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1934 lines
60 KiB
HTML
1934 lines
60 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<meta name="generator" content="HTML Tidy, see www.w3.org">
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<meta name="GENERATOR" content="Microsoft FrontPage Express 2.0">
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<title>Vector Expressions</title>
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</head>
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<body bgcolor="#ffffff">
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<h1><img src="c++boost.gif" alt="c++boost.gif" align="Center">
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Vector Expressions</h1>
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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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forms the base for all static derived vector expression classes
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including class <code>vector</code> itself.</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">
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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.</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">
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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>Interface</h4>
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<pre>
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<code>// Base class for the Barton Nackman trick<br>
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template<class E><br>
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struct vector_expression {<br>
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typedef E expression_type;<br>
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typedef vector_tag type_category;<br>
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<br>
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// This class could define an common interface for all<br>
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// statically derived expression type classes.<br>
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// Due to a compiler deficiency - one can not reference class typedefs of E<br>
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// on MSVC 6.0 (error C2027) - we only implement the casts.<br>
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<br>
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const expression_type &operator () () const;<br>
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expression_type &operator () ();<br>
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};</code>
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</pre>
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<h2><a name="vector_references"></a> Vector References</h2>
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<h3>Constant Reference</h3>
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<h4>Description</h4>
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<p>The templated class <code>vector_const_reference<E></code>
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contains a constant 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">
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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.htm#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.htm#vector_expression">Vector Expression</a> .</p>
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<h4>Public base classes</h4>
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<p><code>vector_expression<vector_const_reference<E>
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></code></p>
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<h4>Members</h4>
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<table border="1">
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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_const_reference (const expression_type
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&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>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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<h4>Interface</h4>
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<pre>
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<code>template<class E><br>
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class vector_const_reference:<br>
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public vector_expression<vector_const_reference<E> > {<br>
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public:<br>
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typedef E expression_type;<br>
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typedef typename E::size_type size_type;<br>
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typedef typename E::difference_type difference_type;<br>
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typedef typename E::value_type value_type;<br>
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typedef typename E::const_reference const_reference;<br>
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typedef const_reference reference;<br>
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typedef typename E::const_pointer const_pointer;<br>
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typedef const_pointer pointer;<br>
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typedef typename E::const_iterator const_iterator_type;<br>
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typedef unknown_storage_tag storage_category;<br>
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<br>
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// Construction and destruction<br>
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vector_const_reference ();<br>
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vector_const_reference (const expression_type &e);<br>
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<br>
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// Accessors<br>
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size_type size () const;<br>
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const expression_type &expression () const;<br>
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<br>
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// Element access<br>
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const_reference operator () (size_type i) const;<br>
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<br>
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const_reference operator [] (size_type i) const;<br>
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<br>
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typedef const_iterator_type const_iterator;<br>
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typedef const_iterator iterator;<br>
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<br>
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// Element lookup<br>
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const_iterator find_first (size_type i) const;<br>
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const_iterator find_last (size_type i) const;<br>
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<br>
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// Iterator is the iterator of the referenced expression.<br>
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<br>
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const_iterator begin () const;<br>
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const_iterator end () const;<br>
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<br>
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// Reverse iterator<br>
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<br>
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typedef reverse_iterator_base<const_iterator> const_reverse_iterator;<br>
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<br>
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const_reverse_iterator rbegin () const;<br>
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const_reverse_iterator rend () const;<br>
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};</code>
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</pre>
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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">
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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.htm#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.htm#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">
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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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<h4>Interface</h4>
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<pre>
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<code>template<class E><br>
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class vector_reference:<br>
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public vector_expression<vector_reference<E> > {<br>
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public:<br>
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typedef E expression_type;<br>
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typedef typename E::size_type size_type;<br>
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typedef typename E::difference_type difference_type;<br>
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typedef typename E::value_type value_type;<br>
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typedef typename E::const_reference const_reference;<br>
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typedef typename E::reference reference;<br>
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typedef typename E::const_pointer const_pointer;<br>
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typedef typename E::pointer pointer;<br>
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typedef typename E::const_iterator const_iterator_type;<br>
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typedef typename E::iterator iterator_type;<br>
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typedef unknown_storage_tag storage_category;<br>
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<br>
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// Construction and destruction<br>
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vector_reference ();<br>
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vector_reference (expression_type &e);<br>
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<br>
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// Accessors<br>
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size_type size () const;<br>
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const expression_type &expression () const;<br>
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expression_type &expression ();<br>
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<br>
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// Resizing<br>
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void resize (size_type size);<br>
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<br>
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// Element access<br>
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const_reference operator () (size_type i) const;<br>
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reference operator () (size_type i);<br>
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<br>
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const_reference operator [] (size_type i) const;<br>
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reference operator [] (size_type i);<br>
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<br>
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typedef const_iterator_type const_iterator;<br>
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typedef iterator_type iterator;<br>
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<br>
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// Element lookup<br>
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const_iterator find_first (size_type i) const;<br>
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iterator find_first (size_type i);<br>
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const_iterator find_last (size_type i) const;<br>
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iterator find_last (size_type i);<br>
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<br>
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// Iterator is the iterator of the referenced expression.<br>
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<br>
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const_iterator begin () const;<br>
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const_iterator end () const;<br>
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<br>
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iterator begin ();<br>
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iterator end ();<br>
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<br>
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// Reverse iterator<br>
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<br>
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typedef reverse_iterator_base<const_iterator> const_reverse_iterator;<br>
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<br>
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const_reverse_iterator rbegin () const;<br>
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const_reverse_iterator rend () const;<br>
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<br>
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typedef reverse_iterator_base<iterator> reverse_iterator;<br>
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<br>
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reverse_iterator rbegin ();<br>
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reverse_iterator rend ();<br>
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};</code>
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</pre>
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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">
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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.htm#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.htm#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">
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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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<h4>Interface</h4>
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|
|
<pre>
|
|
<code>template<class E, class F><br>
|
|
class vector_unary:<br>
|
|
public vector_expression<vector_unary<E, F> > {<br>
|
|
public:<br>
|
|
typedef E expression_type;<br>
|
|
typedef F functor_type;<br>
|
|
typedef typename E::size_type size_type;<br>
|
|
typedef typename E::difference_type difference_type;<br>
|
|
typedef typename F::result_type value_type;<br>
|
|
typedef value_type const_reference;<br>
|
|
typedef const_reference reference;<br>
|
|
typedef const value_type *const_pointer;<br>
|
|
typedef const_pointer pointer;<br>
|
|
typedef const vector_unary<E, F> const_closure_type;<br>
|
|
typedef typename E::const_iterator const_iterator_type;<br>
|
|
typedef unknown_storage_tag storage_category;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
vector_unary ();<br>
|
|
vector_unary (const expression_type &e);<br>
|
|
<br>
|
|
// Accessors<br>
|
|
size_type size () const;<br>
|
|
const expression_type &expression () const;<br>
|
|
<br>
|
|
// Element access<br>
|
|
const_reference operator () (size_type i) const;<br>
|
|
<br>
|
|
const_reference operator [] (size_type i) const;<br>
|
|
<br>
|
|
class const_iterator;<br>
|
|
typedef const_iterator iterator;<br>
|
|
<br>
|
|
// Element lookup<br>
|
|
const_iterator find_first (size_type i) const;<br>
|
|
const_iterator find_last (size_type i) const;<br>
|
|
<br>
|
|
// Iterator enhances the iterator of the referenced expression<br>
|
|
// with the unary functor.<br>
|
|
<br>
|
|
class const_iterator:<br>
|
|
public container_const_reference<vector_unary>,<br>
|
|
public random_access_iterator_base<const_iterator, value_type> {<br>
|
|
public:<br>
|
|
typedef typename E::const_iterator::iterator_category iterator_category;<br>
|
|
typedef typename vector_unary::difference_type difference_type;<br>
|
|
typedef typename vector_unary::value_type value_type;<br>
|
|
typedef typename vector_unary::const_reference reference;<br>
|
|
typedef typename vector_unary::const_pointer pointer;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
const_iterator ();<br>
|
|
const_iterator (const vector_unary &vu, const const_iterator_type &it);<br>
|
|
<br>
|
|
// Arithmetic<br>
|
|
const_iterator &operator ++ ();<br>
|
|
const_iterator &operator -- ();<br>
|
|
const_iterator &operator += (difference_type n);<br>
|
|
const_iterator &operator -= (difference_type n);<br>
|
|
difference_type operator - (const const_iterator &it) const;<br>
|
|
<br>
|
|
// Dereference<br>
|
|
reference operator * () const;<br>
|
|
<br>
|
|
// Index<br>
|
|
size_type index () const;<br>
|
|
<br>
|
|
// Assignment<br>
|
|
const_iterator &operator = (const const_iterator &it);<br>
|
|
<br>
|
|
// Comparison<br>
|
|
bool operator == (const const_iterator &it) const;<br>
|
|
bool operator <(const const_iterator &it) const;<br>
|
|
};<br>
|
|
<br>
|
|
const_iterator begin () const;<br>
|
|
const_iterator end () const;<br>
|
|
<br>
|
|
// Reverse iterator<br>
|
|
<br>
|
|
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;<br>
|
|
<br>
|
|
const_reverse_iterator rbegin () const;<br>
|
|
const_reverse_iterator rend () const;<br>
|
|
};</code>
|
|
</pre>
|
|
|
|
<h3>Unary Operations</h3>
|
|
|
|
<h4>Prototypes</h4>
|
|
|
|
<pre>
|
|
<code>template<class E, class F><br>
|
|
struct vector_unary_traits {<br>
|
|
typedef vector_unary<typename E::const_closure_type, F> expression_type;<br>
|
|
typedef expression_type result_type;<br>
|
|
};<br>
|
|
<br>
|
|
// (- v) [i] = - v [i]<br>
|
|
template<class E><br>
|
|
typename vector_unary_traits<E, scalar_negate<typename E::value_type> >::result_type<br>
|
|
operator - (const vector_expression<E> &e);<br>
|
|
<br>
|
|
// (conj v) [i] = conj (v [i])<br>
|
|
template<class E><br>
|
|
typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type<br>
|
|
conj (const vector_expression<E> &e);<br>
|
|
<br>
|
|
// (real v) [i] = real (v [i])<br>
|
|
template<class E><br>
|
|
typename vector_unary_traits<E, scalar_real<typename E::value_type> >::result_type<br>
|
|
real (const vector_expression<E> &e);<br>
|
|
<br>
|
|
// (imag v) [i] = imag (v [i])<br>
|
|
template<class E><br>
|
|
typename vector_unary_traits<E, scalar_imag<typename E::value_type> >::result_type<br>
|
|
imag (const vector_expression<E> &e);<br>
|
|
<br>
|
|
// (trans v) [i] = v [i]<br>
|
|
template<class E><br>
|
|
typename vector_unary_traits<E, scalar_identity<typename E::value_type> >::result_type<br>
|
|
trans (const vector_expression<E> &e);<br>
|
|
<br>
|
|
// (herm v) [i] = conj (v [i])<br>
|
|
template<class E><br>
|
|
typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type<br>
|
|
herm (const vector_expression<E> &e);</code>
|
|
</pre>
|
|
|
|
<h4>Description</h4>
|
|
|
|
<p><code>operator -</code> computes the additive inverse of a
|
|
vector expression. <code>conj</code> computes the complex conjugate
|
|
of a vector expression. <code>real</code> and <code>imag</code>
|
|
compute the real and imaginary parts of a vector expression.
|
|
<code>trans</code> computes the transpose of a vector expression.
|
|
<code>herm</code> computes the hermitian, i.e. the complex
|
|
conjugate of the transpose of a vector expression.</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=
|
|
"expression.htm#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><br>
|
|
#include <boost/numeric/ublas/io.hpp><br>
|
|
<br>
|
|
int main () {<br>
|
|
using namespace boost::numeric::ublas;<br>
|
|
vector<std::complex<double> > v (3);<br>
|
|
for (unsigned i = 0; i < v.size (); ++ i)<br>
|
|
v (i) = std::complex<double> (i, i);<br>
|
|
<br>
|
|
std::cout << - v << std::endl;<br>
|
|
std::cout << conj (v) << std::endl;<br>
|
|
std::cout << real (v) << std::endl;<br>
|
|
std::cout << imag (v) << std::endl;<br>
|
|
std::cout << trans (v) << std::endl;<br>
|
|
std::cout << herm (v) << std::endl;<br>
|
|
}
|
|
</pre>
|
|
|
|
<h3>Binary Operation Description</h3>
|
|
|
|
<h4>Description</h4>
|
|
|
|
<p>The templated class <code>vector_binary<E1, E2, F></code>
|
|
describes a binary vector operation.</p>
|
|
|
|
<h4>Definition</h4>
|
|
|
|
<p>Defined in the header vector_expression.hpp.</p>
|
|
|
|
<h4>Template parameters</h4>
|
|
|
|
<table border="1">
|
|
<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.htm#vector_expression">Vector Expression</a>
|
|
.</p>
|
|
|
|
<h4>Type requirements</h4>
|
|
|
|
<p>None, except for those imposed by the requirements of <a href=
|
|
"expression.htm#vector_expression">Vector Expression</a> .</p>
|
|
|
|
<h4>Public base classes</h4>
|
|
|
|
<p><code>vector_expression<vector_binary<E1, E2, F>
|
|
></code></p>
|
|
|
|
<h4>Members</h4>
|
|
|
|
<table border="1">
|
|
<tbody>
|
|
<tr>
|
|
<th>Member</th>
|
|
<th>Description</th>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td><code>vector_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 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>
|
|
|
|
<h4>Interface</h4>
|
|
|
|
<pre>
|
|
<code>template<class E1, class E2, class F><br>
|
|
class vector_binary:<br>
|
|
public vector_expression<vector_binary<E1, E2, F> > {<br>
|
|
public:<br>
|
|
typedef E1 expression1_type;<br>
|
|
typedef E2 expression2_type;<br>
|
|
typedef F functor_type;<br>
|
|
typedef typename promote_traits<typename E1::size_type, typename E2::size_type>::promote_type size_type;<br>
|
|
typedef typename promote_traits<typename E1::difference_type, typename E2::difference_type>::promote_type difference_type;<br>
|
|
typedef typename F::result_type value_type;<br>
|
|
typedef value_type const_reference;<br>
|
|
typedef const_reference reference;<br>
|
|
typedef const value_type *const_pointer;<br>
|
|
typedef const_pointer pointer;<br>
|
|
typedef const vector_binary<E1, E2, F> const_closure_type;<br>
|
|
typedef typename E1::const_iterator const_iterator1_type;<br>
|
|
typedef typename E2::const_iterator const_iterator2_type;<br>
|
|
typedef unknown_storage_tag storage_category;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
vector_binary ();<br>
|
|
vector_binary (const expression1_type &e1, const expression2_type &e2);<br>
|
|
<br>
|
|
// Accessors<br>
|
|
size_type size () const;<br>
|
|
const expression1_type &expression1 () const;<br>
|
|
const expression2_type &expression2 () const;<br>
|
|
<br>
|
|
// Element access<br>
|
|
const_reference operator () (size_type i) const;<br>
|
|
<br>
|
|
const_reference operator [] (size_type i) const;<br>
|
|
<br>
|
|
class const_iterator;<br>
|
|
typedef const_iterator iterator;<br>
|
|
<br>
|
|
// Element lookup<br>
|
|
const_iterator find_first (size_type i) const;<br>
|
|
const_iterator find_last (size_type i) const;<br>
|
|
<br>
|
|
// Iterator merges the iterators of the referenced expressions and <br>
|
|
// enhances them with the binary functor.<br>
|
|
<br>
|
|
class const_iterator:<br>
|
|
public container_const_reference<vector_binary>,<br>
|
|
public random_access_iterator_base<const_iterator, value_type> {<br>
|
|
public:<br>
|
|
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,<br>
|
|
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;<br>
|
|
typedef typename vector_binary::difference_type difference_type;<br>
|
|
typedef typename vector_binary::value_type value_type;<br>
|
|
typedef typename vector_binary::const_reference reference;<br>
|
|
typedef typename vector_binary::const_pointer pointer;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
const_iterator ();<br>
|
|
const_iterator (const vector_binary &vb, size_type i,<br>
|
|
const const_iterator1_type &it1, const const_iterator1_type &it1_end,<br>
|
|
const const_iterator2_type &it2, const const_iterator2_type &it2_end);<br>
|
|
<br>
|
|
// Dense specializations<br>
|
|
void increment (dense_random_access_iterator_tag);<br>
|
|
void decrement (dense_random_access_iterator_tag);<br>
|
|
value_type dereference (dense_random_access_iterator_tag) const;<br>
|
|
<br>
|
|
// Packed specializations<br>
|
|
void increment (packed_random_access_iterator_tag);<br>
|
|
void decrement (packed_random_access_iterator_tag);<br>
|
|
value_type dereference (packed_random_access_iterator_tag) const;<br>
|
|
<br>
|
|
// Sparse specializations<br>
|
|
void increment (sparse_bidirectional_iterator_tag);<br>
|
|
void decrement (sparse_bidirectional_iterator_tag);<br>
|
|
value_type dereference (sparse_bidirectional_iterator_tag) const;<br>
|
|
<br>
|
|
// Arithmetic<br>
|
|
const_iterator &operator ++ ();<br>
|
|
const_iterator &operator -- ();<br>
|
|
const_iterator &operator += (difference_type n);<br>
|
|
const_iterator &operator -= (difference_type n);<br>
|
|
difference_type operator - (const const_iterator &it) const;<br>
|
|
<br>
|
|
// Dereference<br>
|
|
reference operator * () const;<br>
|
|
<br>
|
|
// Index<br>
|
|
size_type index () const;<br>
|
|
<br>
|
|
// Assignment<br>
|
|
const_iterator &operator = (const const_iterator &it);<br>
|
|
<br>
|
|
// Comparison<br>
|
|
bool operator == (const const_iterator &it) const;<br>
|
|
bool operator <(const const_iterator &it) const;<br>
|
|
};<br>
|
|
<br>
|
|
const_iterator begin () const;<br>
|
|
const_iterator end () const;<br>
|
|
<br>
|
|
// Reverse iterator<br>
|
|
<br>
|
|
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;<br>
|
|
<br>
|
|
const_reverse_iterator rbegin () const;<br>
|
|
const_reverse_iterator rend () const;<br>
|
|
};<br>
|
|
</code>
|
|
</pre>
|
|
|
|
<h3>Binary Operations</h3>
|
|
|
|
<h4>Prototypes</h4>
|
|
|
|
<pre>
|
|
<code>template<class E1, class E2, class F><br>
|
|
struct vector_binary_traits {<br>
|
|
typedef vector_binary<typename E1::const_closure_type,<br>
|
|
typename E2::const_closure_type, F> expression_type;<br>
|
|
typedef expression_type result_type;<br>
|
|
};<br>
|
|
<br>
|
|
// (v1 + v2) [i] = v1 [i] + v2 [i]<br>
|
|
template<class E1, class E2><br>
|
|
typename vector_binary_traits<E1, E2, scalar_plus<typename E1::value_type,<br>
|
|
typename E2::value_type> >::result_type<br>
|
|
operator + (const vector_expression<E1> &e1,<br>
|
|
const vector_expression<E2> &e2);<br>
|
|
<br>
|
|
// (v1 - v2) [i] = v1 [i] - v2 [i]<br>
|
|
template<class E1, class E2><br>
|
|
typename vector_binary_traits<E1, E2, scalar_minus<typename E1::value_type,<br>
|
|
typename E2::value_type> >::result_type<br>
|
|
operator - (const vector_expression<E1> &e1,<br>
|
|
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.htm#vector_expression">Vector Expression</a> .</li>
|
|
|
|
<li><code>E2</code> is a model of <a href=
|
|
"expression.htm#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><br>
|
|
#include <boost/numeric/ublas/io.hpp><br>
|
|
<br>
|
|
int main () {<br>
|
|
using namespace boost::numeric::ublas;<br>
|
|
vector<double> v1 (3), v2 (3);<br>
|
|
for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i)<br>
|
|
v1 (i) = v2 (i) = i;<br>
|
|
<br>
|
|
std::cout << v1 + v2 << std::endl;<br>
|
|
std::cout << v1 - v2 << std::endl;<br>
|
|
}
|
|
</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">
|
|
<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.htm#matrix_expression">Matrix Expression</a>
|
|
.</p>
|
|
|
|
<h4>Type requirements</h4>
|
|
|
|
<p>None, except for those imposed by the requirements of <a href=
|
|
"expression.htm#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">
|
|
<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>
|
|
|
|
<h4>Interface</h4>
|
|
|
|
<pre>
|
|
<code>template<class E1, class E2, class F><br>
|
|
class vector_matrix_binary:<br>
|
|
public matrix_expression<vector_matrix_binary<E1, E2, F> > {<br>
|
|
public:<br>
|
|
typedef E1 expression1_type;<br>
|
|
typedef E2 expression2_type;<br>
|
|
typedef F functor_type;<br>
|
|
typedef typename promote_traits<typename E1::size_type, typename E2::size_type>::promote_type size_type;<br>
|
|
typedef typename promote_traits<typename E1::difference_type, typename E2::difference_type>::promote_type difference_type;<br>
|
|
typedef typename F::result_type value_type;<br>
|
|
typedef value_type const_reference;<br>
|
|
typedef const_reference reference;<br>
|
|
typedef const value_type *const_pointer;<br>
|
|
typedef const_pointer pointer;<br>
|
|
typedef const vector_matrix_binary<E1, E2, F> const_closure_type;<br>
|
|
typedef unknown_orientation_tag orientation_category;<br>
|
|
typedef typename E1::const_iterator const_iterator1_type;<br>
|
|
typedef typename E2::const_iterator const_iterator2_type;<br>
|
|
typedef unknown_storage_tag storage_category;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
vector_matrix_binary ();<br>
|
|
vector_matrix_binary (const expression1_type &e1, const expression2_type &e2);<br>
|
|
<br>
|
|
// Accessors<br>
|
|
size_type size1 () const;<br>
|
|
size_type size2 () const;<br>
|
|
const expression1_type &expression1 () const;<br>
|
|
const expression2_type &expression2 () const;<br>
|
|
<br>
|
|
// Element access<br>
|
|
const_reference operator () (size_type i, size_type j) const;<br>
|
|
<br>
|
|
class const_iterator1;<br>
|
|
typedef const_iterator1 iterator1;<br>
|
|
class const_iterator2;<br>
|
|
typedef const_iterator2 iterator2;<br>
|
|
<br>
|
|
// Element lookup<br>
|
|
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;<br>
|
|
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;<br>
|
|
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;<br>
|
|
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;<br>
|
|
<br>
|
|
// Iterators enhance the iterators of the referenced expressions<br>
|
|
// with the binary functor.<br>
|
|
<br>
|
|
class const_iterator1:<br>
|
|
public container_const_reference<vector_matrix_binary>,<br>
|
|
public random_access_iterator_base<const_iterator1, value_type> {<br>
|
|
public:<br>
|
|
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,<br>
|
|
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;<br>
|
|
typedef typename vector_matrix_binary::difference_type difference_type;<br>
|
|
typedef typename vector_matrix_binary::value_type value_type;<br>
|
|
typedef typename vector_matrix_binary::const_reference reference;<br>
|
|
typedef typename vector_matrix_binary::const_pointer pointer;<br>
|
|
typedef const_iterator2 dual_iterator_type;<br>
|
|
typedef const_reverse_iterator2 dual_reverse_iterator_type;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
const_iterator1 ();<br>
|
|
const_iterator1 (const vector_matrix_binary &vmb, const const_iterator1_type &it1, const const_iterator2_type &it2);<br>
|
|
<br>
|
|
// Arithmetic<br>
|
|
const_iterator1 &operator ++ ();<br>
|
|
const_iterator1 &operator -- ();<br>
|
|
const_iterator1 &operator += (difference_type n);<br>
|
|
const_iterator1 &operator -= (difference_type n);<br>
|
|
difference_type operator - (const const_iterator1 &it) const;<br>
|
|
<br>
|
|
// Dereference<br>
|
|
reference operator * () const;<br>
|
|
<br>
|
|
const_iterator2 begin () const;<br>
|
|
const_iterator2 end () const;<br>
|
|
const_reverse_iterator2 rbegin () const;<br>
|
|
const_reverse_iterator2 rend () const;<br>
|
|
<br>
|
|
// Indices<br>
|
|
size_type index1 () const;<br>
|
|
size_type index2 () const;<br>
|
|
<br>
|
|
// Assignment<br>
|
|
const_iterator1 &operator = (const const_iterator1 &it);<br>
|
|
<br>
|
|
// Comparison<br>
|
|
bool operator == (const const_iterator1 &it) const;<br>
|
|
bool operator <(const const_iterator1 &it) const;<br>
|
|
};<br>
|
|
<br>
|
|
const_iterator1 begin1 () const;<br>
|
|
const_iterator1 end1 () const;<br>
|
|
<br>
|
|
class const_iterator2:<br>
|
|
public container_const_reference<vector_matrix_binary>,<br>
|
|
public random_access_iterator_base<const_iterator2, value_type> {<br>
|
|
public:<br>
|
|
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,<br>
|
|
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;<br>
|
|
typedef typename vector_matrix_binary::difference_type difference_type;<br>
|
|
typedef typename vector_matrix_binary::value_type value_type;<br>
|
|
typedef typename vector_matrix_binary::const_reference reference;<br>
|
|
typedef typename vector_matrix_binary::const_pointer pointer;<br>
|
|
typedef const_iterator1 dual_iterator_type;<br>
|
|
typedef const_reverse_iterator1 dual_reverse_iterator_type;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
const_iterator2 ();<br>
|
|
const_iterator2 (const vector_matrix_binary &vmb, const const_iterator1_type &it1, const const_iterator2_type &it2);<br>
|
|
<br>
|
|
// Arithmetic<br>
|
|
const_iterator2 &operator ++ ();<br>
|
|
const_iterator2 &operator -- ();<br>
|
|
const_iterator2 &operator += (difference_type n);<br>
|
|
const_iterator2 &operator -= (difference_type n);<br>
|
|
difference_type operator - (const const_iterator2 &it) const;<br>
|
|
<br>
|
|
// Dereference<br>
|
|
reference operator * () const;<br>
|
|
<br>
|
|
const_iterator1 begin () const;<br>
|
|
const_iterator1 end () const;<br>
|
|
const_reverse_iterator1 rbegin () const;<br>
|
|
const_reverse_iterator1 rend () const;<br>
|
|
<br>
|
|
// Indices<br>
|
|
size_type index1 () const;<br>
|
|
size_type index2 () const;<br>
|
|
<br>
|
|
// Assignment<br>
|
|
const_iterator2 &operator = (const const_iterator2 &it);<br>
|
|
<br>
|
|
// Comparison<br>
|
|
bool operator == (const const_iterator2 &it) const;<br>
|
|
bool operator <(const const_iterator2 &it) const;<br>
|
|
};<br>
|
|
<br>
|
|
const_iterator2 begin2 () const;<br>
|
|
const_iterator2 end2 () const;<br>
|
|
<br>
|
|
// Reverse iterators<br>
|
|
<br>
|
|
const_reverse_iterator1 rbegin1 () const;<br>
|
|
const_reverse_iterator1 rend1 () const;<br>
|
|
<br>
|
|
const_reverse_iterator2 rbegin2 () const;<br>
|
|
const_reverse_iterator2 rend2 () const;<br>
|
|
};</code>
|
|
</pre>
|
|
|
|
<h3>Binary Outer Operations</h3>
|
|
|
|
<h4>Prototypes</h4>
|
|
|
|
<pre>
|
|
<code>template<class E1, class E2, class F><br>
|
|
struct vector_matrix_binary_traits {<br>
|
|
typedef vector_matrix_binary<typename E1::const_closure_type,<br>
|
|
typename E2::const_closure_type, F> expression_type;<br>
|
|
typedef expression_type result_type;<br>
|
|
};<br>
|
|
<br>
|
|
// (outer_prod (v1, v2)) [i] [j] = v1 [i] * v2 [j]<br>
|
|
template<class E1, class E2><br>
|
|
typename vector_matrix_binary_traits<E1, E2, scalar_multiplies<typename E1::value_type, typename E2::value_type> >::result_type<br>
|
|
outer_prod (const vector_expression<E1> &e1,<br>
|
|
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.htm#vector_expression">Vector Expression</a> .</li>
|
|
|
|
<li><code>E2</code> is a model of <a href=
|
|
"expression.htm#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><br>
|
|
#include <boost/numeric/ublas/io.hpp><br>
|
|
<br>
|
|
int main () {<br>
|
|
using namespace boost::numeric::ublas;<br>
|
|
vector<double> v1 (3), v2 (3);<br>
|
|
for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i)<br>
|
|
v1 (i) = v2 (i) = i;<br>
|
|
<br>
|
|
std::cout << outer_prod (v1, v2) << std::endl;<br>
|
|
}<br>
|
|
</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">
|
|
<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.htm#vector_expression">Vector Expression</a>
|
|
.</p>
|
|
|
|
<h4>Type requirements</h4>
|
|
|
|
<p>None, except for those imposed by the requirements of <a href=
|
|
"expression.htm#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">
|
|
<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>
|
|
|
|
<h4>Interface</h4>
|
|
|
|
<pre>
|
|
<code>template<class E1, class E2, class F><br>
|
|
class vector_binary_scalar1:<br>
|
|
public vector_expression<vector_binary_scalar1<E1, E2, F> > {<br>
|
|
public:<br>
|
|
typedef E1 expression1_type;<br>
|
|
typedef E2 expression2_type;<br>
|
|
typedef F functor_type;<br>
|
|
typedef typename E2::size_type size_type;<br>
|
|
typedef typename E2::difference_type difference_type;<br>
|
|
typedef typename F::result_type value_type;<br>
|
|
typedef value_type const_reference;<br>
|
|
typedef const_reference reference;<br>
|
|
typedef const value_type *const_pointer;<br>
|
|
typedef const_pointer pointer;<br>
|
|
typedef const vector_binary_scalar1<E1, E2, F> const_closure_type;<br>
|
|
typedef typename E1::value_type const_iterator1_type;<br>
|
|
typedef typename E2::const_iterator const_iterator2_type;<br>
|
|
typedef unknown_storage_tag storage_category;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
vector_binary_scalar1 ();<br>
|
|
vector_binary_scalar1 (const expression1_type &e1, const expression2_type &e2);<br>
|
|
<br>
|
|
// Accessors<br>
|
|
size_type size () const;<br>
|
|
const expression1_type &expression1 () const;<br>
|
|
const expression2_type &expression2 () const;<br>
|
|
<br>
|
|
// Element access<br>
|
|
const_reference operator () (size_type i) const;<br>
|
|
<br>
|
|
const_reference operator [] (size_type i) const;<br>
|
|
<br>
|
|
class const_iterator;<br>
|
|
typedef const_iterator iterator;<br>
|
|
<br>
|
|
// Element lookup<br>
|
|
const_iterator find_first (size_type i) const;<br>
|
|
const_iterator find_last (size_type i) const;<br>
|
|
<br>
|
|
// Iterator enhances the iterator of the referenced vector expression<br>
|
|
// with the binary functor.<br>
|
|
<br>
|
|
class const_iterator:<br>
|
|
public container_const_reference<vector_binary_scalar1>,<br>
|
|
public random_access_iterator_base<const_iterator, value_type> {<br>
|
|
public:<br>
|
|
typedef typename E2::const_iterator::iterator_category iterator_category;<br>
|
|
typedef typename vector_binary_scalar1::difference_type difference_type;<br>
|
|
typedef typename vector_binary_scalar1::value_type value_type;<br>
|
|
typedef typename vector_binary_scalar1::const_reference reference;<br>
|
|
typedef typename vector_binary_scalar1::const_pointer pointer;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
const_iterator ();<br>
|
|
const_iterator (const vector_binary_scalar1 &vbs, const const_iterator1_type &it1, const const_iterator2_type &it2);<br>
|
|
<br>
|
|
// Arithmetic<br>
|
|
const_iterator &operator ++ ();<br>
|
|
const_iterator &operator -- ();<br>
|
|
const_iterator &operator += (difference_type n);<br>
|
|
const_iterator &operator -= (difference_type n);<br>
|
|
difference_type operator - (const const_iterator &it) const;<br>
|
|
<br>
|
|
// Dereference<br>
|
|
reference operator * () const;<br>
|
|
<br>
|
|
// Index<br>
|
|
size_type index () const;<br>
|
|
<br>
|
|
// Assignment<br>
|
|
const_iterator &operator = (const const_iterator &it);<br>
|
|
<br>
|
|
// Comparison<br>
|
|
bool operator == (const const_iterator &it) const;<br>
|
|
bool operator <(const const_iterator &it) const;<br>
|
|
};<br>
|
|
<br>
|
|
const_iterator begin () const;<br>
|
|
const_iterator end () const;<br>
|
|
<br>
|
|
// Reverse iterator<br>
|
|
<br>
|
|
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;<br>
|
|
<br>
|
|
const_reverse_iterator rbegin () const;<br>
|
|
const_reverse_iterator rend () const;<br>
|
|
};<br>
|
|
<br>
|
|
template<class E1, class E2, class F><br>
|
|
class vector_binary_scalar2:<br>
|
|
public vector_expression<vector_binary_scalar2<E1, E2, F> > {<br>
|
|
public:<br>
|
|
typedef E1 expression1_type;<br>
|
|
typedef E2 expression2_type;<br>
|
|
typedef F functor_type;<br>
|
|
typedef typename E1::size_type size_type;<br>
|
|
typedef typename E1::difference_type difference_type;<br>
|
|
typedef typename F::result_type value_type;<br>
|
|
typedef value_type const_reference;<br>
|
|
typedef const_reference reference;<br>
|
|
typedef const value_type *const_pointer;<br>
|
|
typedef const_pointer pointer;<br>
|
|
typedef const vector_binary_scalar2<E1, E2, F> const_closure_type;<br>
|
|
typedef typename E1::const_iterator const_iterator1_type;<br>
|
|
typedef typename E2::value_type const_iterator2_type;<br>
|
|
typedef unknown_storage_tag storage_category;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
vector_binary_scalar2 ();<br>
|
|
vector_binary_scalar2 (const expression1_type &e1, const expression2_type &e2);<br>
|
|
<br>
|
|
// Accessors<br>
|
|
size_type size () const;<br>
|
|
const expression1_type &expression1 () const;<br>
|
|
const expression2_type &expression2 () const;<br>
|
|
<br>
|
|
// Element access<br>
|
|
const_reference operator () (size_type i) const;<br>
|
|
<br>
|
|
const_reference operator [] (size_type i) const ;<br>
|
|
<br>
|
|
class const_iterator;<br>
|
|
typedef const_iterator iterator;<br>
|
|
<br>
|
|
// Element lookup<br>
|
|
const_iterator find_first (size_type i) const;<br>
|
|
const_iterator find_last (size_type i) const;<br>
|
|
<br>
|
|
// Iterator enhances the iterator of the referenced vector expression<br>
|
|
// with the binary functor.<br>
|
|
<br>
|
|
class const_iterator:<br>
|
|
public container_const_reference<vector_binary_scalar2>,<br>
|
|
public random_access_iterator_base<const_iterator, value_type> {<br>
|
|
public:<br>
|
|
typedef typename E1::const_iterator::iterator_category iterator_category;<br>
|
|
typedef typename vector_binary_scalar2::difference_type difference_type;<br>
|
|
typedef typename vector_binary_scalar2::value_type value_type;<br>
|
|
typedef typename vector_binary_scalar2::const_reference reference;<br>
|
|
typedef typename vector_binary_scalar2::const_pointer pointer;<br>
|
|
<br>
|
|
// Construction and destruction<br>
|
|
const_iterator ();<br>
|
|
const_iterator (const vector_binary_scalar2 &vbs, const const_iterator1_type &it1, const const_iterator2_type &it2);<br>
|
|
<br>
|
|
// Arithmetic<br>
|
|
const_iterator &operator ++ ();<br>
|
|
const_iterator &operator -- ();<br>
|
|
const_iterator &operator += (difference_type n);<br>
|
|
const_iterator &operator -= (difference_type n);<br>
|
|
difference_type operator - (const const_iterator &it) const;<br>
|
|
<br>
|
|
// Dereference<br>
|
|
reference operator * () const;<br>
|
|
<br>
|
|
// Index<br>
|
|
size_type index () const;<br>
|
|
<br>
|
|
// Assignment<br>
|
|
const_iterator &operator = (const const_iterator &it);<br>
|
|
<br>
|
|
// Comparison<br>
|
|
bool operator == (const const_iterator &it) const;<br>
|
|
bool operator <(const const_iterator &it) const;<br>
|
|
};<br>
|
|
<br>
|
|
const_iterator begin () const;<br>
|
|
const_iterator end () const;<br>
|
|
<br>
|
|
// Reverse iterator<br>
|
|
<br>
|
|
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;<br>
|
|
<br>
|
|
const_reverse_iterator rbegin () const;<br>
|
|
const_reverse_iterator rend () const;<br>
|
|
};</code>
|
|
</pre>
|
|
|
|
<h3>Scalar Vector Operations</h3>
|
|
|
|
<h4>Prototypes</h4>
|
|
|
|
<pre>
|
|
<code>template<class T1, class E2, class F><br>
|
|
struct vector_binary_scalar1_traits {<br>
|
|
typedef vector_binary_scalar1<scalar_const_reference<T1>,<br>
|
|
typename E2::const_closure_type, F> expression_type;<br>
|
|
typedef expression_type result_type;<br>
|
|
};<br>
|
|
<br>
|
|
// (t * v) [i] = t * v [i]<br>
|
|
template<class T1, class E2><br>
|
|
typename vector_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type<br>
|
|
operator * (const T1 &e1,<br>
|
|
const vector_expression<E2> &e2);<br>
|
|
<br>
|
|
template<class E1, class T2, class F><br>
|
|
struct vector_binary_scalar2_traits {<br>
|
|
typedef vector_binary_scalar2<typename E1::const_closure_type,<br>
|
|
scalar_const_reference<T2>, F> expression_type;<br>
|
|
typedef expression_type result_type;<br>
|
|
};<br>
|
|
<br>
|
|
// (v * t) [i] = v [i] * t<br>
|
|
template<class E1, class T2><br>
|
|
typename vector_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type<br>
|
|
operator * (const vector_expression<E1> &e1,<br>
|
|
const T2 &e2);<br>
|
|
<br>
|
|
// (v / t) [i] = v [i] / t<br>
|
|
template<class E1, class T2><br>
|
|
typename vector_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type<br>
|
|
operator / (const vector_expression<E1> &e1,<br>
|
|
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.htm#scalar_expression">Scalar Expression</a> .</li>
|
|
|
|
<li><code>E2/E1</code> is a model of <a href=
|
|
"expression.htm#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><br>
|
|
#include <boost/numeric/ublas/io.hpp><br>
|
|
<br>
|
|
int main () {<br>
|
|
using namespace boost::numeric::ublas;<br>
|
|
vector<double> v (3);<br>
|
|
for (unsigned i = 0; i < v.size (); ++ i)<br>
|
|
v (i) = i;<br>
|
|
<br>
|
|
std::cout << 2.0 * v << std::endl;<br>
|
|
std::cout << v * 2.0 << std::endl;<br>
|
|
}<br>
|
|
</pre>
|
|
|
|
<h2><a name="vector_reductions"></a> Vector Reductions</h2>
|
|
|
|
<h3>Unary Reductions</h3>
|
|
|
|
<h4>Prototypes</h4>
|
|
|
|
<pre>
|
|
<code>template<class E, class F><br>
|
|
struct vector_scalar_unary_traits {<br>
|
|
typedef typename F::result_type result_type;<br>
|
|
};<br>
|
|
<br>
|
|
// sum v = sum (v [i])<br>
|
|
template<class E><br>
|
|
typename vector_scalar_unary_traits<E, vector_sum<typename E::value_type> >::result_type<br>
|
|
sum (const vector_expression<E> &e);<br>
|
|
<br>
|
|
// norm_1 v = sum (abs (v [i]))<br>
|
|
template<class E><br>
|
|
typename vector_scalar_unary_traits<E, vector_norm_1<typename E::value_type> >::result_type<br>
|
|
norm_1 (const vector_expression<E> &e);<br>
|
|
<br>
|
|
// norm_2 v = sqrt (sum (v [i] * v [i]))<br>
|
|
template<class E><br>
|
|
typename vector_scalar_unary_traits<E, vector_norm_2<typename E::value_type> >::result_type<br>
|
|
norm_2 (const vector_expression<E> &e);<br>
|
|
<br>
|
|
// norm_inf v = max (abs (v [i]))<br>
|
|
template<class E><br>
|
|
typename vector_scalar_unary_traits<E, vector_norm_inf<typename E::value_type> >::result_type<br>
|
|
norm_inf (const vector_expression<E> &e);<br>
|
|
<br>
|
|
// index_norm_inf v = min (i: abs (v [i]) == max (abs (v [i])))<br>
|
|
template<class E><br>
|
|
typename vector_scalar_unary_traits<E, vector_index_norm_inf<typename E::value_type> >::result_type<br>
|
|
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><br>
|
|
<br>
|
|
int main () {<br>
|
|
using namespace boost::numeric::ublas;<br>
|
|
vector<double> v (3);<br>
|
|
for (unsigned i = 0; i < v.size (); ++ i)<br>
|
|
v (i) = i;<br>
|
|
<br>
|
|
std::cout << sum (v) << std::endl;<br>
|
|
std::cout << norm_1 (v) << std::endl;<br>
|
|
std::cout << norm_2 (v) << std::endl;<br>
|
|
std::cout << norm_inf (v) << std::endl;<br>
|
|
std::cout << index_norm_inf (v) << std::endl;<br>
|
|
}<br>
|
|
</pre>
|
|
|
|
<h3>Binary Reductions</h3>
|
|
|
|
<h4>Prototypes</h4>
|
|
|
|
<pre>
|
|
<code>template<class E1, class E2, class F><br>
|
|
struct vector_scalar_binary_traits {<br>
|
|
typedef typename F::result_type result_type;<br>
|
|
};<br>
|
|
<br>
|
|
// inner_prod (v1, v2) = sum (v1 [i] * v2 [i])<br>
|
|
template<class E1, class E2><br>
|
|
typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type,<br>
|
|
typename E2::value_type,<br>
|
|
typename promote_traits<typename E1::value_type,<br>
|
|
typename E2::value_type>::promote_type> >::result_type<br>
|
|
inner_prod (const vector_expression<E1> &e1,<br>
|
|
const vector_expression<E2> &e2);<br>
|
|
<br>
|
|
template<class E1, class E2><br>
|
|
typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type,<br>
|
|
typename E2::value_type,<br>
|
|
typename type_traits<typename promote_traits<typename E1::value_type,<br>
|
|
typename E2::value_type>::promote_type>::precision_type> >::result_type<br>
|
|
prec_inner_prod (const vector_expression<E1> &e1,<br>
|
|
const vector_expression<E2> &e2);</code>
|
|
</pre>
|
|
|
|
<h4>Description</h4>
|
|
|
|
<p><code>inner_prod</code> computes the inner product of the vector
|
|
expressions. <code>prec_inner_prod</code> computes the double
|
|
precision inner product of the vector expressions<code>.</code></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=
|
|
"#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>
|
|
<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><br>
|
|
<br>
|
|
int main () {<br>
|
|
using namespace boost::numeric::ublas;<br>
|
|
vector<double> v1 (3), v2 (3);<br>
|
|
for (unsigned i = 0; i < std::min (v1.size (), v2.size ()); ++ i)<br>
|
|
v1 (i) = v2 (i) = i;<br>
|
|
<br>
|
|
std::cout << inner_prod (v1, v2) << std::endl;<br>
|
|
}<br>
|
|
</pre>
|
|
|
|
<hr>
|
|
<p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br>
|
|
Permission to copy, use, modify, sell and distribute this document
|
|
is granted provided this copyright notice appears in all copies.
|
|
This document is provided ``as is'' without express or implied
|
|
warranty, and with no claim as to its suitability for any
|
|
purpose.</p>
|
|
|
|
<p>Last revised: 1/15/2003</p>
|
|
</body>
|
|
</html>
|
|
|