namespace multi_array_types {
  typedef *unspecified* index;
  typedef *unspecified* size_type;
  typedef *unspecified* difference_type;
  typedef *unspecified* index_range;
  typedef *unspecified* extent_range;
  typedef *unspecified* index_gen;
  typedef *unspecified* extent_gen;
}

Namespace multi_array_types defines types associated with multi_array, multi_array_ref, and const_multi_array_ref that are not dependent upon template parameters. These types find common use with all Boost.Multiarray components. They are defined in a namespace from which they can be accessed conveniently. With the exception of extent_gen and extent_range, these types fulfill the roles of the same name required by MultiArray and are described in its concept definition. extent_gen and extent_range are described below.

extent_range objects define half open intervals. They provide shape and index base information to multi_array, multi_array_ref, and const_multi_array_ref constructors. extent_ranges are passed in aggregate to an array constructor (see extent_gen for more details).

Synopsis. 

class extent_range {
public:
  typedef multi_array_types::index      index;
  typedef multi_array_types::size_type  size_type;

  // Structors
  extent_range(index start, index finish);
  extent_range(index finish);
  ~extent_range();

  // Queries
  index start();
  index finish();
  size_type size();
};

Model Of. DefaultConstructible,CopyConstructible

Methods and Types. 

The extent_gen class defines an interface for aggregating array shape and indexing information to be passed to a multi_array, multi_array_ref, or const_multi_array_ref constructor. Its interface mimics the syntax used to declare built-in array types in C++. For example, while a 3-dimensional array of int values in C++ would be declared as:

int A[3][4][5],

a similar multi_array would be declared:

multi_array<int,3> A(extents[3][4][5]).

Synopsis. 

template <std::size_t NumRanges>
class *implementation_defined* {
public:
  typedef multi_array_types::index index;
  typedef multi_array_types::size_type size_type;

  template <std::size_t NumRanges> class gen_type;

  gen_type<NumRanges+1>::type  operator[](const range& a_range) const;
  gen_type<NumRanges+1>::type  operator[](index idx) const;
};

typedef *implementation_defined*<0> extent_gen;

Methods and Types. 

For syntactic convenience, Boost.MultiArray defines two global objects as part of its interface. These objects play the role of object generators; expressions involving them create other objects of interest.

Under some circumstances, the two global objects may be considered excessive overhead. Their construction can be prevented by defining the preprocessor symbol BOOST_MULTI_ARRAY_NO_GENERATORS before including boost/multi_array.hpp.

namespace boost {
  multi_array_base::extent_gen extents;
}

multi_array<int,3> A(extents[3][3][3]);

namespace boost {
  multi_array_base::index_gen  indices;
}

A[indices[index_range(0,5)][2][index_range(2,4)]];

Boost.MultiArray provides traits classes, subarray_gen, const_subarray_gen, array_view_gen, and const_array_view_gen, for naming of array associated types within function templates. In general this is no more convenient to use than the nested type generators, but the library author found that some C++ compilers do not properly handle templates nested within function template parameter types. These generators constitute a workaround for this deficit. The following code snippet illustrates the correspondence between the array_view_gen traits class and the array_view type associated to an array:

template <typename Array>
void my_function() {
  typedef typename Array::template array_view<3>::type view1_t;
  typedef typename boost::array_view_gen<Array,3>::type view2_t;
  // ...
}

In the above example, view1_t and view2_t have the same type.

While a multidimensional array represents a hierarchy of containers of elements, at some point the elements must be laid out in memory. As a result, a single multidimensional array can be represented in memory more than one way.

For example, consider the two dimensional array shown below in matrix notation:

Here is how the above array is expressed in C++:

int a[3][4] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 };

This is an example of row-major storage, where elements of each row are stored contiguously. While C++ transparently handles accessing elements of an array, you can also manage the array and its indexing manually. One way that this may be expressed in memory is as follows:

int a[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 };
int s[] = { 4, 1 };

With the latter declaration of a and strides s, element a(i,j) of the array can be accessed using the expression

*a+i*s[0]+j*s[1]

.

The same two dimensional array could be laid out by column as follows:

int a[] = { 0, 4, 8, 1, 5, 9, 2, 6, 10, 3, 7, 11 };
int s[] = { 3, 1 };

Notice that the strides here are different. As a result, The expression given above to access values will work with this pair of data and strides as well.

In addition to dimension order, it is also possible to store any dimension in descending order. For example, returning to the first example, the first dimension of the example array, the rows, could be stored in reverse, resulting in the following:

int data[] = { 8, 9, 10, 11, 4, 5, 6, 7, 0, 1, 2, 3 };
int *a = data + 8;
int s[] = { -4, 1 };

Note that in this example a must be explicitly set to the origin. In the previous examples, the first element stored in memory was the origin; here this is no longer the case.

Alternatively, the second dimension, or the columns, could be reversed and the rows stored in ascending order:

int data[] = { 3, 2, 1, 0,  7, 6, 5, 4, 11, 10, 9, 8 };
int *a = data + 3;
int s[] = { 4, -1 };

Finally, both dimensions could be stored in descending order:

int data[] = {11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0};
int *a = data + 11;
int s[] = { -4, -1 };

All of the above arrays are equivalent. The expression given above for a(i,j) will yield the same value regardless of the memory layout. Boost.MultiArray arrays can be created with customized storage parameters as described above. Thus, existing data can be adapted (with multi_array_ref or const_multi_array_ref) as suited to the array abstraction. A common usage of this feature would be to wrap arrays that must interoperate with Fortran routines so they can be manipulated naturally at both the C++ and Fortran levels. The following sections describe the Boost.MultiArray components used to specify memory layout.

class c_storage_order {
  c_storage_order();
};

class fortran_storage_order {
  fortran_storage_order();
};

template <std::size_t NumDims> 
class general_storage_order {

  template <typename OrderingIter, typename AscendingIter>
  general_storage_order(OrderingIter ordering, AscendingIter ascending);
};

By default, the array access methods operator() and operator[] perform range checking. If a supplied index is out of the range defined for an array, an assertion will abort the program. To disable range checking (for performance reasons in production releases), define the BOOST_DISABLE_ASSERTS preprocessor macro prior to including multi_array.hpp in an application.