975 lines
31 KiB
HTML
975 lines
31 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 rel="stylesheet" href="../../../../boost.css" type="text/css"/>
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<link rel="stylesheet" href="ublas.css" type="text/css" />
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<script type="text/javascript" src="js/jquery-1.3.2.min.js" async="async" ></script>
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<script type="text/javascript" src="js/jquery.toc-gw.js" async="async" ></script>
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<title>Vector Expressions</title>
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</head>
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<body>
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<h1><img src="../../../../boost.png" align="middle" />Vector Expressions</h1>
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<div class="toc" id="toc"></div>
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<h2><a name="vector_expression"></a>Vector Expression</h2>
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<h4>Description</h4>
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<p>The templated class <code>vector_expression<E></code>
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is required to be a public base of all classes which model the Vector Expression concept.</p>
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<h4>Definition</h4>
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<p>Defined in the header expression_types.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1" summary="parameters">
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<tbody>
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<tr>
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<th>Parameter</th>
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<th>Description</th>
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<th>Default</th>
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</tr>
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<tr>
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<td><code>E</code></td>
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<td>The type of the vector expression.</td>
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<td> </td>
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</tr>
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</tbody>
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</table>
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<h4>Model of</h4>
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<p>None. <u>Not a Vector Expression</u>!
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</p>
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<h4>Type requirements</h4>
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<p>None.</p>
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<h4>Public base classes</h4>
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<p>None.</p>
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<h4>Members</h4>
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<table border="1" summary="members">
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<tbody>
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<tr>
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<th>Member</th>
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<th>Description</th>
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</tr>
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<tr>
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<td><code>const expression_type &operator () ()
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const</code></td>
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<td>Returns a <code>const</code> reference of the expression.</td>
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</tr>
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<tr>
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<td><code>expression_type &operator () ()</code></td>
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<td>Returns a reference of the expression.</td>
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</tr>
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</tbody>
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</table>
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<h4>Notes</h4>
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<p>The <code>range</code>, <code>slice</code> and <code>project</code> functions have been removed. Use the free functions defined in <a href="vector_proxy.html">vector proxy</a> instead.</p>
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<h2><a name="vector_container"></a>Vector Container</h2>
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<h4>Description</h4>
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<p>The templated class <code>vector_container<C></code>
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is required to be a public base of all classes which model the Vector concept.
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This includes the class <code>vector</code> itself.</p>
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<h4>Definition</h4>
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<p>Defined in the header expression_types.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1" summary="parameters">
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<tbody>
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<tr>
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<th>Parameter</th>
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<th>Description</th>
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<th>Default</th>
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</tr>
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<tr>
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<td><code>C</code></td>
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<td>The type of the vector container.</td>
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<td> </td>
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</tr>
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</tbody>
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</table>
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<h4>Model of</h4>
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<p>None. <u>Not a Vector Expression OR Vector</u>!
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</p>
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<h4>Type requirements</h4>
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<p>None.</p>
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<h4>Public base classes</h4>
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<p><code>vector_expression<C></code></p>
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<h4>Members</h4>
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<table border="1" summary="members">
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<tbody>
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<tr>
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<th>Member</th>
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<th>Description</th>
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</tr>
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<tr>
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<td><code>const container_type &operator () ()
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const</code></td>
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<td>Returns a <code>const</code> reference of the container.</td>
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</tr>
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<tr>
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<td><code>container_type &operator () ()</code></td>
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<td>Returns a reference of the container.</td>
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</tr>
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</tbody>
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</table>
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<h2><a name="vector_references"></a>Vector References</h2>
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<h3>Reference</h3>
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<h4>Description</h4>
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<p>The templated class <code>vector_reference<E></code>
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contains a reference to a vector expression.</p>
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<h4>Definition</h4>
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<p>Defined in the header vector_expression.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1" summary="parameters">
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<tbody>
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<tr>
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<th>Parameter</th>
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<th>Description</th>
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<th>Default</th>
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</tr>
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<tr>
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<td><code>E</code></td>
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<td>The type of the vector expression.</td>
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<td> </td>
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</tr>
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</tbody>
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</table>
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<h4>Model of</h4>
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<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
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.</p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a href=
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"expression_concept.html#vector_expression">Vector Expression</a> .</p>
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<h4>Public base classes</h4>
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<p><code>vector_expression<vector_reference<E>
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></code></p>
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<h4>Members</h4>
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<table border="1" summary="members">
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<tbody>
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<tr>
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<th>Member</th>
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<th>Description</th>
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</tr>
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<tr>
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<td><code>vector_reference (expression_type &e)</code></td>
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<td>Constructs a reference of the expression.</td>
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</tr>
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<tr>
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<td><code>void resize (size_type size)</code></td>
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<td>Resizes the expression to hold at most <code>size</code>
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elements.</td>
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</tr>
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<tr>
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<td><code>size_type size () const</code></td>
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<td>Returns the size of the expression.</td>
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</tr>
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<tr>
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<td><code>const_reference operator () (size_type i)
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const</code></td>
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<td>Returns the value of the <code>i</code>-th element.</td>
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</tr>
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<tr>
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<td><code>reference operator () (size_type i)</code></td>
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<td>Returns a reference of the <code>i</code>-th element.</td>
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</tr>
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<tr>
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<td><code>const_iterator begin () const</code></td>
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<td>Returns a <code>const_iterator</code> pointing to the beginning
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of the expression.</td>
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</tr>
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<tr>
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<td><code>const_iterator end () const</code></td>
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<td>Returns a <code>const_iterator</code> pointing to the end of
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the expression.</td>
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</tr>
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<tr>
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<td><code>iterator begin ()</code></td>
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<td>Returns a <code>iterator</code> pointing to the beginning of
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the expression.</td>
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</tr>
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<tr>
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<td><code>iterator end ()</code></td>
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<td>Returns a <code>iterator</code> pointing to the end of the
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expression.</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator rbegin () const</code></td>
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<td>Returns a <code>const_reverse_iterator</code> pointing to the
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beginning of the reversed expression.</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator rend () const</code></td>
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<td>Returns a <code>const_reverse_iterator</code> pointing to the
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end of the reversed expression.</td>
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</tr>
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<tr>
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<td><code>reverse_iterator rbegin ()</code></td>
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<td>Returns a <code>reverse_iterator</code> pointing to the
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beginning of the reversed expression.</td>
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</tr>
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<tr>
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<td><code>reverse_iterator rend ()</code></td>
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<td>Returns a <code>reverse_iterator</code> pointing to the end of
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the reversed expression.</td>
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</tr>
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</tbody>
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</table>
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<h2><a name="vector_operations"></a>Vector Operations</h2>
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<h3>Unary Operation Description</h3>
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<h4>Description</h4>
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<p>The templated class <code>vector_unary<E, F></code>
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describes a unary vector operation.</p>
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<h4>Definition</h4>
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<p>Defined in the header vector_expression.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1" summary="parameters">
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<tbody>
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<tr>
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<th>Parameter</th>
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<th>Description</th>
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<th>Default</th>
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</tr>
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<tr>
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<td><code>E</code></td>
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<td>The type of the vector expression.</td>
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<td> </td>
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</tr>
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<tr>
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<td><code>F</code></td>
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<td>The type of the operation.</td>
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<td> </td>
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</tr>
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</tbody>
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</table>
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<h4>Model of</h4>
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<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
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.</p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a href=
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"expression_concept.html#vector_expression">Vector Expression</a> .</p>
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<h4>Public base classes</h4>
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<p><code>vector_expression<vector_unary<E, F>
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></code></p>
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<h4>Members</h4>
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<table border="1" summary="members">
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<tbody>
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<tr>
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<th>Member</th>
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<th>Description</th>
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</tr>
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<tr>
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<td><code>vector_unary (const expression_type &e)</code></td>
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<td>Constructs a description of the expression.</td>
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</tr>
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<tr>
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<td><code>size_type size () const</code></td>
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<td>Returns the size of the expression.</td>
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</tr>
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<tr>
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<td><code>const_reference operator () (size_type i)
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const</code></td>
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<td>Returns the value of the <code>i</code>-th element.</td>
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</tr>
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<tr>
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<td><code>const_iterator begin () const</code></td>
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<td>Returns a <code>const_iterator</code> pointing to the beginning
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of the expression.</td>
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</tr>
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<tr>
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<td><code>const_iterator end () const</code></td>
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<td>Returns a <code>const_iterator</code> pointing to the end of
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the expression.</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator rbegin () const</code></td>
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<td>Returns a <code>const_reverse_iterator</code> pointing to the
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beginning of the reversed expression.</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator rend () const</code></td>
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<td>Returns a <code>const_reverse_iterator</code> pointing to the
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end of the reversed expression.</td>
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</tr>
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</tbody>
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</table>
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<h3>Unary Operations</h3>
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<h4>Prototypes</h4>
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<pre>
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<code>template<class E, class F>
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struct vector_unary_traits {
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typedef vector_unary<typename E::const_closure_type, F> expression_type;
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typedef expression_type result_type;
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};
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// (- v) [i] = - v [i]
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template<class E>
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typename vector_unary_traits<E, scalar_negate<typename E::value_type> >::result_type
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operator - (const vector_expression<E> &e);
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// (conj v) [i] = conj (v [i])
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template<class E>
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typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type
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conj (const vector_expression<E> &e);
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// (real v) [i] = real (v [i])
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template<class E>
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typename vector_unary_traits<E, scalar_real<typename E::value_type> >::result_type
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real (const vector_expression<E> &e);
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// (imag v) [i] = imag (v [i])
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template<class E>
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typename vector_unary_traits<E, scalar_imag<typename E::value_type> >::result_type
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imag (const vector_expression<E> &e);
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// (trans v) [i] = v [i]
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template<class E>
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typename vector_unary_traits<E, scalar_identity<typename E::value_type> >::result_type
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trans (const vector_expression<E> &e);
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// (herm v) [i] = conj (v [i])
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template<class E>
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typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type
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herm (const vector_expression<E> &e);</code>
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</pre>
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<h4>Description</h4>
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<p><code>operator -</code> computes the additive inverse of a
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vector expression. <code>conj</code> computes the complex conjugate
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of a vector expression. <code>real</code> and <code>imag</code>
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compute the real and imaginary parts of a vector expression.
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<code>trans</code> computes the transpose of a vector expression.
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<code>herm</code> computes the hermitian, i.e. the complex
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conjugate of the transpose of a vector expression.</p>
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<h4>Definition</h4>
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<p>Defined in the header vector_expression.hpp.</p>
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<h4>Type requirements</h4>
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<ul>
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<li><code>E</code> is a model of <a href=
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"expression_concept.html#vector_expression">Vector Expression</a> .</li>
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</ul>
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<h4>Preconditions</h4>
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<p>None.</p>
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<h4>Complexity</h4>
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<p>Linear depending from the size of the vector expression.</p>
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<h4>Examples</h4>
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<pre>
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#include <boost/numeric/ublas/vector.hpp>
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#include <boost/numeric/ublas/io.hpp>
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int main () {
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using namespace boost::numeric::ublas;
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vector<std::complex<double> > v (3);
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for (unsigned i = 0; i < v.size (); ++ i)
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v (i) = std::complex<double> (i, i);
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std::cout << - v << std::endl;
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std::cout << conj (v) << std::endl;
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std::cout << real (v) << std::endl;
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std::cout << imag (v) << std::endl;
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std::cout << trans (v) << std::endl;
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std::cout << herm (v) << std::endl;
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}
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</pre>
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<h3>Binary Operation Description</h3>
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<h4>Description</h4>
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<p>The templated class <code>vector_binary<E1, E2, F></code>
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describes a binary vector operation.</p>
|
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<h4>Definition</h4>
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<p>Defined in the header vector_expression.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1" summary="parameters">
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<tbody>
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<tr>
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<th>Parameter</th>
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<th>Description</th>
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<th>Default</th>
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</tr>
|
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<tr>
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<td><code>E1</code></td>
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<td>The type of the first vector expression.</td>
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<td></td>
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</tr>
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<tr>
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<td><code>E2</code></td>
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<td>The type of the second vector expression.</td>
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<td></td>
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</tr>
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<tr>
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<td><code>F</code></td>
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<td>The type of the operation.</td>
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<td></td>
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</tr>
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</tbody>
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</table>
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<h4>Model of</h4>
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<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
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.</p>
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<h4>Type requirements</h4>
|
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<p>None, except for those imposed by the requirements of <a href=
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"expression_concept.html#vector_expression">Vector Expression</a> .</p>
|
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<h4>Public base classes</h4>
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<p><code>vector_expression<vector_binary<E1, E2, F>
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></code></p>
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<h4>Members</h4>
|
|
<table border="1" summary="members">
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|
<tbody>
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<tr>
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<th>Member</th>
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<th>Description</th>
|
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</tr>
|
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<tr>
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<td><code>vector_binary (const expression1_type &e1, const
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expression2_type &e2)</code></td>
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<td>Constructs a description of the expression.</td>
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</tr>
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<tr>
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<td><code>size_type size () const</code></td>
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<td>Returns the size of the expression.</td>
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</tr>
|
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<tr>
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<td><code>const_reference operator () (size_type i)
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const</code></td>
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<td>Returns the value of the <code>i</code>-th element.</td>
|
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</tr>
|
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<tr>
|
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<td><code>const_iterator begin () const</code></td>
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<td>Returns a <code>const_iterator</code> pointing to the beginning
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of the expression.</td>
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</tr>
|
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<tr>
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<td><code>const_iterator end () const</code></td>
|
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<td>Returns a <code>const_iterator</code> pointing to the end of
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the expression.</td>
|
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</tr>
|
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<tr>
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<td><code>const_reverse_iterator rbegin () const</code></td>
|
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<td>Returns a <code>const_reverse_iterator</code> pointing to the
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beginning of the reversed expression.</td>
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</tr>
|
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<tr>
|
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<td><code>const_reverse_iterator rend () const</code></td>
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<td>Returns a <code>const_reverse_iterator</code> pointing to the
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end of the reversed expression.</td>
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</tr>
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</tbody>
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</table>
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<h3>Binary Operations</h3>
|
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<h4>Prototypes</h4>
|
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<pre>
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<code>template<class E1, class E2, class F>
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struct vector_binary_traits {
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typedef vector_binary<typename E1::const_closure_type,
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typename E2::const_closure_type, F> expression_type;
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typedef expression_type result_type;
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};
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// (v1 + v2) [i] = v1 [i] + v2 [i]
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template<class E1, class E2>
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|
typename vector_binary_traits<E1, E2, scalar_plus<typename E1::value_type,
|
|
typename E2::value_type> >::result_type
|
|
operator + (const vector_expression<E1> &e1,
|
|
const vector_expression<E2> &e2);
|
|
|
|
// (v1 - v2) [i] = v1 [i] - v2 [i]
|
|
template<class E1, class E2>
|
|
typename vector_binary_traits<E1, E2, scalar_minus<typename E1::value_type,
|
|
typename E2::value_type> >::result_type
|
|
operator - (const vector_expression<E1> &e1,
|
|
const vector_expression<E2> &e2);</code>
|
|
</pre>
|
|
<h4>Description</h4>
|
|
<p><code>operator +</code> computes the sum of two vector
|
|
expressions. <code>operator -</code> computes the difference of two
|
|
vector expressions.</p>
|
|
<h4>Definition</h4>
|
|
<p>Defined in the header vector_expression.hpp.</p>
|
|
<h4>Type requirements</h4>
|
|
<ul>
|
|
<li><code>E1</code> is a model of <a href=
|
|
"expression_concept.html#vector_expression">Vector Expression</a> .</li>
|
|
<li><code>E2</code> is a model of <a href=
|
|
"expression_concept.html#vector_expression">Vector Expression</a> .</li>
|
|
</ul>
|
|
<h4>Preconditions</h4>
|
|
<ul>
|
|
<li><code>e1 ().size () == e2 ().size ()</code></li>
|
|
</ul>
|
|
<h4>Complexity</h4>
|
|
<p>Linear depending from the size of the vector expressions.</p>
|
|
<h4>Examples</h4>
|
|
<pre>
|
|
#include <boost/numeric/ublas/vector.hpp>
|
|
#include <boost/numeric/ublas/io.hpp>
|
|
|
|
int main () {
|
|
using namespace boost::numeric::ublas;
|
|
vector<double> v1 (3), v2 (3);
|
|
for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i)
|
|
v1 (i) = v2 (i) = i;
|
|
|
|
std::cout << v1 + v2 << std::endl;
|
|
std::cout << v1 - v2 << std::endl;
|
|
}
|
|
</pre>
|
|
<h3>Binary Outer Operation Description</h3>
|
|
<h4>Description</h4>
|
|
<p>The templated class <code>vector_matrix_binary<E1, E2,
|
|
F></code> describes a binary outer vector operation.</p>
|
|
<h4>Definition</h4>
|
|
<p>Defined in the header matrix_expression.hpp.</p>
|
|
<h4>Template parameters</h4>
|
|
<table border="1" summary="parameters">
|
|
<tbody>
|
|
<tr>
|
|
<th>Parameter</th>
|
|
<th>Description</th>
|
|
<th>Default</th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>E1</code></td>
|
|
<td>The type of the first vector expression.</td>
|
|
<td></td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>E2</code></td>
|
|
<td>The type of the second vector expression.</td>
|
|
<td></td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>F</code></td>
|
|
<td>The type of the operation.</td>
|
|
<td></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<h4>Model of</h4>
|
|
<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
|
|
.</p>
|
|
<h4>Type requirements</h4>
|
|
<p>None, except for those imposed by the requirements of <a href=
|
|
"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
|
|
<h4>Public base classes</h4>
|
|
<p><code>matrix_expression<vector_matrix_binary<E1, E2, F>
|
|
></code></p>
|
|
<h4>Members</h4>
|
|
<table border="1" summary="members">
|
|
<tbody>
|
|
<tr>
|
|
<th>Member</th>
|
|
<th>Description</th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>vector_matrix_binary (const expression1_type &e1,
|
|
const expression2_type &e2)</code></td>
|
|
<td>Constructs a description of the expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size1 () const</code></td>
|
|
<td>Returns the number of rows.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size2 () const</code></td>
|
|
<td>Returns the number of columns.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reference operator () (size_type i, size_type j)
|
|
const</code></td>
|
|
<td>Returns the value of the <code>j</code>-th element in the
|
|
<code>i</code>-th row.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator1 begin1 () const</code></td>
|
|
<td>Returns a <code>const_iterator1</code> pointing to the
|
|
beginning of the expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator1 end1 () const</code></td>
|
|
<td>Returns a <code>const_iterator1</code> pointing to the end of
|
|
the expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator2 begin2 () const</code></td>
|
|
<td>Returns a <code>const_iterator2</code> pointing to the
|
|
beginning of the expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator2 end2 () const</code></td>
|
|
<td>Returns a <code>const_iterator2</code> pointing to the end of
|
|
the expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
|
|
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
|
|
beginning of the reversed expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reverse_iterator1 rend1 () const</code></td>
|
|
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
|
|
end of the reversed expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
|
|
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
|
|
beginning of the reversed expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reverse_iterator2 rend2 () const</code></td>
|
|
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
|
|
end of the reversed expression.</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<h3>Binary Outer Operations</h3>
|
|
<h4>Prototypes</h4>
|
|
<pre>
|
|
<code>template<class E1, class E2, class F>
|
|
struct vector_matrix_binary_traits {
|
|
typedef vector_matrix_binary<typename E1::const_closure_type,
|
|
typename E2::const_closure_type, F> expression_type;
|
|
typedef expression_type result_type;
|
|
};
|
|
|
|
// (outer_prod (v1, v2)) [i] [j] = v1 [i] * v2 [j]
|
|
template<class E1, class E2>
|
|
typename vector_matrix_binary_traits<E1, E2, scalar_multiplies<typename E1::value_type, typename E2::value_type> >::result_type
|
|
outer_prod (const vector_expression<E1> &e1,
|
|
const vector_expression<E2> &e2);</code>
|
|
</pre>
|
|
<h4>Description</h4>
|
|
<p><code>outer_prod</code> computes the outer product of two vector
|
|
expressions.</p>
|
|
<h4>Definition</h4>
|
|
<p>Defined in the header matrix_expression.hpp.</p>
|
|
<h4>Type requirements</h4>
|
|
<ul>
|
|
<li><code>E1</code> is a model of <a href=
|
|
"expression_concept.html#vector_expression">Vector Expression</a> .</li>
|
|
<li><code>E2</code> is a model of <a href=
|
|
"expression_concept.html#vector_expression">Vector Expression</a> .</li>
|
|
</ul>
|
|
<h4>Preconditions</h4>
|
|
<p>None.</p>
|
|
<h4>Complexity</h4>
|
|
<p>Quadratic depending from the size of the vector expressions.</p>
|
|
<h4>Examples</h4>
|
|
<pre>
|
|
#include <boost/numeric/ublas/matrix.hpp>
|
|
#include <boost/numeric/ublas/io.hpp>
|
|
|
|
int main () {
|
|
using namespace boost::numeric::ublas;
|
|
vector<double> v1 (3), v2 (3);
|
|
for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i)
|
|
v1 (i) = v2 (i) = i;
|
|
|
|
std::cout << outer_prod (v1, v2) << std::endl;
|
|
}
|
|
</pre>
|
|
<h3>Scalar Vector Operation Description</h3>
|
|
<h4>Description</h4>
|
|
<p>The templated classes <code>vector_binary_scalar1<E1, E2,
|
|
F></code> and <code>vector_binary_scalar2<E1, E2,
|
|
F></code> describe binary operations between a scalar and a
|
|
vector.</p>
|
|
<h4>Definition</h4>
|
|
<p>Defined in the header vector_expression.hpp.</p>
|
|
<h4>Template parameters</h4>
|
|
<table border="1" summary="parameters">
|
|
<tbody>
|
|
<tr>
|
|
<th>Parameter</th>
|
|
<th>Description</th>
|
|
<th>Default</th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>E1/E2</code></td>
|
|
<td>The type of the scalar expression.</td>
|
|
<td></td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>E2/E1</code></td>
|
|
<td>The type of the vector expression.</td>
|
|
<td></td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>F</code></td>
|
|
<td>The type of the operation.</td>
|
|
<td></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<h4>Model of</h4>
|
|
<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
|
|
.</p>
|
|
<h4>Type requirements</h4>
|
|
<p>None, except for those imposed by the requirements of <a href=
|
|
"expression_concept.html#vector_expression">Vector Expression</a> .</p>
|
|
<h4>Public base classes</h4>
|
|
<p><code>vector_expression<vector_binary_scalar1<E1, E2,
|
|
F> ></code> and
|
|
<code>vector_expression<vector_binary_scalar2<E1, E2, F>
|
|
></code> resp.</p>
|
|
<h4>Members</h4>
|
|
<table border="1" summary="members">
|
|
<tbody>
|
|
<tr>
|
|
<th>Member</th>
|
|
<th>Description</th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>vector_binary_scalar1 (const expression1_type &e1,
|
|
const expression2_type &e2)</code></td>
|
|
<td>Constructs a description of the expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>vector_binary_scalar2 (const expression1_type &e1,
|
|
const expression2_type &e2)</code></td>
|
|
<td>Constructs a description of the expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size () const</code></td>
|
|
<td>Returns the size of the expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reference operator () (size_type i)
|
|
const</code></td>
|
|
<td>Returns the value of the <code>i</code>-th element.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator begin () const</code></td>
|
|
<td>Returns a <code>const_iterator</code> pointing to the beginning
|
|
of the expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator end () const</code></td>
|
|
<td>Returns a <code>const_iterator</code> pointing to the end of
|
|
the expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reverse_iterator rbegin () const</code></td>
|
|
<td>Returns a <code>const_reverse_iterator</code> pointing to the
|
|
beginning of the reversed expression.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reverse_iterator rend () const</code></td>
|
|
<td>Returns a <code>const_reverse_iterator</code> pointing to the
|
|
end of the reversed expression.</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<h3>Scalar Vector Operations</h3>
|
|
<h4>Prototypes</h4>
|
|
<pre>
|
|
<code>template<class T1, class E2, class F>
|
|
struct vector_binary_scalar1_traits {
|
|
typedef vector_binary_scalar1<scalar_const_reference<T1>,
|
|
typename E2::const_closure_type, F> expression_type;
|
|
typedef expression_type result_type;
|
|
};
|
|
|
|
// (t * v) [i] = t * v [i]
|
|
template<class T1, class E2>
|
|
typename vector_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type
|
|
operator * (const T1 &e1,
|
|
const vector_expression<E2> &e2);
|
|
|
|
template<class E1, class T2, class F>
|
|
struct vector_binary_scalar2_traits {
|
|
typedef vector_binary_scalar2<typename E1::const_closure_type,
|
|
scalar_const_reference<T2>, F> expression_type;
|
|
typedef expression_type result_type;
|
|
};
|
|
|
|
// (v * t) [i] = v [i] * t
|
|
template<class E1, class T2>
|
|
typename vector_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type
|
|
operator * (const vector_expression<E1> &e1,
|
|
const T2 &e2);
|
|
|
|
// (v / t) [i] = v [i] / t
|
|
template<class E1, class T2>
|
|
typename vector_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type
|
|
operator / (const vector_expression<E1> &e1,
|
|
const T2 &e2);</code>
|
|
</pre>
|
|
<h4>Description</h4>
|
|
<p><code>operator *</code> computes the product of a scalar and a
|
|
vector expression. <code>operator /</code> multiplies the vector
|
|
with the reciprocal of the scalar.</p>
|
|
<h4>Definition</h4>
|
|
<p>Defined in the header vector_expression.hpp.</p>
|
|
<h4>Type requirements</h4>
|
|
<ul>
|
|
<li><code>T1/T2</code> is a model of <a href=
|
|
"expression_concept.html#scalar_expression">Scalar Expression</a> .</li>
|
|
<li><code>E2/E1</code> is a model of <a href=
|
|
"expression_concept.html#vector_expression">Vector Expression</a> .</li>
|
|
</ul>
|
|
<h4>Preconditions</h4>
|
|
<p>None.</p>
|
|
<h4>Complexity</h4>
|
|
<p>Linear depending from the size of the vector expression.</p>
|
|
<h4>Examples</h4>
|
|
<pre>
|
|
#include <boost/numeric/ublas/vector.hpp>
|
|
#include <boost/numeric/ublas/io.hpp>
|
|
|
|
int main () {
|
|
using namespace boost::numeric::ublas;
|
|
vector<double> v (3);
|
|
for (unsigned i = 0; i < v.size (); ++ i)
|
|
v (i) = i;
|
|
|
|
std::cout << 2.0 * v << std::endl;
|
|
std::cout << v * 2.0 << std::endl;
|
|
}
|
|
</pre>
|
|
<h2><a name="vector_reductions"></a>Vector Reductions</h2>
|
|
<h3>Unary Reductions</h3>
|
|
<h4>Prototypes</h4>
|
|
<pre>
|
|
<code>template<class E, class F>
|
|
struct vector_scalar_unary_traits {
|
|
typedef typename F::result_type result_type;
|
|
};
|
|
|
|
// sum v = sum (v [i])
|
|
template<class E>
|
|
typename vector_scalar_unary_traits<E, vector_sum<typename E::value_type> >::result_type
|
|
sum (const vector_expression<E> &e);
|
|
|
|
// norm_1 v = sum (abs (v [i]))
|
|
template<class E>
|
|
typename vector_scalar_unary_traits<E, vector_norm_1<typename E::value_type> >::result_type
|
|
norm_1 (const vector_expression<E> &e);
|
|
|
|
// norm_2 v = sqrt (sum (v [i] * v [i]))
|
|
template<class E>
|
|
typename vector_scalar_unary_traits<E, vector_norm_2<typename E::value_type> >::result_type
|
|
norm_2 (const vector_expression<E> &e);
|
|
|
|
// norm_2_square v = sum (v [i] * v [i])
|
|
template<class E>
|
|
typename vector_scalar_unary_traits<E, vector_norm_2_square<typename E::value_type> >::result_type
|
|
norm_2_square (const vector_expression<E> &e);
|
|
|
|
// norm_inf v = max (abs (v [i]))
|
|
template<class E>
|
|
typename vector_scalar_unary_traits<E, vector_norm_inf<typename E::value_type> >::result_type
|
|
norm_inf (const vector_expression<E> &e);
|
|
|
|
// index_norm_inf v = min (i: abs (v [i]) == max (abs (v [i])))
|
|
template<class E>
|
|
typename vector_scalar_unary_traits<E, vector_index_norm_inf<typename E::value_type> >::result_type
|
|
index_norm_inf (const vector_expression<E> &e);</code>
|
|
</pre>
|
|
<h4>Description</h4>
|
|
<p><code>sum</code> computes the sum of the vector expression's
|
|
elements. <code>norm_1</code>, <code>norm_2</code> and
|
|
<code>norm_inf</code> compute the corresponding
|
|
<em>||.||</em><sub><em>1</em></sub>,
|
|
<em>||.||</em><sub><em>2</em></sub> and
|
|
<em>||.||</em><sub><em>inf</em></sub> vector norms.
|
|
<code>index_norm_1</code> computes the index of the vector
|
|
expression's first element having maximal absolute value.</p>
|
|
<h4>Definition</h4>
|
|
<p>Defined in the header vector_expression.hpp.</p>
|
|
<h4>Type requirements</h4>
|
|
<ul>
|
|
<li><code>E</code> is a model of <a href=
|
|
"#vector_expression">Vector Expression</a> .</li>
|
|
</ul>
|
|
<h4>Preconditions</h4>
|
|
<p>None.</p>
|
|
<h4>Complexity</h4>
|
|
<p>Linear depending from the size of the vector expression.</p>
|
|
<h4>Examples</h4>
|
|
<pre>
|
|
#include <boost/numeric/ublas/vector.hpp>
|
|
|
|
int main () {
|
|
using namespace boost::numeric::ublas;
|
|
vector<double> v (3);
|
|
for (unsigned i = 0; i < v.size (); ++ i)
|
|
v (i) = i;
|
|
|
|
std::cout << sum (v) << std::endl;
|
|
std::cout << norm_1 (v) << std::endl;
|
|
std::cout << norm_2 (v) << std::endl;
|
|
std::cout << norm_inf (v) << std::endl;
|
|
std::cout << index_norm_inf (v) << std::endl;
|
|
}
|
|
</pre>
|
|
<h3>Binary Reductions</h3>
|
|
<h4>Prototypes</h4>
|
|
<pre>
|
|
<code>template<class E1, class E2, class F>
|
|
struct vector_scalar_binary_traits {
|
|
typedef typename F::result_type result_type;
|
|
};
|
|
|
|
// inner_prod (v1, v2) = sum (v1 [i] * v2 [i])
|
|
template<class E1, class E2>
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typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type,
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typename E2::value_type,
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typename promote_traits<typename E1::value_type,
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typename E2::value_type>::promote_type> >::result_type
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inner_prod (const vector_expression<E1> &e1,
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const vector_expression<E2> &e2);
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|
|
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template<class E1, class E2>
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typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type,
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typename E2::value_type,
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typename type_traits<typename promote_traits<typename E1::value_type,
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|
typename E2::value_type>::promote_type>::precision_type> >::result_type
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prec_inner_prod (const vector_expression<E1> &e1,
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const vector_expression<E2> &e2);</code>
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</pre>
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<h4>Description</h4>
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|
<p><code>inner_prod</code> computes the inner product of the vector
|
|
expressions. <code>prec_inner_prod</code> computes the double
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|
precision inner product of the vector expressions<code>.</code></p>
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<h4>Definition</h4>
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|
<p>Defined in the header vector_expression.hpp.</p>
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<h4>Type requirements</h4>
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|
<ul>
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|
<li><code>E1</code> is a model of <a href=
|
|
"#vector_expression">Vector Expression</a> .</li>
|
|
<li><code>E2</code> is a model of <a href=
|
|
"#vector_expression">Vector Expression</a> .</li>
|
|
</ul>
|
|
<h4>Preconditions</h4>
|
|
<ul>
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|
<li><code>e1 ().size () == e2 ().size ()</code></li>
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|
</ul>
|
|
<h4>Complexity</h4>
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|
<p>Linear depending from the size of the vector expressions.</p>
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<h4>Examples</h4>
|
|
<pre>
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#include <boost/numeric/ublas/vector.hpp>
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|
|
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int main () {
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using namespace boost::numeric::ublas;
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vector<double> v1 (3), v2 (3);
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for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i)
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v1 (i) = v2 (i) = i;
|
|
|
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std::cout << inner_prod (v1, v2) << std::endl;
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}
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</pre>
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<hr />
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<p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br />
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|
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
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</a>).
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</p>
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