| <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" |
| "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> |
| <html xmlns="http://www.w3.org/1999/xhtml"> |
| <head> |
| <meta name="generator" content= |
| "HTML Tidy for Linux/x86 (vers 1st March 2004), see www.w3.org" /> |
| <meta http-equiv="Content-Type" content= |
| "text/html; charset=us-ascii" /> |
| <link rel="stylesheet" href="../../../../boost.css" type="text/css"/> |
| <link rel="stylesheet" href="ublas.css" type="text/css" /> |
| <script type="text/javascript" src="js/jquery-1.3.2.min.js" async="async" ></script> |
| <script type="text/javascript" src="js/jquery.toc-gw.js" async="async" ></script> |
| <title>Iterator Concepts</title> |
| </head> |
| <body> |
| <h1><img src="../../../../boost.png" align="middle" />Iterator Concepts</h1> |
| <div class="toc" id="toc"></div> |
| <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" summary="associated types"> |
| <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" summary="notation"> |
| <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" summary="expressions"> |
| <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> </td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td>Dereference</td> |
| <td><code>*it</code></td> |
| <td> </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> </td> |
| </tr> |
| <tr> |
| <td>Member access</td> |
| <td><code>it->m</code></td> |
| <td><code>T</code> is a type for which <code>t.m</code> is |
| defined.</td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td>Preincrement</td> |
| <td><code>++ it</code></td> |
| <td> </td> |
| <td><code>I &</code></td> |
| </tr> |
| <tr> |
| <td>Postincrement</td> |
| <td><code>it ++</code></td> |
| <td> </td> |
| <td><code>I</code></td> |
| </tr> |
| <tr> |
| <td>Predecrement</td> |
| <td><code>-- it</code></td> |
| <td> </td> |
| <td><code>I &</code></td> |
| </tr> |
| <tr> |
| <td>Postdecrement</td> |
| <td><code>it --</code></td> |
| <td> </td> |
| <td><code>I</code></td> |
| </tr> |
| <tr> |
| <td>Index</td> |
| <td><code>it.index ()</code></td> |
| <td> </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" summary="semantics"> |
| <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> </td> |
| <td> </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> </td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td>Dereference assignment</td> |
| <td><code>*it = t</code></td> |
| <td>Same as for <code>*it</code>.</td> |
| <td> </td> |
| <td><code>*it</code> is a copy of t.</td> |
| </tr> |
| <tr> |
| <td>Member access</td> |
| <td><code>it->m</code></td> |
| <td><code>it</code> is dereferenceable.</td> |
| <td>Equivalent to <code>(*it).m</code></td> |
| <td> </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 /> |
| &it == &++ 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 /> |
| I itt = it;<br /> |
| ++ it;<br /> |
| 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>&it = &-- it</code>.<br /> |
| If <code>it1 == it2</code>,<br /> |
| then <code>-- it1 == -- it2</code>.<br /> |
| If <code>it2</code> is dereferenceable and <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 /> |
| I itt = it;<br /> |
| -- it;<br /> |
| return itt;<br /> |
| }</code></td> |
| <td><code>it</code> is dereferenceable. </td> |
| </tr> |
| <tr> |
| <td>Index</td> |
| <td><code>it.index ()</code></td> |
| <td><code>it</code> is dereferenceable.</td> |
| <td><code>it.index () >= 0</code><br /> |
| and<br /> |
| <code>it.index () < it ().size ()</code></td> |
| <td>If <code>it1 == it2</code>,<br /> |
| then <code>it1.index () == it2.index ()</code>.<br /> |
| If <code>it1 == it2</code>,<br /> |
| then <code>it1.index () < (++ it2).index |
| ()</code>.<br /> |
| If <code>it1 == it2</code>,<br /> |
| then <code>it1.index () > (-- it2).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" summary="invariants"> |
| <tbody> |
| <tr> |
| <td>Identity</td> |
| <td><code>it1 == it2</code> if and only if <code>&*it1 == |
| &*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::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" summary="associated types"> |
| <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" summary="notation"> |
| <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" summary="expressions"> |
| <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> </td> |
| <td><code>I &</code></td> |
| </tr> |
| <tr> |
| <td>Iterator addition</td> |
| <td><code>it + n</code></td> |
| <td> </td> |
| <td><code>I</code></td> |
| </tr> |
| <tr> |
| <td>Backward motion</td> |
| <td><code>i -= n</code></td> |
| <td> </td> |
| <td><code>I &</code></td> |
| </tr> |
| <tr> |
| <td>Iterator subtraction</td> |
| <td><code>it - n</code></td> |
| <td> </td> |
| <td><code>I</code> </td> |
| </tr> |
| <tr> |
| <td>Difference</td> |
| <td><code>it1 - it2</code></td> |
| <td> </td> |
| <td><code>C::difference_type</code></td> |
| </tr> |
| <tr> |
| <td>Element operator</td> |
| <td><code>it [n]</code></td> |
| <td> </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" summary="semantics"> |
| <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 > 0</code>, equivalent to executing <code>++ |
| it</code> <code>n</code> times. If <code>n < 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 /> |
| I itt = it;<br /> |
| 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 /> |
| I itt = it;<br /> |
| 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> </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> </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> </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" summary="invariants"> |
| <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 >= 0</code>.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Models</h4> |
| <ul> |
| <li><code>vector::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" summary="associated types"> |
| <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" summary="notation"> |
| <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" summary="expressions"> |
| <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 it</code></td> |
| <td> </td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td>Dereference</td> |
| <td><code>*it</code></td> |
| <td> </td> |
| <td>Convertible to <code>T</code>.</td> |
| </tr> |
| <tr> |
| <td>Dereference assignment</td> |
| <td><code>*it = t</code></td> |
| <td><code>I1</code> is mutable.</td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td>Member access</td> |
| <td><code>it->m</code></td> |
| <td><code>T</code> is a type for which <code>t.m</code> is |
| defined.</td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td>Preincrement</td> |
| <td><code>++ it</code></td> |
| <td> </td> |
| <td><code>I1 &</code></td> |
| </tr> |
| <tr> |
| <td>Postincrement</td> |
| <td><code>it ++</code></td> |
| <td> </td> |
| <td><code>I1</code></td> |
| </tr> |
| <tr> |
| <td>Predecrement</td> |
| <td><code>-- it</code></td> |
| <td> </td> |
| <td><code>I1 &</code></td> |
| </tr> |
| <tr> |
| <td>Postdecrement</td> |
| <td><code>it --</code></td> |
| <td> </td> |
| <td><code>I1</code></td> |
| </tr> |
| <tr> |
| <td>Row Index</td> |
| <td><code>it.index1 ()</code></td> |
| <td> </td> |
| <td><code>C::size_type</code></td> |
| </tr> |
| <tr> |
| <td>Column Index</td> |
| <td><code>it.index2 ()</code></td> |
| <td> </td> |
| <td><code>C::size_type</code></td> |
| </tr> |
| <tr> |
| <td>Row/Column Begin</td> |
| <td><code>it.begin ()</code></td> |
| <td> </td> |
| <td><code>I2</code></td> |
| </tr> |
| <tr> |
| <td>Row/Column End</td> |
| <td><code>it.end ()</code></td> |
| <td> </td> |
| <td><code>I2</code></td> |
| </tr> |
| <tr> |
| <td>Reverse Row/Column Begin</td> |
| <td><code>it.rbegin ()</code></td> |
| <td> </td> |
| <td><code>reverse_iterator<I2></code></td> |
| </tr> |
| <tr> |
| <td>Reverse Row/Column End</td> |
| <td><code>it.rend ()</code></td> |
| <td> </td> |
| <td><code>reverse_iterator<I2></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" summary="semantics"> |
| <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 it</code></td> |
| <td> </td> |
| <td> </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> </td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td>Dereference assignment</td> |
| <td><code>*it = t</code></td> |
| <td>Same as for <code>*it</code>.</td> |
| <td> </td> |
| <td><code>*it</code> is a copy of t.</td> |
| </tr> |
| <tr> |
| <td>Member access</td> |
| <td><code>it->m</code></td> |
| <td><code>it</code> is dereferenceable.</td> |
| <td>Equivalent to <code>(*it).m</code></td> |
| <td> </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 of |
| the column/row, i.e. for column iterators holds<br /> |
| <code>it.index1 () < (++ it).index1 ()</code> and<br /> |
| <code>it.index2 () == (++ it).index2 ()</code>,<br /> |
| for row iterators holds<br /> |
| <code>it.index1 () == (++ it).index1 ()</code> and<br /> |
| <code>it.index2 () < (++ it).index2 ()</code>.<br /></td> |
| <td><code>it</code> is dereferenceable or past-the-end. |
| <code><br /> |
| &it == &++ 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 /> |
| I1 itt = it;<br /> |
| ++ it;<br /> |
| 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 of the column/row, i.e. for column iterators holds<br /> |
| <code>it.index1 () > (-- it).index1 ()</code> and<br /> |
| <code>it.index2 () == (-- it).index2 ()</code>,<br /> |
| for row iterators holds<br /> |
| <code>it.index1 () == (-- it).index1 ()</code> and<br /> |
| <code>it.index2 () > (-- it).index2 ()</code>.</td> |
| <td><code>it</code> is dereferenceable.<br /> |
| <code>&it = &-- 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 /> |
| I1 itt = it;<br /> |
| -- it;<br /> |
| return itt;<br /> |
| }</code></td> |
| <td><code>it</code> is dereferenceable. </td> |
| </tr> |
| <tr> |
| <td>Row Index</td> |
| <td><code>it.index1 ()</code></td> |
| <td>If <code>it</code> is a Row iterator then <code>it</code> must be dereferenceable.</td> |
| <td><code>it.index1 () >= 0</code> and<br /> |
| <code>it.index1 () < it () .size1 ()</code></td> |
| <td>If <code>it1 == it2</code>,<br /> |
| then <code>it1.index1 () == 12.index1 ()</code>.<br /> |
| If <code>it1</code>, <code>it2</code> are Row Iterators with <code>it1 == it2</code>,<br /> |
| then <code>it1.index1 () < (++ it2</code>).<code>index1 ()</code>.<br /> |
| and <code>it1.index1 () > (-- it2</code>).<code>index1 ()</code>.</td> |
| </tr> |
| <tr> |
| <td>Column Index</td> |
| <td><code>it.index2 ()</code></td> |
| <td>If <code>it</code> is a Column iterator then <code>it</code> must be dereferenceable.</td> |
| <td><code>it.index2 () >= 0</code> and<br /> |
| <code>it.index2 () < it () .size2 ()</code></td> |
| <td>If <code>it1 == it2</code>,<br /> |
| then <code>it1.index2 () == it2</code>.<code>index2 ()</code> |
| .<br /> |
| If <code>it1</code>, <code>it2</code> are Column Iterators with <code>it1 == i12</code>,<br /> |
| then <code>it1.index2 () < (++ it2</code>).<code>index2 ()</code>.<br /> |
| end <code>it1.index2 () > (-- it2</code>).<code>index2 ()</code>.</td> |
| </tr> |
| <tr> |
| <td>Row/Column Begin</td> |
| <td><code>it.begin ()</code></td> |
| <td><code>it</code> is dereferenceable.</td> |
| <td>If <code>it</code> is a Column Iterator,<br /> |
| then <code>it2 = it.begin ()</code> is a Row Iterator<br /> |
| with <code>it2.index1 () == it.index1 ()</code>. |
| <p>If <code>it</code> is a Row Iterator,<br /> |
| then <code>it2 = it.begin ()</code> is a Column Iterator<br /> |
| with <code>it2.index2 () == it.index2 ()</code>.</p> |
| </td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td>Row/Column End</td> |
| <td><code>it.end ()</code></td> |
| <td><code>it</code> is dereferenceable.</td> |
| <td>If <code>it</code> is a Column Iterator,<br /> |
| then <code>it2 = it.end ()</code> is a Row Iterator<br /> |
| with <code>it2.index1 () == it.index1 ()</code>. |
| <p>If <code>it</code> is a Row Iterator,<br /> |
| then <code>it2 = it.end ()</code> is a Column Iterator<br /> |
| with <code>it2.index2 () == it.index2 ()</code>.</p> |
| </td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td>Reverse Row/Column Begin</td> |
| <td><code>it.rbegin ()</code></td> |
| <td><code>it</code> is dereferenceable.</td> |
| <td>Equivalent to <code>reverse_iterator<I2> (it.end |
| ())</code>.</td> |
| <td> </td> |
| </tr> |
| <tr> |
| <td>Reverse Row/Column End</td> |
| <td><code>it.rend ()</code></td> |
| <td><code>it</code> is dereferenceable.</td> |
| <td>Equivalent to <code>reverse_iterator<I2> (it.begin |
| ())</code>.</td> |
| <td> </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" summary="invariants"> |
| <tbody> |
| <tr> |
| <td>Identity</td> |
| <td><code>it1 == it2</code> if and only if <code>&*it1 == |
| &*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.index1 (), it.index2 ())</code></td> |
| </tr> |
| <tr> |
| <td>Relation between iterator column/row begin and iterator |
| index</td> |
| <td>If <code>it</code> is a Column Iterator |
| and <code>it2 = it.begin ()</code> then <code>it2.index2 () < |
| it2t.index2 ()</code> for all <code>it2t</code> with <code>it2t () |
| == it2 ()</code> and <code>it2t ().index1 () == it2 ().index1 |
| ()</code>. |
| <p>If <code>it</code> is a Row Iterator and |
| <code>it2 = it.begin ()</code> then <code>it2.index1 () < |
| 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>it</code> is a Column Iterator |
| and <code>it2 = it.end ()</code> then <code>it2.index2 () > |
| it2t.index2 ()</code> for all <code>it2t</code> with <code>it2t () |
| == it2 ()</code> and <code>it2t ().index1 () == it2 ().index1 |
| ()</code>. |
| <p>If <code>it</code> is a Row Iterator and |
| <code>it2 = it.end ()</code> then <code>it2.index1 () > |
| 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::iterator1</code></li> |
| <li><code>sparse_matrix::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" summary="associated types"> |
| <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" summary="notation"> |
| <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" summary="expressions"> |
| <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> </td> |
| <td><code>I &</code></td> |
| </tr> |
| <tr> |
| <td>Iterator addition</td> |
| <td><code>it + n</code></td> |
| <td> </td> |
| <td><code>I</code></td> |
| </tr> |
| <tr> |
| <td>Backward motion</td> |
| <td><code>i -= n</code></td> |
| <td> </td> |
| <td><code>I &</code></td> |
| </tr> |
| <tr> |
| <td>Iterator subtraction</td> |
| <td><code>it - n</code></td> |
| <td> </td> |
| <td><code>I</code> </td> |
| </tr> |
| <tr> |
| <td>Difference</td> |
| <td><code>it1 - it2</code></td> |
| <td> </td> |
| <td><code>C::difference_type</code></td> |
| </tr> |
| <tr> |
| <td>Element operator</td> |
| <td><code>it [n]</code></td> |
| <td> </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" summary="semantics"> |
| <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 > 0</code>, equivalent to executing <code>++ |
| it</code> <code>n</code> times. If <code>n < 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 /> |
| I itt = it;<br /> |
| 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 /> |
| I itt = it;<br /> |
| 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> </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> </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> </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" summary="invariants"> |
| <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 >= 0</code>.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Models</h4> |
| <ul> |
| <li><code>matrix::iterator1</code></li> |
| <li><code>matrix::iterator2</code></li> |
| </ul> |
| <hr /> |
| <p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br /> |
| Use, modification and distribution are subject to the |
| Boost Software License, Version 1.0. |
| (See accompanying file LICENSE_1_0.txt |
| or copy at <a href="http://www.boost.org/LICENSE_1_0.txt"> |
| http://www.boost.org/LICENSE_1_0.txt |
| </a>). |
| </p> |
| <script type="text/javascript"> |
| (function($) { |
| $('#toc').toc(); |
| })(jQuery); |
| </script> |
| </body> |
| </html> |