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<html><head><meta content="text/html; charset=ISO-8859-1" http-equiv="Content-Type"><title>Boost.MultiArray Reference Manual</title><meta name="generator" content="DocBook XSL Stylesheets V1.49"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="article"><div class="titlepage"><div><h1 class="title"><a name="id170468"></a>Boost.MultiArray Reference Manual</h1></div><div><h3 class="author">Ronald Garcia</h3><div class="affiliation"><span class="orgname">Indiana University<br></span><span class="orgdiv">Open Systems Lab<br></span></div></div><div><p class="copyright">Copyright © 2002 Ronald Garcia</p></div><hr></div><div class="toc"><p><b>Table of Contents</b></p><dl><dt><a href="#synopsis">Library Synopsis</a></dt><dt><a href="#MultiArray">MultiArray Concept</a></dt><dd><dl><dt><a href="#id179006">Notation</a></dt><dt><a href="#id175494">Associated Types</a></dt><dt><a href="#id250868">Valid expressions</a></dt><dt><a href="#id251805">Complexity guarantees</a></dt><dt><a href="#id251847">Invariants</a></dt><dt><a href="#view_types">Associated Types for Views</a></dt><dd><dl><dt><a href="#index_range">index_range</a></dt><dt><a href="#index_gen">index_gen</a></dt></dl></dd><dt><a href="#id253521">Models</a></dt></dl></dd><dt><a href="#array_types">Array Components</a></dt><dd><dl><dt><a href="#multi_array">multi_array</a></dt><dt><a href="#multi_array_ref">multi_array_ref</a></dt><dt><a href="#const_multi_array_ref">const_multi_array_ref</a></dt></dl></dd><dt><a href="#auxiliary">Auxiliary Components</a></dt><dd><dl><dt><a href="#multi_array_types">multi_array_types</a></dt><dt><a href="#extent_range">extent_range</a></dt><dt><a href="#extent_gen">extent_gen</a></dt><dt><a href="#id253863">Global Objects</a></dt><dd><dl><dt><a href="#extents">extents</a></dt><dt><a href="#indices">indices</a></dt></dl></dd><dt><a href="#generators">View and SubArray Generators</a></dt><dt><a href="#memory_layout">Memory Layout Specifiers</a></dt><dd><dl><dt><a href="#c_storage_order">c_storage_order</a></dt><dt><a href="#fortran_storage_order">fortran_storage_order</a></dt><dt><a href="#general_storage_order">general_storage_order</a></dt></dl></dd></dl></dd></dl></div><fake><p>Boost.MultiArray is composed of several components.
The MultiArray concept defines a generic interface to multidimensional
containers.
<tt>multi_array</tt> is a general purpose container class
that models MultiArray. <tt>multi_array_ref</tt>
and <tt>const_multi_array_ref</tt> are adapter
classes. Using them,
you can manipulate any block of contiguous data as though it were a
<tt>multi_array</tt>.
<tt>const_multi_array_ref</tt> differs from
<tt>multi_array_ref</tt> in that its elements cannot
be modified through its interface. Finally, several auxiliary classes are used
to create and specialize arrays and some global objects are defined as
part of the library interface.</p></fake><div class="sect1"><div class="titlepage"><div><h2 class="title" style="clear: both"><a name="synopsis"></a>Library Synopsis</h2></div></div><fake><p>To use Boost.MultiArray, you must include the header
<tt>boost/multi_array.hpp</tt> in your source. This file
brings the following declarations into scope:</p></fake><pre class="programlisting">
namespace boost {
namespace multi_array_types {
typedef *implementation-defined* index;
typedef *implementation-defined* size_type;
typedef *implementation-defined* difference_type;
typedef *implementation-defined* index_range;
typedef *implementation-defined* extent_range;
typedef *implementation-defined* index_gen;
typedef *implementation-defined* extent_gen;
}
template &lt;typename ValueType,
std::size_t NumDims,
typename Allocator = std::allocator&lt;ValueType&gt; &gt;
class multi_array;
template &lt;typename ValueType,
std::size_t NumDims&gt;
class multi_array_ref;
template &lt;typename ValueType,
std::size_t NumDims&gt;
class const_multi_array_ref;
multi_array_types::extent_gen extents;
multi_array_types::index_gen indices;
template &lt;typename Array, int N&gt; class subarray_gen;
template &lt;typename Array, int N&gt; class const_subarray_gen;
template &lt;typename Array, int N&gt; class array_view_gen;
template &lt;typename Array, int N&gt; class const_array_view_gen;
class c_storage_order;
class fortran_storage_order;
template &lt;std::size_t NumDims&gt; class general_storage_order;
}
</pre></div><div class="sect1"><div class="titlepage"><div><h2 class="title" style="clear: both"><a name="MultiArray"></a>MultiArray Concept</h2></div></div><fake><p>The MultiArray
concept defines an interface to hierarchically nested
containers. It specifies operations for accessing elements,
traversing containers, and creating views
of array data.
MultiArray defines
a flexible memory model that accomodates
a variety of data layouts.
</p></fake><fake><p>
At each level (or dimension) of a MultiArray's
container hierarchy lie a set of ordered containers, each of which
contains the same number and type of values. The depth of this
container hierarchy is the MultiArray's <span class="emphasis"><i>dimensionality</i></span>.
MultiArray is recursively defined; the
containers at each level of the container hierarchy model
MultiArray as well. While each dimension of a MultiArray
has its own size, the list of sizes for all dimensions
defines the <span class="emphasis"><i>shape</i></span> of the entire MultiArray.
At the base of this hierarchy lie 1-dimensional
MultiArrays. Their values are the contained
objects of interest and not part of the container hierarchy. These are
the MultiArray's elements.
</p></fake><fake><p>
Like other container concepts, MultiArray exports
iterators to traverse its values. In addition, values can be
addressed directly using the familiar bracket notation.
</p></fake><fake><p>
MultiArray also specifies
routines for creating
specialized views. A <span class="emphasis"><i>view</i></span> lets you treat a
subset of the underlying
elements in a MultiArray as though it were a separate
MultiArray. Since a view refers to the same underlying elements,
changes made to a view's elements will be reflected in the original
MultiArray. For
example, given a 3-dimensional &quot;cube&quot; of elements, a 2-dimensional
slice can be viewed as if it were an independent
MultiArray.
Views are created using <tt>index_gen</tt> and
<tt>index_range</tt> objects.
<tt>index_range</tt>s denote elements from a certain
dimension that are to be included in a
view. <tt>index_gen</tt> aggregates range data and performs
bookkeeping to determine the view type to be returned.
MultiArray's <tt>operator[]</tt>
must be passed the result
of <tt>N</tt> chained calls to
<tt>index_gen::operator[]</tt>, i.e.
<pre class="programlisting">indices[a0][a1]...[aN];
</pre>
where <tt>N</tt> is the
MultiArray's dimensionality and
<tt>indices</tt> an object of type <tt>index_gen</tt>.
The view type is dependent upon the number of degenerate dimensions
specified to <tt>index_gen</tt>. A degenerate dimension
occurs when a single-index is specified to
<tt>index_gen</tt> for a certain dimension. For example, if
<tt>indices</tt> is an object of type
<tt>index_gen</tt>, then the following example:
<pre class="programlisting">indices[index_range(0,5)][2][index_range(0,4)];
</pre>
has a degenerate second dimension. The view generated from the above
specification will have 2 dimensions with shape <tt>5 x 2</tt>.
If the &quot;<tt>2</tt>&quot; above were replaced with
another <tt>index_range</tt> object, for example:
<pre class="programlisting">indices[index_range(0,5)][index_range(0,2)][index_range(0,4)];
</pre>
then the view would have 3 dimensions.</p></fake><fake><p>
MultiArray exports
information regarding the memory
layout of its contained elements. Its memory model for elements is
completely defined by 4 properties: the origin, shape, index bases,
and strides. The origin is the address in memory of the element
accessed as <tt>a[0][0]...[0]</tt>, where
<tt>a</tt> is a MultiArray. The shape is a list of numbers
specifying the size of containers at each dimension. For example, the
first extent is the size of the outermost container, the second extent
is the size of its subcontainers, and so on. The index bases are a
list of signed values specifying the index of the first value in a
container. All containers at the same dimension share the same index
base. Note that since positive index bases are
possible, the origin need not exist in order to determine the location
in memory of the MultiArray's elements.
The strides determine how index values are mapped to memory offsets.
They accomodate a
number of possible element layouts. For example, the elements of a 2
dimensional array can be stored by row (i.e., the elements of each row
are stored contiguously) or by column (i.e., the elements of each
column are stored contiguously).
</p></fake><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="id179006"></a>Notation</h3></div></div><fake><p>What follows are the descriptions of symbols that will be used
to describe the MultiArray interface.</p></fake><div class="table"><p><b>Table 1. Notation</b></p><table summary="Notation" border="1"><colgroup><col><col></colgroup><tbody><tr><td><tt>A</tt></td><td>A type that is a model of MultiArray
</td></tr><tr><td><tt>a</tt></td><td>An object of type <tt>A</tt></td></tr><tr><td><tt>NumDims</tt></td><td>The numeric dimension parameter associated with
<tt>A</tt>.</td></tr><tr><td><tt>Dims</tt></td><td>Some numeric dimension parameter such that
<tt>0&lt;Dims&lt;NumDims</tt>.
</td></tr><tr><td><tt>indices</tt></td><td>An object created by some number of chained calls
to <tt>index_gen::operator[](index_range)</tt>.</td></tr><tr><td><tt>index_list</tt></td><td>An object whose type models
<a href="../../utility/Collection.html" target="_top">Collection</a></td></tr><tr><td><tt>idx</tt></td><td>A signed integral value.</td></tr><tr><td><tt>tmp</tt></td><td>An object of type
<tt>boost::array&lt;index,NumDims&gt;</tt></td></tr></tbody></table></div></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="id175494"></a>Associated Types</h3></div></div><fake><p>
</p></fake><div class="table"><p><b>Table 2. Associated Types</b></p><table summary="Associated Types" border="1"><colgroup><col><col></colgroup><thead><tr><th>Type</th><th>Description</th></tr></thead><tbody><tr><td><tt>value_type</tt></td><td>This is the value type of the container.
If <tt>NumDims == 1</tt>, then this is
<tt>element</tt>. Otherwise, this is the value type of the
immediately nested containers.
</td></tr><tr><td><tt>reference</tt></td><td>
This is the reference type of the contained value.
If <tt>NumDims == 1</tt>, then this is
<tt>element&amp;</tt>. Otherwise, this is the same type as
<tt>template subarray&lt;NumDims-1&gt;::type</tt>.
</td></tr><tr><td><tt>const_reference</tt></td><td>
This is the const reference type of the contained value.
If <tt>NumDims == 1</tt>, then this is
<tt>const element&amp;</tt>. Otherwise, this is the same
type as
<tt>template const_subarray&lt;NumDims-1&gt;::type</tt>.
</td></tr><tr><td><tt>size_type</tt></td><td>
This is an unsigned integral type. It is primarily used to specify array shape.
</td></tr><tr><td><tt>difference_type</tt></td><td>
This is a signed integral type used to represent the distance between two
iterators. It is the same type as
<tt>std::iterator_traits&lt;iterator&gt;::difference_type</tt>.
</td></tr><tr><td><tt>iterator</tt></td><td>
This is an iterator over the values of <tt>A</tt>.
If <tt>NumDims == 1</tt>, then it models
<a href="http://www.sgi.com/tech/stl/RandomAccessIterator.html" target="_top">
<tt>Random Access Iterator</tt></a>.
Otherwise it models
<a href="./iterator_categories.html#concept_RandomAccessTraversalIterator" target="_top">
Random Access Traversal Iterator</a>,
<a href="./iterator_categories.html#concept_ReadableIterator" target="_top">
Readable Iterator</a>, and
<a href="./iterator_categories.html#concept_WritableIterator" target="_top">
Writable Iterator</a>.
</td></tr><tr><td><tt>const_iterator</tt></td><td>
This is the const iterator over the values of <tt>A</tt>.
</td></tr><tr><td><tt>reverse_iterator</tt></td><td>
This is the reversed iterator, used to iterate backwards over the values of
<tt>A</tt>.
</td></tr><tr><td><tt>const_reverse_iterator</tt></td><td>
This is the reversed const iterator.
<tt>A</tt>.
</td></tr><tr><td><tt>element</tt></td><td>
This is the type of objects stored at the base of the
hierarchy of MultiArrays. It is the same as
<tt>template subarray&lt;1&gt;::value_type</tt></td></tr><tr><td><tt>index</tt></td><td>
This is a signed integral type used for indexing into <tt>A</tt>. It
is also used to represent strides and index bases.
</td></tr><tr><td><tt>index_gen</tt></td><td>
This type is used to create a tuple of <tt>index_range</tt>s
passed to <tt>operator[]</tt> to create
an <tt>array_view&lt;Dims&gt;::type</tt> object.
</td></tr><tr><td><tt>index_range</tt></td><td>
This type specifies a range of indices over some dimension of a
MultiArray. This range will be visible through an
<tt>array_view&lt;Dims&gt;::type</tt> object.
</td></tr><tr><td><tt>template subarray&lt;Dims&gt;::type</tt></td><td>
This is subarray type with <tt>Dims</tt> dimensions.
It is the reference type of the <tt>(NumDims - Dims)</tt>
dimension of <tt>A</tt> and also models
MultiArray.
</td></tr><tr><td><tt>template const_subarray&lt;Dims&gt;::type</tt></td><td>
This is the const subarray type.
</td></tr><tr><td><tt>template array_view&lt;Dims&gt;::type</tt></td><td>
This is the view type with <tt>Dims</tt> dimensions. It is
returned by calling <tt>operator[](<tt>indices</tt>)</tt>.
It models MultiArray.
</td></tr><tr><td><tt>template
const_array_view&lt;Dims&gt;::type</tt></td><td>
This is the const view type with <tt>Dims</tt> dimensions.
</td></tr></tbody></table></div></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="id250868"></a>Valid expressions</h3></div></div><div class="table"><p><b>Table 3. Valid Expressions</b></p><table summary="Valid Expressions" border="1"><colgroup><col><col><col></colgroup><thead><tr><th>Expression</th><th>Return type</th><th>Semantics</th></tr></thead><tbody><tr><td><tt>a.shape()</tt></td><td><tt>const size_type*</tt></td><td>
This returns a list of <tt>NumDims</tt> elements specifying the
extent of each array dimension.
</td></tr><tr><td><tt>a.strides()</tt></td><td><tt>const index*</tt></td><td>
This returns a list of <tt>NumDims</tt> elements specifying the
stride associated with each array dimension. When accessing values,
strides is used to calculate an element's location in memory.
</td></tr><tr><td><tt>a.index_bases()</tt></td><td><tt>const index*</tt></td><td>
This returns a list of <tt>NumDims</tt> elements specifying the
numeric index of the first element for each array dimension.
</td></tr><tr><td><tt>a.origin()</tt></td><td><tt>element*</tt> if <tt>a</tt> is mutable,
<tt>const element*</tt> otherwise.
</td><td>
This returns the address of the element accessed by the expression
<tt>a[0][0]...[0].</tt>. If the index bases are positive,
this element won't exist, but the address can still be used to locate
a valid element given its indices.
</td></tr><tr><td><tt>a.num_dimensions()</tt></td><td><tt>size_type</tt></td><td>This returns the number of dimensions of the array
(note that <tt>a.num_dimensions() == NumDims</tt>).</td></tr><tr><td><tt>a.num_elements()</tt></td><td><tt>size_type</tt></td><td>This returns the number of elements contained
in the array. It is equivalent to the following code:
<pre class="programlisting">
std::accumulate(a.shape(),a.shape+a.num_dimensions(),
size_type(1),std::multiplies&lt;size_type&gt;());
</pre></td></tr><tr><td><tt>a.size()</tt></td><td><tt>size_type</tt></td><td>
This returns the number of values contained in
<tt>a</tt>. It is equivalent to <tt>a.shape()[0];</tt></td></tr><tr><td><tt>a(index_list)</tt></td><td><tt>element&amp;</tt>; if <tt>a</tt> is mutable,
<tt>const element&amp;</tt> otherwise.
</td><td>
This expression accesses a specific element of
<tt>a</tt>.<tt>index_list</tt> is the unique set
of indices that address the element returned. It is
equivalent to the following code (disregarding intermediate temporaries):
<pre class="programlisting">
// multiply indices by strides
std::transform(index_list.begin(), index_list.end(),
a.strides(), tmp.begin(), std::multiplies&lt;index&gt;()),
// add the sum of the products to the origin
*std::accumulate(tmp.begin(), tmp.end(), a.origin());
</pre></td></tr><tr><td><tt>a.begin()</tt></td><td><tt>iterator</tt> if <tt>a</tt> is mutable,
<tt>const_iterator</tt> otherwise.
</td><td>This returns an iterator pointing to the beginning of
<tt>a</tt>.</td></tr><tr><td><tt>a.end()</tt></td><td><tt>iterator</tt> if <tt>a</tt> is mutable,
<tt>const_iterator</tt> otherwise.
</td><td>This returns an iterator pointing to the end of
<tt>a</tt>.</td></tr><tr><td><tt>a.rbegin()</tt></td><td><tt>reverse_iterator</tt> if <tt>a</tt> is mutable,
<tt>const_reverse_iterator</tt> otherwise.
</td><td>This returns a reverse iterator pointing to the
beginning of <tt>a</tt> reversed.
</td></tr><tr><td><tt>a.rend()</tt></td><td><tt>reverse_iterator</tt> if <tt>a</tt> is mutable,
<tt>const_reverse_iterator</tt> otherwise.
</td><td>
This returns a reverse iterator pointing to the end of <tt>a</tt>
reversed.
</td></tr><tr><td><tt>a[idx]</tt></td><td><tt>reference</tt> if <tt>a</tt> is mutable,
<tt>const_reference</tt> otherwise.
</td><td>
This returns a reference type that is bound to the index
<tt>idx</tt> value of <tt>a</tt>. Note that if
<tt>i</tt> is the index base for this dimension, the above
expression returns the <tt>(idx-i)</tt>th element (counting
from zero). The expression is equivalent to
<tt>*(a.begin()+idx-a.index_bases()[0]);</tt>.
</td></tr><tr><td><tt>a[indices]</tt></td><td><tt>array_view&lt;Dims&gt;::type</tt> if
<tt>a</tt> is mutable,
<tt>const_array_view&lt;Dims&gt;::type</tt> otherwise.
</td><td>
This expression generates a view of the array determined by the
<tt>index_range</tt> and <tt>index</tt> values
used to construct <tt>indices</tt>.
</td></tr><tr><td><tt>a == b</tt></td><td>bool</td><td>This performs a lexicographical comparison of the
values of <tt>a</tt> and <tt>b</tt>. The element
type must model <a href="http://www.sgi.com/tech/stl/EqualityComparable.html" target="_top">EqualityComparable</a> for this
expression to be valid.</td></tr><tr><td><tt>a &lt; b</tt></td><td>bool</td><td>This performs a lexicographical comparison of the
values of <tt>a</tt> and <tt>b</tt>. The element
type must model <a href="http://www.sgi.com/tech/stl/LessThanComparable.html" target="_top">LessThanComparable</a> for this
expression to be valid.</td></tr><tr><td><tt>a &lt;= b</tt></td><td>bool</td><td>This performs a lexicographical comparison of the
values of <tt>a</tt> and <tt>b</tt>. The element
type must model <a href="http://www.sgi.com/tech/stl/EqualityComparable.html" target="_top">EqualityComparable</a> and
<a href="http://www.sgi.com/tech/stl/LessThanComparable.html" target="_top">LessThanComparable</a> for this
expression to be valid.</td></tr><tr><td><tt>a &gt; b</tt></td><td>bool</td><td>This performs a lexicographical comparison of the
values of <tt>a</tt> and <tt>b</tt>. The element
type must model <a href="http://www.sgi.com/tech/stl/EqualityComparable.html" target="_top">EqualityComparable</a> and
<a href="http://www.sgi.com/tech/stl/LessThanComparable.html" target="_top">LessThanComparable</a> for this
expression to be valid.</td></tr><tr><td><tt>a &gt;= b</tt></td><td>bool</td><td>This performs a lexicographical comparison of the
values of <tt>a</tt> and <tt>b</tt>. The element
type must model <a href="http://www.sgi.com/tech/stl/LessThanComparable.html" target="_top">LessThanComparable</a> for this
expression to be valid.</td></tr></tbody></table></div></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="id251805"></a>Complexity guarantees</h3></div></div><tt>begin()</tt> and <tt>end()</tt> execute in amortized
constant time.
<tt>size()</tt> executes in at most linear time in the
MultiArray's size.
</div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="id251847"></a>Invariants</h3></div></div><div class="table"><p><b>Table 4. Invariants</b></p><table summary="Invariants" border="1"><colgroup><col><col></colgroup><tbody><tr><td>Valid range</td><td><tt>[a.begin(),a.end())</tt> is a valid range.
</td></tr><tr><td>Range size</td><td><tt>a.size() == std::distance(a.begin(),a.end());</tt>.
</td></tr><tr><td>Completeness</td><td>
Iteration through the range
<tt>[a.begin(),a.end())</tt> will traverse across every
<tt>value_type</tt> of <tt>a</tt>.
</td></tr><tr><td>Accessor Equivalence</td><td>
Calling <tt>a[a1][a2]...[aN]</tt> where <tt>N==NumDims</tt>
yields the same result as calling
<tt>a(index_list)</tt>, where <tt>index_list</tt>
is a <a href="../../utility/Collection.html" target="_top">Collection</a> containing the values <tt>a1...aN</tt>.
</td></tr></tbody></table></div></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="view_types"></a>Associated Types for Views</h3></div></div><fake><p>The following MultiArray associated
types define the interface for creating views of existing
MultiArrays. Their interfaces and roles in the
concept are described below.</p></fake><div class="sect3"><div class="titlepage"><div><h4 class="title"><a name="index_range"></a><tt>index_range</tt></h4></div></div><fake><p><tt>index_range</tt> objects represent half-open
strided intervals. They are aggregated (using an
<tt>index_gen</tt> object) and passed to
a MultiArray's <tt>operator[]</tt>
to create an array view. When creating a view,
each <tt>index_range</tt> denotes a range of
valid indices along one dimension of a MultiArray.
Elements that are accessed through the set of ranges specified will be
included in the constructed view. In some cases, an
<tt>index_range</tt> is created without specifying start
or finish values. In those cases, the object is interpreted to
start at the beginning of a MultiArray dimension
and end at its end.</p></fake><fake><p>
<tt>index_range</tt> objects can be constructed and modified
several ways in order to allow convenient and clear expression of a
range of indices. To specify ranges, <tt>index_range</tt>
supports a set of constructors, mutating member functions, and a novel
specification involving inequality operators. Using inequality
operators, a half open range [5,10) can be specified as follows:
<pre class="programlisting">5 &lt;= index_range() &lt; 10;</pre> or
<pre class="programlisting">4 &lt; index_range() &lt;= 9;</pre> and so on.
The following describes the
<tt>index_range</tt> interface.
</p></fake><div class="table"><p><b>Table 5. Notation</b></p><table summary="Notation" border="1"><colgroup><col><col></colgroup><tbody><tr><td><tt>i</tt></td><td>An object of type <tt>index_range</tt>.</td></tr><tr><td><tt>idx,idx1,idx2,idx3</tt></td><td>Objects of type <tt>index</tt>.</td></tr></tbody></table></div><div class="table"><p><b>Table 6. Associated Types</b></p><table summary="Associated Types" border="1"><colgroup><col><col></colgroup><thead><tr><th>Type</th><th>Description</th></tr></thead><tbody><tr><td><tt>index</tt></td><td>This is a signed integral type. It is used to
specify the start, finish, and stride values.</td></tr><tr><td><tt>size_type</tt></td><td>This is an unsigned integral type. It is used to
report the size of the range an <tt>index_range</tt>
represents.</td></tr></tbody></table></div><div class="table"><p><b>Table 7. Valid Expressions</b></p><table summary="Valid Expressions" border="1"><colgroup><col><col><col></colgroup><thead><tr><th>Expression</th><th>Return type</th><th>Semantics</th></tr></thead><tbody><tr><td><tt>index_range(idx1,idx2,idx3)</tt></td><td><tt>index_range</tt></td><td>This constructs an <tt>index_range</tt>
representing the interval <tt>[idx1,idx2)</tt>
with stride <tt>idx3</tt>.</td></tr><tr><td><tt>index_range(idx1,idx2)</tt></td><td><tt>index_range</tt></td><td>This constructs an <tt>index_range</tt>
representing the interval <tt>[idx1,idx2)</tt>
with unit stride. It is equivalent to
<tt>index_range(idx1,idx2,1)</tt>.</td></tr><tr><td><tt>index_range()</tt></td><td><tt>index_range</tt></td><td>This construct an <tt>index_range</tt>
with unspecified start and finish values.</td></tr><tr><td><tt>i.start(idx1)</tt></td><td><tt>index&amp;</tt></td><td>This sets the start index of <tt>i</tt> to
<tt>idx</tt>.</td></tr><tr><td><tt>i.finish(idx)</tt></td><td><tt>index&amp;</tt></td><td>This sets the finish index of <tt>i</tt> to
<tt>idx</tt>.</td></tr><tr><td><tt>i.stride(idx)</tt></td><td><tt>index&amp;</tt></td><td>This sets the stride length of <tt>i</tt> to
<tt>idx</tt>.</td></tr><tr><td><tt>i.start()</tt></td><td><tt>index</tt></td><td>This returns the start index of <tt>i</tt>.</td></tr><tr><td><tt>i.finish()</tt></td><td><tt>index</tt></td><td>This returns the finish index of <tt>i</tt>.</td></tr><tr><td><tt>i.stride()</tt></td><td><tt>index</tt></td><td>This returns the stride length of <tt>i</tt>.</td></tr><tr><td><tt>i.get_start(idx)</tt></td><td><tt>index</tt></td><td>If <tt>i</tt> specifies a start
value, this is equivalent to <tt>i.start()</tt>. Otherwise it
returns <tt>idx</tt>.</td></tr><tr><td><tt>i.get_finish(idx)</tt></td><td><tt>index</tt></td><td>If <tt>i</tt> specifies a finish
value, this is equivalent to <tt>i.finish()</tt>. Otherwise it
returns <tt>idx</tt>.</td></tr><tr><td><tt>i.size(idx)</tt></td><td><tt>size_type</tt></td><td>If <tt>i</tt> specifies a both finish and
start values, this is equivalent to
<tt>(i.finish()-i.start())/i.stride()</tt>. Otherwise it
returns <tt>idx</tt>.</td></tr><tr><td><tt>i &lt; idx</tt></td><td><tt>index</tt></td><td>This is another syntax for specifying the finish
value. This notation does not include
<tt>idx</tt> in the range of valid indices. It is equivalent to
<tt>index_range(r.start(), idx, r.stride())</tt></td></tr><tr><td><tt>i &lt;= idx</tt></td><td><tt>index</tt></td><td>This is another syntax for specifying the finish
value. This notation includes
<tt>idx</tt> in the range of valid indices. It is equivalent to
<tt>index_range(r.start(), idx + 1, r.stride())</tt></td></tr><tr><td><tt>idx &lt; i</tt></td><td><tt>index</tt></td><td>This is another syntax for specifying the start
value. This notation does not include
<tt>idx</tt> in the range of valid indices. It is equivalent to
<tt>index_range(idx + 1, i.finish(), i.stride())</tt>.</td></tr><tr><td><tt>idx &lt;= i</tt></td><td><tt>index</tt></td><td>This is another syntax for specifying the start
value. This notation includes
<tt>idx1</tt> in the range of valid indices. It is equivalent to
<tt>index_range(idx, i.finish(), i.stride())</tt>.</td></tr><tr><td><tt>i + idx</tt></td><td><tt>index</tt></td><td>This expression shifts the start and finish values
of <tt>i</tt> up by <tt>idx</tt>. It is equivalent to
<tt>index_range(r.start()+idx1, r.finish()+idx, r.stride())</tt></td></tr><tr><td><tt>i - idx</tt></td><td><tt>index</tt></td><td>This expression shifts the start and finish values
of <tt>i</tt> up by <tt>idx</tt>. It is equivalent to
<tt>index_range(r.start()-idx1, r.finish()-idx, r.stride())</tt></td></tr></tbody></table></div></div><div class="sect3"><div class="titlepage"><div><h4 class="title"><a name="index_gen"></a><tt>index_gen</tt></h4></div></div><fake><p> <tt>index_gen</tt> aggregates
<tt>index_range</tt> objects in order to specify view
parameters. Chained calls to <tt>operator[]</tt> store
range and dimension information used to
instantiate a new view into a MultiArray.
</p></fake><div class="table"><p><b>Table 8. Notation</b></p><table summary="Notation" border="1"><colgroup><col><col></colgroup><tbody><tr><td><tt>Dims,Ranges</tt></td><td>Unsigned integral values.</td></tr><tr><td><tt>x</tt></td><td>An object of type
<tt>template gen_type&lt;Dims,Ranges&gt;::type</tt>.</td></tr><tr><td><tt>i</tt></td><td>An object of type
<tt>index_range</tt>.</td></tr><tr><td><tt>idx</tt></td><td>Objects of type <tt>index</tt>.</td></tr></tbody></table></div><div class="table"><p><b>Table 9. Associated Types</b></p><table summary="Associated Types" border="1"><colgroup><col><col></colgroup><thead><tr><th>Type</th><th>Description</th></tr></thead><tbody><tr><td><tt>index</tt></td><td>This is a signed integral type. It is used to
specify degenerate dimensions.</td></tr><tr><td><tt>size_type</tt></td><td>This is an unsigned integral type. It is used to
report the size of the range an <tt>index_range</tt>
represents.</td></tr><tr><td><tt>template gen_type::&lt;Dims,Ranges&gt;::type</tt></td><td>This type generator names the result of
<tt>Dims</tt> chained calls to
<tt>index_gen::operator[]</tt>. The
<tt>Ranges</tt> parameter is determined by the number of
degenerate ranges specified (i.e. calls to
<tt>operator[](index)</tt>). Note that
<tt>index_gen</tt> and
<tt>gen_type&lt;0,0&gt;::type</tt> are the same type.</td></tr></tbody></table></div><div class="table"><p><b>Table 10. Valid Expressions</b></p><table summary="Valid Expressions" border="1"><colgroup><col><col><col></colgroup><thead><tr><th>Expression</th><th>Return type</th><th>Semantics</th></tr></thead><tbody><tr><td><tt>index_gen()</tt></td><td><tt>gen_type&lt;0,0&gt;::type</tt></td><td>This constructs an <tt>index_gen</tt>
object. This object can then be used to generate tuples of
<tt>index_range</tt> values.</td></tr><tr><td><tt>x[i]</tt></td><td><tt>gen_type&lt;Dims+1,Ranges+1&gt;::type</tt></td><td>Returns a new object containing all previous
<tt>index_range</tt> objects in addition to
<tt>i.</tt> Chained calls to
<tt>operator[]</tt> are the means by which
<tt>index_range</tt> objects are aggregated.</td></tr><tr><td><tt>x[idx]</tt></td><td><tt>gen_type&lt;Dims,Ranges&gt;::type</tt></td><td>Returns a new object containing all previous
<tt>index_range</tt> objects in addition to a degenerate
range, <tt>index_range(idx,idx).</tt> Note that this is NOT
equivalent to <tt>x[index_range(idx,idx)].</tt>, which will
return an object of type
<tt>gen_type&lt;Dims+1,Ranges+1&gt;::type</tt>.
</td></tr></tbody></table></div></div></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="id253521"></a>Models</h3></div></div><div class="itemizedlist"><ul type="disc"><li><tt>multi_array</tt></li><li><tt>multi_array_ref</tt></li><li><tt>const_multi_array_ref</tt></li><li><tt>template array_view&lt;Dims&gt;::type</tt></li><li><tt>template const_array_view&lt;Dims&gt;::type</tt></li><li><tt>template subarray&lt;Dims&gt;::type</tt></li><li><tt>template const_subarray&lt;Dims&gt;::type</tt></li></ul></div></div></div><div class="sect1"><div class="titlepage"><div><h2 class="title" style="clear: both"><a name="array_types"></a>Array Components</h2></div></div><fake><p>
Boost.MultiArray defines an array class,
<tt>multi_array</tt>, and two adapter classes,
<tt>multi_array_ref</tt> and
<tt>const_multi_array_ref</tt>. The three classes model
MultiArray and so they share a lot of functionality.
<tt>multi_array_ref</tt> differs from
<tt>multi_array</tt> in that the
<tt>multi_array</tt> manages its own memory, while
<tt>multi_array_ref</tt> is passed a block of memory that it
expects to be externally managed.
<tt>const_multi_array_ref</tt> differs from
<tt>multi_array_ref</tt> in that the underlying elements it
adapts cannot be modified through its interface, though some array
properties, including the array shape and index bases, can be altered.
Functionality the classes have in common is described
below.
</p></fake><p><b>Note: Preconditions, Effects, and Implementation. </b>
Throughout the following sections, small pieces of C++ code are
used to specify constraints such as preconditions, effects, and
postconditions. These do not necessarily describe the underlying
implementation of array components; rather, they describe the
expected input to and
behavior of the specified operations. Failure to meet
preconditions results in undefined behavior. Not all effects
(i.e. copy constructors, etc.) must be mimicked exactly. The code
snippets for effects intend to capture the essence of the described
operation.
</p><p><b>Queries. </b><div class="variablelist"><dl><dt><span class="term"><pre class="programlisting">element* data();
const element* data() const;</pre></span></dt><dd><fake><p>This returns a pointer to the beginning of the
contiguous block that contains the array's data. If all dimensions of
the array are 0-indexed and stored in ascending order, this is
equivalent to <tt>origin()</tt>. Note that
<tt>const_multi_array_ref</tt> only provides the const
version of this function.
</p></fake></dd><dt><span class="term"><pre class="programlisting">element* origin();
const element* origin() const;</pre></span></dt><dd><fake><p>This returns the origin element of the
<tt>multi_array</tt>. Note that
<tt>const_multi_array_ref</tt> only provides the const
version of this function. (Required by MultiArray)
</p></fake></dd><dt><span class="term"><tt>const index* index_bases();</tt></span></dt><dd><fake><p>This returns the index bases for the
<tt>multi_array</tt>. (Required by MultiArray)
</p></fake></dd><dt><span class="term"><tt>const index* strides();</tt></span></dt><dd><fake><p>This returns the strides for the
<tt>multi_array</tt>. (Required by MultiArray)
</p></fake></dd><dt><span class="term"><tt>const size_type* shape();</tt></span></dt><dd><fake><p>This returns the shape of the
<tt>multi_array</tt>. (Required by MultiArray)
</p></fake></dd></dl></div></p><p><b>Comparators. </b><div class="variablelist"><dl><dt><span class="term"><pre class="programlisting">
bool operator==(const *array-type*&amp; rhs);
bool operator!=(const *array-type*&amp; rhs);
bool operator&lt;(const *array-type*&amp; rhs);
bool operator&gt;(const *array-type*&amp; rhs);
bool operator&gt;=(const *array-type*&amp; rhs);
bool operator&lt;=(const *array-type*&amp; rhs);</pre></span></dt><dd><fake><p>Each comparator executes a lexicographical compare over
the value types of the two arrays.
(Required by MultiArray)
</p></fake><p><b>Preconditions. </b><tt>element</tt> must support the
comparator corresponding to that called on
<tt>multi_array</tt>.</p><p><b>Complexity. </b>O(<tt>num_elements()</tt>).</p></dd></dl></div></p><p><b>Modifiers. </b><div class="variablelist"><dl><dt><span class="term">
<pre class="programlisting">
template &lt;typename SizeList&gt;
void reshape(const SizeList&amp; sizes)
</pre>
</span></dt><dd><fake><p>This changes the shape of the <tt>multi_array</tt>. The
number of elements and the index bases remain the same, but the number
of values at each level of the nested container hierarchy may
change.</p></fake><p><b><tt>SizeList</tt> Requirements. </b><tt>SizeList</tt> must model
<a href="../../utility/Collection.html" target="_top">Collection</a>.</p><p><b>Preconditions. </b>
<pre class="programlisting">
std::accumulate(sizes.begin(),sizes.end(),size_type(1),std::times&lt;size_type&gt;()) == this-&gt;num_elements();
sizes.size() == NumDims;
</pre></p><p><b>Postconditions. </b>
<tt>std::equal(sizes.begin(),sizes.end(),this-&gt;shape) == true;</tt>
</p></dd><dt><span class="term">
<pre class="programlisting">
template &lt;typename BaseList&gt;
void reindex(const BaseList&amp; values);
</pre>
</span></dt><dd><fake><p>This changes the index bases of the <tt>multi_array</tt> to
correspond to the the values in <tt>values</tt>.</p></fake><p><b><tt>BaseList</tt> Requirements. </b><tt>BaseList</tt> must model
<a href="../../utility/Collection.html" target="_top">Collection</a>.</p><p><b>Preconditions. </b><tt>values.size() == NumDims;</tt></p><p><b>Postconditions. </b><tt>std::equal(values.begin(),values.end(),this-&gt;index_bases());
</tt></p></dd><dt><span class="term">
<pre class="programlisting">
void reindex(index value);
</pre>
</span></dt><dd><fake><p>This changes the index bases of all dimensions of the
<tt>multi_array</tt> to <tt>value</tt>.</p></fake><p><b>Postconditions. </b>
<pre class="programlisting">
std::count_if(this-&gt;index_bases(),this-&gt;index_bases()+this-&gt;num_dimensions(),
std::bind_2nd(std::equal_to&lt;index&gt;(),value)) ==
this-&gt;num_dimensions();
</pre>
</p></dd></dl></div></p><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="multi_array"></a><tt>multi_array</tt></h3></div></div><fake><p>
<tt>multi_array</tt> is a multi-dimensional container that
supports random access iteration. Its number of dimensions is
fixed at compile time, but its shape and the number of elements it
contains are specified during its construction. The number of elements
will remain fixed for the duration of a
<tt>multi_array</tt>'s lifetime, but the shape of the container can
be changed. A <tt>multi_array</tt> manages its data elements
using a replaceable allocator.
</p></fake><p><b>Model Of. </b>
<a href="#MultiArray" title="MultiArray Concept">MultiArray</a>,
<a href="../../../libs/utility/CopyConstructible.html" target="_top">CopyConstructible</a>. Depending on the element type,
it may also model <a href="http://www.sgi.com/tech/stl/EqualityComparable.html" target="_top">EqualityComparable</a> and <a href="http://www.sgi.com/tech/stl/LessThanComparable.html" target="_top">LessThanComparable</a>.
</p><p><b>Synopsis. </b><pre class="programlisting">
namespace boost {
template &lt;typename ValueType,
std::size_t NumDims,
typename Allocator = std::allocator&lt;ValueType&gt; &gt;
class multi_array {
public:
// types:
typedef ValueType element;
typedef *implementation-defined* value_type;
typedef *implementation-defined* reference;
typedef *implementation-defined* const_reference;
typedef *implementation-defined* difference_type;
typedef *implementation-defined* iterator;
typedef *implementation-defined* const_iterator;
typedef *implementation-defined* reverse_iterator;
typedef *implementation-defined* const_reverse_iterator;
typedef multi_array_types::size_type size_type;
typedef multi_array_types::index index;
typedef multi_array_types::index_gen index_gen;
typedef multi_array_types::index_range index_range;
typedef multi_array_types::extent_gen extent_gen;
typedef multi_array_types::extent_range extent_range;
typedef *implementation-defined* storage_order_type;
// template typedefs
template &lt;std::size_t Dims&gt; struct subarray;
template &lt;std::size_t Dims&gt; struct const_subarray;
template &lt;std::size_t Dims&gt; struct array_view;
template &lt;std::size_t Dims&gt; struct const_array_view;
// constructors and destructors
multi_array();
template &lt;typename ExtentList&gt;
explicit multi_array(const ExtentList&amp; sizes,
const storage_order_type&amp; store = c_storage_order(),
const Allocator&amp; alloc = Allocator());
explicit multi_array(const extents_tuple&amp; ranges,
const storage_order_type&amp; store = c_storage_order(),
const Allocator&amp; alloc = Allocator());
multi_array(const multi_array&amp; x);
~multi_array();
// modifiers
multi_array&amp; operator=(const multi_array&amp; x);
template &lt;class Array&gt; multi_array&amp; operator=(const Array&amp; x);
// iterators:
iterator begin();
iterator end();
const_iterator begin() const;
const_iterator end() const;
reverse_iterator rbegin();
reverse_iterator rend();
const_reverse_iterator rbegin() const;
const_reverse_iterator rend() const;
// capacity:
size_type size() const;
size_type num_elements() const;
size_type num_dimensions() const;
// element access:
template &lt;typename IndexList&gt;
element&amp; operator()(const IndexList&amp; indices);
template &lt;typename IndexList&gt;
const element&amp; operator()(const IndexList&amp; indices) const;
reference operator[](index i);
const_reference operator[](index i) const;
array_view&lt;Dims&gt;::type operator[](const indices_tuple&amp; r);
const_array_view&lt;Dims&gt;::type operator[](const indices_tuple&amp; r) const;
// queries
element* data();
const element* data() const;
element* origin();
const element* origin() const;
const size_type* shape() const;
const index* strides() const;
const index* index_bases() const;
const storage_order_type&amp; storage_order() const;
// comparators
bool operator==(const multi_array&amp; rhs);
bool operator!=(const multi_array&amp; rhs);
bool operator&lt;(const multi_array&amp; rhs);
bool operator&gt;(const multi_array&amp; rhs);
bool operator&gt;=(const multi_array&amp; rhs);
bool operator&lt;=(const multi_array&amp; rhs);
// modifiers:
template &lt;typename InputIterator&gt;
void assign(InputIterator begin, InputIterator end);
template &lt;typename SizeList&gt;
void reshape(const SizeList&amp; sizes)
template &lt;typename BaseList&gt; void reindex(const BaseList&amp; values);
void reindex(index value);
multi_array&amp; resize(extents_tuple&amp; extents);
};
</pre></p><p><b>Constructors. </b><div class="variablelist"><dl><dt><span class="term"><pre class="programlisting">template &lt;typename ExtentList&gt;
explicit multi_array(const ExtentList&amp; sizes,
const storage_order_type&amp; store = c_storage_order(),
const Allocator&amp; alloc = Allocator());
</pre></span></dt><dd><fake><p>
This constructs a <tt>multi_array</tt> using the specified
parameters. <tt>sizes</tt> specifies the shape of the
constructed <tt>multi_array</tt>. <tt>store</tt>
specifies the storage order or layout in memory of the array
dimensions. <tt>alloc</tt> is used to
allocate the contained elements.
</p></fake><p><b><tt>ExtentList</tt> Requirements. </b>
<tt>ExtentList</tt> must model <a href="../../utility/Collection.html" target="_top">Collection</a>.
</p><p><b>Preconditions. </b><tt>sizes.size() == NumDims;</tt></p></dd><dt><span class="term">
<pre class="programlisting">explicit multi_array(extent_gen::gen_type&lt;NumDims&gt;::type ranges,
const storage_order_type&amp; store = c_storage_order(),
const Allocator&amp; alloc = Allocator());
</pre></span></dt><dd><fake><p>
This constructs a <tt>multi_array</tt> using the specified
parameters. <tt>ranges</tt> specifies the shape and
index bases of the constructed multi_array. It is the result of
<tt>NumDims</tt> chained calls to
<tt>extent_gen::operator[]</tt>. <tt>store</tt>
specifies the storage order or layout in memory of the array
dimensions. <tt>alloc</tt> is the allocator used to
allocate the memory used to store <tt>multi_array</tt>
elements.
</p></fake></dd><dt><span class="term"><pre class="programlisting">
multi_array(const multi_array&amp; x);
</pre></span></dt><dd><fake><p>This constructs a <tt>multi_array</tt> and performs a deep
copy of <tt>x</tt>.
</p></fake><p><b>Complexity. </b> This performs O(<tt>x.num_elements()</tt>) calls to
<tt>element</tt>'s copy
constructor.
</p></dd><dt><span class="term"><pre class="programlisting">
multi_array();
</pre></span></dt><dd><fake><p>This constructs a <tt>multi_array</tt> whose shape is (0,...,0) and contains no elements.
</p></fake></dd></dl></div><p><b>Note on Constructors. </b>
The <tt>multi_array</tt> construction expressions,
<pre class="programlisting">
multi_array&lt;int,3&gt; A(boost::extents[5][4][3]);
</pre>
and
<pre class="programlisting">
boost::array&lt;multi_array_base::index,3&gt; my_extents = {{5, 4, 3}};
multi_array&lt;int,3&gt; A(my_extents);
</pre>
are equivalent.
</p></p><p><b>Modifiers. </b><div class="variablelist"><dl><dt><span class="term"><pre class="programlisting">
multi_array&amp; operator=(const multi_array&amp; x);
template &lt;class Array&gt; multi_array&amp; operator=(const Array&amp; x);
</pre>
</span></dt><dd><fake><p>This performs an element-wise copy of <tt>x</tt>
into the current <tt>multi_array</tt>.</p></fake><p><b><tt>Array</tt> Requirements. </b><tt>Array</tt> must model MultiArray.
</p><p><b>Preconditions. </b>
<pre class="programlisting">std::equal(this-&gt;shape(),this-&gt;shape()+this-&gt;num_dimensions(),
x.shape());</pre></p><p><b>Postconditions. </b>
<pre class="programlisting">(*.this) == x;</pre>
</p><p><b>Complexity. </b>The assignment operators perform
O(<tt>x.num_elements()</tt>) calls to <tt>element</tt>'s
copy constructor.</p></dd><dt><span class="term">
<pre class="programlisting">
template &lt;typename InputIterator&gt;
void assign(InputIterator begin, InputIterator end);
</pre>
</span></dt><dd><fake><p>This copies the elements in the range
<tt>[begin,end)</tt> into the array. It is equivalent to
<tt>std::copy(begin,end,this-&gt;data())</tt>.
</p></fake><p><b>Preconditions. </b><tt>std::distance(begin,end) == this-&gt;num_elements();</tt>
</p><p><b>Complexity. </b>
The <tt>assign</tt> member function performs
O(<tt>this-&gt;num_elements()</tt>) calls to
<tt>ValueType</tt>'s copy constructor.
</p></dd><dt><span class="term">
<pre class="programlisting">multi_array&amp; resize(extent_gen::gen_type&lt;NumDims&gt;::type ranges);
</pre></span></dt><dd><fake><p>
This function resizes an array to the shape specified by
<tt>ranges</tt>. The contents of the array are preserved
whenever possible; if the new array size is smaller, then some data will
be lost. Any new elements created by resizing the array are initialized with
the <tt>element</tt> default constructor.
</p></fake></dd></dl></div></p><p><b>Queries. </b><div class="variablelist"><dl><dt><span class="term"><pre class="programlisting">
storage_order_type&amp; storage_order() const;
</pre>
</span></dt><dd><fake><p>This query returns the storage order object associated with the
<tt>multi_array</tt> in question. It can be used to construct a new array with the same storage order.</p></fake></dd></dl></div></p></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="multi_array_ref"></a><tt>multi_array_ref</tt></h3></div></div><fake><p>
<tt>multi_array_ref</tt> is a multi-dimensional container
adaptor. It provides the MultiArray interface over any contiguous
block of elements. <tt>multi_array_ref</tt> exports the
same interface as <tt>multi_array</tt>, with the exception
of the constructors.
</p></fake><p><b>Model Of. </b>
<tt>multi_array_ref</tt> models
<a href="#MultiArray" title="MultiArray Concept">MultiArray</a>,
<a href="../../../libs/utility/CopyConstructible.html" target="_top">CopyConstructible</a>.
and depending on the element type, it may also model
<a href="http://www.sgi.com/tech/stl/EqualityComparable.html" target="_top">EqualityComparable</a> and <a href="http://www.sgi.com/tech/stl/LessThanComparable.html" target="_top">LessThanComparable</a>.
Detailed descriptions are provided here only for operations that are
not described in the <tt>multi_array</tt> reference.
</p><p><b>Synopsis. </b><pre class="programlisting">
namespace boost {
template &lt;typename ValueType,
std::size_t NumDims,
typename Allocator = std::allocator&lt;ValueType&gt; &gt;
class multi_array_ref {
public:
// types:
typedef ValueType element;
typedef *implementation-defined* value_type;
typedef *implementation-defined* reference;
typedef *implementation-defined* const_reference;
typedef *implementation-defined* difference_type;
typedef *implementation-defined* iterator;
typedef *implementation-defined* const_iterator;
typedef *implementation-defined* reverse_iterator;
typedef *implementation-defined* const_reverse_iterator;
typedef multi_array_types::size_type size_type;
typedef multi_array_types::index index;
typedef multi_array_types::index_gen index_gen;
typedef multi_array_types::index_range index_range;
typedef multi_array_types::extent_gen extent_gen;
typedef multi_array_types::extent_range extent_range;
typedef *implementation-defined* storage_order_type;
// template typedefs
template &lt;std::size_t Dims&gt; struct subarray;
template &lt;std::size_t Dims&gt; struct const_subarray;
template &lt;std::size_t Dims&gt; struct array_view;
template &lt;std::size_t Dims&gt; struct const_array_view;
// structors
template &lt;typename ExtentList&gt;
explicit multi_array_ref(element* data, const ExtentList&amp; sizes,
const storage_order_type&amp; store = c_storage_order());
explicit multi_array_ref(element* data, const extents_tuple&amp; ranges,
const storage_order_type&amp; store = c_storage_order());
multi_array_ref(const multi_array_ref&amp; x);
~multi_array_ref();
// modifiers
multi_array_ref&amp; operator=(const multi_array_ref&amp; x);
template &lt;class Array&gt; multi_array_ref&amp; operator=(const Array&amp; x);
// iterators:
iterator begin();
iterator end();
const_iterator begin() const;
const_iterator end() const;
reverse_iterator rbegin();
reverse_iterator rend();
const_reverse_iterator rbegin() const;
const_reverse_iterator rend() const;
// capacity:
size_type size() const;
size_type num_elements() const;
size_type num_dimensions() const;
// element access:
template &lt;typename IndexList&gt;
element&amp; operator()(const IndexList&amp; indices);
template &lt;typename IndexList&gt;
const element&amp; operator()(const IndexList&amp; indices) const;
reference operator[](index i);
const_reference operator[](index i) const;
array_view&lt;Dims&gt;::type operator[](const indices_tuple&amp; r);
const_array_view&lt;Dims&gt;::type operator[](const indices_tuple&amp; r) const;
// queries
element* data();
const element* data() const;
element* origin();
const element* origin() const;
const size_type* shape() const;
const index* strides() const;
const index* index_bases() const;
const storage_order_type&amp; storage_order() const;
// comparators
bool operator==(const multi_array_ref&amp; rhs);
bool operator!=(const multi_array_ref&amp; rhs);
bool operator&lt;(const multi_array_ref&amp; rhs);
bool operator&gt;(const multi_array_ref&amp; rhs);
bool operator&gt;=(const multi_array_ref&amp; rhs);
bool operator&lt;=(const multi_array_ref&amp; rhs);
// modifiers:
template &lt;typename InputIterator&gt;
void assign(InputIterator begin, InputIterator end);
template &lt;typename SizeList&gt;
void reshape(const SizeList&amp; sizes)
template &lt;typename BaseList&gt; void reindex(const BaseList&amp; values);
void reindex(index value);
};
</pre></p><p><b>Constructors. </b><div class="variablelist"><dl><dt><span class="term"><pre class="programlisting">template &lt;typename ExtentList&gt;
explicit multi_array_ref(element* data,
const ExtentList&amp; sizes,
const storage_order&amp; store = c_storage_order(),
const Allocator&amp; alloc = Allocator());
</pre></span></dt><dd><fake><p>
This constructs a <tt>multi_array_ref</tt> using the specified
parameters. <tt>sizes</tt> specifies the shape of the
constructed <tt>multi_array_ref</tt>. <tt>store</tt>
specifies the storage order or layout in memory of the array
dimensions. <tt>alloc</tt> is used to
allocate the contained elements.
</p></fake><p><b><tt>ExtentList</tt> Requirements. </b>
<tt>ExtentList</tt> must model <a href="../../utility/Collection.html" target="_top">Collection</a>.
</p><p><b>Preconditions. </b><tt>sizes.size() == NumDims;</tt></p></dd><dt><span class="term">
<pre class="programlisting">explicit multi_array_ref(element* data,
extent_gen::gen_type&lt;NumDims&gt;::type ranges,
const storage_order&amp; store = c_storage_order());
</pre></span></dt><dd><fake><p>
This constructs a <tt>multi_array_ref</tt> using the specified
parameters. <tt>ranges</tt> specifies the shape and
index bases of the constructed multi_array_ref. It is the result of
<tt>NumDims</tt> chained calls to
<tt>extent_gen::operator[]</tt>. <tt>store</tt>
specifies the storage order or layout in memory of the array
dimensions.
</p></fake></dd><dt><span class="term"><pre class="programlisting">
multi_array_ref(const multi_array_ref&amp; x);
</pre></span></dt><dd><fake><p>This constructs a shallow copy of <tt>x</tt>.
</p></fake><p><b>Complexity. </b> Constant time (for contrast, compare this to
the <tt>multi_array</tt> class copy constructor.
</p></dd></dl></div></p><p><b>Modifiers. </b><div class="variablelist"><dl><dt><span class="term"><pre class="programlisting">
multi_array_ref&amp; operator=(const multi_array_ref&amp; x);
template &lt;class Array&gt; multi_array_ref&amp; operator=(const Array&amp; x);
</pre>
</span></dt><dd><fake><p>This performs an element-wise copy of <tt>x</tt>
into the current <tt>multi_array_ref</tt>.</p></fake><p><b><tt>Array</tt> Requirements. </b><tt>Array</tt> must model MultiArray.
</p><p><b>Preconditions. </b>
<pre class="programlisting">std::equal(this-&gt;shape(),this-&gt;shape()+this-&gt;num_dimensions(),
x.shape());</pre></p><p><b>Postconditions. </b>
<pre class="programlisting">(*.this) == x;</pre>
</p><p><b>Complexity. </b>The assignment operators perform
O(<tt>x.num_elements()</tt>) calls to <tt>element</tt>'s
copy constructor.</p></dd></dl></div></p></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="const_multi_array_ref"></a><tt>const_multi_array_ref</tt></h3></div></div><fake><p>
<tt>const_multi_array_ref</tt> is a multi-dimensional container
adaptor. It provides the MultiArray interface over any contiguous
block of elements. <tt>const_multi_array_ref</tt> exports the
same interface as <tt>multi_array</tt>, with the exception
of the constructors.
</p></fake><p><b>Model Of. </b>
<tt>const_multi_array_ref</tt> models
<a href="#MultiArray" title="MultiArray Concept">MultiArray</a>,
<a href="../../../libs/utility/CopyConstructible.html" target="_top">CopyConstructible</a>.
and depending on the element type, it may also model
<a href="http://www.sgi.com/tech/stl/EqualityComparable.html" target="_top">EqualityComparable</a> and <a href="http://www.sgi.com/tech/stl/LessThanComparable.html" target="_top">LessThanComparable</a>.
Detailed descriptions are provided here only for operations that are
not described in the <tt>multi_array</tt> reference.
</p><p><b>Synopsis. </b><pre class="programlisting">
namespace boost {
template &lt;typename ValueType,
std::size_t NumDims,
typename Allocator = std::allocator&lt;ValueType&gt; &gt;
class const_multi_array_ref {
public:
// types:
typedef ValueType element;
typedef *implementation-defined* value_type;
typedef *implementation-defined* reference;
typedef *implementation-defined* const_reference;
typedef *implementation-defined* difference_type;
typedef *implementation-defined* iterator;
typedef *implementation-defined* const_iterator;
typedef *implementation-defined* reverse_iterator;
typedef *implementation-defined* const_reverse_iterator;
typedef multi_array_types::size_type size_type;
typedef multi_array_types::index index;
typedef multi_array_types::index_gen index_gen;
typedef multi_array_types::index_range index_range;
typedef multi_array_types::extent_gen extent_gen;
typedef multi_array_types::extent_range extent_range;
typedef *implementation-defined* storage_order_type;
// template typedefs
template &lt;std::size_t Dims&gt; struct subarray;
template &lt;std::size_t Dims&gt; struct const_subarray;
template &lt;std::size_t Dims&gt; struct array_view;
template &lt;std::size_t Dims&gt; struct const_array_view;
// structors
template &lt;typename ExtentList&gt;
explicit const_multi_array_ref(const element* data, const ExtentList&amp; sizes,
const storage_order_type&amp; store = c_storage_order());
explicit const_multi_array_ref(const element* data, const extents_tuple&amp; ranges,
const storage_order_type&amp; store = c_storage_order());
const_multi_array_ref(const const_multi_array_ref&amp; x);
~const_multi_array_ref();
// iterators:
const_iterator begin() const;
const_iterator end() const;
const_reverse_iterator rbegin() const;
const_reverse_iterator rend() const;
// capacity:
size_type size() const;
size_type num_elements() const;
size_type num_dimensions() const;
// element access:
template &lt;typename IndexList&gt;
const element&amp; operator()(const IndexList&amp; indices) const;
const_reference operator[](index i) const;
const_array_view&lt;Dims&gt;::type operator[](const indices_tuple&amp; r) const;
// queries
const element* data() const;
const element* origin() const;
const size_type* shape() const;
const index* strides() const;
const index* index_bases() const;
const storage_order_type&amp; storage_order() const;
// comparators
bool operator==(const const_multi_array_ref&amp; rhs);
bool operator!=(const const_multi_array_ref&amp; rhs);
bool operator&lt;(const const_multi_array_ref&amp; rhs);
bool operator&gt;(const const_multi_array_ref&amp; rhs);
bool operator&gt;=(const const_multi_array_ref&amp; rhs);
bool operator&lt;=(const const_multi_array_ref&amp; rhs);
// modifiers:
template &lt;typename SizeList&gt;
void reshape(const SizeList&amp; sizes)
template &lt;typename BaseList&gt; void reindex(const BaseList&amp; values);
void reindex(index value);
};
</pre></p><p><b>Constructors. </b><div class="variablelist"><dl><dt><span class="term"><pre class="programlisting">template &lt;typename ExtentList&gt;
explicit const_multi_array_ref(const element* data,
const ExtentList&amp; sizes,
const storage_order&amp; store = c_storage_order());
</pre></span></dt><dd><fake><p>
This constructs a <tt>const_multi_array_ref</tt> using the specified
parameters. <tt>sizes</tt> specifies the shape of the
constructed <tt>const_multi_array_ref</tt>. <tt>store</tt>
specifies the storage order or layout in memory of the array
dimensions.
</p></fake><p><b><tt>ExtentList</tt> Requirements. </b>
<tt>ExtentList</tt> must model <a href="../../utility/Collection.html" target="_top">Collection</a>.
</p><p><b>Preconditions. </b><tt>sizes.size() == NumDims;</tt></p></dd><dt><span class="term">
<pre class="programlisting">explicit const_multi_array_ref(const element* data,
extent_gen::gen_type&lt;NumDims&gt;::type ranges,
const storage_order&amp; store = c_storage_order());
</pre></span></dt><dd><p><b>Effects. </b>
This constructs a <tt>const_multi_array_ref</tt> using the specified
parameters. <tt>ranges</tt> specifies the shape and
index bases of the constructed const_multi_array_ref. It is the result of
<tt>NumDims</tt> chained calls to
<tt>extent_gen::operator[]</tt>. <tt>store</tt>
specifies the storage order or layout in memory of the array
dimensions.
</p></dd><dt><span class="term"><pre class="programlisting">
const_multi_array_ref(const const_multi_array_ref&amp; x);
</pre></span></dt><dd><p><b>Effects. </b>This constructs a shallow copy of <tt>x</tt>.
</p></dd></dl></div></p></div></div><div class="sect1"><div class="titlepage"><div><h2 class="title" style="clear: both"><a name="auxiliary"></a>Auxiliary Components</h2></div></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="multi_array_types"></a><tt>multi_array_types</tt></h3></div></div><pre class="programlisting">
namespace multi_array_types {
typedef *implementation-defined* index;
typedef *implementation-defined* size_type;
typedef *implementation-defined* difference_type;
typedef *implementation-defined* index_range;
typedef *implementation-defined* extent_range;
typedef *implementation-defined* index_gen;
typedef *implementation-defined* extent_gen;
}
</pre><fake><p>Namespace <tt>multi_array_types</tt> defines types
associated with <tt>multi_array</tt>,
<tt>multi_array_ref</tt>, and
<tt>const_multi_array_ref</tt> 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 <tt>extent_gen</tt> and
<tt>extent_range</tt>, these types fulfill the roles of the
same name required by MultiArray and are described in its
concept definition. <tt>extent_gen</tt> and
<tt>extent_range</tt> are described below.
</p></fake></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="extent_range"></a><tt>extent_range</tt></h3></div></div><fake><p><tt>extent_range</tt> objects define half open
intervals. They provide shape and index base information to
<tt>multi_array</tt>, <tt>multi_array_ref</tt>,
and <tt>const_multi_array_ref</tt> constructors.
<tt>extent_range</tt>s are passed in
aggregate to an array constructor (see
<tt>extent_gen</tt> for more details).
</p></fake><p><b>Synopsis. </b><pre class="programlisting">
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();
};</pre></p><p><b>Model Of. </b>DefaultConstructible,CopyConstructible</p><p><b>Methods and Types. </b><div class="variablelist"><dl><dt><span class="term"><tt>extent_range(index start, index finish)</tt></span></dt><dd><fake><p> This constructor defines the half open interval
<tt>[start,finish)</tt>. The expression
<tt>finish</tt> must be greater than <tt>start</tt>.
</p></fake></dd><dt><span class="term"><tt>extent_range(index finish)</tt></span></dt><dd><fake><p>This constructor defines the half open interval
<tt>[0,finish)</tt>. The value of <tt>finish</tt>
must be positive.</p></fake></dd><dt><span class="term"><tt>index start()</tt></span></dt><dd><fake><p>This function returns the first index represented by the range</p></fake></dd><dt><span class="term"><tt>index finish()</tt></span></dt><dd><fake><p>This function returns the upper boundary value of the half-open
interval. Note that the range does not include this value.</p></fake></dd><dt><span class="term"><tt>size_type size()</tt></span></dt><dd><fake><p>This function returns the size of the specified range. It is
equivalent to <tt>finish()-start()</tt>.</p></fake></dd></dl></div></p></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="extent_gen"></a><tt>extent_gen</tt></h3></div></div><fake><p>The <tt>extent_gen</tt> class defines an
interface for aggregating array shape and indexing information to be
passed to a <tt>multi_array</tt>,
<tt>multi_array_ref</tt>, or <tt>const_multi_array_ref</tt>
constructor. Its interface mimics
the syntax used to declare built-in array types
in C++. For example, while a 3-dimensional array of
<tt>int</tt> values in C++ would be
declared as:
<pre class="programlisting">int A[3][4][5],</pre>
a similar <tt>multi_array</tt> would be declared:
<pre class="programlisting">multi_array&lt;int,3&gt; A(extents[3][4][5]).</pre>
</p></fake><p><b>Synopsis. </b><pre class="programlisting">
template &lt;std::size_t NumRanges&gt;
class *implementation_defined* {
public:
typedef multi_array_types::index index;
typedef multi_array_types::size_type size_type;
template &lt;std::size_t NumRanges&gt; class gen_type;
gen_type&lt;NumRanges+1&gt;::type operator[](const range&amp; a_range) const;
gen_type&lt;NumRanges+1&gt;::type operator[](index idx) const;
};
typedef *implementation_defined*&lt;0&gt; extent_gen;
</pre></p><p><b>Methods and Types. </b><div class="variablelist"><dl><dt><span class="term"><tt>template gen_type::&lt;Ranges&gt;::type</tt></span></dt><dd><fake><p>This type generator is used to specify the result of
<tt>Ranges</tt> chained calls to
<tt>extent_gen::operator[].</tt> The types
<tt>extent_gen</tt> and
<tt>gen_type&lt;0&gt;::type</tt> are the same.</p></fake></dd><dt><span class="term"><tt>gen_type&lt;NumRanges+1&gt;::type
operator[](const extent_range&amp; a_range) const;</tt></span></dt><dd><fake><p>This function returns a new object containing all previous
<tt>extent_range</tt> objects in addition to
<tt>a_range.</tt> <tt>extent_range</tt>
objects are aggregated by chained calls to
<tt>operator[]</tt>.</p></fake></dd><dt><span class="term"><tt>gen_type&lt;NumRanges+1&gt;::type
operator[](index idx) const;</tt></span></dt><dd><fake><p>This function returns a new object containing all previous
<tt>extent_range</tt> objects in addition to
<tt>extent_range(0,idx).</tt> This function gives the array
constructors a similar syntax to traditional C multidimensional array
declaration.</p></fake></dd></dl></div></p></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="id253863"></a>Global Objects</h3></div></div><fake><p>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.
</p></fake><fake><p> Under some circumstances, the two global objects may be
considered excessive overhead. Their construction can be prevented by
defining the preprocessor symbol
<tt>BOOST_MULTI_ARRAY_NO_GENERATORS</tt> before including
<tt>boost/multi_array.hpp.</tt></p></fake><div class="sect3"><div class="titlepage"><div><h4 class="title"><a name="extents"></a><tt>extents</tt></h4></div></div><pre class="programlisting">
namespace boost {
multi_array_base::extent_gen extents;
}
</pre><fake><p>Boost.MultiArray's array classes use the
<tt>extents</tt> global object to specify
array shape during their construction.
For example,
a 3 by 3 by 3 <tt>multi_array</tt> is constructed as follows:
<pre class="programlisting">multi_array&lt;int,3&gt; A(extents[3][3][3]);</pre>
The same array could also be created by explicitly declaring an <tt>extent_gen</tt>
object locally,, but the global object makes this declaration unnecessary.
</p></fake></div><div class="sect3"><div class="titlepage"><div><h4 class="title"><a name="indices"></a><tt>indices</tt></h4></div></div><pre class="programlisting">
namespace boost {
multi_array_base::index_gen indices;
}
</pre><fake><p>The MultiArray concept specifies an
<tt>index_gen</tt> associated type that is used to
create views.
<tt>indices</tt> is a global object that serves the role of
<tt>index_gen</tt> for all array components provided by this
library and their associated subarrays and views.
</p></fake><fake><p>For example, using the <tt>indices</tt> object,
a view of an array <tt>A</tt> is constructed as follows:
<pre class="programlisting">
A[indices[index_range(0,5)][2][index_range(2,4)]];
</pre>
</p></fake></div></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="generators"></a>View and SubArray Generators</h3></div></div><fake><p>
Boost.MultiArray provides traits classes, <tt>subarray_gen</tt>,
<tt>const_subarray_gen</tt>,
<tt>array_view_gen</tt>,
and <tt>const_array_view_gen</tt>, 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 <tt>array_view_gen</tt>
traits class and the <tt>array_view</tt> type associated to
an array:
<pre class="programlisting">
template &lt;typename Array&gt;
void my_function() {
typedef typename Array::template array_view&lt;3&gt;::type view1_t;
typedef typename boost::array_view_gen&lt;Array,3&gt;::type view2_t;
// ...
}
</pre>
In the above example, <tt>view1_t</tt> and
<tt>view2_t</tt> have the same type.
</p></fake></div><div class="sect2"><div class="titlepage"><div><h3 class="title"><a name="memory_layout"></a>Memory Layout Specifiers</h3></div></div><fake><p>
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.
</p></fake><fake><p>For example, consider the two dimensional array shown below in
matrix notation:
</p><p><img src="matrix.gif"></p><p>
Here is how the above array is expressed in C++:
<pre class="programlisting">
int a[3][4] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 };
</pre>
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:
<pre class="programlisting">
int a[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 };
int s[] = { 4, 1 };
</pre>
With the latter declaration of <tt>a</tt> and
strides <tt>s</tt>, element <tt>a(i,j)</tt>
of the array can be
accessed using the expression
<pre class="programlisting">*a+i*s[0]+j*s[1]</pre>.
</p></fake><fake><p>The same two dimensional array could be laid out by column as follows:
<pre class="programlisting">
int a[] = { 0, 4, 8, 1, 5, 9, 2, 6, 10, 3, 7, 11 };
int s[] = { 3, 1 };
</pre>
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.
</p></fake><fake><p>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:
<pre class="programlisting">
int data[] = { 8, 9, 10, 11, 4, 5, 6, 7, 0, 1, 2, 3 };
int *a = data + 8;
int s[] = { -4, 1 };
</pre>
Note that in this example <tt>a</tt> 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.
</p></fake><fake><p>
Alternatively, the second dimension, or the columns, could be reversed
and the rows stored in ascending order:
<pre class="programlisting">
int data[] = { 3, 2, 1, 0, 7, 6, 5, 4, 11, 10, 9, 8 };
int *a = data + 3;
int s[] = { 4, -1 };
</pre>
</p></fake><fake><p>
Finally, both dimensions could be stored in descending order:
<pre class="programlisting">
int data[] = {11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0};
int *a = data + 11;
int s[] = { -4, -1 };
</pre>
<tt>
</tt>
</p></fake><fake><p>
All of the above arrays are equivalent. The expression
given above for <tt>a(i,j)</tt> 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 <tt>multi_array_ref</tt> or
<tt>const_multi_array_ref</tt>) 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.
</p></fake><div class="sect3"><div class="titlepage"><div><h4 class="title"><a name="c_storage_order"></a><tt>c_storage_order</tt></h4></div></div><pre class="programlisting">
class c_storage_order {
c_storage_order();
};
</pre><fake><p><tt>c_storage_order</tt> is used to specify that an
array should store its elements using the same layout as that used by
primitive C++ multidimensional arrays, that is, from last dimension
to first. This is the default storage order for the arrays provided by
this library.</p></fake></div><div class="sect3"><div class="titlepage"><div><h4 class="title"><a name="fortran_storage_order"></a><tt>fortran_storage_order</tt></h4></div></div><pre class="programlisting">
class fortran_storage_order {
fortran_storage_order();
};
</pre><fake><p><tt>fortran_storage_order</tt> is used to specify that
an array should store its elements using the same memory layout as a
Fortran multidimensional array would, that is, from first dimension to
last.</p></fake></div><div class="sect3"><div class="titlepage"><div><h4 class="title"><a name="general_storage_order"></a><tt>general_storage_order</tt></h4></div></div><pre class="programlisting">
template &lt;std::size_t NumDims&gt;
class general_storage_order {
template &lt;typename OrderingIter, typename AscendingIter&gt;
general_storage_order(OrderingIter ordering, AscendingIter ascending);
};
</pre><fake><p><tt>general_storage_order</tt> allows the user to
specify an arbitrary memory layout for the contents of an array. The
constructed object is passed to the array constructor in order to
specify storage order.</p></fake><fake><p>
<tt>OrderingIter</tt> and <tt>AscendingIter</tt>
must model the <tt>InputIterator</tt> concept. Both
iterators must refer to a range of <tt>NumDims</tt>
elements. <tt>AscendingIter</tt> points to objects
convertible to <tt>bool</tt>. A value of
<tt>true</tt> means that a dimension is stored in ascending
order while <tt>false</tt> means that a dimension is stored
in descending order. <tt>OrderingIter</tt> specifies the
order in which dimensions are stored.
</p></fake></div></div></div></div></body></html>
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