<!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>Container Concepts</title> </head> <body> <h1><img src="../../../../boost.png" align="middle" />Container Concepts</h1> <div class="toc" id="toc"></div> <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="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>, <a href="expression_concept.htm#vector_expression">Vector Expression</a> <a href="#vector_expression_note">[1]</a>.</p> <h4>Associated types</h4> <p>In addition to the types defined by <a href="expression_concept.htm#vector_expression">Vector Expression</a></p> <table border="1" summary="types"> <tbody> <tr> <td>Public base</td> <td>vector_container<V></td> <td>V must be derived from this public base type.</td> </tr> <tr> <td>Storage array</td> <td>V::array_type</td> <td> Dense Vector ONLY. The type of underlying storage array used to store the elements. The array_type must model the <a href="storage_concept.htm"><b>Storage</b></a> concept.</td> </tr> </tbody> </table> <h4>Notation</h4> <table border="0" summary="notation"> <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> <tr> <td><code>p</code></td> <td>Object of a type convertible to <code>bool</code></td> </tr> </tbody> </table> <h4>Definitions</h4> <h4>Valid expressions</h4> <p>In addition to the expressions defined in <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>, <a href="expression_concept.htm#vector_expression">Vector Expression</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>Sizing constructor</td> <td><code>V v (n)</code></td> <td> </td> <td><code>V</code></td> </tr> <tr> <td>Insert</td> <td><code>v.insert_element (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_element (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><br /> <code>v.resize (n, p)</code></td> <td><code>v</code> is mutable.</td> <td><code>void</code></td> </tr> <tr> <td>Storage</td> <td><code>v.data()</code></td> <td><code>v</code> is mutable and Dense.</td> <td><code>array_type&</code> if <code>v</code> is mutable, <code>const array_type&</code> otherwise</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_concept.htm#vector_expression">Vector Expression</a> .</p> <table border="1" summary="semantics"> <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 >= 0</code></td> <td>Allocates a vector of<code>n</code> elements.</td> <td><code>v.size () == n</code>.</td> </tr> <tr> <td>Element access <a href="#element_access_note">[2]</a></td> <td><code>v[n]</code></td> <td><code>0<n>v.size()</code></td> <td>returns the n-th element in v</td> <td> </td> </tr> <tr> <td>Insert</td> <td><code>v.insert_element (i, t)</code></td> <td><code>0 <= i < v.size ()</code>.</td> <td>Inserts an element at <code>v (i)</code> with value <code>t</code>. The storage requirement of the Vector may be increased.</td> <td><code>v (i)</code> is equal to <code>t</code>.</td> </tr> <tr> <td>Erase</td> <td><code>v.erase_element (i)</code></td> <td><code>0 <= i < v.size ()</code></td> <td>Destroys the element as <code>v (i)</code> and replaces it with the default <code>value_type ()</code>. The storage requirement of the Vector may be decreased.</td> <td><code>v (i)</code> is equal to <code>value_type ()</code>.</td> </tr> <tr> <td>Clear</td> <td><code>v.clear ()</code></td> <td> </td> <td>Equivalent to<br /> <code>for (i = 0; i < v.size (); ++ i)</code><br /> <code>v.erase_element (i);</code></td> <td> </td> </tr> <tr> <td>Resize</td> <td><code>v.resize (n) <br />v.resize (n, p)</code></td> <td> </td> <td>Reallocates the vector so that it can hold <code>n</code> elements.<br /> Erases or appends elements in order to bring the vector to the prescribed size. Appended elements copies of <code>value_type()</code>. <br /> When <code>p == false</code> then existing elements are not preserved and elements will not appended as normal. Instead the vector is in the same state as that after an equivalent sizing constructor.</td> <td><code>v.size () == n</code>.</td> </tr> <tr> <td>Storage</td> <td><code>v.data()</code></td> <td></td> <td>Returns a reference to the underlying dense storage.</td> <td> </td> </tr> </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_element and erase_element is specific for the Vector model and it depends on increases/decreases in storage requirements.</p> <p>The run-time complexity of resize is linear in the vector's size.</p> <h4>Invariants</h4> <h4>Models</h4> <ul> <li><code>vector</code>, <code>bounded_vector</code>, <code>c_vector</code></li> <li><code>unit_vector</code>, <code>zero_vector</code>, <code>scalar_vector</code></li> <li><code>mapped_vector;</code>, <code>compressed_vector</code>, <code>coordinate_vector</code></li> </ul> <h4>Notes</h4> <p><a name="vector_expression_note">[1]</a> As a user you need not care about <tt>Vector</tt> being a refinement of the VectorExpression. Being a refinement of the VectorExpression is only important for the template-expression engine but not the user.</p> <p><a name="element_access_note">[2]</a> The <code>operator[]</code> is added purely for convenience and compatibility with the <code>std::vector</code>. In uBLAS however, generally <code>operator()</code> is used for indexing because this can be used for both vectors and matrices.</p> <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="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>, <a href="expression_concept.htm#matrix_expression">Matrix Expression</a> <a href="#matrix_expression_note">[1]</a> .</p> <h4>Associated types</h4> <p>In addition to the types defined by <a href="expression_concept.htm#matrix_expression">Matrix Expression</a></p> <table border="1" summary="types"> <tbody> <tr> <td>Public base</td> <td>matrix_container<M></td> <td>M must be derived from this public base type.</td> </tr> <tr> <td>Storage array</td> <td>M::array_type</td> <td>Dense Matrix ONLY. The type of underlying storage array used to store the elements. The array_type must model the <a href="storage_concept.htm"><b>Storage</b></a> concept.</td> </tr> </tbody> </table> <h4>Notation</h4> <table border="0" summary="notation"> <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> <tr> <td><code>p</code></td> <td>Object of a type convertible to <code>bool</code></td> </tr> </tbody> </table> <h4>Definitions</h4> <h4>Valid expressions</h4> <p>In addition to the expressions defined in <a href= "expression_concept.htm#matrix_expression">Matrix Expression</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>Sizing constructor</td> <td><code>M m (n1, n2)</code></td> <td> </td> <td><code>M</code></td> </tr> <tr> <td>Insert</td> <td><code>m.insert_element (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_element (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><br /> <code>m.resize (n1, n2, p)</code></td> <td><code>m</code> is mutable.</td> <td><code>void</code></td> </tr> <tr> <td>Storage</td> <td><code>m.data()</code></td> <td><code>m</code> is mutable and Dense.</td> <td><code>array_type&</code> if <code>m</code> is mutable, <code>const array_type&</code> otherwise</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_concept.htm#matrix_expression">Matrix Expression</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>Sizing constructor</td> <td><code>M m (n1, n2)</code></td> <td><code>n1 >= 0</code> and <code>n2 >= 0</code></td> <td>Allocates 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_element (i, j, t)</code></td> <td><code>0 <= i < m.size1 ()</code>,<br /> <code>0 <= j < m.size2 ()</code>.</td> <td>Inserts an element at <code>m (i, j)</code> with value <code>t</code>. The storage requirement of the Matrix may be increased.</td> <td><code>m (i, j)</code> is equal to <code>t</code>.</td> </tr> <tr> <td>Erase</td> <td><code>m.erase_element (i, j)</code></td> <td><code>0 <= i < m.size1 ()</code>and <code><br /> 0 <= j < m.size2</code></td> <td>Destroys the element as <code>m (i, j)</code> and replaces it with the default <code>value_type ()</code>. The storage requirement of the Matrix may be decreased.</td> <td><code>m (i, j)</code> is equal to <code>value_type ()</code>.</td> </tr> <tr> <td>Clear</td> <td><code>m.clear ()</code></td> <td> </td> <td>Equivalent to<br /> <code>for (i = 0; i < m.size1 (); ++ i)</code><br /> <code>for (j = 0; j < m.size2 (); ++ j)</code><br /> <code>m.erase_element (i, j);</code></td> <td> </td> </tr> <tr> <td>Resize</td> <td><code>m.resize (n1, n2) <br /> m.resize (n1, n2, p) </code></td> <td> </td> <td>Reallocate the matrix so that it can hold <code>n1</code> rows and <code>n2</code> columns.<br /> Erases or appends elements in order to bring the matrix to the prescribed size. Appended elements are <code>value_type()</code> copies.<br /> When <code>p == false</code> then existing elements are not preserved and elements will not appended as normal. Instead the matrix is in the same state as that after an equivalent sizing constructor.</td> <td><code>m.size1 () == n1</code> and <code>m.size2 () == n2</code>.</td> </tr> <tr> <td>Storage</td> <td><code>m.data()</code></td> <td></td> <td>Returns a reference to the underlying dense storage.</td> <td> </td> </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_element and erase_element is specific for the Matrix model and it depends on increases/decreases in storage requirements.</p> <p>The run-time complexity of resize is quadratic in the matrix's size.</p> <h4>Invariants</h4> <h4>Models</h4> <ul> <li><code>matrix</code>, <code>bounded_matrix</code>, <code>c_matrix</code></li> <li><code>identity_matrix</code> , <code>zero_matrix</code> , <code>scalar_matrix</code></li> <li><code>triangular_matrix</code> , <code>symmetric_matrix</code> , <code>banded_matrix</code></li> <li><code>mapped_matrix</code> , <code>compressed_matrix</code> , <code>coordinate_matrix</code></li> </ul> <h4>Notes</h4> <p><a name="matrix_expression_note">[1]</a> As a user you need not care about <tt>Matrix</tt> being a refinement of the MatrixExpression. Being a refinement of the MatrixExpression is only important for the template-expression engine but not the user.</p> <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>