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1761 lines
58 KiB
HTML
1761 lines
58 KiB
HTML
<html>
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<head>
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<meta http-equiv="Content-Type"
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content="text/html; charset=iso-8859-1">
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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">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>forms
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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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<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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</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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<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 () () const</code></td>
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<td>Returns a <code>const </code>reference of the
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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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</table>
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<h4>Interface</h4>
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<pre><code> // Base class for the Barton Nackman trick
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template<class E>
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struct vector_expression {
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typedef E expression_type;
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typedef vector_tag type_category;
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// This class could define an common interface for all
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// statically derived expression type classes.
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// Due to a compiler deficiency - one can not reference class typedefs of E
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// on MSVC 6.0 (error C2027) - we only implement the casts.
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const expression_type &operator () () const;
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expression_type &operator () ();
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};</code></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>contains
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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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||
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<table border="1">
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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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</table>
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<h4>Model of</h4>
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<p><a href="expression.htm#vector_expression">Vector Expression</a>.</p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a
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href="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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||
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||
<table border="1">
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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) 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
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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_iterator end () const</code></td>
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<td>Returns a <code>const_iterator</code> pointing to the
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||
end of 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>
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||
pointing to the 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>
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||
pointing to the end of the reversed expression. </td>
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</tr>
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</table>
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||
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<h4>Interface</h4>
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||
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<pre><code> template<class E>
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class vector_const_reference:
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public vector_expression<vector_const_reference<E> > {
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public:
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typedef E expression_type;
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typedef typename E::size_type size_type;
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typedef typename E::difference_type difference_type;
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typedef typename E::value_type value_type;
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typedef typename E::const_reference const_reference;
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typedef const_reference reference;
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typedef typename E::const_pointer const_pointer;
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typedef const_pointer pointer;
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typedef typename E::const_iterator const_iterator_type;
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typedef unknown_storage_tag storage_category;
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// Construction and destruction
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vector_const_reference ();
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vector_const_reference (const expression_type &e);
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// Accessors
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size_type size () const;
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const expression_type &expression () const;
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// Element access
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const_reference operator () (size_type i) const;
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const_reference operator [] (size_type i) const;
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typedef const_iterator_type const_iterator;
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typedef const_iterator iterator;
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// Element lookup
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const_iterator find_first (size_type i) const;
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const_iterator find_last (size_type i) const;
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||
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// Iterator is the iterator of the referenced expression.
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const_iterator begin () const;
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const_iterator end () const;
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// Reverse iterator
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||
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typedef reverse_iterator_base<const_iterator> const_reverse_iterator;
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const_reverse_iterator rbegin () const;
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const_reverse_iterator rend () const;
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};</code></pre>
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<h3>Reference</h3>
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||
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||
<h4>Description</h4>
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||
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<p>The templated class <code>vector_reference<E> </code>contains
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||
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">
|
||
<tr>
|
||
<th>Parameter </th>
|
||
<th>Description </th>
|
||
<th>Default </th>
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||
</tr>
|
||
<tr>
|
||
<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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||
</table>
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||
|
||
<h4>Model of</h4>
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||
|
||
<p><a href="expression.htm#vector_expression">Vector Expression</a>.</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="expression.htm#vector_expression">Vector Expression</a>.</p>
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||
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||
<h4>Public base classes</h4>
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||
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||
<p><code>vector_expression<vector_reference<E> ></code></p>
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||
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||
<h4>Members</h4>
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||
|
||
<table border="1">
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||
<tr>
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||
<th>Member </th>
|
||
<th>Description </th>
|
||
</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>
|
||
<tr>
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||
<td><code>const_reference operator () (size_type i) 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.
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||
</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 of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator end () const</code></td>
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||
<td>Returns a <code>const_iterator</code> pointing to the
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||
end of 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
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||
beginning of the expression. </td>
|
||
</tr>
|
||
<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 expression. </td>
|
||
</tr>
|
||
<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>
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||
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>
|
||
<tr>
|
||
<td><code>reverse_iterator rbegin () </code></td>
|
||
<td>Returns a <code>reverse_iterator</code> pointing to
|
||
the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>reverse_iterator rend () </code></td>
|
||
<td>Returns a <code>reverse_iterator</code> pointing to
|
||
the end of the reversed expression. </td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> template<class E>
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class vector_reference:
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||
public vector_expression<vector_reference<E> > {
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public:
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||
typedef E expression_type;
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||
typedef typename E::size_type size_type;
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||
typedef typename E::difference_type difference_type;
|
||
typedef typename E::value_type value_type;
|
||
typedef typename E::const_reference const_reference;
|
||
typedef typename E::reference reference;
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||
typedef typename E::const_pointer const_pointer;
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||
typedef typename E::pointer pointer;
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typedef typename E::const_iterator const_iterator_type;
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typedef typename E::iterator iterator_type;
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typedef unknown_storage_tag storage_category;
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|
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// Construction and destruction
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vector_reference ();
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vector_reference (expression_type &e);
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// Accessors
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size_type size () const;
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const expression_type &expression () const;
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expression_type &expression ();
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|
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// Resizing
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void resize (size_type size);
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||
|
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// Element access
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||
const_reference operator () (size_type i) const;
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reference operator () (size_type i);
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|
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const_reference operator [] (size_type i) const;
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reference operator [] (size_type i);
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||
|
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typedef const_iterator_type const_iterator;
|
||
typedef iterator_type iterator;
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||
|
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// Element lookup
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const_iterator find_first (size_type i) const;
|
||
iterator find_first (size_type i);
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||
const_iterator find_last (size_type i) const;
|
||
iterator find_last (size_type i);
|
||
|
||
// Iterator is the iterator of the referenced expression.
|
||
|
||
const_iterator begin () const;
|
||
const_iterator end () const;
|
||
|
||
iterator begin ();
|
||
iterator end ();
|
||
|
||
// Reverse iterator
|
||
|
||
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;
|
||
|
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const_reverse_iterator rbegin () const;
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||
const_reverse_iterator rend () const;
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||
|
||
typedef reverse_iterator_base<iterator> reverse_iterator;
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||
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||
reverse_iterator rbegin ();
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||
reverse_iterator rend ();
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||
};</code></pre>
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||
|
||
<h2><a name="vector_operations"></a>Vector Operations</h2>
|
||
|
||
<h3>Unary Operation Description</h3>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p>The templated class <code>vector_unary<E, F> </code>describes
|
||
a unary vector operation.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header vector_expression.hpp.</p>
|
||
|
||
<h4>Template parameters</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Parameter </th>
|
||
<th>Description </th>
|
||
<th>Default </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>E</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>
|
||
</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_unary<E, F> ></code></p>
|
||
|
||
<h4>Members</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Member </th>
|
||
<th>Description </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>vector_unary (const expression_type &e)</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>
|
||
</table>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> template<class E, class F>
|
||
class vector_unary:
|
||
public vector_expression<vector_unary<E, F> > {
|
||
public:
|
||
typedef E expression_type;
|
||
typedef F functor_type;
|
||
typedef typename E::size_type size_type;
|
||
typedef typename E::difference_type difference_type;
|
||
typedef typename F::result_type value_type;
|
||
typedef value_type const_reference;
|
||
typedef const_reference reference;
|
||
typedef const value_type *const_pointer;
|
||
typedef const_pointer pointer;
|
||
typedef const vector_unary<E, F> const_closure_type;
|
||
typedef typename E::const_iterator const_iterator_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
vector_unary ();
|
||
vector_unary (const expression_type &e);
|
||
|
||
// Accessors
|
||
size_type size () const;
|
||
const expression_type &expression () const;
|
||
|
||
// Element access
|
||
const_reference operator () (size_type i) const;
|
||
|
||
const_reference operator [] (size_type i) const;
|
||
|
||
class const_iterator;
|
||
typedef const_iterator iterator;
|
||
|
||
// Element lookup
|
||
const_iterator find_first (size_type i) const;
|
||
const_iterator find_last (size_type i) const;
|
||
|
||
// Iterator enhances the iterator of the referenced expression
|
||
// with the unary functor.
|
||
|
||
class const_iterator:
|
||
public container_const_reference<vector_unary>,
|
||
public random_access_iterator_base<const_iterator, value_type> {
|
||
public:
|
||
typedef typename E::const_iterator::iterator_category iterator_category;
|
||
typedef typename vector_unary::difference_type difference_type;
|
||
typedef typename vector_unary::value_type value_type;
|
||
typedef typename vector_unary::const_reference reference;
|
||
typedef typename vector_unary::const_pointer pointer;
|
||
|
||
// Construction and destruction
|
||
const_iterator ();
|
||
const_iterator (const vector_unary &vu, const const_iterator_type &it);
|
||
|
||
// Arithmetic
|
||
const_iterator &operator ++ ();
|
||
const_iterator &operator -- ();
|
||
const_iterator &operator += (difference_type n);
|
||
const_iterator &operator -= (difference_type n);
|
||
difference_type operator - (const const_iterator &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
// Index
|
||
size_type index () const;
|
||
|
||
// Assignment
|
||
const_iterator &operator = (const const_iterator &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator &it) const;
|
||
bool operator <(const const_iterator &it) const;
|
||
};
|
||
|
||
const_iterator begin () const;
|
||
const_iterator end () const;
|
||
|
||
// Reverse iterator
|
||
|
||
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;
|
||
|
||
const_reverse_iterator rbegin () const;
|
||
const_reverse_iterator rend () const;
|
||
};</code></pre>
|
||
|
||
<h3>Unary Operations</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class E, class F>
|
||
struct vector_unary_traits {
|
||
typedef vector_unary<typename E::const_closure_type, F> expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
// (- v) [i] = - v [i]
|
||
template<class E>
|
||
typename vector_unary_traits<E, scalar_negate<typename E::value_type> >::result_type
|
||
operator - (const vector_expression<E> &e);
|
||
|
||
// (conj v) [i] = conj (v [i])
|
||
template<class E>
|
||
typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type
|
||
conj (const vector_expression<E> &e);
|
||
|
||
// (real v) [i] = real (v [i])
|
||
template<class E>
|
||
typename vector_unary_traits<E, scalar_real<typename E::value_type> >::result_type
|
||
real (const vector_expression<E> &e);
|
||
|
||
// (imag v) [i] = imag (v [i])
|
||
template<class E>
|
||
typename vector_unary_traits<E, scalar_imag<typename E::value_type> >::result_type
|
||
imag (const vector_expression<E> &e);
|
||
|
||
// (trans v) [i] = v [i]
|
||
template<class E>
|
||
typename vector_unary_traits<E, scalar_identity<typename E::value_type> >::result_type
|
||
trans (const vector_expression<E> &e);
|
||
|
||
// (herm v) [i] = conj (v [i])
|
||
template<class E>
|
||
typename vector_unary_traits<E, scalar_conj<typename E::value_type> >::result_type
|
||
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>
|
||
|
||
<dir>
|
||
<li><code>E</code> is a model of <a
|
||
href="expression.htm#vector_expression">Vector Expression</a>.</li>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<p>None.</p>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Linear depending from the size of the vector expression.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
vector<std::complex<double> > v (3);
|
||
for (int i = 0; i < v.size (); ++ i)
|
||
v (i) = std::complex (i, i);
|
||
|
||
std::cout << - v << std::endl;
|
||
std::cout << conj (v) << std::endl;
|
||
std::cout << real (v) << std::endl;
|
||
std::cout << imag (v) << std::endl;
|
||
std::cout << trans (v) << std::endl;
|
||
std::cout << herm (v) << std::endl;
|
||
}</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">
|
||
<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>
|
||
</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">
|
||
<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>
|
||
</table>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
class vector_binary:
|
||
public vector_expression<vector_binary<E1, E2, F> > {
|
||
public:
|
||
typedef E1 expression1_type;
|
||
typedef E2 expression2_type;
|
||
typedef F functor_type;
|
||
typedef typename promote_traits<typename E1::size_type, typename E2::size_type>::promote_type size_type;
|
||
typedef typename promote_traits<typename E1::difference_type, typename E2::difference_type>::promote_type difference_type;
|
||
typedef typename F::result_type value_type;
|
||
typedef value_type const_reference;
|
||
typedef const_reference reference;
|
||
typedef const value_type *const_pointer;
|
||
typedef const_pointer pointer;
|
||
typedef const vector_binary<E1, E2, F> const_closure_type;
|
||
typedef typename E1::const_iterator const_iterator1_type;
|
||
typedef typename E2::const_iterator const_iterator2_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
vector_binary ();
|
||
vector_binary (const expression1_type &e1, const expression2_type &e2);
|
||
|
||
// Accessors
|
||
size_type size () const;
|
||
const expression1_type &expression1 () const;
|
||
const expression2_type &expression2 () const;
|
||
|
||
// Element access
|
||
const_reference operator () (size_type i) const;
|
||
|
||
const_reference operator [] (size_type i) const;
|
||
|
||
class const_iterator;
|
||
typedef const_iterator iterator;
|
||
|
||
// Element lookup
|
||
const_iterator find_first (size_type i) const;
|
||
const_iterator find_last (size_type i) const;
|
||
|
||
// Iterator merges the iterators of the referenced expressions and
|
||
// enhances them with the binary functor.
|
||
|
||
class const_iterator:
|
||
public container_const_reference<vector_binary>,
|
||
public random_access_iterator_base<const_iterator, value_type> {
|
||
public:
|
||
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,
|
||
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;
|
||
typedef typename vector_binary::difference_type difference_type;
|
||
typedef typename vector_binary::value_type value_type;
|
||
typedef typename vector_binary::const_reference reference;
|
||
typedef typename vector_binary::const_pointer pointer;
|
||
|
||
// Construction and destruction
|
||
const_iterator ();
|
||
const_iterator (const vector_binary &vb, size_type i,
|
||
const const_iterator1_type &it1, const const_iterator1_type &it1_end,
|
||
const const_iterator2_type &it2, const const_iterator2_type &it2_end);
|
||
|
||
// Dense specializations
|
||
void increment (dense_random_access_iterator_tag);
|
||
void decrement (dense_random_access_iterator_tag);
|
||
value_type dereference (dense_random_access_iterator_tag) const;
|
||
|
||
// Packed specializations
|
||
void increment (packed_random_access_iterator_tag);
|
||
void decrement (packed_random_access_iterator_tag);
|
||
value_type dereference (packed_random_access_iterator_tag) const;
|
||
|
||
// Sparse specializations
|
||
void increment (sparse_bidirectional_iterator_tag);
|
||
void decrement (sparse_bidirectional_iterator_tag);
|
||
value_type dereference (sparse_bidirectional_iterator_tag) const;
|
||
|
||
// Arithmetic
|
||
const_iterator &operator ++ ();
|
||
const_iterator &operator -- ();
|
||
const_iterator &operator += (difference_type n);
|
||
const_iterator &operator -= (difference_type n);
|
||
difference_type operator - (const const_iterator &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
// Index
|
||
size_type index () const;
|
||
|
||
// Assignment
|
||
const_iterator &operator = (const const_iterator &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator &it) const;
|
||
bool operator <(const const_iterator &it) const;
|
||
};
|
||
|
||
const_iterator begin () const;
|
||
const_iterator end () const;
|
||
|
||
// Reverse iterator
|
||
|
||
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;
|
||
|
||
const_reverse_iterator rbegin () const;
|
||
const_reverse_iterator rend () const;
|
||
};
|
||
</code></pre>
|
||
|
||
<h3>Binary Operations</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
struct vector_binary_traits {
|
||
typedef vector_binary<typename E1::const_closure_type,
|
||
typename E2::const_closure_type, F> expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
// (v1 + v2) [i] = v1 [i] + v2 [i]
|
||
template<class E1, class E2>
|
||
typename vector_binary_traits<E1, E2, scalar_plus<typename E1::value_type,
|
||
typename E2::value_type> >::result_type
|
||
operator + (const vector_expression<E1> &e1,
|
||
const vector_expression<E2> &e2);
|
||
|
||
// (v1 - v2) [i] = v1 [i] - v2 [i]
|
||
template<class E1, class E2>
|
||
typename vector_binary_traits<E1, E2, scalar_minus<typename E1::value_type,
|
||
typename E2::value_type> >::result_type
|
||
operator - (const vector_expression<E1> &e1,
|
||
const vector_expression<E2> &e2);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>operator +</code> computes the sum of two vector
|
||
expressions. <code>operator - </code>computes the difference of
|
||
two vector expressions.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header vector_expression.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<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>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<dir>
|
||
<li><code>e1 ().size () == e2 ().size ()</code></li>
|
||
</dir>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Linear depending from the size of the vector expressions.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
vector<double> v1 (3), v2 (3);
|
||
for (int i = 0; i < std::min (v1.size (), v2.size ()); ++ i)
|
||
v1 (i) = v2 (i) = i;
|
||
|
||
std::cout << v1 + v2 << std::endl;
|
||
std::cout << v1 - v2 << std::endl;
|
||
}</pre>
|
||
|
||
<h3>Binary Outer Operation Description</h3>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p>The templated class <code>vector_matrix_binary<E1, E2,
|
||
F> </code>describes a binary outer vector operation.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Template parameters</h4>
|
||
|
||
<table border="1">
|
||
<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>
|
||
</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">
|
||
<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>
|
||
</table>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
class vector_matrix_binary:
|
||
public matrix_expression<vector_matrix_binary<E1, E2, F> > {
|
||
public:
|
||
typedef E1 expression1_type;
|
||
typedef E2 expression2_type;
|
||
typedef F functor_type;
|
||
typedef typename promote_traits<typename E1::size_type, typename E2::size_type>::promote_type size_type;
|
||
typedef typename promote_traits<typename E1::difference_type, typename E2::difference_type>::promote_type difference_type;
|
||
typedef typename F::result_type value_type;
|
||
typedef value_type const_reference;
|
||
typedef const_reference reference;
|
||
typedef const value_type *const_pointer;
|
||
typedef const_pointer pointer;
|
||
typedef const vector_matrix_binary<E1, E2, F> const_closure_type;
|
||
typedef unknown_orientation_tag orientation_category;
|
||
typedef typename E1::const_iterator const_iterator1_type;
|
||
typedef typename E2::const_iterator const_iterator2_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
vector_matrix_binary ();
|
||
vector_matrix_binary (const expression1_type &e1, const expression2_type &e2);
|
||
|
||
// Accessors
|
||
size_type size1 () const;
|
||
size_type size2 () const;
|
||
const expression1_type &expression1 () const;
|
||
const expression2_type &expression2 () const;
|
||
|
||
// Element access
|
||
const_reference operator () (size_type i, size_type j) const;
|
||
|
||
class const_iterator1;
|
||
typedef const_iterator1 iterator1;
|
||
class const_iterator2;
|
||
typedef const_iterator2 iterator2;
|
||
|
||
// Element lookup
|
||
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
|
||
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
|
||
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
|
||
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
|
||
|
||
// Iterators enhance the iterators of the referenced expressions
|
||
// with the binary functor.
|
||
|
||
class const_iterator1:
|
||
public container_const_reference<vector_matrix_binary>,
|
||
public random_access_iterator_base<const_iterator1, value_type> {
|
||
public:
|
||
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,
|
||
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;
|
||
typedef typename vector_matrix_binary::difference_type difference_type;
|
||
typedef typename vector_matrix_binary::value_type value_type;
|
||
typedef typename vector_matrix_binary::const_reference reference;
|
||
typedef typename vector_matrix_binary::const_pointer pointer;
|
||
typedef const_iterator2 dual_iterator_type;
|
||
typedef const_reverse_iterator2 dual_reverse_iterator_type;
|
||
|
||
// Construction and destruction
|
||
const_iterator1 ();
|
||
const_iterator1 (const vector_matrix_binary &vmb, const const_iterator1_type &it1, const const_iterator2_type &it2);
|
||
|
||
// Arithmetic
|
||
const_iterator1 &operator ++ ();
|
||
const_iterator1 &operator -- ();
|
||
const_iterator1 &operator += (difference_type n);
|
||
const_iterator1 &operator -= (difference_type n);
|
||
difference_type operator - (const const_iterator1 &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
const_iterator2 begin () const;
|
||
const_iterator2 end () const;
|
||
const_reverse_iterator2 rbegin () const;
|
||
const_reverse_iterator2 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
const_iterator1 &operator = (const const_iterator1 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator1 &it) const;
|
||
bool operator <(const const_iterator1 &it) const;
|
||
};
|
||
|
||
const_iterator1 begin1 () const;
|
||
const_iterator1 end1 () const;
|
||
|
||
class const_iterator2:
|
||
public container_const_reference<vector_matrix_binary>,
|
||
public random_access_iterator_base<const_iterator2, value_type> {
|
||
public:
|
||
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,
|
||
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;
|
||
typedef typename vector_matrix_binary::difference_type difference_type;
|
||
typedef typename vector_matrix_binary::value_type value_type;
|
||
typedef typename vector_matrix_binary::const_reference reference;
|
||
typedef typename vector_matrix_binary::const_pointer pointer;
|
||
typedef const_iterator1 dual_iterator_type;
|
||
typedef const_reverse_iterator1 dual_reverse_iterator_type;
|
||
|
||
// Construction and destruction
|
||
const_iterator2 ();
|
||
const_iterator2 (const vector_matrix_binary &vmb, const const_iterator1_type &it1, const const_iterator2_type &it2);
|
||
|
||
// Arithmetic
|
||
const_iterator2 &operator ++ ();
|
||
const_iterator2 &operator -- ();
|
||
const_iterator2 &operator += (difference_type n);
|
||
const_iterator2 &operator -= (difference_type n);
|
||
difference_type operator - (const const_iterator2 &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
const_iterator1 begin () const;
|
||
const_iterator1 end () const;
|
||
const_reverse_iterator1 rbegin () const;
|
||
const_reverse_iterator1 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
const_iterator2 &operator = (const const_iterator2 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator2 &it) const;
|
||
bool operator <(const const_iterator2 &it) const;
|
||
};
|
||
|
||
const_iterator2 begin2 () const;
|
||
const_iterator2 end2 () const;
|
||
|
||
// Reverse iterators
|
||
|
||
const_reverse_iterator1 rbegin1 () const;
|
||
const_reverse_iterator1 rend1 () const;
|
||
|
||
const_reverse_iterator2 rbegin2 () const;
|
||
const_reverse_iterator2 rend2 () const;
|
||
};</code></pre>
|
||
|
||
<h3>Binary Outer Operations</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
struct vector_matrix_binary_traits {
|
||
typedef vector_matrix_binary<typename E1::const_closure_type,
|
||
typename E2::const_closure_type, F> expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
// (outer_prod (v1, v2)) [i] [j] = v1 [i] * v2 [j]
|
||
template<class E1, class E2>
|
||
typename vector_matrix_binary_traits<E1, E2, scalar_multiplies<typename E1::value_type, typename E2::value_type> >::result_type
|
||
outer_prod (const vector_expression<E1> &e1,
|
||
const vector_expression<E2> &e2);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>outer_prod </code>computes the outer product of two
|
||
vector expressions.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<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>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<p>None.</p>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Quadratic depending from the size of the vector expressions.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
vector<double> v1 (3), v2 (3);
|
||
for (int i = 0; i < std::min (v1.size (), v2.size ()); ++ i)
|
||
v1 (i) = v2 (i) = i;
|
||
|
||
std::cout << outer_prod (v1, v2) << std::endl;
|
||
}</pre>
|
||
|
||
<h3>Scalar Vector Operation Description</h3>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p>The templated classes <code>vector_binary_scalar1<E1, E2,
|
||
F> </code>and <code>vector_binary_scalar2<E1, E2, F></code>
|
||
describe binary operations between a scalar and a vector.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header vector_expression.hpp.</p>
|
||
|
||
<h4>Template parameters</h4>
|
||
|
||
<table border="1">
|
||
<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>
|
||
</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">
|
||
<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>
|
||
</table>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
class vector_binary_scalar1:
|
||
public vector_expression<vector_binary_scalar1<E1, E2, F> > {
|
||
public:
|
||
typedef E1 expression1_type;
|
||
typedef E2 expression2_type;
|
||
typedef F functor_type;
|
||
typedef typename E2::size_type size_type;
|
||
typedef typename E2::difference_type difference_type;
|
||
typedef typename F::result_type value_type;
|
||
typedef value_type const_reference;
|
||
typedef const_reference reference;
|
||
typedef const value_type *const_pointer;
|
||
typedef const_pointer pointer;
|
||
typedef const vector_binary_scalar1<E1, E2, F> const_closure_type;
|
||
typedef typename E1::value_type const_iterator1_type;
|
||
typedef typename E2::const_iterator const_iterator2_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
vector_binary_scalar1 ();
|
||
vector_binary_scalar1 (const expression1_type &e1, const expression2_type &e2);
|
||
|
||
// Accessors
|
||
size_type size () const;
|
||
const expression1_type &expression1 () const;
|
||
const expression2_type &expression2 () const;
|
||
|
||
// Element access
|
||
const_reference operator () (size_type i) const;
|
||
|
||
const_reference operator [] (size_type i) const;
|
||
|
||
class const_iterator;
|
||
typedef const_iterator iterator;
|
||
|
||
// Element lookup
|
||
const_iterator find_first (size_type i) const;
|
||
const_iterator find_last (size_type i) const;
|
||
|
||
// Iterator enhances the iterator of the referenced vector expression
|
||
// with the binary functor.
|
||
|
||
class const_iterator:
|
||
public container_const_reference<vector_binary_scalar1>,
|
||
public random_access_iterator_base<const_iterator, value_type> {
|
||
public:
|
||
typedef typename E2::const_iterator::iterator_category iterator_category;
|
||
typedef typename vector_binary_scalar1::difference_type difference_type;
|
||
typedef typename vector_binary_scalar1::value_type value_type;
|
||
typedef typename vector_binary_scalar1::const_reference reference;
|
||
typedef typename vector_binary_scalar1::const_pointer pointer;
|
||
|
||
// Construction and destruction
|
||
const_iterator ();
|
||
const_iterator (const vector_binary_scalar1 &vbs, const const_iterator1_type &it1, const const_iterator2_type &it2);
|
||
|
||
// Arithmetic
|
||
const_iterator &operator ++ ();
|
||
const_iterator &operator -- ();
|
||
const_iterator &operator += (difference_type n);
|
||
const_iterator &operator -= (difference_type n);
|
||
difference_type operator - (const const_iterator &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
// Index
|
||
size_type index () const;
|
||
|
||
// Assignment
|
||
const_iterator &operator = (const const_iterator &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator &it) const;
|
||
bool operator <(const const_iterator &it) const;
|
||
};
|
||
|
||
const_iterator begin () const;
|
||
const_iterator end () const;
|
||
|
||
// Reverse iterator
|
||
|
||
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;
|
||
|
||
const_reverse_iterator rbegin () const;
|
||
const_reverse_iterator rend () const;
|
||
};
|
||
|
||
template<class E1, class E2, class F>
|
||
class vector_binary_scalar2:
|
||
public vector_expression<vector_binary_scalar2<E1, E2, F> > {
|
||
public:
|
||
typedef E1 expression1_type;
|
||
typedef E2 expression2_type;
|
||
typedef F functor_type;
|
||
typedef typename E1::size_type size_type;
|
||
typedef typename E1::difference_type difference_type;
|
||
typedef typename F::result_type value_type;
|
||
typedef value_type const_reference;
|
||
typedef const_reference reference;
|
||
typedef const value_type *const_pointer;
|
||
typedef const_pointer pointer;
|
||
typedef const vector_binary_scalar2<E1, E2, F> const_closure_type;
|
||
typedef typename E1::const_iterator const_iterator1_type;
|
||
typedef typename E2::value_type const_iterator2_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
vector_binary_scalar2 ();
|
||
vector_binary_scalar2 (const expression1_type &e1, const expression2_type &e2);
|
||
|
||
// Accessors
|
||
size_type size () const;
|
||
const expression1_type &expression1 () const;
|
||
const expression2_type &expression2 () const;
|
||
|
||
// Element access
|
||
const_reference operator () (size_type i) const;
|
||
|
||
const_reference operator [] (size_type i) const ;
|
||
|
||
class const_iterator;
|
||
typedef const_iterator iterator;
|
||
|
||
// Element lookup
|
||
const_iterator find_first (size_type i) const;
|
||
const_iterator find_last (size_type i) const;
|
||
|
||
// Iterator enhances the iterator of the referenced vector expression
|
||
// with the binary functor.
|
||
|
||
class const_iterator:
|
||
public container_const_reference<vector_binary_scalar2>,
|
||
public random_access_iterator_base<const_iterator, value_type> {
|
||
public:
|
||
typedef typename E1::const_iterator::iterator_category iterator_category;
|
||
typedef typename vector_binary_scalar2::difference_type difference_type;
|
||
typedef typename vector_binary_scalar2::value_type value_type;
|
||
typedef typename vector_binary_scalar2::const_reference reference;
|
||
typedef typename vector_binary_scalar2::const_pointer pointer;
|
||
|
||
// Construction and destruction
|
||
const_iterator ();
|
||
const_iterator (const vector_binary_scalar2 &vbs, const const_iterator1_type &it1, const const_iterator2_type &it2);
|
||
|
||
// Arithmetic
|
||
const_iterator &operator ++ ();
|
||
const_iterator &operator -- ();
|
||
const_iterator &operator += (difference_type n);
|
||
const_iterator &operator -= (difference_type n);
|
||
difference_type operator - (const const_iterator &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
// Index
|
||
size_type index () const;
|
||
|
||
// Assignment
|
||
const_iterator &operator = (const const_iterator &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator &it) const;
|
||
bool operator <(const const_iterator &it) const;
|
||
};
|
||
|
||
const_iterator begin () const;
|
||
const_iterator end () const;
|
||
|
||
// Reverse iterator
|
||
|
||
typedef reverse_iterator_base<const_iterator> const_reverse_iterator;
|
||
|
||
const_reverse_iterator rbegin () const;
|
||
const_reverse_iterator rend () const;
|
||
};</code></pre>
|
||
|
||
<h3>Scalar Vector Operations </h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class T1, class E2, class F>
|
||
struct vector_binary_scalar1_traits {
|
||
typedef vector_binary_scalar1<scalar_const_reference<T1>,
|
||
typename E2::const_closure_type, F> expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
// (t * v) [i] = t * v [i]
|
||
template<class T1, class E2>
|
||
typename vector_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type
|
||
operator * (const T1 &e1,
|
||
const vector_expression<E2> &e2);
|
||
|
||
template<class E1, class T2, class F>
|
||
struct vector_binary_scalar2_traits {
|
||
typedef vector_binary_scalar2<typename E1::const_closure_type,
|
||
scalar_const_reference<T2>, F> expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
// (v * t) [i] = v [i] * t
|
||
template<class E1, class T2>
|
||
typename vector_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type
|
||
operator * (const vector_expression<E1> &e1,
|
||
const T2 &e2);
|
||
|
||
// (v / t) [i] = v [i] / t
|
||
template<class E1, class T2>
|
||
typename vector_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type
|
||
operator / (const vector_expression<E1> &e1,
|
||
const T2 &e2);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>operator *</code> computes the product of a scalar and a
|
||
vector expression. <code>operator /</code> multiplies the vector
|
||
with the reciprocal of the scalar. </p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header vector_expression.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<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>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<p>None.</p>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Linear depending from the size of the vector expression.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
vector<double> v (3);
|
||
for (int i = 0; i < v.size (); ++ i)
|
||
v (i) = i;
|
||
|
||
std::cout << 2.0 * v << std::endl;
|
||
std::cout << v * 2.0 << std::endl;
|
||
}</pre>
|
||
|
||
<h2><a name="vector_reductions"></a>Vector Reductions</h2>
|
||
|
||
<h3>Unary Reductions</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class E, class F>
|
||
struct vector_scalar_unary_traits {
|
||
typedef typename F::result_type result_type;
|
||
};
|
||
|
||
// sum v = sum (v [i])
|
||
template<class E>
|
||
typename vector_scalar_unary_traits<E, vector_sum<typename E::value_type> >::result_type
|
||
sum (const vector_expression<E> &e);
|
||
|
||
// norm_1 v = sum (abs (v [i]))
|
||
template<class E>
|
||
typename vector_scalar_unary_traits<E, vector_norm_1<typename E::value_type> >::result_type
|
||
norm_1 (const vector_expression<E> &e);
|
||
|
||
// norm_2 v = sqrt (sum (v [i] * v [i]))
|
||
template<class E>
|
||
typename vector_scalar_unary_traits<E, vector_norm_2<typename E::value_type> >::result_type
|
||
norm_2 (const vector_expression<E> &e);
|
||
|
||
// norm_inf v = max (abs (v [i]))
|
||
template<class E>
|
||
typename vector_scalar_unary_traits<E, vector_norm_inf<typename E::value_type> >::result_type
|
||
norm_inf (const vector_expression<E> &e);
|
||
|
||
// index_norm_inf v = min (i: abs (v [i]) == max (abs (v [i])))
|
||
template<class E>
|
||
typename vector_scalar_unary_traits<E, vector_index_norm_inf<typename E::value_type> >::result_type
|
||
index_norm_inf (const vector_expression<E> &e);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>sum</code> computes the sum of the vector expression's
|
||
elements. <code>norm_1</code>, <code>norm_2</code> and <code>norm_inf</code>
|
||
compute the corresponding <em>||.||</em><sub><em>1</em></sub>, <em>||.||</em><sub><em>2</em></sub>
|
||
and <em>||.||</em><sub><em>inf</em></sub> vector norms.<code>
|
||
index_norm_1</code> computes the index of the vector expression's
|
||
first element having maximal absolute value.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header vector_expression.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<li><code>E</code> is a model of <a href="#vector_expression">Vector
|
||
Expression</a>.</li>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<p>None.</p>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Linear depending from the size of the vector expression.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
vector<double> v (3);
|
||
for (int i = 0; i < v.size (); ++ i)
|
||
v (i) = i;
|
||
|
||
std::cout << sum (v) << std::endl;
|
||
std::cout << norm_1 (v) << std::endl;
|
||
std::cout << norm_2 (v) << std::endl;
|
||
std::cout << norm_inf (v) << std::endl;
|
||
std::cout << index_norm_inf (v) << std::endl;
|
||
}</pre>
|
||
|
||
<h3>Binary Reductions</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
struct vector_scalar_binary_traits {
|
||
typedef typename F::result_type result_type;
|
||
};
|
||
|
||
// inner_prod (v1, v2) = sum (v1 [i] * v2 [i]
|
||
template<class E1, class E2>
|
||
typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type,
|
||
typename E2::value_type,
|
||
typename promote_traits<typename E1::value_type,
|
||
typename E2::value_type>::promote_type> >::result_type
|
||
inner_prod (const vector_expression<E1> &e1,
|
||
const vector_expression<E2> &e2);
|
||
|
||
template<class E1, class E2>
|
||
typename vector_scalar_binary_traits<E1, E2, vector_inner_prod<typename E1::value_type,
|
||
typename E2::value_type,
|
||
typename type_traits<typename promote_traits<typename E1::value_type,
|
||
typename E2::value_type>::promote_type>::precision_type> >::result_type
|
||
prec_inner_prod (const vector_expression<E1> &e1,
|
||
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>
|
||
|
||
<dir>
|
||
<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>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<dir>
|
||
<li><code>e1 ().size () == e2 ().size ()</code></li>
|
||
</dir>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Linear depending from the size of the vector expressions.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
vector<double> v1 (3), v2 (3);
|
||
for (int i = 0; i < std::min (v1.size (), v2.size ()); ++ i)
|
||
v1 (i) = v2 (i) = i;
|
||
|
||
std::cout << inner_prod (v1, v2) << std::endl;
|
||
}</pre>
|
||
|
||
<hr>
|
||
|
||
<p>Copyright (<28>) 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: 8/3/2002</p>
|
||
|
||
</body>
|
||
</html>
|