README

/*! \file libaff/README
 * \brief C++ containers for numbers (libaff)
 *
 * ----------------------------------------------------------------------------
 *
 * $Id$
 * 
 * Copyright (c) 2002 by Thomas Forbriger (IMG Frankfurt) 
 * 
 * C++ containers for numbers (libaff)
 *
 * This file contains:
 *  - documentation of namespace aff
 *  - mainpage text
 *  - documentation for pages:
 *    - \ref page_design
 *    - \ref page_using
 *    - \ref page_notes
 *    - \ref page_naming
 * 
 * REVISIONS and CHANGES 
 *  - 06/12/2002   V1.0   Thomas Forbriger (copied from libcontxx)
 *  - 20/12/2002   V1.1   (thof)
 *                        - complete revision of this file
 *                        - there are major gaps in
 *                          -# \ref sec_design_multidimensional
 *                          -# \ref page_using
 *  - 28/12/2002   V1.2   (thof)
 *                        - new term for containers of const elements
 *                        - added documentation regarding the concept of 
 *                          const correctness
 *                        - added documentation regarding member typedefs
 *  - 29/12/2002   V1.3   (thof)
 *                        - added section about replicated shared heap base
 *                          class (\ref sec_design_replicated)
 *                        - added section about sparse interface
 *                          (\ref sec_design_interface_sparse)
 *                        - added section about accessing internals
 *                          (\ref sec_design_interface_internals)
 *                        - reflect changes to Subarray and Slice
 *                        - tell about class hierarchies and member data vs.
 *                          inheritance
 *  - 04/01/2003   V1.4   (thof)
 *                        - added section about Tcontainer typedef 
 *                          (\ref sec_design_interface_tcontainer)
 *  - 10/02/2004   V1.5   (thof)
 *                        - added section about decision against interface
 *                          base classes
 *                          (\ref sec_design_interface_nobaseclass)
 *  - 10/11/2010   V1.6   (thof)
 *                        - code fragments for precompiled templates are
 *                          removed from the library (\ref sec_design_binary)
 *  - 14/05/2011   V1.7   (thof)
 *                        - add info on raw-major and column-major order
 *  - 15/05/2011   V1.8   (thof)
 *                        - reordered documentation, movde modules to
 *                          README.groups
 * 
 * ============================================================================
 */

/*! \brief Root namespace of library
  
  This namespace contains all modules of the library
  (see \ref sec_main_modules). 
  Here you should find all components, the user needs to work with this
  library.
 */
namespace aff {
} // namespace aff

/*======================================================================*/

/*! \mainpage

\author Thomas Forbriger
\author Wolfgang Friederich
\since December 2002
\date December 2002
\version V1.0
$Id$

  Contents of this page:
  - \ref sec_main_aims
  - \ref sec_main_need
  - \ref sec_main_peculiar
  - \ref sec_main_modules

  Additional information:
  - \ref page_changelog
  - \ref page_project_status
  - \ref page_using
  - \ref page_array_layout
  - \ref page_design
  - \ref page_naming
  - \ref page_representation
  - \ref page_fortran

\section sec_main_aims Aims of the library
  
  The AFF (Array of Friederich and Forbriger) is a lightweight class library.
  It offers a simple and easy to use container for numbers as is necessary in
  numerical code. The offered array always has a rectangular strided layout,
  reference semantics (through counted references) and a Fortran layout in
  memory. The interface is intentionally kept sparse to keep compilation times
  small. The array itself is meant to be used to pass numbers from one program
  module to the other. If you want to exploit the power of expression
  templates, pass the array contents to something like Blitz++.


  Contents of this page:

\section sec_main_peculiar Peculiarities of AFF

\par Containers use counted references
All containers (e.g. aff::Array, aff::Series) use counted references to access
global memory. Assigning one container object to another just assigns the
reference. Both will use the same data in memory afterwards. 
\sa \ref page_representation.

\par Const-correctness for array elements
In this library we follow provide functionality to write const-correct code
with regard to the array container and with regard to its element values.
\sa \ref sec_design_const.

\par Multidimensional arrays
Every aff::Array of this class has aff::Strided::Mmax_dimen dimensions.
Construction and access for lower dimensionality is provided. In the case of
using less dimensions, the size of the unused dimensions is 1 by default and
its index is inherently set to the first index.
\sa \ref sec_design_multidimensional.

\section sec_main_need Why do we need this array library
  
  One major reason for replacing Fortran77 by C++ in numerical code is the
  convenience in expressing logistics. Data of different type and size may be
  packed into classes and encapsulated from the outside world. Most numerical
  results are to be stored in arrays, multi-dimensional arrays in particular.
  This library provides the basic functionality for storing many data of the
  same type in memory, passing them around between subroutines in an efficient
  way and accessing them through convenient interfaces. The main purpose of
  this library is not calculation but managing (passing between program
  modules, selection of subsets of the data) large amounts of numbers. In the
  future it might provide interfaces to libraries like blitz++ for finite
  difference calculations, MTL for linear algebra calculations, and POOMA for
  parallel computations.

  \sa http://www.sophya.org/, http://www.boost.org

\section sec_main_modules Modules of the library

  The main module is the array class aff::Array. It provides basic
  functionality through its interface. See the explanation there.
  It is presented in aff/array.h
  The object code is placed in libaff.a.

  \sa \ref group_array, \ref group_array_extensions
*/

/*======================================================================*/

/*! \page page_design Design decisions

  Contents of this page:
  - \ref sec_design_interface
    - \ref sec_design_interface_sparse
    - \ref sec_design_interface_typedef
    - \ref sec_design_interface_tcontainer
    - \ref sec_design_interface_internals
    - \ref sec_design_interface_nobaseclass
  - \ref sec_design_hierarchy
  - \ref sec_design_replicated
    - \ref sec_design_replicated_fact
    - \ref sec_design_replicated_problem
    - \ref sec_design_replicated_solution
  - \ref sec_design_copy
  - \ref sec_design_namespaces
  - \ref sec_design_binary
  - \ref sec_design_multidimensional
  - \ref sec_design_const
    - \ref sec_design_const_problem
    - \ref sec_design_const_approach
    - \ref sec_design_const_alternatives
    - \ref sec_design_const_general

\section sec_design_interface Common interface concepts

\subsection sec_design_interface_sparse Sparse interfaces

  The class library is intended to be a  light-weight library. This means it
  should offer basic functionality in terms of multidimensional containers
  with counted references (and not more in first place). We do not like to
  include a tremendous amount of code for specialized concepts (like subranges
  or expression templates in Blitz++) each time we just need a small array.
  Thus the header files providing array declarations (aff/array.h and the
  files included therein) should be as sparse as possible. All extra
  functionality like iterators (aff::Iterator presented in aff/iterator.h) or
  slices (aff::Slice presented in aff/slice.h) should be external to the
  aff::Array class. This allows us to load their definitions only where
  needed. However, this approach requires that the internals of aff::Array are
  exposed to the outside through appropriate functions (see 
  \ref sec_design_interface_internals).

\subsection sec_design_interface_typedef Member typedefs

  Class templates like aff::Iterator may be used with any container class,
  that provides an appropriate interface. This interface convention concerns
  the access to the type of related objects. I will explain by example:

  We use an iterator \c i which was declared
  \code aff::Iterator<Cont> i \endcode
  for a container of type \c Cont, it expects to find a corresponding
  container class that promises constness of the elements through 
  \code Cont::Tcontainer_of_const \endcode
  or short
  \code Cont::Tcoc \endcode

  For aff::ConstArray the type aff::ConstArray::Tcoc is just the class itself.
  However aff::Array::Tcoc gives an aff::ConstArray.

  \sa aff::SharedHeap::Tcontainer_of_const
  \sa aff::ConstSharedHeap::Tcontainer_of_const
  \sa aff::Array::Tcontainer_of_const
  \sa aff::ConstArray::Tcontainer_of_const
  \sa aff::Series::Tcontainer_of_const
  \sa aff::ConstSeries::Tcontainer_of_const

  In the same way we may access the appropriate element type through
  \code Cont::Tvalue \endcode
  which is \c T for aff::Array<T> and \c const \T for aff::ConstArray<T>.
  However a 
  \code Cont::Tconst_value \endcode
  will always provide a type with const qualifier.

  \sa aff::Array::Tvalue
  \sa aff::Array::Tconst_value
  \sa aff::ConstArray::Tvalue
  \sa aff::ConstArray::Tconst_value
  \sa aff::Series::Tvalue
  \sa aff::Series::Tconst_value
  \sa aff::ConstSeries::Tvalue
  \sa aff::ConstSeries::Tconst_value

  In the same way we may access the type of the appropriate representation
  by \code Cont::Trepresentation \endcode

  \sa aff::Array::Trepresentation
  \sa aff::ConstArray::Trepresentation
  \sa aff::Series::Trepresentation
  \sa aff::ConstSeries::Trepresentation

  \b Notice: Using these typedefs (and also the typedefs for the shape class,
  etc.) improves the maintainability of your code. Think of using the $HOME
  variable in shell scripts. Once the name of your home directory changes, you
  need not modify all your shell scripts. Now consider one day your shape
  class might be renamed...

\subsection sec_design_interface_tcontainer Member typedef Tcontainer

  \par Design decision:
  Every class that can be converted to a container type, should provide a
  member typedef \c Tcontainer and an appropriate conversion operator.

  \sa aff::util::Slice
  \sa aff::util::Subarray
  \sa aff::deepcopy

  \par Background
  aff::deepcopy is a good example for function designed to deal with any
  container. There may be others in the future, like global arithmetic
  operators or sum-reduction. Due to its generality the function template puts
  no restrictions on its template arguments. You may instantiate that template
  for any class. In some sense this is bad practice and we have to resolve
  ambiguities and support type conversions. In particular, think of feeding a
  subarray (class aff::util::Subarray) to one of these whole-array functions
  (this might be one of the most interesting uses). aff::util::Subarray easily
  matches the template parameter, but does not offer the member functions
  necessary for element access.

  \par 
  Hence we must ensure conversion of the aff::util::Subarray to its container
  class. In our concept this is done with in aff::deepcopy. It looks for a
  Tcontainer typedef in the argument class definitions and converts the class
  objects to its corresponding container class before the copy operation.

  \par
  Barton and Nackman propose another concept. Using their scheme we would
  introduce a general Container class,
  \code
  template<class C>
  class Container {
    public:
      typedef C& Tcontainer_reference;
      Container(Tcontainer_reference c): M(c) { }
      operator Tcontainer_reference() { return(M); }
    private:
      Tcontainer_reference M;
  };
  \endcode
  that takes a special container class as
  a template argument and initializes a member data reference to an object of
  this class in its constructors. We would then derive aff::Array from this
  class by
  \code
  template<class T>
  class Array: public Container<Array <T> > { };
  \endcode
  This way any reference to a container (aff::Array, aff:Series,
  aff::ConstArray, etc.) can be converted to a Container class object, which
  agein offers a conversion operator to a reference to its leaf class.
  Container-specific functions then are declared
  \code
  template<class S, class T>
  void deecopy(const Container<S>& source, Container<T>& target);
  \endcode
  deepcopy than can only be called for objects that are derived from
  Container.

  \par Trade-offs
  The Barton and Nackman trick involves another member data field in each
  container class to hold the reference in the Container base class.
  aff::Array would have to extra member data fields, because aff::Array and
  aff::ConstArray both must inherit from Container. I regard this as a partial
  violation to our concept of sparse interfaces. and small data types and
  discard this option.

  \par
  However, our concept requires to create a full copy of at least the target
  container in each whole-array operation. This would not be necessary
  generally. Generally we would operate directly on the aff::Array reference
  passed as target of the operation.

  \par
  With the Barton and Nackman trick this copy operation would only be
  necessary with class objects, that are not directly derived from Container,
  as are aff::util::Subarray and companions. However, for those we would have
  to introduce specializations (overloaded functions) of whole-array
  operations, that first perform the conversion (creating an aff::Array or
  else) and then call the function that takes Container arguments.

  \par Alternative
  The cheapest alternative (with respect to runtime overhead in the
  whole-array function and in the container classes aff::Array, etc.) is to
  delegate the problem to aff::util::Subarray and companions. We could
  introduce a member data field in them of type Tarray. This would allow for a
  member function returning a reference to this member. There should be no
  runtime overhead, since every subarray must once be converted to an array to
  be useful (now this conversion takes place outside aff::util::Subarray).
  But this would involve the inconvenience to call an extra member function in
  Subarray, when passing to a whole-array function.
  The template argument type of the corresponding whole-array function remains
  unrestricted (totally unchecked).

\subsection sec_design_interface_internals Accessing internals

  Providing extended functionality outside of aff::Array (see 
  \ref sec_design_interface_sparse) requires, that aff::Array,
  aff::ConstArray, aff::Series, and aff::ConstSeries expose some of their
  internals. This concerns the underlying shape as well as the represented
  data.

  aff::ConstArray and aff::ConstSeries provide a read-only reference to the
  data (i.e. an aff::ConstSharedHeap object) through their member-functions
  aff::ConstArray::representation and
  aff::ConstSeries::representation, respectively.
  In the same way aff::Array and aff::Series return an aff::SharedHeap through
  their representation member function.

  All of them return a copy of their shape through the member functions
  aff::Array::shape, aff::ConstArray::shape, aff::Series::shape, and
  aff::ConstSeries::shape, respectively. The type of the appropriate shape is
  available through a member typedef (see \ref sec_design_interface_typedef).

  In return all containers provide a constructor that takes a representation
  and a shape object and checks for their consistency.

\subsection sec_design_interface_nobaseclass Decision against a base class to express common interface

  This library contains different classes that provide common interfaces. For
  example all aff::ConstArray, aff::Array, aff::Series and aff::ConstSeries
  provide the necessary interface to be used together with aff::Iterator or
  aff::Browser. A rather elegant way to express this commonality in a template
  context is the Barton and Nackman trick. All containers that can work
  together with aff::Iterater sould have to inherit from a class
  aff::Iteratable. The base class is templated, takes the iteratable class as
  template parameter and stores a reference to the instance of the iteratable
  class. This way each iteratable class can be converted to aff::Iteratable,
  which again returns a reference to the classes iteratable features in the
  appropriate context.

  This way of expressing common interfaces makes the whole classes more
  complicated than necessary to provide their elementary functionality. We
  have to store an extra reference to the leaf class object for each feature,
  we will express this way. And we have to include a whole bunsch of extra
  code for each feature. Since we prefer \ref sec_design_interface_sparse this
  method was rejected.

<HR>
\section sec_design_hierarchy Class hierarchy: member data vs. inheritance

  Containers like aff::Array rely on functionality provided by other classes.
  They are based on shapes like aff::Strided and memory representations like
  aff::SharedHeap (see \ref page_representation).

  \par An array isn't a shape. 
    Thus it would look like better design to use shapes as member data.
    We prefer, \b however, to derive privately from the shape classes. 
    This hides them from the outside (apart from explicit access - 
    see \ref sec_design_interface_internals).
    At the same time we make use of using declarations to provide access to
    member functions like aff::Strided::size() that make also sense as a member
    of aff::Array.

  \par An array is some kind of memory representation.
    Thus it would look like proper design to derive an array from a
    representation class.
    We prefer, \b however, to use the memory representation as a private
    member. 
    We think of the representation as an individual and independent object
    that can be passed (e.g.) from an aff::Array to and aff::Series.
    Also due to the replication of the representation in aff::Array 
    (see \ref sec_design_replicated) and the distinction between containers
    that allow data modification and containers that allow only read access
    this leads to a clearer design.
    This is reflected by the conciseness of the array constructors.
    Use the representation class as member data should introduce no runtime
    overhead. 
    The full class specification including member data is available at
    compile-time. 
    This should enable compilers to do excessive inlining.

<HR>
\section sec_design_replicated Replicated ConstSharedHeap 

\subsection sec_design_replicated_fact Design decision
  aff::Array has a member of type aff::SharedHeap (which is exposed to the
  outside through aff::Array::representation), which itself inherits from
  aff::ConstSharedHeap. 
  At the same time aff::ConstArray has a member of type aff::Array and
  inherits itself from aff::ConstSharedHeap (which is exposed to the outside
  through aff::ConstArray::representation).
  Thus the class aff::ConstSharedHeap is replicated in aff::Array and it
  is not replicated by deriving from virtual base classes a virtual base
  class.

  The same applies to aff::Series and aff::ConstSeries.

\subsection sec_design_replicated_problem Where is the problem?
  Having an array object \c a declared
  \code aff::Array<T> a; \endcode where \c T is any type, we want to pass this
  object to a function that promises constness of the elements (see 
  \ref sec_design_const). The function is thus declared
  \code void func(const aff::ConstArray<T>&); \endcode
  and we want to use it like
  \code func(a) \endcode
  Consequently we must offer a way to convert an
  \code aff::Array<T>& \endcode
  to an
  \code aff::ConstArray<T>& \endcode
  implicitely.
  This is done by deriving aff::Array<T> publicly from aff::ConstArray<T>.

  The memory representation is needed by both, aff::Array<T> and its base
  class. Hence aff::ConstArray<T> has to inherit from the representation. It
  would be natural for aff::ConstArray<T> to inherit from aff::ConstSharedHeap
  only. However, since the derived aff::Array<T> needs full access to an
  aff::SharedHeap<T> (to expose the representation to the outside), we might
  tend to derive aff::ConstArray<T> from aff::SharedHeap<T> privately,
  allowing only read access and conversion to aff::ConstSharedHeap.

  Why is this a problem?
  Consider the inside of the above function. We might know, that the columns
  of the passed array contain seismogram waveforms. And we might like to
  access them in an appropriate way (i.e. through an interface that provides
  waveform operations), though just reading - not modifying - the data. Then
  we would like to code something like
  \code
  template<class T>
  void func(const aff::ConstArray<T>& a)
  {
    // cycle all seismograms
    for (Tsubscript iseis=a.f(1); iseis<=a.l(1); iseis++)
    {
      // extract shape
      aff::Strided shape(a.shape());
      // collapse to waveform iseis
      shape.collapse(1,iseis);
      // create a time series
      aff::ConstSeries<T> waveform(a.representation(),
                            shape.size(), shape.first_offset());
      // operate on time series (e.g. recursive filter)
      some_waveform_operation(waveform);
    }
  }
  \endcode

  The above example requires that we can construct an aff::ConstSeries<T> from
  an aff::ConstSharedHeap<T> (which is returned by
  aff::ConstArray::representation). The same problem appears together with
  aff::ConstArray, when creating a subarray or slice from an aff::ConstArray
  with aff::subarray or aff::slice and aff::ConstArray itself knowing nothing
  about slices, etc.

  Constructing aff::ConstArray from an aff::ConstSharedHeap sounds a natural
  operation. However, aff::ConstArray will ask for an aff::SharedHeap, if we
  derive from aff::SharedHeap (as sketched above). Conclusion: aff::ConstArray
  must use an aff::ConstSharedHeap only. At the same time we must hold
  the full aff::SharedHeap together with the aff::Array object, since this must
  return an aff::SharedHeap through aff::Array::representation to allow the
  above operation (accessing data through aff::Series or constructing a
  slice - see \ref sec_design_interface_sparse).

\subsection sec_design_replicated_solution Solution
  The most convincing solution (IMHO) to this problem is to use an
  (additional) member of type aff::SharedHeap<T> in aff::Array<T> which
  inherits from aff::ConstArray<T>.
  In consequence aff::ConstSharedHeap<T> is then a replicated within
  aff::Array<T>. For a proper design we might consider to make
  aff::ConstSharedHeap a virtual base, thus avoiding member data duplication.
  This would, however, introduce an extra level of indirection (additional to
  the indirection when accessing the heap data through the pointer to the
  aff::util::SHeap struct in aff::ConstSharedHeap). On the other hand, fully
  replicating the base aff::ConstSharedHeap just adds one member data pointer
  (the pointer to the aff::util::SHeap struct) to the data block in aff::Array
  (which already contains many bytes from the aff::Strided base). This
  overhead is not considered significant. 

  \b But \b notice: We now must take care to synchronize the aff::SharedHeap
  base of aff::Array and the aff::ConstSharedHeap base of aff::ConstArray
  during construction. This is no major concern, but it is error-prone to some
  degree. It is, however, much easier to keep them synchronous when using
  member data instead of inheritance.

<HR>
\section sec_design_copy Copy constructor and copy operator
  
  Usually we would expect the copy operator and the copy constructor to have
  the same semantics. Here the copy constructor of aff::Array must have
  reference semantics (it does a shallow copy). This is necessary to allow
  arrays as return values from functions. In this case the copy constructor is
  automatically invoked. Reference semantics ensure a minimal overhead. in
  terms of memory usage and execution time.

  In the case of the copy (assignment) operator things are less clear: 
  If we define the
  copy operator to have reference semantics, it has the same behaviour as the
  copy constructor. That is what we usually would expect. An expression like
  \code
  A=B;
  \endcode
  means that array \c A drops its reference to the memory location it was
  pointing to and forgets its previous shape. Following this statement array
  \c A will refer to the same memory location as array \c B and will have the
  same shape. Both are indistinguishable.

  However, in many cases (most cases?) we will use the copy (assignment)
  operator in the
  sense of a mathematical equation. This may read like
  \code
  A=B+C;
  \endcode
  although expressions like this are not yet supported by the library
  features. In this case we do not mean that \c A should drop it reference. 
  \c A may refer to an array in memory which is also referred by other array
  instances. And we want these values to be set to the result of the operation
  \c B + \c C. In that case the copy operator should have deep copy semantics.

  \par Design decision
  The classes aff::Array and aff::Series provide copy (assignment) operators
  with shallow copy semantics. 
  The automatically created copy constructor and copy operator do just right
  for this.
  This is sensible, because we are not offering mathematical array operations.
  This operations may be delegated to a wrapper class in the future, which
  then also may provide expression templates and an appropriate assignment
  operator.

<HR>
\section sec_design_namespaces Namespaces

  We group all code in two namespaces. Major modules which will be accessed by
  the user are placed in namepsace aff. Modules meant to be used internally are
  placed in aff::util.
  Use directives like
  \code
  using namespace aff;
  \endcode
  or
  \code
  using aff::Array;
  \endcode
  for convenient access.

<HR>
\section sec_design_binary Binary library

\note
  The option to provide precompiled templates is finally removed from the
  library. 
\date 10/11/2010

<HR>
\section sec_design_multidimensional Multidimensional arrays

  \todo
  Explain Wolfgangs idea of multidimensional arrays.

<HR>
\section sec_design_const Notes on the const-correctness of arrays

\subsection sec_design_const_problem Where is the problem?
  When passing a container (i.e. an array) to a function, we would like to
  promise that the values in the container are not modified, in case the
  function uses only read-access. Consider a declaration
  \code void func(const int& v) \endcode
  of a function that takes and argument of type \c int an promises that this
  will not be modified. Passing by reference is used, because this is more
  efficient than passing by value (in particular for large objects - which is
  not the case for \c int, but for an array).
  And qualifying the type \c const promises that the
  value passed by reference will not be changed.

  A declaration
  \code void func(const Array<int>& v) \endcode
  does not what we want (see \ref sec_design_const_general). It just
  promises the constness of the container, not of the data. Within the
  function the passed reference may be assigned to a non-const \c Array<int>,
  which allows modification of the data (see \ref page_representation).

  Thus we must use something like
  \code void func(const ConstArray<int>& v) \endcode
  where \c ConstArray<int> does not allow modification of the data (be no
  means - copying and conversions included) and may be derived from an 
  \c Array<int> by a trivial conversion (like a conversion to a public base
  class).

\subsection sec_design_const_approach The approach used in this library

  We distinguish between the constness of the array and the constness of the
  elements. A definition
  \code
  aff::Array<int> A(12,12);
  const aff::Array<int> B(A);
  \endcode
  means that array \c B is a constant array initialized to array \c A. This
  means, that the container is constant. Its shape and reference may not be
  changed.

  If you want to define constness of the contained values (e.g. when passing
  an array to a function), you have to use
  \code
  aff::ConstArray<int> C(A);
  \endcode
  which defines that the contents of \c C may not be changed (i.e. they are of
  type \c const \c int. 
  They are still refering to the same data in memory. 
  If you modify data elements through \c A, this will be visible through \c C.

  An array for elements of type \c T is derived from an array for elements of
  type \c const \c T. 
  Functions that only need read access to arrays should be declared like
  \code
  void func(const aff::ConstArray<int>& array);
  \endcode
  and may be called like
  \code
  aff::Array<int> A(12,12);
  func(A);
  \endcode
  The type conversion from \code aff::Array<int> \endcode to 
  \code const aff::ConstArray<int>& \endcode is trivial and has no runtime
  overhead.

  Each container class must deal with this issue on its own. Sorry...

  \sa aff::ConstSharedHeap
  \sa aff::ConstArray
  \sa aff::ConstSeries

\par Restrictions for containers with const qualifier
  In 7/2005 we changed the design decision of not allowing data modification
  through containers that are declared const.
  Strictly distinguishing between constness of the container and constness of
  the contained data allows to modify data through an object \c c that
  was declared
  \code const Array<int> c; \endcode
  The containers in this library (aff::Array, etc.) allow data modification 
  through instances declared const. This may appear surprising to users of the
  library. However, since it is possible to create a copy of a const container
  at any place and modifying the data through this copy, we would regard a
  different behaviour as a false promise.

  To ensure true constness of the data, you have to assign to the base class
  of the container. 
  Any container class (e.g. \c Cont) provides the type of container for const
  elements through a typedef Tcontainer_of_const 
  (i.e. \c Cont::Tcontainer_of_const) or short Tcoc.
  Remember that a \c const \c aff::Array always
  may be assigned to a mutable aff::Array, which in turn allows modification
  of the data!

\subsection sec_design_const_alternatives Alternatives

  Three alternatives to this concept have been discussed (and discarded).
  Both have the appealing property of needing only one class definition for
  each container (in contrast to a class and a base class in our case).
  Additionally both would offer name commonality for containers of non-const
  elements and containers of const elements.

\par Using arrays with element type const T
  A rather straight approach is to use the element type \c const \c T
  where an array of elements of type \c T should be used, that we do not allow
  to be changed. This design concept can be accomplished with a special traits
  class that is specialized for \c const \c T and allows to derive a mutable
  or const version of any type. By further providing appropriate conversion
  operators, an \code Array<T> \endcode could be converted to an
  \code Array<const T>, \endcode both sharing the same elements in memory.
  In this approach, however, both container classes are completely
  independent (although having the same name) due to their different template
  arguments. The conversion to the container for const elements is not a
  trivial conversion (like for a reference to a reference of a public base
  class) and must be done explicitely. That's inconvenient for the most common
  use (i.e. passing a container to a function).

\par Deriving from a template specialization
  The name commonality could still be achieved by deriving the Array<T> from
  template specialization Array<const T>. In this case the specialization must
  be used as a base class before it is actually defined. That's improper
  design.

\par Ensuring constness of elements through const qualifier of functions
  We could strictly follow the concept (as we do anyway to some extent) to
  couple the constness of the container to the constness of the contained
  data. This is done by const qualifiers to member functions that allow
  modification of the data. To avoid pitfalls,
  we have to consider copy operators
  and copy constructors then too. Both must not promise const-ness to their
  arguments. While this works in principle, we would end up with a container
  class which doesn't allow copies of const instances. Hence we could not
  return a container from a function, that ensures that the accessed data
  cannot be modified.

\subsection sec_design_const_general General considerations

  Arrays using the shared heap representation have reference semantics.
  Different instances will access the same data in memory. Copying an array
  instance just copies a reference to the data. This mechanism is not obvious
  to the compiler. The array instances are values in the sense of C++ types
  and not references. Passing an \c const \c aff::Array to a function does
  not prohibit the function from assigning this instance to a non-const
  \c aff::Array, which then references the same memory area and allows the
  modification of the values contained in the array.

  Generally it has to be defined, what is meant by declaring an array instance
  to be \c const. In the first place this means constness of the container to
  the compiler. The compiler will ensure, that the container (array class) is
  not changed, thus no data member of the array is changed. This means that
  the array will keep the reference to the same data and that the
  index-mapping defined by the array shape may not be changed. However, the
  compiler will not prevent to change any data, the array refers to. 

  We may define access operators that have a non-const version that returns a
  reference to the data, allowing to change the data values together with a
  const version that returns a value of const reference, thus preventing the
  data from being changed through an instance that is declared const. However,
  the compiler will always allow to create a non-const copy of a const array
  instance. In the sense of const-ness of C++ data, this does not violate the
  const-ness of the source of the copy. The shape of the original array may
  not be changed. Only the shape of the copy may be changed. But the data of
  the original array may now be changed through the copied instance, since our
  array classes implicitly have reference semantic. Thus we have to
  distinguish between const-ness of the container (array class instance) and
  the contained data (values in memory the arrays refers to).

  In this library we will not provide a const and a non-const version of the
  array classes. With templated code it is more convenient to use an array
  with element type \c const \c T as the const version of an array with
  element type \c T. To allow conversion of an instance with element type \c T
  to an instance of type \c const \c T, we use the version for elements of
  type \c const \c T as a base classe.

   -  The need of const-correctness is discussed in "Chapter 1 Introduction,
      C++ Conventions, Implementation of Vector and Matrix Classes" of
      "Numerical Recipes in C++". A link to a PDF file of this chapter is
      provided at "http://www.nr.com/cpp-blurb.html".
   - The "C++ FAQ Lite" discusses many aspects of const-correctness in Chapter
     18, which you find at
     "http://www.inf.uni-konstanz.de/~kuehl/cpp/cppfaq.htm/const-correctness.html".
   -  You may find my thoughts about const-correctness with containers that
      have reference semantics at
      "http://www.geophysik.uni-frankfurt.de/~forbrig/txt/cxx/tutorial/consthandle.doc/doc/html/index.html".

*/

/*======================================================================*/

/*! \page page_using HOWTO use this library

  Contents of this page:
  - \ref sec_using_constructor
  - \ref sec_using_examples

\section sec_using_constructor Constructing arrays
  Arrays are most easy constructed by means of the aff::Shaper.
  If you want e.g. define an array \c A of element type int with Fortran
  layout, three dimensions and the index ranges [-2:2], [1:4], and [6:10] you
  have to code
  \code
  using namespace aff;
  Array<int> A(Shaper(-2,2)(4)(6,10));
  \endcode
  The shaper is presented in aff/shaper.h.

\section sec_using_examples Example code
  The test programs may serve as examples for using this library:
  - tests/arraytest.cc
  - tests/shapetest.cc
  - tests/reprtest.cc
  - tests/simplearraytest.cc

\todo
We need more text and examples.

*/


/*======================================================================*/

/*! \page page_naming Naming conventions

  Contents of this page:
  - \ref sec_naming_identifiers
  - \ref sec_naming_macros
  - \ref sec_naming_files

\section sec_naming_identifiers Classes, Typedefs, etc.

  During coding it is sometimes helpfull to recognize the meaning of an
  identifier due to some signals in irs name. Therefor the following
  guidelines are used. The nameing of template parameters is left free for
  convenience.

  \par Classes
   
  Class names always start with a capital letter.

  \par Typedefs

  Typedefs always start with a capital \c T.

  \par Member data

  Member data identifiers always start with a capital \c M.

\section sec_naming_macros Preprocessor macros

  Preprocessor macros like include-guards should have the prefix "AFF_".
  The macros in the \ref group_helpers are an exception to this rule.

\section sec_naming_files Filenames

  Files with the extension \c .cc contain only non-template definitions. Files
  with the extension \c .h may contain prototypes, class declarations or
  template code. Files ending on \c def.h contain template code definitions
  that is factored out to be compilable into a binary library for explicit
  instantiation.

  The main directory %aff contains headers that are usually included by the
  user. A subdirectory %aff/lib contains additional headers that are mostly
  used internally.

*/

/*======================================================================*/

/*! \page page_array_layout Array layout
 
  The array class template aff::Array uses the shape class aff::Strided.
  Usually and in particular when constructed by using aff::Shaper,
  aff::Strided uses a Fortran like column-major layout in memory.
  aff::FortranArray and aff::util::FortranShape are provided to interface
  Fortran code with such kind of arrays.
  Nevertheless aff::Array together with aff::Strided is able to address a
  row-major C like memory layout too.
  Classes to interface raw memory arrays are presented in Carray.h.

  By definition the first index \f$ i \f$ on a two-dimenional matrix 
  \f$ A_{ij} \f$ as represented by the array
  \c A(i,j) is the row index while the second index \f$ j \f$ is the
  column index.
  If elements of the two-dimensional matrix or array are arranged in linear
  computer memory, there are two options:

  \section sec_array_layout_column_major Column major layout

  When traversing the linear representation in memory byte by byte in
     increasing address order the elements of the first column in order of
     increasing row index are passed first.
     Next the elements of the second column are passed in increasing row order
     and so forth.
     When labelling the array elements in linear memory, the first index
     varies quicker than the second index of the array if the elements are
     traversed in increasing address order.
     This is called the "column major order" and is the usualy layout of
     Fortran arrays.

  Column major layout is described in detail at
  http://en.wikipedia.org/wiki/Row-major_order#Column-major_order

  \section sec_array_layout_row_major Row major layout

  When traversing the linear representation in memory byte by byte in
     increasing address order the elements of the first row in order of
     increasing column index are passed first.
     Next the elements of the second row are passed in increasing column order
     and so forth.
     When labelling the array elements in linear memory, the second index
     varies quicker than the first index of the array if the elements are
     traversed in increasing address order.
     This is called the "row major order" and is the usualy layout of
     C arrays.

  Row major layout is described in detail at
  http://en.wikipedia.org/wiki/Row-major_order#Row-major_order
 
  \todo
  Provide details on indexing raw memory in both layouts here.
 */

// ----- END OF README -----