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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<meta name="GENERATOR" content="Microsoft FrontPage Express 2.0">
<title>Iterator Concepts</title>
</head>
<body bgcolor="#ffffff">
<h1><img src="c++boost.gif" alt="c++boost.gif" align="Center">
Iterator Concepts</h1>
<p>An Iterator is a restricted pointer-like object pointing into a vector
or matrix container.</p>
<h2><a name="indexed_bidirectional_iterator"></a>
Indexed Bidirectional Iterator</h2>
<h4>Description</h4>
<p>An Indexed Bidirectional Iterator is an iterator of a container that can
be dereferenced, incremented, decremented and carries index information. </p>
<h4>Refinement of</h4>
<p>Assignable, Equality Comparable, Default Constructible.</p>
<h4>Associated types</h4>
<table border="1">
<tbody>
<tr>
<td>Value type </td>
<td>The type of the value obtained by dereferencing a Indexed
Bidirectional Iterator </td>
</tr>
<tr>
<td>Container type</td>
<td>The type of the container a Indexed Bidirectional Iterator
points into.</td>
</tr>
</tbody>
</table>
<h4>Notation</h4>
<table border="0">
<tbody>
<tr>
<td><code>I</code> </td>
<td>A type that is a model of Indexed Bidirectional Iterator
</td>
</tr>
<tr>
<td><code>T</code> </td>
<td>The value type of <code>I</code> </td>
</tr>
<tr>
<td><code>C</code></td>
<td>The container type of <code>I</code></td>
</tr>
<tr>
<td><code>it</code>, <code>itt, it1</code>,<code> it2 </code></td>
<td>Objects of type <code>I</code> </td>
</tr>
<tr>
<td><code>t</code> </td>
<td>Object of type <code>T</code> </td>
</tr>
<tr>
<td><code>c</code></td>
<td>Object of type <code>C</code></td>
</tr>
</tbody>
</table>
<h4>Definitions</h4>
<p>A Indexed Bidirectional Iterator may be <i>mutable</i>, meaning that the
values referred to by objects of that type may be modified, or <i>constant</i>
, meaning that they may not. If an iterator type is mutable, this implies
that its value type is a model of Assignable; the converse, though, is not
necessarily true. </p>
<p>A Indexed Bidirectional Iterator may have a <i>singular</i> value, meaning
that the results of most operations, including comparison for equality, are
undefined. The only operation that is guaranteed to be supported is assigning
a nonsingular iterator to a singular iterator. </p>
<p>A Indexed Bidirectional Iterator may have a <i>dereferenceable</i> value,
meaning that dereferencing it yields a well-defined value. Dereferenceable
iterators are always nonsingular, but the converse is not true. </p>
<p>An Indexed Bidirectional Iterator is <i>past-the-end</i> if it points beyond
the last element of a container. Past-the-end values are nonsingular and
nondereferenceable. </p>
<h4>Valid expressions</h4>
<p>In addition to the expressions defined for Assignable, Equality Comparable
and Default Constructible, the following expressions must be valid. </p>
<table border="1">
<tbody>
<tr>
<th>Name </th>
<th>Expression </th>
<th>Type requirements </th>
<th>Return type </th>
</tr>
<tr>
<td>Default constructor </td>
<td><code>I it</code> </td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Dereference </td>
<td><code>*it</code> </td>
<td>&nbsp; </td>
<td>Convertible to <code>T</code>. </td>
</tr>
<tr>
<td>Dereference assignment </td>
<td><code>*it = t</code> </td>
<td><code>I</code> is mutable. </td>
<td>&nbsp; </td>
</tr>
<tr>
<td>Member access </td>
<td><code>it-&gt;m</code> </td>
<td><code>T</code> is a type for which <code>t.m</code>
is defined. </td>
<td>&nbsp; </td>
</tr>
<tr>
<td>Preincrement</td>
<td><code>++ it</code> </td>
<td>&nbsp;</td>
<td><code>I &amp;</code> </td>
</tr>
<tr>
<td>Postincrement </td>
<td><code>it ++</code> </td>
<td>&nbsp;</td>
<td><code>I</code></td>
</tr>
<tr>
<td>Predecrement </td>
<td><code>-- it</code></td>
<td>&nbsp;</td>
<td><code>I &amp;</code></td>
</tr>
<tr>
<td>Postdecrement </td>
<td><code>it --</code> </td>
<td>&nbsp; </td>
<td><code>I</code> </td>
</tr>
<tr>
<td>Function call</td>
<td><code>it ()</code></td>
<td>&nbsp;</td>
<td>Convertible to <code>C &amp;</code>.</td>
</tr>
<tr>
<td>Index</td>
<td><code>it.index ()</code></td>
<td>&nbsp;</td>
<td><code>C::size_type</code></td>
</tr>
</tbody>
</table>
<h4>Expression Semantics</h4>
<p>Semantics of an expression is defined only where it differs from, or is
not defined in, Assignable, Equality Comparable and Default Constructible.</p>
<table border="1">
<tbody>
<tr>
<th>Name </th>
<th>Expression </th>
<th>Precondition </th>
<th>Semantics </th>
<th>Postcondition </th>
</tr>
<tr>
<td>Default constructor </td>
<td><code>I it</code> </td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td><code>it</code> is singular.</td>
</tr>
<tr>
<td>Dereference </td>
<td><code>*it</code> </td>
<td><code>it</code> is dereferenceable. </td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Dereference assignment </td>
<td><code>*it = t</code></td>
<td>Same as for <code>*it</code>.</td>
<td>&nbsp;</td>
<td><code>*it</code> is a copy of t.</td>
</tr>
<tr>
<td>Member access </td>
<td><code>it-&gt;m</code></td>
<td><code>it</code> is dereferenceable. </td>
<td>Equivalent to <code>(*it).m</code></td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Preincrement </td>
<td><code>++ it</code> </td>
<td><code>it</code> is dereferenceable. </td>
<td><code>it</code> is modified to point to the next element.
</td>
<td><code>it</code> is dereferenceable or past-the-end. <code><br>
&amp;it == &amp;++ it</code>. <br>
If <code>it1 == it2</code>, <br>
then <code>++ it1 == ++ it2</code>.</td>
</tr>
<tr>
<td>Postincrement </td>
<td><code>it ++</code> </td>
<td>Same as for <code>++ it</code>.</td>
<td>Equivalent to <br>
<code>{ <br>
&nbsp;I itt = it; <br>
&nbsp;++ it; <br>
&nbsp;return itt; <br>
}</code> </td>
<td><code>it</code> is dereferenceable or past-the-end.</td>
</tr>
<tr>
<td>Predecrement </td>
<td><code>-- it</code> </td>
<td><code>it</code> is dereferenceable or past-the-end. <br>
There exists a dereferenceable iterator <code>itt</code>
such that <code>it == ++ itt</code>. </td>
<td><code>it</code> is modified to point to the previous
element. </td>
<td><code>it</code> is dereferenceable. <br>
<code>&amp;it = &amp;-- it</code>. <br>
If <code>it1 == it2</code>, <br>
then <code>-- it1 == -- it2</code>. </td>
</tr>
<tr>
<td>Postdecrement </td>
<td><code>it --</code> </td>
<td>Same as for --<code> it</code>.</td>
<td>Equivalent to <br>
<code>{ <br>
&nbsp;I itt = it; <br>
&nbsp;-- it; <br>
&nbsp;return itt; <br>
}</code> </td>
<td><code>it</code> is dereferenceable.&nbsp; </td>
</tr>
<tr>
<td>Function call</td>
<td><code>it ()</code></td>
<td><code>it</code> is dereferenceable or past-the-end. </td>
<td>If<code> it </code>points into container <code>c</code>
then<code> it () = c</code>.</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Index</td>
<td><code>it.index ()</code></td>
<td><code>it</code> is dereferenceable or past-the-end. </td>
<td><code>it.index () &gt;= 0</code><br>
and<br>
<code>it.index () &lt;= it ().size ()</code></td>
<td>If <code>it1 == it2</code>, <br>
then <code>it1.index () == it2</code>.<code>index ()</code>.<br>
If <code>it1 == it2</code>, <br>
then <code>it1.index () &lt; (++ it2</code>).<code>index
()</code>.<br>
If <code>it1 == it2</code>, <br>
then <code>it1.index () &gt; (-- it2</code>).<code>index
()</code>.</td>
</tr>
</tbody>
</table>
<h4>Complexity guarantees</h4>
<p>The complexity of operations on indexed bidirectional iterators is guaranteed
to be amortized constant time.</p>
<h4>Invariants</h4>
<table border="1">
<tbody>
<tr>
<td>Identity </td>
<td><code>it1 == it2</code> if and only if <code>&amp;*it1
== &amp;*it2</code>.</td>
</tr>
<tr>
<td>Symmetry of increment and decrement </td>
<td>If <code>it</code> is dereferenceable, then <code>++
it; --it;</code> is a null operation. Similarly, <code>-- it; ++
it;</code> is a null operation. </td>
</tr>
<tr>
<td>Relation between iterator index and container element
operator </td>
<td>If <code>it</code> is dereferenceable, <code>*it ==
it () (it.index ())</code>.</td>
</tr>
</tbody>
</table>
<h4>Models</h4>
<ul>
<li><code>sparse_vector&lt;T&gt;::iterator</code> </li>
</ul>
<h2><a name="indexed_random_access_iterator"></a>
Indexed Random Access Iterator</h2>
<h4>Description</h4>
<p>An Indexed Random Access Iterator is an iterator of a container that can
be dereferenced, moved forward, moved backward and carries index information.
</p>
<h4>Refinement of</h4>
<p>LessThanComparable, <a href="#indexed_bidirectional_iterator">Indexed
Bidirectional Iterator</a>
.</p>
<h4>Associated types</h4>
<table border="1">
<tbody>
<tr>
<td>Value type </td>
<td>The type of the value obtained by dereferencing a Indexed
Random Access Iterator </td>
</tr>
<tr>
<td>Container type</td>
<td>The type of the container a Indexed Random Access Iterator
points into.</td>
</tr>
</tbody>
</table>
<h4>Notation</h4>
<table border="0">
<tbody>
<tr>
<td><code>I</code> </td>
<td>A type that is a model of Indexed Random Access Iterator
</td>
</tr>
<tr>
<td><code>T</code> </td>
<td>The value type of <code>I</code> </td>
</tr>
<tr>
<td><code>C</code></td>
<td>The container type of <code>I</code></td>
</tr>
<tr>
<td><code>it</code>, <code>itt, it1</code>,<code> it2 </code></td>
<td>Objects of type <code>I</code> </td>
</tr>
<tr>
<td><code>t</code> </td>
<td>Object of type <code>T</code> </td>
</tr>
<tr>
<td><code>n</code></td>
<td>Object of type <code>C::difference_type</code></td>
</tr>
</tbody>
</table>
<h4>Definitions</h4>
<p>An Indexed Random Access Iterator <code>it1</code> is <i>reachable</i>
from an Indexed Random Access Iterator <code>it2</code> if, after applying
<code>operator ++</code> to <code>it2</code> a finite number of times, <code>
it1 == it2</code>. </p>
<h4>Valid expressions</h4>
<p>In addition to the expressions defined for <a href="#indexed_bidirectional_iterator">
Indexed Bidirectional Iterator</a>
, the following expressions must be valid. </p>
<table border="1">
<tbody>
<tr>
<th>Name </th>
<th>Expression </th>
<th>Type requirements </th>
<th>Return type </th>
</tr>
<tr>
<td>Forward motion </td>
<td><code>it += n</code></td>
<td>&nbsp;</td>
<td><code>I &amp;</code> </td>
</tr>
<tr>
<td>Iterator addition </td>
<td><code>it + n</code> </td>
<td>&nbsp; </td>
<td><code>I</code></td>
</tr>
<tr>
<td>Backward motion</td>
<td><code>i -= n</code> </td>
<td>&nbsp;</td>
<td><code>I &amp;</code> </td>
</tr>
<tr>
<td>Iterator subtraction </td>
<td><code>it - n</code> </td>
<td>&nbsp;</td>
<td><code>I</code>&nbsp; </td>
</tr>
<tr>
<td>Difference </td>
<td><code>it1 - it2</code></td>
<td>&nbsp;</td>
<td><code>C::difference_type</code> </td>
</tr>
<tr>
<td>Element operator </td>
<td><code>it [n]</code></td>
<td>&nbsp;</td>
<td>Convertible to <code>T</code>. </td>
</tr>
<tr>
<td>Element assignment </td>
<td><code>it [n] = t</code></td>
<td><code>I</code> is mutable </td>
<td>Convertible to <code>T</code>. </td>
</tr>
</tbody>
</table>
<h4>Expression Semantics</h4>
<p>Semantics of an expression is defined only where it differs from, or is
not defined in, <a href="#indexed_bidirectional_iterator">Indexed Bidirectional
Iterator</a>
. </p>
<table border="1">
<tbody>
<tr>
<th>Name </th>
<th>Expression </th>
<th>Precondition </th>
<th>Semantics </th>
<th>Postcondition </th>
</tr>
<tr>
<td>Forward motion </td>
<td><code>it += n</code> </td>
<td>Including <code>it</code> itself, there must be <code>n</code>
dereferenceable or past-the-end iterators following or
preceding <code>it</code>, depending on whether <code>n</code>
is positive or negative. </td>
<td>If <code>n &gt; 0</code>, equivalent to executing <code>++
it</code> <code>n</code> times. If <code>n &lt; 0</code>,
equivalent to executing <code>-- it</code> <code>n</code> times.
If <code>n == 0</code>, this is a null operation. </td>
<td><code>it</code> is dereferenceable or past-the-end. </td>
</tr>
<tr>
<td>Iterator addition </td>
<td><code>it + n</code></td>
<td>Same as for <code>i += n</code>.</td>
<td>Equivalent to <br>
<code>{ <br>
&nbsp;I itt = it; <br>
&nbsp;return itt += n; <br>
}</code></td>
<td>Result is dereferenceable or past-the-end. </td>
</tr>
<tr>
<td>Backward motion</td>
<td><code>it -= n</code></td>
<td>Including <code>it</code> itself, there must be <code>n</code>
dereferenceable or past-the-end iterators preceding or
following <code>it</code>, depending on whether <code>n</code>
is positive or negative. </td>
<td>Equivalent to <code>it += (-n)</code>. </td>
<td><code>it</code> is dereferenceable or past-the-end. </td>
</tr>
<tr>
<td>Iterator subtraction </td>
<td><code>it - n</code></td>
<td>Same as for <code>i -= n</code>.</td>
<td>Equivalent to <br>
<code>{ <br>
&nbsp;I itt = it; <br>
&nbsp;return itt -= n; <br>
}</code></td>
<td>Result is dereferenceable or past-the-end. </td>
</tr>
<tr>
<td>Difference </td>
<td><code>it1 - it2</code> </td>
<td>Either <code>it1</code> is reachable from <code>it2</code>
or <code>it2</code> is reachable from <code>it1</code>, or
both. </td>
<td>Returns a number <code>n</code> such that <code>it1
== it2 + n</code> </td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Element operator</td>
<td><code>it [n]</code> </td>
<td><code>it + n</code> exists and is dereferenceable. </td>
<td>Equivalent to <code>*(it + n)</code></td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Element assignment </td>
<td><code>i[n] = t</code> </td>
<td>Same as for <code>it [n]</code>.</td>
<td>Equivalent to <code>*(it + n) = t</code></td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<h4>Complexity guarantees</h4>
<p>The complexity of operations on indexed random access iterators is guaranteed
to be amortized constant time.</p>
<h4>Invariants</h4>
<table border="1">
<tbody>
<tr>
<td>Symmetry of addition and subtraction </td>
<td>If <code>it + n</code> is well-defined, then <code>it
+= n; it -= n;</code> and <code>(it + n) - n</code> are null operations.
Similarly, if <code>it - n</code> is well-defined, then <code>it -=
n; it += n;</code> and <code>(it - n) + n</code> are null operations.
</td>
</tr>
<tr>
<td>Relation between distance and addition </td>
<td>If <code>it1 - it2</code> is well-defined, then <code>it1
== it2 + (it1 - it2)</code>. </td>
</tr>
<tr>
<td>Reachability and distance</td>
<td>If <code>it1</code> is reachable from <code>it2</code>,
then <code>it1 - it2 &gt;= 0</code>. </td>
</tr>
</tbody>
</table>
<h4>Models</h4>
<ul>
<li><code>vector&lt;T&gt;::iterator</code> </li>
</ul>
<h2><a name="indexed_bidirectional_cr_iterator"></a>
Indexed Bidirectional Column/Row Iterator</h2>
<h4>Description</h4>
<p>An Indexed Bidirectional Column/Row Iterator is an iterator of a container
that can be dereferenced, incremented, decremented and carries index information.
</p>
<h4>Refinement of</h4>
<p>Assignable, Equality Comparable, Default Constructible.</p>
<h4>Associated types</h4>
<table border="1">
<tbody>
<tr>
<td>Value type </td>
<td>The type of the value obtained by dereferencing a Indexed
Bidirectional Column/Row Iterator </td>
</tr>
<tr>
<td>Container type</td>
<td>The type of the container a Indexed Bidirectional Column/Row
Iterator points into.</td>
</tr>
</tbody>
</table>
<h4>Notation</h4>
<table border="0">
<tbody>
<tr>
<td><code>I1</code> </td>
<td>A type that is a model of Indexed Bidirectional Column/Row
Iterator </td>
</tr>
<tr>
<td><code>I2</code></td>
<td>A type that is a model of Indexed Bidirectional Row/Column
Iterator </td>
</tr>
<tr>
<td><code>T</code> </td>
<td>The value type of <code>I1 </code>and <code>I2 </code></td>
</tr>
<tr>
<td><code>C</code></td>
<td>The container type of <code>I1 </code>and <code>I2 </code></td>
</tr>
<tr>
<td><code>it1</code>, <code>it1t, it11</code>,<code> it12
</code></td>
<td>Objects of type <code>I1</code> </td>
</tr>
<tr>
<td><code>it2</code>, <code>it2t</code></td>
<td>Objects of type <code>I2</code> </td>
</tr>
<tr>
<td><code>t</code> </td>
<td>Object of type <code>T</code> </td>
</tr>
<tr>
<td><code>c</code></td>
<td>Object of type <code>C</code></td>
</tr>
</tbody>
</table>
<h4>Definitions</h4>
<h4>Valid expressions</h4>
<p>In addition to the expressions defined for Assignable, Equality Comparable
and Default Constructible, the following expressions must be valid. </p>
<table border="1">
<tbody>
<tr>
<th>Name </th>
<th>Expression </th>
<th>Type requirements </th>
<th>Return type </th>
</tr>
<tr>
<td>Default constructor </td>
<td><code>I1 it1</code> </td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Dereference </td>
<td><code>*it1</code> </td>
<td>&nbsp; </td>
<td>Convertible to <code>T</code>. </td>
</tr>
<tr>
<td>Dereference assignment </td>
<td><code>*it1 = t</code> </td>
<td><code>I1</code> is mutable. </td>
<td>&nbsp; </td>
</tr>
<tr>
<td>Member access </td>
<td><code>it1-&gt;m</code> </td>
<td><code>T</code> is a type for which <code>t.m</code>
is defined. </td>
<td>&nbsp; </td>
</tr>
<tr>
<td>Preincrement</td>
<td><code>++ it1</code> </td>
<td>&nbsp;</td>
<td><code>I1 &amp;</code> </td>
</tr>
<tr>
<td>Postincrement </td>
<td><code>it1 ++</code> </td>
<td>&nbsp;</td>
<td><code>I1</code></td>
</tr>
<tr>
<td>Predecrement </td>
<td><code>-- it1</code></td>
<td>&nbsp;</td>
<td><code>I1 &amp;</code></td>
</tr>
<tr>
<td>Postdecrement </td>
<td><code>it1 --</code> </td>
<td>&nbsp; </td>
<td><code>I1</code> </td>
</tr>
<tr>
<td>Function call</td>
<td><code>it1 ()</code></td>
<td>&nbsp;</td>
<td>Convertible to <code>C &amp;</code>.</td>
</tr>
<tr>
<td>Row Index</td>
<td><code>it1.index1 ()</code></td>
<td>&nbsp;</td>
<td><code>C::size_type</code></td>
</tr>
<tr>
<td>Column Index</td>
<td><code>it1.index2 ()</code></td>
<td>&nbsp;</td>
<td><code>C::size_type</code></td>
</tr>
<tr>
<td>Row/Column Begin</td>
<td><code>it1.begin ()</code></td>
<td>&nbsp;</td>
<td><code>I2 </code></td>
</tr>
<tr>
<td>Row/Column End</td>
<td><code>it1.end ()</code></td>
<td>&nbsp;</td>
<td><code>I2 </code></td>
</tr>
<tr>
<td>Reverse Row/Column Begin</td>
<td><code>it1.rbegin ()</code></td>
<td>&nbsp;</td>
<td><code>reverse_iterator&lt;I2&gt; </code></td>
</tr>
<tr>
<td>Reverse Row/Column End</td>
<td><code>it1.rend ()</code></td>
<td>&nbsp;</td>
<td><code>reverse_iterator&lt;I2&gt; </code></td>
</tr>
</tbody>
</table>
<h4>Expression Semantics</h4>
<p>Semantics of an expression is defined only where it differs from, or is
not defined in, Assignable, Equality Comparable and Default Constructible.</p>
<table border="1">
<tbody>
<tr>
<th>Name </th>
<th>Expression </th>
<th>Precondition </th>
<th>Semantics </th>
<th>Postcondition </th>
</tr>
<tr>
<td>Default constructor </td>
<td><code>I1 it1</code> </td>
<td>&nbsp;</td>
<td>&nbsp;</td>
<td><code>it1</code> is singular.</td>
</tr>
<tr>
<td>Dereference </td>
<td><code>*it1</code> </td>
<td><code>it1</code> is dereferenceable. </td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Dereference assignment </td>
<td><code>*it1 = t</code></td>
<td>Same as for <code>*it1</code>.</td>
<td>&nbsp;</td>
<td><code>*it1</code> is a copy of t.</td>
</tr>
<tr>
<td>Member access </td>
<td><code>it1-&gt;m</code></td>
<td><code>it1</code> is dereferenceable. </td>
<td>Equivalent to <code>(*it1).m</code></td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Preincrement </td>
<td><code>++ it1</code> </td>
<td><code>it1</code> is dereferenceable. </td>
<td><code>it1</code> is modified to point to the next element
of the column/row, i.e. for column iterators holds<br>
<code>it1.index1 () &lt; (++ it1).index1 () </code>and<br>
<code>it1.index2 () == (++ it1).index2 ()</code>,<br>
for row iterators holds<br>
<code>it1.index1 () == (++ it1).index1 () </code>and<br>
<code>it1.index2 () &lt; (++ it1).index2 ()</code>.<br>
</td>
<td><code>it1</code> is dereferenceable or past-the-end. <code><br>
&amp;it1 == &amp;++ it1</code>. <br>
If <code>it11 == it12</code>, <br>
then <code>++ it11 == ++ it12</code>.</td>
</tr>
<tr>
<td>Postincrement </td>
<td><code>it1 ++</code> </td>
<td>Same as for <code>++ it1</code>.</td>
<td>Equivalent to <br>
<code>{ <br>
&nbsp;I1 it1t = it1; <br>
&nbsp;++ it1; <br>
&nbsp;return it1t; <br>
}</code> </td>
<td><code>it1</code> is dereferenceable or past-the-end.</td>
</tr>
<tr>
<td>Predecrement </td>
<td><code>-- it1</code> </td>
<td><code>it1</code> is dereferenceable or past-the-end. <br>
There exists a dereferenceable iterator <code>it1t</code>
such that <code>it1 == ++ it1t</code>. </td>
<td><code>it1</code> is modified to point to the previous&nbsp;
element of the column/row, i.e. for column iterators holds<br>
<code>it1.index1 () &gt; (-- it1).index1 () </code>and<br>
<code>it1.index2 () == (-- it1).index2 ()</code>,<br>
for row iterators holds<br>
<code>it1.index1 () == (-- it1).index1 () </code>and<br>
<code>it1.index2 () &gt; (-- it1).index2 ()</code>. </td>
<td><code>it1</code> is dereferenceable. <br>
<code>&amp;it1 = &amp;-- it1</code>. <br>
If <code>it11 == it12</code>, <br>
then <code>-- it11 == -- it12</code>. </td>
</tr>
<tr>
<td>Postdecrement </td>
<td><code>it1 --</code> </td>
<td>Same as for --<code> it1</code>.</td>
<td>Equivalent to <br>
<code>{ <br>
&nbsp;I1 it1t = it1; <br>
&nbsp;-- it1; <br>
&nbsp;return it1t; <br>
}</code> </td>
<td><code>it1</code> is dereferenceable.&nbsp; </td>
</tr>
<tr>
<td>Function call</td>
<td><code>it1 ()</code></td>
<td><code>it1</code> is dereferenceable or past-the-end. </td>
<td>If<code> it1 </code>points into container <code>c</code>
then<code> it1 () = c</code>.</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Row Index</td>
<td><code>it1.index1 ()</code></td>
<td><code>it1</code> is dereferenceable or past-the-end. </td>
<td><code>it1.index1 () &gt;= 0</code> and<br>
<code>it1.index1 () &lt;= it () .size1 ()</code></td>
<td>If <code>it11 == it12</code>, <br>
then <code>it11.index1 () == it12</code>.<code>index1 ()</code>
.<br>
If <code>it11</code>, <code>it12</code> are Indexed Bidirectional
Row Iterators with<code> it11 == it12</code>, <br>
then <code>it11.index1 () &lt; (++ it12</code>).<code>index1
()</code>.<br>
If <code>it11</code>, <code>it12</code> are Indexed Bidirectional
Row Iterators with<code> it11 == it12</code>, <br>
then <code>it11.index1 () &gt; (-- it12</code>).<code>index1
()</code>.</td>
</tr>
<tr>
<td>Column Index</td>
<td><code>it1.index2 ()</code></td>
<td><code>it1</code> is dereferenceable or past-the-end.</td>
<td><code>it1.index2 () &gt;= 0</code> and<br>
<code>it1.index2 () &lt;= it () .size2 ()</code></td>
<td>If <code>it11 == it12</code>, <br>
then <code>it11.index2 () == it12</code>.<code>index2 ()</code>
.<br>
If <code>it11</code>, <code>it12</code> are Indexed Bidirectional
Column Iterators with<code> it11 == it12</code>, <br>
then <code>it11.index2 () &lt; (++ it12</code>).<code>index2
()</code>.<br>
If <code>it11</code>, <code>it12</code> are Indexed Bidirectional
Column Iterators with<code> it11 == it12</code>, <br>
then <code>it11.index2 () &gt; (-- it12</code>).<code>index2
()</code>.</td>
</tr>
<tr>
<td>Row/Column Begin</td>
<td><code>it1.begin ()</code></td>
<td><code>it1</code> is dereferenceable.</td>
<td>If <code>it1</code> is a Indexed Bidirectional Column
Iterator, <br>
then <code>it2 = it1.begin () </code>is a Indexed Bidirectional
Row Iterator <br>
with<code> it2.index1 () == it1.index1 ()</code>.
<p>If <code>it1</code> is a Indexed Bidirectional Row Iterator,
<br>
then <code>it2 = it1.begin () </code>is a Indexed Bidirectional
Column Iterator <br>
with <code>it2.index2 () == it1.index2 ()</code>.</p>
</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Row/Column End</td>
<td><code>it1.end ()</code></td>
<td><code>it1</code> is dereferenceable.</td>
<td>If <code>it1</code> is a Indexed Bidirectional Column
Iterator, <br>
then <code>it2 = it1.end ()</code> is a Indexed Bidirectional
Row Iterator <br>
with<code> it2.index1 () == it1.index1 ()</code>.
<p>If <code>it1</code> is a Indexed Bidirectional Row Iterator,
<br>
then<code> it2 = it1.end ()</code> is a Indexed Bidirectional
Column Iterator <br>
with <code>it2.index2 () == it1.index2 ()</code>.</p>
</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Reverse Row/Column Begin</td>
<td><code>it1.rbegin ()</code></td>
<td><code>it1</code> is dereferenceable.</td>
<td>Equivalent to <code>reverse_iterator&lt;I2&gt; (it1.end
())</code>.</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Reverse Row/Column End</td>
<td><code>it1.rend ()</code></td>
<td><code>it1</code> is dereferenceable.</td>
<td>Equivalent to <code>reverse_iterator&lt;I2&gt; (it1.begin
())</code>.</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<h4>Complexity guarantees</h4>
<p>The complexity of operations on indexed bidirectional column/row iterators
is guaranteed to be logarithmic depending on the size of the container. The
complexity of one iterator (depending on the storage layout) can be lifted
to be amortized constant time. The complexity of the other iterator (depending
on the storage layout and the container) can be lifted to be amortized constant
time for the first row/first column respectively.</p>
<h4>Invariants</h4>
<table border="1">
<tbody>
<tr>
<td>Identity </td>
<td><code>it11 == it12</code> if and only if <code>&amp;*it11
== &amp;*it12</code>. </td>
</tr>
<tr>
<td>Symmetry of increment and decrement </td>
<td>If <code>it1</code> is dereferenceable, then <code>++
it1; --it1;</code> is a null operation. Similarly, <code>-- it1;
++ it1;</code> is a null operation. </td>
</tr>
<tr>
<td>Relation between iterator index and container element
operator </td>
<td>If <code>it1</code> is dereferenceable, <code>*it1 ==
it1 () (it1.index1 (), it2.index2 ())</code></td>
</tr>
<tr>
<td>Relation between iterator column/row begin and iterator
index</td>
<td>If <code>it1</code> is a Indexed Bidirectional Column
Iterator and <code>it2 = it1.begin ()</code> then<code> it2.index2
() &lt; it2t.index2 ()</code> for all <code>it2t </code>with <code>
it2t () == it2 () </code>and <code>it2t ().index1 () == it2 ().index1
()</code>.
<p>If <code>it1</code> is a Indexed Bidirectional Row Iterator
and <code>it2 = it1.begin ()</code> then<code> it2.index1 () &lt;
it2t.index1 ()</code> for all <code>it2t </code>with <code>it2t
() == it2 () </code>and <code>it2t ().index2 () == it2 ().index2
()</code>.</p>
</td>
</tr>
<tr>
<td>Relation between iterator column/row end and iterator
index</td>
<td>If <code>it1</code> is a Indexed Bidirectional Column
Iterator and <code>it2 = it1.end ()</code> then<code> it2.index2
() &gt; it2t.index2 ()</code> for all <code>it2t </code>with <code>
it2t () == it2 () </code>and <code>it2t ().index1 () == it2 ().index1
()</code>.
<p>If <code>it1</code> is a Indexed Bidirectional Row Iterator
and <code>it2 = it1.end () </code>then<code> it2.index1 () &gt;
it2t.index1 ()</code> for all <code>it2t </code>with <code>it2t
() == it2 () </code>and <code>it2t ().index2 () == it2 ().index2
()</code>.</p>
</td>
</tr>
</tbody>
</table>
<h4>Models</h4>
<ul>
<li><code>sparse_matrix&lt;T&gt;::iterator1</code></li>
<li><code>sparse_matrix&lt;T&gt;::iterator2</code></li>
</ul>
<h2><a name="indexed_random_access_cr_iterator"></a>
Indexed Random Access Column/Row Iterator</h2>
<h4>Description</h4>
<p>An Indexed Random Access Column/Row Iterator is an iterator of a container
that can be dereferenced, incremented, decremented and carries index information.
</p>
<h4>Refinement of</h4>
<p><a href="#indexed_bidirectional_cr_iterator">Indexed Bidirectional Column/Row
Iterator</a>
.</p>
<h4>Associated types</h4>
<table border="1">
<tbody>
<tr>
<td>Value type </td>
<td>The type of the value obtained by dereferencing a Indexed
Random Access Column/Row Iterator </td>
</tr>
<tr>
<td>Container type</td>
<td>The type of the container a Indexed Random Access Column/Row
Iterator points into.</td>
</tr>
</tbody>
</table>
<h4>Notation</h4>
<table border="0">
<tbody>
<tr>
<td><code>I</code> </td>
<td>A type that is a model of Indexed Random Access Column/Row
Iterator </td>
</tr>
<tr>
<td><code>T</code> </td>
<td>The value type of <code>I</code></td>
</tr>
<tr>
<td><code>C</code></td>
<td>The container type of <code>I</code></td>
</tr>
<tr>
<td><code>it</code>, <code>itt, it1</code>,<code> it2 </code></td>
<td>Objects of type <code>I</code> </td>
</tr>
<tr>
<td><code>t</code> </td>
<td>Object of type <code>T</code> </td>
</tr>
<tr>
<td><code>c</code></td>
<td>Object of type <code>C</code></td>
</tr>
</tbody>
</table>
<h4>Definitions</h4>
<h4>Valid expressions</h4>
<p>In addition to the expressions defined for <a href="#indexed_bidirectional_cr_iterator">
Indexed Bidirectional Column/Row Iterator</a>
, the following expressions must be valid. </p>
<table border="1">
<tbody>
<tr>
<th>Name </th>
<th>Expression </th>
<th>Type requirements </th>
<th>Return type </th>
</tr>
<tr>
<td>Forward motion </td>
<td><code>it += n</code></td>
<td>&nbsp;</td>
<td><code>I &amp;</code> </td>
</tr>
<tr>
<td>Iterator addition </td>
<td><code>it + n</code> </td>
<td>&nbsp; </td>
<td><code>I</code></td>
</tr>
<tr>
<td>Backward motion</td>
<td><code>i -= n</code> </td>
<td>&nbsp;</td>
<td><code>I &amp;</code> </td>
</tr>
<tr>
<td>Iterator subtraction </td>
<td><code>it - n</code> </td>
<td>&nbsp;</td>
<td><code>I</code>&nbsp; </td>
</tr>
<tr>
<td>Difference </td>
<td><code>it1 - it2</code></td>
<td>&nbsp;</td>
<td><code>C::difference_type</code> </td>
</tr>
<tr>
<td>Element operator </td>
<td><code>it [n]</code></td>
<td>&nbsp;</td>
<td>Convertible to <code>T</code>. </td>
</tr>
<tr>
<td>Element assignment </td>
<td><code>it [n] = t</code></td>
<td><code>I</code> is mutable </td>
<td>Convertible to <code>T</code>. </td>
</tr>
</tbody>
</table>
<h4>Expression Semantics</h4>
<p>Semantics of an expression is defined only where it differs from, or is
not defined in, <a href="#indexed_bidirectional_cr_iterator">Indexed Bidirectional
Column/Row Iterator</a>
.</p>
<table border="1">
<tbody>
<tr>
<th>Name </th>
<th>Expression </th>
<th>Precondition </th>
<th>Semantics </th>
<th>Postcondition </th>
</tr>
<tr>
<td>Forward motion </td>
<td><code>it += n</code> </td>
<td>Including <code>it</code> itself, there must be <code>n</code>
dereferenceable or past-the-end iterators following or
preceding <code>it</code>, depending on whether <code>n</code>
is positive or negative. </td>
<td>If <code>n &gt; 0</code>, equivalent to executing <code>++
it</code> <code>n</code> times. If <code>n &lt; 0</code>,
equivalent to executing <code>-- it</code> <code>n</code> times.
If <code>n == 0</code>, this is a null operation. </td>
<td><code>it</code> is dereferenceable or past-the-end. </td>
</tr>
<tr>
<td>Iterator addition </td>
<td><code>it + n</code></td>
<td>Same as for <code>i += n</code>.</td>
<td>Equivalent to <br>
<code>{ <br>
&nbsp;I itt = it; <br>
&nbsp;return itt += n; <br>
}</code></td>
<td>Result is dereferenceable or past-the-end. </td>
</tr>
<tr>
<td>Backward motion</td>
<td><code>it -= n</code></td>
<td>Including <code>it</code> itself, there must be <code>n</code>
dereferenceable or past-the-end iterators preceding or
following <code>it</code>, depending on whether <code>n</code>
is positive or negative. </td>
<td>Equivalent to <code>it += (-n)</code>. </td>
<td><code>it</code> is dereferenceable or past-the-end. </td>
</tr>
<tr>
<td>Iterator subtraction </td>
<td><code>it - n</code></td>
<td>Same as for <code>i -= n</code>.</td>
<td>Equivalent to <br>
<code>{ <br>
&nbsp;I itt = it; <br>
&nbsp;return itt -= n; <br>
}</code></td>
<td>Result is dereferenceable or past-the-end. </td>
</tr>
<tr>
<td>Difference </td>
<td><code>it1 - it2</code> </td>
<td>Either <code>it1</code> is reachable from <code>it2</code>
or <code>it2</code> is reachable from <code>it1</code>, or
both. </td>
<td>Returns a number <code>n</code> such that <code>it1
== it2 + n</code> </td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Element operator</td>
<td><code>it [n]</code> </td>
<td><code>it + n</code> exists and is dereferenceable. </td>
<td>Equivalent to <code>*(it + n)</code></td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Element assignment </td>
<td><code>i[n] = t</code> </td>
<td>Same as for <code>it [n]</code>.</td>
<td>Equivalent to <code>*(it + n) = t</code></td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<h4>Complexity guarantees</h4>
<p>The complexity of operations on indexed random access Column/Row iterators
is guaranteed to be amortized constant time.</p>
<h4>Invariants</h4>
<table border="1">
<tbody>
<tr>
<td>Symmetry of addition and subtraction </td>
<td>If <code>it + n</code> is well-defined, then <code>it
+= n; it -= n;</code> and <code>(it + n) - n</code> are null operations.
Similarly, if <code>it - n</code> is well-defined, then <code>it -=
n; it += n;</code> and <code>(it - n) + n</code> are null operations.
</td>
</tr>
<tr>
<td>Relation between distance and addition </td>
<td>If <code>it1 - it2</code> is well-defined, then <code>it1
== it2 + (it1 - it2)</code>. </td>
</tr>
<tr>
<td>Reachability and distance</td>
<td>If <code>it1</code> is reachable from <code>it2</code>,
then <code>it1 - it2 &gt;= 0</code>. </td>
</tr>
</tbody>
</table>
<h4>Models</h4>
<ul>
<li><code>matrix&lt;T&gt;::iterator1</code></li>
<li><code>matrix&lt;T&gt;::iterator2</code></li>
</ul>
<hr>
<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch <br>
Permission to copy, use, modify, sell and distribute this document is granted
provided this copyright notice appears in all copies. This document is provided
``as is'' without express or implied warranty, and with no claim as to its
suitability for any purpose.</p>
<p>Last revised: 1/15/2003</p>
</body>
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