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1429 lines
48 KiB
HTML
1429 lines
48 KiB
HTML
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<!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>Matrix Expressions</title>
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</head>
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<body>
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<h1><img src="../../../../boost.png" align="middle" />Matrix Expressions</h1>
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<div class="toc" id="toc"></div>
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<h2><a name="matrix_expression"></a>Matrix Expression</h2>
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<h4>Description</h4>
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<p>The templated class <code>matrix_expression<E></code>
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is required to be a public base of all classes which model the Matrix 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 matrix 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 Matrix 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>operator[]</code>, <code>row</code>, <code>column</code>, <code>range</code>, <code>slice</code> and <code>project</code> functions have been removed. Use the free functions defined in <a href="matrix_proxy.html">matrix proxy</a> instead.</p>
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<h2><a name="matrix_container"></a>Matrix Container</h2>
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<h4>Description</h4>
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<p>The templated class <code>matrix_container<C></code>
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is required to be a public base of all classes which model the Matrix concept.
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This includes the class <code>matrix</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>E</code></td>
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<td>The type of the matrix 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 Matrix Expression OR Matrix</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>matrix_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="matrix_references"></a>Matrix 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>matrix_reference<E></code>
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contains a reference to a matrix expression.</p>
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<h4>Definition</h4>
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<p>Defined in the header matrix_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 matrix 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#matrix_expression">Matrix 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#matrix_expression">Matrix Expression</a> .</p>
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<h4>Public base classes</h4>
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<p><code>matrix_expression<matrix_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>matrix_reference (expression_type &e)</code></td>
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<td>Constructs a constant 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 size1, size2)</code></td>
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<td>Resizes the expression to hold at most <code>size1</code> rows
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of <code>size2</code> elements.</td>
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</tr>
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<tr>
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<td><code>size_type size1 () const</code></td>
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<td>Returns the number of rows.</td>
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</tr>
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<tr>
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<td><code>size_type size2 () const</code></td>
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<td>Returns the number of columns.</td>
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</tr>
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<tr>
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<td><code>const_reference operator () (size_type i, size_type j)
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const</code></td>
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<td>Returns the value of the <code>j</code>-th element in the
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<code>i</code>-th row.</td>
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</tr>
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<tr>
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<td><code>reference operator () (size_type i, size_type
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j)</code></td>
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<td>Returns a reference of the <code>j</code>-th element in the
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<code>i</code>-th row.</td>
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</tr>
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<tr>
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<td><code>const_iterator1 begin1 () const</code></td>
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<td>Returns a <code>const_iterator1</code> pointing to the
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beginning of the expression.</td>
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</tr>
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<tr>
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<td><code>const_iterator1 end1 () const</code></td>
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<td>Returns a <code>const_iterator1</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>iterator1 begin1 ()</code></td>
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<td>Returns a <code>iterator1</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>iterator1 end1 ()</code></td>
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<td>Returns a <code>iterator1</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_iterator2 begin2 () const</code></td>
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<td>Returns a <code>const_iterator2</code> pointing to the
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beginning of the expression.</td>
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</tr>
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<tr>
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<td><code>const_iterator2 end2 () const</code></td>
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<td>Returns a <code>const_iterator2</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>iterator2 begin2 ()</code></td>
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<td>Returns a <code>iterator2</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>iterator2 end2 ()</code></td>
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<td>Returns a <code>iterator2</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_iterator1 rbegin1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</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_iterator1 rend1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</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_iterator1 rbegin1 ()</code></td>
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<td>Returns a <code>reverse_iterator1</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_iterator1 rend1 ()</code></td>
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<td>Returns a <code>reverse_iterator1</code> pointing to the end of
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the reversed expression.</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</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_iterator2 rend2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</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_iterator2 rbegin2 ()</code></td>
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<td>Returns a <code>reverse_iterator2</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_iterator2 rend2 ()</code></td>
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<td>Returns a <code>reverse_iterator2</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="matrix_operations"></a>Matrix 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 classes <code>matrix_unary1<E, F></code> and
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<code>matrix_unary2<E, F></code> describe unary matrix
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operations.</p>
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<h4>Definition</h4>
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<p>Defined in the header matrix_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 matrix 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#matrix_expression">Matrix Expression</a>
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.</p>
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<h4>Type requirements</h4>
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||
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<p>None, except for those imposed by the requirements of <a href=
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"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
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<h4>Public base classes</h4>
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<p><code>matrix_expression<matrix_unary1<E, F> ></code>
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and <code>matrix_expression<matrix_unary2<E, F>
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></code> resp.</p>
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<h4>Members</h4>
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||
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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>matrix_unary1 (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>matrix_unary2 (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 size1 () const</code></td>
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<td>Returns the number of rows.</td>
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</tr>
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<tr>
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<td><code>size_type size2 () const</code></td>
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<td>Returns the number of columns.</td>
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</tr>
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<tr>
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<td><code>const_reference operator () (size_type i, size_type j)
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const</code></td>
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<td>Returns the value of the <code>j</code>-th element in the
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<code>i</code>-th row.</td>
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</tr>
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<tr>
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<td><code>const_iterator1 begin1 () const</code></td>
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<td>Returns a <code>const_iterator1</code> pointing to the
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beginning of the expression.</td>
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</tr>
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<tr>
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<td><code>const_iterator1 end1 () const</code></td>
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<td>Returns a <code>const_iterator1</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_iterator2 begin2 () const</code></td>
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<td>Returns a <code>const_iterator2</code> pointing to the
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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>Unary Operations</h3>
|
||
|
|
<h4>Prototypes</h4>
|
||
|
|
<pre>
|
||
|
|
<code>template<class E, class F>
|
||
|
|
struct matrix_unary1_traits {
|
||
|
|
typedef matrix_unary1<typename E::const_closure_type, F> expression_type;
|
||
|
|
typedef expression_type result_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
// (- m) [i] [j] = - m [i] [j]
|
||
|
|
template<class E>
|
||
|
|
typename matrix_unary1_traits<E, scalar_negate<typename E::value_type> >::result_type
|
||
|
|
operator - (const matrix_expression<E> &e);
|
||
|
|
|
||
|
|
// (conj m) [i] [j] = conj (m [i] [j])
|
||
|
|
template<class E>
|
||
|
|
typename matrix_unary1_traits<E, scalar_conj<typename E::value_type> >::result_type
|
||
|
|
conj (const matrix_expression<E> &e);
|
||
|
|
|
||
|
|
// (real m) [i] [j] = real (m [i] [j])
|
||
|
|
template<class E>
|
||
|
|
typename matrix_unary1_traits<E, scalar_real<typename E::value_type> >::result_type
|
||
|
|
real (const matrix_expression<E> &e);
|
||
|
|
|
||
|
|
// (imag m) [i] [j] = imag (m [i] [j])
|
||
|
|
template<class E>
|
||
|
|
typename matrix_unary1_traits<E, scalar_imag<typename E::value_type> >::result_type
|
||
|
|
imag (const matrix_expression<E> &e);
|
||
|
|
|
||
|
|
template<class E, class F>
|
||
|
|
struct matrix_unary2_traits {
|
||
|
|
typedef matrix_unary2<typename E::const_closure_type, F> expression_type;
|
||
|
|
typedef expression_type result_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
// (trans m) [i] [j] = m [j] [i]
|
||
|
|
template<class E>
|
||
|
|
typename matrix_unary2_traits<E, scalar_identity<typename E::value_type> >::result_type
|
||
|
|
trans (const matrix_expression<E> &e);
|
||
|
|
|
||
|
|
// (herm m) [i] [j] = conj (m [j] [i])
|
||
|
|
template<class E>
|
||
|
|
typename matrix_unary2_traits<E, scalar_conj<typename E::value_type> >::result_type
|
||
|
|
herm (const matrix_expression<E> &e);</code>
|
||
|
|
</pre>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p><code>operator -</code> computes the additive inverse of a
|
||
|
|
matrix expression. <code>conj</code> computes the complex conjugate
|
||
|
|
of a matrix expression. <code>real</code> and <code>imag</code>
|
||
|
|
compute the real and imaginary parts of a matrix expression.
|
||
|
|
<code>trans</code> computes the transpose of a matrix expression.
|
||
|
|
<code>herm</code> computes the hermitian, i.e. the complex
|
||
|
|
conjugate of the transpose of a matrix expression.</p>
|
||
|
|
<h4>Definition</h4>
|
||
|
|
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
|
<h4>Type requirements</h4>
|
||
|
|
<ul>
|
||
|
|
<li><code>E</code> is a model of <a href=
|
||
|
|
"expression_concept.html#matrix_expression">Matrix Expression</a> .</li>
|
||
|
|
</ul>
|
||
|
|
<h4>Preconditions</h4>
|
||
|
|
<p>None.</p>
|
||
|
|
<h4>Complexity</h4>
|
||
|
|
<p>Quadratic depending from the size of the matrix expression.</p>
|
||
|
|
<h4>Examples</h4>
|
||
|
|
<pre>
|
||
|
|
#include <boost/numeric/ublas/matrix.hpp>
|
||
|
|
#include <boost/numeric/ublas/io.hpp>
|
||
|
|
|
||
|
|
int main () {
|
||
|
|
using namespace boost::numeric::ublas;
|
||
|
|
matrix<std::complex<double> > m (3, 3);
|
||
|
|
for (unsigned i = 0; i < m.size1 (); ++ i)
|
||
|
|
for (unsigned j = 0; j < m.size2 (); ++ j)
|
||
|
|
m (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
|
||
|
|
|
||
|
|
std::cout << - m << std::endl;
|
||
|
|
std::cout << conj (m) << std::endl;
|
||
|
|
std::cout << real (m) << std::endl;
|
||
|
|
std::cout << imag (m) << std::endl;
|
||
|
|
std::cout << trans (m) << std::endl;
|
||
|
|
std::cout << herm (m) << std::endl;
|
||
|
|
}
|
||
|
|
</pre>
|
||
|
|
<h3>Binary Operation Description</h3>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p>The templated class <code>matrix_binary<E1, E2, F></code>
|
||
|
|
describes a binary matrix 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 matrix expression.</td>
|
||
|
|
<td></td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td><code>E2</code></td>
|
||
|
|
<td>The type of the second matrix 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<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>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 Operations</h3>
|
||
|
|
<h4>Prototypes</h4>
|
||
|
|
<pre>
|
||
|
|
<code>template<class E1, class E2, class F>
|
||
|
|
struct matrix_binary_traits {
|
||
|
|
typedef matrix_binary<typename E1::const_closure_type,
|
||
|
|
typename E2::const_closure_type, F> expression_type;
|
||
|
|
typedef expression_type result_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
// (m1 + m2) [i] [j] = m1 [i] [j] + m2 [i] [j]
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_binary_traits<E1, E2, scalar_plus<typename E1::value_type,
|
||
|
|
typename E2::value_type> >::result_type
|
||
|
|
operator + (const matrix_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2);
|
||
|
|
|
||
|
|
// (m1 - m2) [i] [j] = m1 [i] [j] - m2 [i] [j]
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_binary_traits<E1, E2, scalar_minus<typename E1::value_type,
|
||
|
|
typename E2::value_type> >::result_type
|
||
|
|
operator - (const matrix_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2);</code>
|
||
|
|
</pre>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p><code>operator +</code> computes the sum of two matrix
|
||
|
|
expressions. <code>operator -</code> computes the difference of two
|
||
|
|
matrix 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#matrix_expression">Matrix Expression</a> .</li>
|
||
|
|
<li><code>E2</code> is a model of <a href=
|
||
|
|
"expression_concept.html#matrix_expression">Matrix Expression</a> .</li>
|
||
|
|
</ul>
|
||
|
|
<h4>Preconditions</h4>
|
||
|
|
<ul>
|
||
|
|
<li><code>e1 ().size1 () == e2 ().size1 ()</code></li>
|
||
|
|
<li><code>e1 ().size2 () == e2 ().size2 ()</code></li>
|
||
|
|
</ul>
|
||
|
|
<h4>Complexity</h4>
|
||
|
|
<p>Quadratic depending from the size of the matrix 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;
|
||
|
|
matrix<double> m1 (3, 3), m2 (3, 3);
|
||
|
|
for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i)
|
||
|
|
for (unsigned j = 0; j < std::min (m1.size2 (), m2.size2 ()); ++ j)
|
||
|
|
m1 (i, j) = m2 (i, j) = 3 * i + j;
|
||
|
|
|
||
|
|
std::cout << m1 + m2 << std::endl;
|
||
|
|
std::cout << m1 - m2 << std::endl;
|
||
|
|
}
|
||
|
|
</pre>
|
||
|
|
<h3>Scalar Matrix Operation Description</h3>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p>The templated classes <code>matrix_binary_scalar1<E1, E2,
|
||
|
|
F></code> and <code>matrix_binary_scalar2<E1, E2,
|
||
|
|
F></code> describe binary operations between a scalar and a
|
||
|
|
matrix.</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/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 matrix 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<matrix_binary_scalar1<E1, E2,
|
||
|
|
F> ></code> and
|
||
|
|
<code>matrix_expression<matrix_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>matrix_binary_scalar1 (const expression1_type &e1,
|
||
|
|
const expression2_type &e2)</code></td>
|
||
|
|
<td>Constructs a description of the expression.</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td><code>matrix_binary_scalar1 (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>Scalar Matrix Operations</h3>
|
||
|
|
<h4>Prototypes</h4>
|
||
|
|
<pre>
|
||
|
|
<code>template<class T1, class E2, class F>
|
||
|
|
struct matrix_binary_scalar1_traits {
|
||
|
|
typedef matrix_binary_scalar1<scalar_const_reference<T1>,
|
||
|
|
typename E2::const_closure_type, F> expression_type;
|
||
|
|
typedef expression_type result_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
// (t * m) [i] [j] = t * m [i] [j]
|
||
|
|
template<class T1, class E2>
|
||
|
|
typename matrix_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type
|
||
|
|
operator * (const T1 &e1,
|
||
|
|
const matrix_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class E1, class T2, class F>
|
||
|
|
struct matrix_binary_scalar2_traits {
|
||
|
|
typedef matrix_binary_scalar2<typename E1::const_closure_type,
|
||
|
|
scalar_const_reference<T2>, F> expression_type;
|
||
|
|
typedef expression_type result_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
// (m * t) [i] [j] = m [i] [j] * t
|
||
|
|
template<class E1, class T2>
|
||
|
|
typename matrix_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type
|
||
|
|
operator * (const matrix_expression<E1> &e1,
|
||
|
|
const T2 &e2);
|
||
|
|
|
||
|
|
// (m / t) [i] [j] = m [i] [j] / t
|
||
|
|
template<class E1, class T2>
|
||
|
|
typename matrix_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type
|
||
|
|
operator / (const matrix_expression<E1> &e1,
|
||
|
|
const T2 &e2);</code>
|
||
|
|
</pre>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p><code>operator *</code> computes the product of a scalar and a
|
||
|
|
matrix expression. <code>operator /</code> multiplies the matrix
|
||
|
|
with the reciprocal of the scalar.</p>
|
||
|
|
<h4>Definition</h4>
|
||
|
|
<p>Defined in the header matrix_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#matrix_expression">Matrix Expression</a> .</li>
|
||
|
|
</ul>
|
||
|
|
<h4>Preconditions</h4>
|
||
|
|
<p>None.</p>
|
||
|
|
<h4>Complexity</h4>
|
||
|
|
<p>Quadratic depending from the size of the matrix expression.</p>
|
||
|
|
<h4>Examples</h4>
|
||
|
|
<pre>
|
||
|
|
#include <boost/numeric/ublas/matrix.hpp>
|
||
|
|
#include <boost/numeric/ublas/io.hpp>
|
||
|
|
|
||
|
|
int main () {
|
||
|
|
using namespace boost::numeric::ublas;
|
||
|
|
matrix<double> m (3, 3);
|
||
|
|
for (unsigned i = 0; i < m.size1 (); ++ i)
|
||
|
|
for (unsigned j = 0; j < m.size2 (); ++ j)
|
||
|
|
m (i, j) = 3 * i + j;
|
||
|
|
|
||
|
|
std::cout << 2.0 * m << std::endl;
|
||
|
|
std::cout << m * 2.0 << std::endl;
|
||
|
|
}
|
||
|
|
</pre>
|
||
|
|
<h2><a name="matrix_vector_operations"></a>Matrix Vector Operations</h2>
|
||
|
|
<h3>Binary Operation Description</h3>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p>The templated classes <code>matrix_vector_binary1<E1, E2,
|
||
|
|
F></code> and <code>matrix_vector_binary2<E1, E2,
|
||
|
|
F></code> describe binary matrix vector operations.</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 matrix or vector expression.</td>
|
||
|
|
<td></td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td><code>E2</code></td>
|
||
|
|
<td>The type of the vector or matrix 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<matrix_vector_binary1<E1, E2,
|
||
|
|
F> ></code> and
|
||
|
|
<code>vector_expression<matrix_vector_binary2<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>matrix_vector_binary1 (const expression1_type &e1,
|
||
|
|
const expression2_type &e2)</code></td>
|
||
|
|
<td>Constructs a description of the expression.</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td><code>matrix_vector_binary2 (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>Binary Operations</h3>
|
||
|
|
<h4>Prototypes</h4>
|
||
|
|
<pre>
|
||
|
|
<code>template<class T1, class E1, class T2, class E2>
|
||
|
|
struct matrix_vector_binary1_traits {
|
||
|
|
typedef row_major_tag dispatch_category;
|
||
|
|
typedef typename promote_traits<T1, T2>::promote_type promote_type;
|
||
|
|
typedef matrix_vector_binary1<typename E1::const_closure_type,
|
||
|
|
typename E2::const_closure_type,
|
||
|
|
matrix_vector_prod1<T1, T2, promote_type> > expression_type;
|
||
|
|
typedef expression_type result_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_vector_binary1_traits<typename E1::value_type, E1,
|
||
|
|
typename E2::value_type, E2>::result_type
|
||
|
|
prod (const matrix_expression<E1> &e1,
|
||
|
|
const vector_expression<E2> &e2,
|
||
|
|
row_major_tag);
|
||
|
|
|
||
|
|
// Dispatcher
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_vector_binary1_traits<typename E1::value_type, E1,
|
||
|
|
typename E2::value_type, E2>::result_type
|
||
|
|
prod (const matrix_expression<E1> &e1,
|
||
|
|
const vector_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_vector_binary1_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
|
|
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
|
|
prec_prod (const matrix_expression<E1> &e1,
|
||
|
|
const vector_expression<E2> &e2,
|
||
|
|
row_major_tag);
|
||
|
|
|
||
|
|
// Dispatcher
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_vector_binary1_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
|
|
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
|
|
prec_prod (const matrix_expression<E1> &e1,
|
||
|
|
const vector_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class V, class E1, class E2>
|
||
|
|
V
|
||
|
|
prod (const matrix_expression<E1> &e1,
|
||
|
|
const vector_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class V, class E1, class E2>
|
||
|
|
V
|
||
|
|
prec_prod (const matrix_expression<E1> &e1,
|
||
|
|
const vector_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class T1, class E1, class T2, class E2>
|
||
|
|
struct matrix_vector_binary2_traits {
|
||
|
|
typedef column_major_tag dispatch_category;
|
||
|
|
typedef typename promote_traits<T1, T2>::promote_type promote_type;
|
||
|
|
typedef matrix_vector_binary2<typename E1::const_closure_type,
|
||
|
|
typename E2::const_closure_type,
|
||
|
|
matrix_vector_prod2<T1, T2, promote_type> > expression_type;
|
||
|
|
typedef expression_type result_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_vector_binary2_traits<typename E1::value_type, E1,
|
||
|
|
typename E2::value_type, E2>::result_type
|
||
|
|
prod (const vector_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2,
|
||
|
|
column_major_tag);
|
||
|
|
|
||
|
|
// Dispatcher
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_vector_binary2_traits<typename E1::value_type, E1,
|
||
|
|
typename E2::value_type, E2>::result_type
|
||
|
|
prod (const vector_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_vector_binary2_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
|
|
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
|
|
prec_prod (const vector_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2,
|
||
|
|
column_major_tag);
|
||
|
|
|
||
|
|
// Dispatcher
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_vector_binary2_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
|
|
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
|
|
prec_prod (const vector_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class V, class E1, class E2>
|
||
|
|
V
|
||
|
|
prod (const vector_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class V, class E1, class E2>
|
||
|
|
V
|
||
|
|
prec_prod (const vector_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2);</code>
|
||
|
|
</pre>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p><code>prod</code> computes the product of the matrix and the
|
||
|
|
vector expression. <code>prec_prod</code> computes the double
|
||
|
|
precision product of the matrix and the vector expression.</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#matrix_expression">Matrix Expression</a> or
|
||
|
|
<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> or
|
||
|
|
<a href="expression_concept.html#matrix_expression">Matrix Expression</a>
|
||
|
|
.</li>
|
||
|
|
</ul>
|
||
|
|
<h4>Preconditions</h4>
|
||
|
|
<ul>
|
||
|
|
<li><code>e1 ().size2 () == e2 ().size ()</code></li>
|
||
|
|
<li><code>e1 ().size () == e2 ().size1 ()</code></li>
|
||
|
|
</ul>
|
||
|
|
<h4>Complexity</h4>
|
||
|
|
<p>Quadratic depending from the size of the matrix expression.</p>
|
||
|
|
<h4>Examples</h4>
|
||
|
|
<pre>
|
||
|
|
#include <boost/numeric/ublas/matrix.hpp>
|
||
|
|
#include <boost/numeric/ublas/io.hpp>
|
||
|
|
|
||
|
|
int main () {
|
||
|
|
using namespace boost::numeric::ublas;
|
||
|
|
matrix<double> m (3, 3);
|
||
|
|
vector<double> v (3);
|
||
|
|
for (unsigned i = 0; i < std::min (m.size1 (), v.size ()); ++ i) {
|
||
|
|
for (unsigned j = 0; j < m.size2 (); ++ j)
|
||
|
|
m (i, j) = 3 * i + j;
|
||
|
|
v (i) = i;
|
||
|
|
}
|
||
|
|
|
||
|
|
std::cout << prod (m, v) << std::endl;
|
||
|
|
std::cout << prod (v, m) << std::endl;
|
||
|
|
}
|
||
|
|
</pre>
|
||
|
|
<h3>Triangular Solver</h3>
|
||
|
|
<h4>Prototypes</h4>
|
||
|
|
<pre>
|
||
|
|
<code>template<class E1, class E2>
|
||
|
|
struct matrix_vector_solve_traits {
|
||
|
|
typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type;
|
||
|
|
typedef vector<promote_type> result_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (const matrix_expression<E1> &e1,
|
||
|
|
E2 &e2,
|
||
|
|
lower_tag,
|
||
|
|
vector_tag);
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (const matrix_expression<E1> &e1,
|
||
|
|
E2 &e2,
|
||
|
|
upper_tag,
|
||
|
|
vector_tag);
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (const matrix_expression<E1> &e1,
|
||
|
|
E2 &e2,
|
||
|
|
unit_lower_tag,
|
||
|
|
vector_tag);
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (const matrix_expression<E1> &e1,
|
||
|
|
E2 &e2,
|
||
|
|
unit_upper_tag,
|
||
|
|
vector_tag);
|
||
|
|
|
||
|
|
template<class E1, class E2, class C>
|
||
|
|
typename matrix_vector_solve_traits<E1, E2>::result_type
|
||
|
|
solve (const matrix_expression<E1> &e1,
|
||
|
|
const vector_expression<E2> &e2,
|
||
|
|
C);
|
||
|
|
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (E1 &e1,
|
||
|
|
const matrix_expression<E2> &e2,
|
||
|
|
vector_tag,
|
||
|
|
lower_tag);
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (E1 &e1,
|
||
|
|
const matrix_expression<E2> &e2,
|
||
|
|
vector_tag,
|
||
|
|
upper_tag);
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (E1 &e1,
|
||
|
|
const matrix_expression<E2> &e2,
|
||
|
|
vector_tag,
|
||
|
|
unit_lower_tag);
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (E1 &e1,
|
||
|
|
const matrix_expression<E2> &e2,
|
||
|
|
vector_tag,
|
||
|
|
unit_upper_tag);
|
||
|
|
|
||
|
|
template<class E1, class E2, class C>
|
||
|
|
typename matrix_vector_solve_traits<E1, E2>::result_type
|
||
|
|
solve (const vector_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2,
|
||
|
|
C);</code>
|
||
|
|
</pre>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p><code>solve</code> solves a linear equation for lower or upper
|
||
|
|
(unit) triangular matrices.</p>
|
||
|
|
<h4>Definition</h4>
|
||
|
|
<p>Defined in the header triangular.hpp.</p>
|
||
|
|
<h4>Type requirements</h4>
|
||
|
|
<ul>
|
||
|
|
<li><code>E1</code> is a model of <a href=
|
||
|
|
"expression_concept.html#matrix_expression">Matrix Expression</a> or
|
||
|
|
<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> or
|
||
|
|
<a href="expression_concept.html#matrix_expression">Matrix Expression</a>
|
||
|
|
.</li>
|
||
|
|
</ul>
|
||
|
|
<h4>Preconditions</h4>
|
||
|
|
<ul>
|
||
|
|
<li><code>e1 ().size1 () == e1 ().size2 ()</code></li>
|
||
|
|
<li><code>e1 ().size2 () == e2 ().size ()</code></li>
|
||
|
|
<li><code>e1 ().size () == e2 ().size1 ()</code></li>
|
||
|
|
<li><code>e2 ().size1 () == e2 ().size2 ()</code></li>
|
||
|
|
</ul>
|
||
|
|
<h4>Complexity</h4>
|
||
|
|
<p>Quadratic depending from the size of the matrix expression.</p>
|
||
|
|
<h4>Examples</h4>
|
||
|
|
<pre>
|
||
|
|
#include <boost/numeric/ublas/triangular.hpp>
|
||
|
|
#include <boost/numeric/ublas/io.hpp>
|
||
|
|
|
||
|
|
int main () {
|
||
|
|
using namespace boost::numeric::ublas;
|
||
|
|
matrix<double> m (3, 3);
|
||
|
|
vector<double> v (3);
|
||
|
|
for (unsigned i = 0; i < std::min (m.size1 (), v.size ()); ++ i) {
|
||
|
|
for (unsigned j = 0; j <= i; ++ j)
|
||
|
|
m (i, j) = 3 * i + j + 1;
|
||
|
|
v (i) = i;
|
||
|
|
}
|
||
|
|
|
||
|
|
std::cout << solve (m, v, lower_tag ()) << std::endl;
|
||
|
|
std::cout << solve (v, m, lower_tag ()) << std::endl;
|
||
|
|
}
|
||
|
|
</pre>
|
||
|
|
<h2><a name="matrix_matrix_operations"></a>Matrix Matrix Operations</h2>
|
||
|
|
<h3>Binary Operation Description</h3>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p>The templated class <code>matrix_matrix_binary<E1, E2,
|
||
|
|
F></code> describes a binary matrix 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 matrix expression.</td>
|
||
|
|
<td></td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<td><code>E2</code></td>
|
||
|
|
<td>The type of the second matrix 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<matrix_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>matrix_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 Operations</h3>
|
||
|
|
<h4>Prototypes</h4>
|
||
|
|
<pre>
|
||
|
|
<code>template<class T1, class E1, class T2, class E2>
|
||
|
|
struct matrix_matrix_binary_traits {
|
||
|
|
typedef unknown_orientation_tag dispatch_category;
|
||
|
|
typedef typename promote_traits<T1, T2>::promote_type promote_type;
|
||
|
|
typedef matrix_matrix_binary<typename E1::const_closure_type,
|
||
|
|
typename E2::const_closure_type,
|
||
|
|
matrix_matrix_prod<T1, T2, promote_type> > expression_type;
|
||
|
|
typedef expression_type result_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_matrix_binary_traits<typename E1::value_type, E1,
|
||
|
|
typename E2::value_type, E2>::result_type
|
||
|
|
prod (const matrix_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2,
|
||
|
|
unknown_orientation_tag);
|
||
|
|
|
||
|
|
// Dispatcher
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_matrix_binary_traits<typename E1::value_type, E1,
|
||
|
|
typename E2::value_type, E2>::result_type
|
||
|
|
prod (const matrix_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_matrix_binary_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
|
|
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
|
|
prec_prod (const matrix_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2,
|
||
|
|
unknown_orientation_tag);
|
||
|
|
|
||
|
|
// Dispatcher
|
||
|
|
template<class E1, class E2>
|
||
|
|
typename matrix_matrix_binary_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
|
|
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
|
|
prec_prod (const matrix_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class M, class E1, class E2>
|
||
|
|
M
|
||
|
|
prod (const matrix_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2);
|
||
|
|
|
||
|
|
template<class M, class E1, class E2>
|
||
|
|
M
|
||
|
|
prec_prod (const matrix_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2);</code>
|
||
|
|
</pre>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p><code>prod</code> computes the product of the matrix
|
||
|
|
expressions. <code>prec_prod</code> computes the double precision
|
||
|
|
product of the matrix 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#matrix_expression">Matrix Expression</a> .</li>
|
||
|
|
<li><code>E2</code> is a model of <a href=
|
||
|
|
"expression_concept.html#matrix_expression">Matrix Expression</a> .</li>
|
||
|
|
</ul>
|
||
|
|
<h4>Preconditions</h4>
|
||
|
|
<ul>
|
||
|
|
<li><code>e1 ().size2 () == e2 ().size1 ()</code></li>
|
||
|
|
</ul>
|
||
|
|
<h4>Complexity</h4>
|
||
|
|
<p>Cubic depending from the size of the matrix expression.</p>
|
||
|
|
<h4>Examples</h4>
|
||
|
|
<pre>
|
||
|
|
#include <boost/numeric/ublas/matrix.hpp>
|
||
|
|
#include <boost/numeric/ublas/io.hpp>
|
||
|
|
|
||
|
|
int main () {
|
||
|
|
using namespace boost::numeric::ublas;
|
||
|
|
matrix<double> m1 (3, 3), m2 (3, 3);
|
||
|
|
for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i)
|
||
|
|
for (unsigned j = 0; j < std::min (m1.size2 (), m2.size2 ()); ++ j)
|
||
|
|
m1 (i, j) = m2 (i, j) = 3 * i + j;
|
||
|
|
|
||
|
|
std::cout << prod (m1, m2) << std::endl;
|
||
|
|
}
|
||
|
|
</pre>
|
||
|
|
<h3>Triangular Solvers</h3>
|
||
|
|
<h4>Prototypes</h4>
|
||
|
|
<pre>
|
||
|
|
<code>template<class E1, class E2>
|
||
|
|
struct matrix_matrix_solve_traits {
|
||
|
|
typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type;
|
||
|
|
typedef matrix<promote_type> result_type;
|
||
|
|
};
|
||
|
|
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (const matrix_expression<E1> &e1,
|
||
|
|
E2 &e2,
|
||
|
|
lower_tag,
|
||
|
|
matrix_tag);
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (const matrix_expression<E1> &e1,
|
||
|
|
E2 &e2,
|
||
|
|
upper_tag,
|
||
|
|
matrix_tag);
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (const matrix_expression<E1> &e1,
|
||
|
|
E2 &e2,
|
||
|
|
unit_lower_tag,
|
||
|
|
matrix_tag);
|
||
|
|
template<class E1, class E2>
|
||
|
|
void inplace_solve (const matrix_expression<E1> &e1,
|
||
|
|
E2 &e2,
|
||
|
|
unit_upper_tag,
|
||
|
|
matrix_tag);
|
||
|
|
|
||
|
|
template<class E1, class E2, class C>
|
||
|
|
typename matrix_matrix_solve_traits<E1, E2>::result_type
|
||
|
|
solve (const matrix_expression<E1> &e1,
|
||
|
|
const matrix_expression<E2> &e2,
|
||
|
|
C);</code>
|
||
|
|
</pre>
|
||
|
|
<h4>Description</h4>
|
||
|
|
<p><code>solve</code> solves a linear equation for lower or upper
|
||
|
|
(unit) triangular matrices.</p>
|
||
|
|
<h4>Definition</h4>
|
||
|
|
<p>Defined in the header triangular.hpp.</p>
|
||
|
|
<h4>Type requirements</h4>
|
||
|
|
<ul>
|
||
|
|
<li><code>E1</code> is a model of <a href=
|
||
|
|
"expression_concept.html#matrix_expression">Matrix Expression</a> .</li>
|
||
|
|
<li><code>E2</code> is a model of <a href=
|
||
|
|
"expression_concept.html#matrix_expression">Matrix Expression</a> .</li>
|
||
|
|
</ul>
|
||
|
|
<h4>Preconditions</h4>
|
||
|
|
<ul>
|
||
|
|
<li><code>e1 ().size1 () == e1 ().size2 ()</code></li>
|
||
|
|
<li><code>e1 ().size2 () == e2 ().size1 ()</code></li>
|
||
|
|
</ul>
|
||
|
|
<h4>Complexity</h4>
|
||
|
|
<p>Cubic depending from the size of the matrix expressions.</p>
|
||
|
|
<h4>Examples</h4>
|
||
|
|
<pre>
|
||
|
|
#include <boost/numeric/ublas/triangular.hpp>
|
||
|
|
#include <boost/numeric/ublas/io.hpp>
|
||
|
|
|
||
|
|
int main () {
|
||
|
|
using namespace boost::numeric::ublas;
|
||
|
|
matrix<double> m1 (3, 3), m2 (3, 3);
|
||
|
|
for (unsigned i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i)
|
||
|
|
for (unsigned j = 0; j <= i; ++ j)
|
||
|
|
m1 (i, j) = m2 (i, j) = 3 * i + j + 1;
|
||
|
|
|
||
|
|
std::cout << solve (m1, m2, lower_tag ()) << std::endl;
|
||
|
|
}
|
||
|
|
</pre>
|
||
|
|
<hr />
|
||
|
|
<p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br />
|
||
|
|
Use, modification and distribution are subject to the
|
||
|
|
Boost Software License, Version 1.0.
|
||
|
|
(See accompanying file LICENSE_1_0.txt
|
||
|
|
or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
|
||
|
|
http://www.boost.org/LICENSE_1_0.txt
|
||
|
|
</a>).
|
||
|
|
</p>
|
||
|
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