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398 lines
12 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml">
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<head>
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<meta name="generator" content=
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"HTML Tidy for Linux/x86 (vers 1st March 2004), see www.w3.org" />
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<meta http-equiv="Content-Type" content=
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"text/html; charset=us-ascii" />
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<link href="ublas.css" type="text/css" />
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<title>Container Concepts</title>
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</head>
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<body>
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<h1><img src="c++boost.gif" alt="c++boost.gif" align="middle" />
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Container Concepts</h1>
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<h2><a name="vector" id="vector"></a> Vector</h2>
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<h4>Description</h4>
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<p>A Vector describes common aspects of dense, packed and sparse
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vectors.</p>
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<h4>Refinement of</h4>
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<p><a href="expression_concept.htm#vector_expression">Vector Expression</a>
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.</p>
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<h4>Associated types</h4>
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<p>
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In addition to the types defined int
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<a href="expression_concept.htm#vector_expression">Vector Expression</a>
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</p>
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<table border="0" summary="types">
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<tbody>
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<tr>
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<td>Storage</td>
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<td>array_type</td>
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<td>The type of underlying storage used to store the elements</td>
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</tr>
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</tbody>
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</table>
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<h4>Notation</h4>
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<table border="0" summary="notation">
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<tbody>
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<tr>
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<td><code>V</code></td>
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<td>A type that is a model of Vector</td>
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</tr>
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<tr>
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<td><code>v</code></td>
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<td>Objects of type <code>V</code></td>
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</tr>
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<tr>
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<td><code>n, i</code></td>
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<td>Objects of a type convertible to <code>size_type</code></td>
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</tr>
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<tr>
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<td><code>t</code></td>
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<td>Object of a type convertible to <code>value_type</code></td>
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</tr>
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<tr>
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<td><code>p</code></td>
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<td>Object of a type convertible to <code>bool</code></td>
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</tr>
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</tbody>
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</table>
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<h4>Definitions</h4>
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<h4>Valid expressions</h4>
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<p>In addition to the expressions defined in <a href=
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"expression_concept.htm#vector_expression">Vector Expression</a> the
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following expressions must be valid.</p>
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<table border="1" summary="expressions">
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<tbody>
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<tr>
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<th>Name</th>
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<th>Expression</th>
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<th>Type requirements</th>
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<th>Return type</th>
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</tr>
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<tr>
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<td>Sizing constructor</td>
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<td><code>V v (n)</code></td>
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<td> </td>
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<td><code>V</code></td>
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</tr>
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<tr>
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<td>Element access <a href="#element_access_note">[1]</a></td>
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<td><code>v[n]</code></td>
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<td><code>n</code> is convertible to <code>size_type</code></td>
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<td><code>reference</code> if v is mutable, <code>const_reference</code> otherwise</td>
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</tr>
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<tr>
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<td>Insert</td>
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<td><code>v.insert_element (i, t)</code></td>
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<td><code>v</code> is mutable.</td>
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<td><code>void</code></td>
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</tr>
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<tr>
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<td>Erase</td>
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<td><code>v.erase_element (i)</code></td>
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<td><code>v</code> is mutable.</td>
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<td><code>void</code></td>
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</tr>
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<tr>
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<td>Clear</td>
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<td><code>v.clear ()</code></td>
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<td><code>v</code> is mutable.</td>
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<td><code>void</code></td>
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</tr>
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<tr>
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<td>Resize</td>
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<td><code>v.resize (n)</code><br />
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<code>v.resize (n, p)</code></td>
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<td><code>v</code> is mutable.</td>
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<td><code>void</code></td>
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</tr>
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<tr>
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<td>Storage</td>
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<td><code>data() const</code></td>
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<td></td>
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<td><code>const array_type&</code></td>
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</tr>
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<tr>
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<td>Storage</td>
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<td><code>data()</code></td>
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<td><code>v</code> is mutable</td>
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<td><code>array_type&</code></td>
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</tr>
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</tbody>
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</table>
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<h4>Expression semantics</h4>
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<p>Semantics of an expression is defined only where it differs
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from, or is not defined in <a href=
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"expression_concept.htm#vector_expression">Vector Expression</a> .</p>
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<table border="1" summary="semantics">
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<tr>
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<th>Name</th>
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<th>Expression</th>
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<th>Precondition</th>
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<th>Semantics</th>
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<th>Postcondition</th>
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</tr>
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<tr>
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<td>Sizing constructor</td>
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<td><code>V v (n)</code></td>
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<td><code>n >= 0</code></td>
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<td>Allocates a vector of<code>n</code> elements.</td>
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<td><code>v.size () == n</code>.</td>
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</tr>
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<tr>
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<td>Element access <a href="#element_access_note">[1]</a></td>
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<td><code>v[n]</code></td>
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<td><code>0<n>v.size()</code></td>
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<td>returns the n-th element in v</td>
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<td></td>
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</tr>
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<tr>
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<td>Insert</td>
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<td><code>v.insert_element (i, t)</code></td>
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<td><code>0 <= i < v.size ()</code> and<br />
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<code>v (i)</code> is equal to <code>value_type (0)</code>.</td>
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<td>A copy of <code>t</code> is inserted in <code>v</code>.</td>
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<td><code>v (i)</code> is a copy of <code>t</code>.</td>
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</tr>
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<tr>
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<td>Erase</td>
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<td><code>v.erase_element (i)</code></td>
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<td><code>0 <= i < v.size ()</code></td>
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<td>Destroys the element <code>v (i)</code> and replaces it with
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<code>value_type ()</code>.</td>
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<td><code>v (i)</code> is a copy of <code>value_type
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()</code>.</td>
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</tr>
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<tr>
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<td>Clear</td>
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<td><code>v.clear ()</code></td>
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<td> </td>
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<td>Equivalent to<br />
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<code>for (i = 0; i < v.size (); ++ i)</code><br />
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<code>v.erase (i);</code></td>
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<td> </td>
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</tr>
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<tr>
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<td>Resize</td>
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<td><code>v.resize (n)
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<br />v.resize (n, p)</code></td>
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<td> </td>
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<td>Reallocates the vector so that it can hold <code>n</code>
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elements.<br />
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Erases or appends elements in order to bring the vector to the prescribed size. Appended elements copies of <code>value_type()</code>.
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<br />
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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>
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<td><code>v.size () == n</code>.</td>
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</tr>
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<tr>
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<td>Storage</td>
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<td><code>v.data()</code></td>
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<td><code>v</code> is const</td>
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<td>Returns a reference to the underlying storage</td>
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<td></td>
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</tr>
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<tr>
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<td>Storage</td>
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<td><code>v.data()</code></td>
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<td><code>v</code> is mutable</td>
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<td>Returns a reference to the underlying storage</td>
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<td></td>
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</tr>
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</table>
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<h4>Complexity guarantees</h4>
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<p>The run-time complexity of the sizing constructor is linear in
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the vector's size.</p>
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<p>The run-time complexity of insert_element and erase_element is specific for the
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vector.</p>
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<p>The run-time complexity of resize is linear in the vector's
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size.</p>
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<h4>Invariants</h4>
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<h4>Models</h4>
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<ul>
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<li><code>vector<T></code> , <code>bounded_vector<T, N></code></li>
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<li><code>unit_vector<T></code> , <code>zero_vector<T></code> , <code>scalar_vector<T></code></li>
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<li><code>mapped_vector<T></code> , <code>compressed_vector</code> , <code>coordinate_vector</code></li>
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</ul>
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<h4>Notes</h4>
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<a name="element_access_note">[1]</a>The <code>operator[]</code> is added purely for convenience
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and compatibility with the <code>std::vector</code>. In uBLAS however,
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generally <code>operator()</code> is used for indexing because this can be
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used for both vectors and matrices.
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<h2><a name="matrix" id="matrix"></a> Matrix</h2>
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<h4>Description</h4>
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<p>A Matrix describes common aspects of dense, packed and sparse
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matrices.</p>
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<h4>Refinement of</h4>
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<p><a href="expression_concept.htm#matrix_expression">Matrix Expression</a>
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.</p>
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<h4>Associated types</h4>
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<p>
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See <a href="expression_concept.htm#matrix_expression">Matrix Expression</a>
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</p>
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<h4>Notation</h4>
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<table border="0" summary="notation">
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<tbody>
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<tr>
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<td><code>M</code></td>
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<td>A type that is a model of Matrix</td>
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</tr>
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<tr>
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<td><code>m</code></td>
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<td>Objects of type <code>M</code></td>
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</tr>
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<tr>
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<td><code>n1, n2, i, j</code></td>
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<td>Objects of a type convertible to <code>size_type</code></td>
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</tr>
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<tr>
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<td><code>t</code></td>
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<td>Object of a type convertible to <code>value_type</code></td>
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</tr>
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<tr>
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<td><code>p</code></td>
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<td>Object of a type convertible to <code>bool</code></td>
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</tr>
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</tbody>
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</table>
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<h4>Definitions</h4>
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<h4>Valid expressions</h4>
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<p>In addition to the expressions defined in <a href=
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"expression_concept.htm#matrix_expression">Matrix Expression</a> the
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following expressions must be valid.</p>
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<table border="1" summary="expressions">
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<tbody>
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<tr>
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<th>Name</th>
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<th>Expression</th>
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<th>Type requirements</th>
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<th>Return type</th>
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</tr>
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<tr>
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<td>Sizing constructor</td>
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<td><code>M m (n1, n2)</code></td>
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<td> </td>
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<td><code>M</code></td>
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</tr>
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<tr>
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<td>Insert</td>
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<td><code>m.insert_element (i, j, t)</code></td>
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<td><code>m</code> is mutable.</td>
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<td><code>void</code></td>
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</tr>
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<tr>
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<td>Erase</td>
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<td><code>m.erase_element (i, j)</code></td>
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<td><code>m</code> is mutable.</td>
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<td><code>void</code></td>
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</tr>
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<tr>
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<td>Clear</td>
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<td><code>m.clear ()</code></td>
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<td><code>m</code> is mutable.</td>
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<td><code>void</code></td>
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</tr>
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<tr>
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<td>Resize</td>
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<td><code>m.resize (n1, n2)</code><br />
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<code>m.resize (n1, n2, p)</code></td>
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<td><code>m</code> is mutable.</td>
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<td><code>void</code></td>
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</tr>
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</tbody>
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</table>
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<h4>Expression semantics</h4>
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<p>Semantics of an expression is defined only where it differs
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from, or is not defined in <a href=
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"expression_concept.htm#matrix_expression">Matrix Expression</a> .</p>
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<table border="1" summary="semantics">
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<tbody>
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<tr>
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<th>Name</th>
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<th>Expression</th>
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<th>Precondition</th>
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<th>Semantics</th>
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<th>Postcondition</th>
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</tr>
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<tr>
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<td>Sizing constructor</td>
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<td><code>M m (n1, n2)</code></td>
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<td><code>n1 >= 0</code> and <code>n2 >= 0</code></td>
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<td>Allocates a matrix of <code>n1</code> rows and <code>n2</code>
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columns.</td>
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<td><code>m.size1 () == n1</code> and <code>m.size2 () ==
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n2</code>.</td>
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</tr>
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<tr>
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<td>Insert</td>
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<td><code>m.insert_element (i, j, t)</code></td>
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<td><code>0 <= i < m.size1 ()</code>,<br />
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<code>0 <= j < m.size2 ()</code>and <code><br />
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m (i, j)</code> is equal to <code>value_type (0)</code>.</td>
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<td>A copy of <code>t</code> is inserted in <code>m</code>.</td>
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<td><code>m (i, j)</code> is a copy of <code>t</code>.</td>
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</tr>
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<tr>
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<td>Erase</td>
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<td><code>m.erase (i, j)</code></td>
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<td><code>0 <= i < m.size1 ()</code>and <code><br />
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0 <= j < m.size2</code></td>
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<td>Destroys the element <code>m (i, j)</code> and replaces it with
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<code>value_type ()</code>.</td>
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<td><code>m (i, j)</code> is a copy of <code>value_type
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()</code>.</td>
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</tr>
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<tr>
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<td>Clear</td>
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<td><code>m.clear ()</code></td>
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<td> </td>
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<td>Equivalent to<br />
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<code>for (i = 0; i < m.size1 (); ++ i)</code><br />
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<code>for (j = 0; j < m.size2 (); ++ j)</code><br />
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<code>m.erase (i, j);</code></td>
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<td> </td>
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</tr>
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<tr>
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<td>Resize</td>
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<td><code>m.resize (n1, n2)
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<br />
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m.resize (n1, n2, p)
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</code></td>
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<td> </td>
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<td>Reallocate the matrix so that it can hold <code>n1</code> rows
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and <code>n2</code> columns.<br />
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Erases or appends elements in order to bring the matrix to the
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prescribed size. Appended elements are <code>value_type()</code>
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copies.<br />
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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>
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<td><code>m.size1 () == n1</code> and <code>m.size2 () == n2</code>.</td>
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</tr>
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</tbody>
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</table>
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<h4>Complexity guarantees</h4>
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<p>The run-time complexity of the sizing constructor is quadratic
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in the matrix's size.</p>
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<p>The run-time complexity of insert_element and erase_element is specific for the
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matrix.</p>
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<p>The run-time complexity of resize is quadratic in the matrix's
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size.</p>
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<h4>Invariants</h4>
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<h4>Models</h4>
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<ul>
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<li><code>matrix<T></code> , <code>bounded_matrix<T, M, N></code></li>
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<li><code>identity_matrix<T></code> , <code>zero_matrix<T></code> , <code>scalar_matrix<T></code></li>
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<li><code>triangular_matrix<T></code> , <code>symmetric_matrix<T></code> , <code>banded_matrix<T></code></li>
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<li><code>mapped_matrix<T></code> , <code>compressed_matrix</code> , <code>coordinate_matrix</code></li>
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</ul>
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<hr />
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<p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br />
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Permission to copy, use, modify, sell and distribute this document
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is granted provided this copyright notice appears in all copies.
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This document is provided ``as is'' without express or implied
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warranty, and with no claim as to its suitability for any
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purpose.</p>
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<p>Last revised: 24/06/2004</p>
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</body>
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</html>
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