 Eigen's class hierarchy is designed so that virtual functions are avoided where their overhead would
     15 significantly impair performance. Instead, Eigen achieves polymorphism with the Curiously Recurring Template
     16 Pattern (CRTP). In this pattern, the base class (for instance, \c MatrixBase) is in fact a template class, and
     17 the derived class (for instance, \c Matrix) inherits the base class with the derived class itself as a
     18 template argument (in this case, \c Matrix inherits from \c MatrixBase<Matrix>). This allows Eigen to
     19 resolve the polymorphic function calls at compile time.
     20 
     21 In addition, the design avoids multiple inheritance. One reason for this is that in our experience, some
     22 compilers (like MSVC) fail to perform empty base class optimization, which is crucial for our fixed-size
     23 types.
     24 
     25 
     26 \section TopicClassHierarchyCoreClasses The core classes
     27 
     28 These are the classes that you need to know about if you want to write functions that accept or return Eigen
     29 objects.
     30 
     31   - Matrix means plain dense matrix. If \c m is a \c %Matrix, then, for instance, \c m+m is no longer a 
     32     \c %Matrix, it is a "matrix expression".
     33   - MatrixBase means dense matrix expression. This means that a \c %MatrixBase is something that can be
     34     added, matrix-multiplied, LU-decomposed, QR-decomposed... All matrix expression classes, including 
     35     \c %Matrix itself, inherit \c %MatrixBase.
     36   - Array means plain dense array. If \c x is an \c %Array, then, for instance, \c x+x is no longer an 
     37     \c %Array, it is an "array expression".
     38   - ArrayBase means dense array expression. This means that an \c %ArrayBase is something that can be
     39     added, array-multiplied, and on which you can perform all sorts of array operations... All array
     40     expression classes, including \c %Array itself, inherit \c %ArrayBase.
     41   - DenseBase means dense (matrix or array) expression. Both \c %ArrayBase and \c %MatrixBase inherit
     42     \c %DenseBase. \c %DenseBase is where all the methods go that apply to dense expressions regardless of
     43     whether they are matrix or array expressions. For example, the \link DenseBase::block() block(...) \endlink
     44     methods are in \c %DenseBase.
     45 
     46 \section TopicClassHierarchyBaseClasses Base classes
     47 
     48 These classes serve as base classes for the five core classes mentioned above. They are more internal and so
     49 less interesting for users of the Eigen library.
     50 
     51   - PlainObjectBase means dense (matrix or array) plain object, i.e. something that stores its own dense
     52     array of coefficients. This is where, for instance, the \link PlainObjectBase::resize() resize() \endlink
     53     methods go. \c %PlainObjectBase is inherited by \c %Matrix and by \c %Array. But above, we said that 
     54     \c %Matrix inherits \c %MatrixBase and \c %Array inherits \c %ArrayBase. So does that mean multiple
     55     inheritance? No, because \c %PlainObjectBase \e itself inherits \c %MatrixBase or \c %ArrayBase depending
     56     on whether we are in the matrix or array case. When we said above that \c %Matrix inherited 
     57     \c %MatrixBase, we omitted to say it does so indirectly via \c %PlainObjectBase. Same for \c %Array.
     58   - DenseCoeffsBase means something that has dense coefficient accessors. It is a base class for
     59     \c %DenseBase. The reason for \c %DenseCoeffsBase to exist is that the set of available coefficient
     60     accessors is very different depending on whether a dense expression has direct memory access or not (the
     61     \c DirectAccessBit flag). For example, if \c x is a plain matrix, then \c x has direct access, and 
     62     \c x.transpose() and \c x.block(...) also have direct access, because their coefficients can be read right
     63     off memory, but for example, \c x+x does not have direct memory access, because obtaining any of its
     64     coefficients requires a computation (an addition), it can't be just read off memory.
     65   - EigenBase means anything that can be evaluated into a plain dense matrix or array (even if that would
     66     be a bad idea). \c %EigenBase is really the absolute base class for anything that remotely looks like a
     67     matrix or array. It is a base class for \c %DenseCoeffsBase, so it sits below all our dense class
     68     hierarchy, but it is not limited to dense expressions. For example, \c %EigenBase is also inherited by
     69     diagonal matrices, sparse matrices, etc...
     70 
     71 
     72 \section TopicClassHierarchyInheritanceDiagrams Inheritance diagrams
     73 
     74 The inheritance diagram for Matrix looks as follows:
     75 
     76 <pre>
     77 EigenBase&lt;%Matrix&gt;
     78   <-- DenseCoeffsBase&lt;%Matrix&gt;    (direct access case)
     79     <-- DenseBase&lt;%Matrix&gt;
     80       <-- MatrixBase&lt;%Matrix&gt;
     81         <-- PlainObjectBase&lt;%Matrix&gt;    (matrix case)
     82           <-- Matrix
     83 </pre>
     84 
     85 The inheritance diagram for Array looks as follows:
     86 
     87 <pre>
     88 EigenBase&lt;%Array&gt;
     89   <-- DenseCoeffsBase&lt;%Array&gt;    (direct access case)
     90     <-- DenseBase&lt;%Array&gt;
     91       <-- ArrayBase&lt;%Array&gt;
     92         <-- PlainObjectBase&lt;%Array&gt;    (array case)
     93           <-- Array
     94 </pre>
     95 
     96 The inheritance diagram for some other matrix expression class, here denoted by \c SomeMatrixXpr, looks as
     97 follows:
     98 
     99 <pre>
    100 EigenBase&lt;SomeMatrixXpr&gt;
    101   <-- DenseCoeffsBase&lt;SomeMatrixXpr&gt;    (direct access or no direct access case)
    102     <-- DenseBase&lt;SomeMatrixXpr&gt;
    103       <-- MatrixBase&lt;SomeMatrixXpr&gt;
    104         <-- SomeMatrixXpr
    105 </pre>
    106 
    107 The inheritance diagram for some other array expression class, here denoted by \c SomeArrayXpr, looks as
    108 follows:
    109 
    110 <pre>
    111 EigenBase&lt;SomeArrayXpr&gt;
    112   <-- DenseCoeffsBase&lt;SomeArrayXpr&gt;    (direct access or no direct access case)
    113     <-- DenseBase&lt;SomeArrayXpr&gt;
    114       <-- ArrayBase&lt;SomeArrayXpr&gt;
    115         <-- SomeArrayXpr
    116 </pre>
    117 
    118 Finally, consider an example of something that is not a dense expression, for instance a diagonal matrix. The
    119 corresponding inheritance diagram is:
    120 
    121 <pre>
    122 EigenBase&lt;%DiagonalMatrix&gt;
    123   <-- DiagonalBase&lt;%DiagonalMatrix&gt;
    124     <-- DiagonalMatrix
    125 </pre>
    126 
    127 
    128 */
    129 }
    130