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985 lines
64 KiB
HTML
985 lines
64 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<html>
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<meta http-equiv="Content-Type" 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">
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Vector Expressions</h1>
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<h2><a name="vector_expression"></a>
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Vector Expression</h2>
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<h4>Description</h4>
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<p>The templated class <code>vector_expression<E> </code>forms the base
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for all static derived vector expression classes including class <code> vector</code>
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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 () () const</code></td>
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<td>Returns a <code>const </code>reference of the expression.
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</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><code> // Base class for the Barton Nackman trick<br> template<class E><br> struct vector_expression {<br> typedef E expression_type;<br> typedef vector_tag type_category;<br><br> // This class could define an common interface for all<br> // statically derived expression type classes.<br> // Due to a compiler deficiency - one can not reference class typedefs of E<br> // on MSVC 6.0 (error C2027) - we only implement the casts.<br><br> const expression_type &operator () () const;<br> expression_type &operator () ();<br> };</code></pre>
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<h2><a name="vector_references"></a>
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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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<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="expression.htm#vector_expression">
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Vector Expression</a>
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.</p>
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<h4>Public base classes</h4>
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<p><code>vector_expression<vector_const_reference<E> ></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) 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> pointing
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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> pointing
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to the 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><br> class vector_const_reference:<br> public vector_expression<vector_const_reference<E> > {<br> public:<br> typedef E expression_type;<br> typedef typename E::size_type size_type;<br> typedef typename E::difference_type difference_type;<br> typedef typename E::value_type value_type;<br> typedef typename E::const_reference const_reference;<br> typedef const_reference reference;<br> typedef typename E::const_pointer const_pointer;<br> typedef const_pointer pointer;<br> typedef typename E::const_iterator const_iterator_type;<br> typedef unknown_storage_tag storage_category;<br><br> // Construction and destruction<br> vector_const_reference ();<br> vector_const_reference (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> typedef const_iterator_type 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 is the iterator of the referenced expression.<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>
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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>contains a reference
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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="expression.htm#vector_expression">
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Vector Expression</a>
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.</p>
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<h4>Public base classes</h4>
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<p><code>vector_expression<vector_reference<E> ></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) 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
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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>iterator begin () </code></td>
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<td>Returns a <code>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>iterator end () </code></td>
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<td>Returns a <code>iterator</code> pointing to the end
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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_reverse_iterator rbegin () const</code></td>
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<td>Returns a <code>const_reverse_iterator</code> pointing
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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> pointing
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to the 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
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the 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
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the 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><br> class vector_reference: <br> public vector_expression<vector_reference<E> > {<br> public:<br> typedef E expression_type;<br> typedef typename E::size_type size_type;<br> typedef typename E::difference_type difference_type;<br> typedef typename E::value_type value_type;<br> typedef typename E::const_reference const_reference;<br> typedef typename E::reference reference;<br> typedef typename E::const_pointer const_pointer;<br> typedef typename E::pointer pointer;<br> typedef typename E::const_iterator const_iterator_type;<br> typedef typename E::iterator iterator_type;<br> typedef unknown_storage_tag storage_category;<br><br> // Construction and destruction<br> vector_reference ();<br> vector_reference (expression_type &e);<br><br> // Accessors<br> size_type size () const;<br> const expression_type &expression () const;<br> expression_type &expression ();<br><br> // Resizing<br> void resize (size_type size);<br><br> // Element access<br> const_reference operator () (size_type i) const;<br> reference operator () (size_type i);<br><br> const_reference operator [] (size_type i) const;<br> reference operator [] (size_type i);<br><br> typedef const_iterator_type const_iterator;<br> typedef iterator_type iterator;<br><br> // Element lookup<br> const_iterator find_first (size_type i) const;<br> iterator find_first (size_type i);<br> const_iterator find_last (size_type i) const;<br> iterator find_last (size_type i);<br><br> // Iterator is the iterator of the referenced expression.<br><br> const_iterator begin () const;<br> const_iterator end () const;<br><br> iterator begin ();<br> iterator end ();<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> typedef reverse_iterator_base<iterator> reverse_iterator;<br><br> reverse_iterator rbegin ();<br> reverse_iterator rend ();<br> };</code></pre>
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<h2><a name="vector_operations"></a>
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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>describes a unary
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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="expression.htm#vector_expression">
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Vector Expression</a>
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.</p>
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<h4>Public base classes</h4>
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<p><code>vector_expression<vector_unary<E, F> ></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) 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> pointing
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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> pointing
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to the 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>
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<h3>Unary Operations</h3>
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<h4>Prototypes</h4>
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<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>
|
|
|
|
<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>#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>
|
|
|
|
<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>#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>
|
|
|
|
<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>#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>
|
|
|
|
<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>#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>
|
|
|
|
<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>
|
|
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<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>
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<h3>Binary Reductions</h3>
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<h4>Prototypes</h4>
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<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>
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<h4>Description</h4>
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<p><code>inner_prod </code>computes the inner product of the vector expressions.
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<code>prec_inner_prod </code>computes the double precision inner product of
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the vector expressions<code>.</code></p>
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<h4>Definition</h4>
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<p>Defined in the header vector_expression.hpp.</p>
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<h4>Type requirements</h4>
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<dir> <li><code>E1</code> is a model of <a href="#vector_expression">
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Vector Expression</a>
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.</li>
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<li><code>E2</code> is a model of <a href="#vector_expression">Vector
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Expression</a>
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.</li>
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</dir>
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<h4>Preconditions</h4>
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<dir> <li><code>e1 ().size () == e2 ().size ()</code></li>
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</dir>
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<h4>Complexity</h4>
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<p>Linear depending from the size of the vector expressions.</p>
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<h4>Examples</h4>
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<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>
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<hr>
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<p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch <br>
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Permission to copy, use, modify, sell and distribute this document is granted
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provided this copyright notice appears in all copies. This document is provided
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``as is'' without express or implied warranty, and with no claim as to its
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suitability for any purpose.</p>
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<p>Last revised: 1/15/2003</p>
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</body>
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</html>
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