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Jörg Walter bbca4f92fa A couple of fixes and improvements
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2003-05-26 20:55:45 +00:00

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<title>Container Concepts</title>
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<h1><img src="c++boost.gif" alt="c++boost.gif" align="Center">
Container Concepts</h1>
<h2><a name="vector"></a> Vector</h2>
<h4>Description</h4>
<p>A Vector describes common aspects of dense, packed and sparse
vectors.</p>
<h4>Refinement of</h4>
<p><a href="expression.htm#vector_expression">Vector Expression</a>
.</p>
<h4>Associated types</h4>
<table border="1">
<tbody>
<tr>
<td>Value type</td>
<td><code>value_type</code> </td>
<td>The type of the vector.</td>
</tr>
<tr>
<td>Distance type</td>
<td><code>difference_type</code> </td>
<td>A signed integral type used to represent the distance between
two of the vector's iterators.</td>
</tr>
<tr>
<td>Size type</td>
<td><code>size_type</code> </td>
<td>An unsigned integral type that can represent any nonnegative
value of the vector's distance type.</td>
</tr>
</tbody>
</table>
<h4>Notation</h4>
<table border="0">
<tbody>
<tr>
<td><code>V</code> </td>
<td>A type that is a model of Vector</td>
</tr>
<tr>
<td><code>v</code></td>
<td>Objects of type <code>V</code> </td>
</tr>
<tr>
<td><code>n, i</code></td>
<td>Objects of a type convertible to <code>size_type</code> </td>
</tr>
<tr>
<td><code>t</code></td>
<td>Object of a type convertible to <code>value_type</code> </td>
</tr>
</tbody>
</table>
<h4>Definitions</h4>
<h4>Valid expressions</h4>
<p>In addition to the expressions defined in <a href=
"expression.htm#vector_expression">Vector Expression</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>Sizing constructor</td>
<td><code>V v (n)</code> </td>
<td>&nbsp;</td>
<td><code>V</code></td>
</tr>
<tr>
<td>Insert</td>
<td><code>v.insert (i, t)</code> </td>
<td><code>v</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Erase</td>
<td><code>v.erase (i)</code> </td>
<td><code>v</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Clear</td>
<td><code>v.clear ()</code> </td>
<td><code>v</code> is mutable.</td>
<td><code>void</code> </td>
</tr>
<tr>
<td>Resize</td>
<td><code>v.resize (n)</code> </td>
<td><code>v</code> is mutable.</td>
<td><code>void</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=
"expression.htm#vector_expression">Vector Expression</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>Sizing constructor</td>
<td><code>V v (n)</code> </td>
<td><code>n &gt;= 0</code> </td>
<td>Creates a vector of <code>n</code> elements.</td>
<td><code>v.size () == n</code>.</td>
</tr>
<tr>
<td>Insert</td>
<td><code>v.insert (i, t)</code> </td>
<td><code>0 &lt;= i &lt; v.size ()</code> and<br>
<code>v (i)</code> is a copy of <code>value_type ()</code>.</td>
<td>A copy of <code>t</code> is inserted in <code>v</code>.</td>
<td><code>v (i)</code> is a copy of <code>t</code>.</td>
</tr>
<tr>
<td>Erase</td>
<td><code>v.erase (i)</code> </td>
<td><code>0 &lt;= i &lt; v.size ()</code> </td>
<td>Destroys the element <code>v (i)</code> and replaces it with
<code>value_type ()</code>.</td>
<td><code>v (i)</code> is a copy of <code>value_type
()</code>.</td>
</tr>
<tr>
<td>Clear</td>
<td><code>v.clear ()</code> </td>
<td>&nbsp;</td>
<td>Equivalent to<br>
<code>for (i = 0; i &lt; v.size (); ++ i)</code><br>
&nbsp; <code>v.erase (i);</code> </td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Resize</td>
<td><code>v.resize (n)</code> </td>
<td>&nbsp;</td>
<td>Modifies the vector so that it can hold <code>n</code>
elements.</td>
<td><code>v.size () == n</code>.</td>
</tr>
</tbody>
</table>
<h4>Complexity guarantees</h4>
<p>The run-time complexity of the sizing constructor is linear in
the vector's size.</p>
<p>The run-time complexity of insert and erase is specific for the
vector.</p>
<h4>Invariants</h4>
<h4>Models</h4>
<ul>
<li><code>vector&lt;T, A&gt;</code></li>
<li><code>unit_vector&lt;T&gt;</code></li>
<li><code>zero_vector&lt;T&gt;</code></li>
<li><code>sparse_vector&lt;T, A&gt;</code></li>
</ul>
<h2><a name="matrix"></a> Matrix</h2>
<h4>Description</h4>
<p>A Matrix describes common aspects of dense, packed and sparse
matrices.</p>
<h4>Refinement of</h4>
<p><a href="expression.htm#matrix_expression">Matrix Expression</a>
.</p>
<h4>Associated types</h4>
<table border="1">
<tbody>
<tr>
<td>Value type</td>
<td><code>value_type</code> </td>
<td>The type of the matrix.</td>
</tr>
<tr>
<td>Distance type</td>
<td><code>difference_type</code> </td>
<td>A signed integral type used to represent the distance between
two of the matrix's iterators.</td>
</tr>
<tr>
<td>Size type</td>
<td><code>size_type</code> </td>
<td>An unsigned integral type that can represent any nonnegative
value of the matrix's distance type.</td>
</tr>
</tbody>
</table>
<h4>Notation</h4>
<table border="0">
<tbody>
<tr>
<td><code>M</code> </td>
<td>A type that is a model of Matrix</td>
</tr>
<tr>
<td><code>m</code></td>
<td>Objects of type <code>M</code> </td>
</tr>
<tr>
<td><code>n1, n2, i, j</code></td>
<td>Objects of a type convertible to <code>size_type</code> </td>
</tr>
<tr>
<td><code>t</code></td>
<td>Object of a type convertible to <code>value_type</code> </td>
</tr>
</tbody>
</table>
<h4>Definitions</h4>
<h4>Valid expressions</h4>
<p>In addition to the expressions defined in <a href=
"expression.htm#matrix_expression">Matrix Expression</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>Sizing constructor</td>
<td><code>M m (n1, n2)</code> </td>
<td>&nbsp;</td>
<td><code>M</code></td>
</tr>
<tr>
<td>Insert</td>
<td><code>m.insert (i, j, t)</code> </td>
<td><code>m</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Erase</td>
<td><code>m.erase (i, j)</code> </td>
<td><code>m</code> is mutable.</td>
<td><code>void</code></td>
</tr>
<tr>
<td>Clear</td>
<td><code>m.clear ()</code> </td>
<td><code>m</code> is mutable.</td>
<td><code>void</code> </td>
</tr>
<tr>
<td>Resize</td>
<td><code>m.resize (n1, n2)</code> </td>
<td><code>m</code> is mutable.</td>
<td><code>void</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=
"expression.htm#matrix_expression">Matrix Expression</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>Sizing constructor</td>
<td><code>M m (n1, n2)</code> </td>
<td><code>n1 &gt;= 0</code> and <code>n2 &gt;= 0</code></td>
<td>Creates a matrix of <code>n1</code> rows and <code>n2</code>
columns.</td>
<td><code>m.size1 () == n1</code> and <code>m.size2 () ==
n2</code>.</td>
</tr>
<tr>
<td>Insert</td>
<td><code>m.insert (i, j, t)</code> </td>
<td><code>0 &lt;= i &lt; m.size1 ()</code>,<br>
<code>0 &lt;= j &lt; m.size2 ()</code>and <code><br>
m (i, j)</code> is a copy of <code>value_type ()</code>.</td>
<td>A copy of <code>t</code> is inserted in <code>m</code>.</td>
<td><code>m (i, j)</code> is a copy of <code>t</code>.</td>
</tr>
<tr>
<td>Erase</td>
<td><code>m.erase (i, j)</code> </td>
<td><code>0 &lt;= i &lt; m.size1 ()</code>and <code><br>
0 &lt;= j &lt; m.size2</code> </td>
<td>Destroys the element <code>m (i, j)</code> and replaces it with
<code>value_type ()</code>.</td>
<td><code>m (i, j)</code> is a copy of <code>value_type
()</code>.</td>
</tr>
<tr>
<td>Clear</td>
<td><code>m.clear ()</code> </td>
<td>&nbsp;</td>
<td>Equivalent to<br>
<code>for (i = 0; i &lt; m.size1 (); ++ i)</code><br>
&nbsp; <code>for (j = 0; j &lt; m.size2 (); ++ j)</code><br>
&nbsp; &nbsp; <code>m.erase (i, j);</code> </td>
<td>&nbsp;</td>
</tr>
<tr>
<td>Resize</td>
<td><code>m.resize (n1, n2)</code> </td>
<td>&nbsp;</td>
<td>Modifies the vector so that it can hold <code>n1</code> rows
and <code>n2</code> columns.</td>
<td><code>m.size1 () == n1</code> and <code>m.size2 () ==
n2</code>.</td>
</tr>
</tbody>
</table>
<h4>Complexity guarantees</h4>
<p>The run-time complexity of the sizing constructor is quadratic
in the matrix's size.</p>
<p>The run-time complexity of insert and erase is specific for the
matrix.</p>
<h4>Invariants</h4>
<h4>Models</h4>
<ul>
<li><code>matrix&lt;T, F, A&gt;</code></li>
<li><code>identity_matrix&lt;T&gt;</code></li>
<li><code>zero_matrix&lt;T&gt;</code></li>
<li><code>triangular_matrix&lt;T, F1, F2, A&gt;</code></li>
<li><code>symmetric_matrix&lt;T, F1, F2, A&gt;</code></li>
<li><code>banded_matrix&lt;T, F, A&gt;</code></li>
<li><code>sparse_matrix&lt;T, F, A&gt;</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>
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