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219 lines
7.0 KiB
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<title>DenseVector Concept</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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DenseVector Concept</h1>
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<h2>DenseVector</h2>
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<h4>Description</h4>
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<p>A dense-vector is a, exactly as the name says, a dense vector that is intended to behave well for linear algebra operations</p>
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<h4>Refinement of</h4>
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<p><a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>, <a href="http://www.sgi.com/tech/stl/RandomAccessContainer.html">RandomAccessContainer</a> and <a href="expression_concept.htm#vector_expression">Vector Expression</a><a href="#footnote1">[1]</a>.</p>
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<h4>Associated types</h4>
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<p>In addition to the types defined by <a href="http://www.sgi.com/tech/stl/RandomAccessContainer.html">RandomAccessContainer</a> and <a href="expression_concept.htm#vector_expression">Vector Expression</a></p>
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<table border="1" summary="types">
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<tbody>
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<tr>
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<td>StorageArray</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>T</code></td>
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<td>The value_type of elements of V</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>T</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="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a> and <a href="expression_concept.htm#vector_expression">Vector Expression</a> the 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>Size-constructor</td>
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<td><code>V v(n)</code></td>
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<td>T is <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a></td>
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<td><code>V</code></td>
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</tr>
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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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<p><a name="footnote1">[1]</a>
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As a user you should not care about <tt>DenseVector</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.
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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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</body>
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</html>
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