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3003 lines
108 KiB
HTML
3003 lines
108 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>Matrix 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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width="277" height="86">Matrix Expressions</h1>
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<h2><a name="matrix_expression"></a>Matrix Expression</h2>
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<h4>Description</h4>
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<p>The templated class <code>matrix_expression<E> </code>forms
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the base for all static derived matrix expression classes
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including class <code>matrix</code> itself.</p>
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<h4>Definition</h4>
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<p>Defined in the header matrix_expression.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1">
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<tr>
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<th>Parameter </th>
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<th>Description </th>
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<th>Default </th>
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</tr>
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<tr>
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<td><code>E</code> </td>
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<td>The type of the matrix expression. </td>
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<td> </td>
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</tr>
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</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 matrix_expression {
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typedef E expression_type;
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typedef matrix_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="matrix_references"></a>Matrix 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>matrix_const_reference<E> </code>contains
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a constant reference to a matrix expression.</p>
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<h4>Definition</h4>
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<p>Defined in the header matrix_expression.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1">
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<tr>
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<th>Parameter </th>
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<th>Description </th>
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<th>Default </th>
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</tr>
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<tr>
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<td><code>E</code> </td>
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<td>The type of the matrix expression. </td>
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<td> </td>
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</tr>
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</table>
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<h4>Model of</h4>
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<p><a href="expression.htm#matrix_expression">Matrix Expression</a>.
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</p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a
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href="expression.htm#matrix_expression">Matrix Expression</a>.</p>
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<h4>Public base classes</h4>
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<p><code>matrix_expression<matrix_const_reference<E>
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></code></p>
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<h4>Members</h4>
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<table border="1">
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<tr>
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<th>Member </th>
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<th>Description </th>
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</tr>
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<tr>
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<td><code>matrix_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 size1 () const</code></td>
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<td>Returns the number of rows. </td>
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</tr>
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<tr>
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<td><code>size_type size2 () const</code></td>
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<td>Returns the number of columns. </td>
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</tr>
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<tr>
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<td><code>const_reference operator () (size_type i,
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size_type j) const</code></td>
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<td>Returns the value of the <code>j</code>-th element in
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the<code> i</code>-th row. </td>
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</tr>
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<tr>
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<td><code>const_iterator1 begin1 () const</code></td>
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<td>Returns a <code>const_iterator1</code> pointing to
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the beginning of the expression. </td>
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</tr>
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<tr>
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<td><code>const_iterator1 end1 () const</code></td>
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<td>Returns a <code>const_iterator1</code> pointing to
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the end of the expression. </td>
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</tr>
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<tr>
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<td><code>const_iterator2 begin2 () const</code></td>
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<td>Returns a <code>const_iterator2</code> pointing to
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the beginning of the expression. </td>
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</tr>
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<tr>
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<td><code>const_iterator2 end2 () const</code></td>
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<td>Returns a <code>const_iterator2</code> pointing to
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the end of the expression. </td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code>
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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_iterator1 rend1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code>
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pointing to the end of the reversed expression. </td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</code>
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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_iterator2 rend2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</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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<p>Interface </p>
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<pre><code> template<class E>
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class matrix_const_reference:
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public matrix_expression<matrix_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::orientation_category orientation_category;
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typedef typename E::const_iterator1 const_iterator1_type;
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typedef typename E::const_iterator2 const_iterator2_type;
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typedef unknown_storage_tag storage_category;
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// Construction and destruction
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matrix_const_reference ();
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matrix_const_reference (const expression_type &e);
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// Accessors
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size_type size1 () const;
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size_type size2 () 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, size_type j) const;
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typedef const_iterator1_type const_iterator1;
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typedef const_iterator1 iterator1;
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typedef const_iterator2_type const_iterator2;
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typedef const_iterator2 iterator2;
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// Element lookup
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const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
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const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
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const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
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const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
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// Iterators are the iterators of the referenced expression.
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const_iterator1 begin1 () const;
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const_iterator1 end1 () const;
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const_iterator2 begin2 () const;
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const_iterator2 end2 () const;
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// Reverse iterators
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typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
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const_reverse_iterator1 rbegin1 () const;
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const_reverse_iterator1 rend1 () const;
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typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
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const_reverse_iterator2 rbegin2 () const;
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const_reverse_iterator2 rend2 () const;
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};</code></pre>
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||
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||
<h3>Reference</h3>
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||
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||
<h4>Description</h4>
|
||
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||
<p>The templated class <code>matrix_reference<E> </code>contains
|
||
a reference to a matrix expression.</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>
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||
</tr>
|
||
<tr>
|
||
<td><code>E</code> </td>
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||
<td>The type of the matrix expression. </td>
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||
<td> </td>
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||
</tr>
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||
</table>
|
||
|
||
<h4>Model of</h4>
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||
|
||
<p><a href="expression.htm#matrix_expression">Matrix Expression</a>.
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||
</p>
|
||
|
||
<h4>Type requirements</h4>
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||
|
||
<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<matrix_reference<E> ></code></p>
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||
|
||
<h4>Members</h4>
|
||
|
||
<table border="1">
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||
<tr>
|
||
<th>Member </th>
|
||
<th>Description </th>
|
||
</tr>
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||
<tr>
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||
<td><code>matrix_reference (expression_type &e)</code>
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||
</td>
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||
<td>Constructs a constant reference of the expression.</td>
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||
</tr>
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||
<tr>
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||
<td><code>void resize (size_type size1, size2)</code></td>
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||
<td>Resizes the expression to hold at most <code>size1 </code>rows
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of <code>size2 </code>elements. </td>
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</tr>
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||
<tr>
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||
<td><code>size_type size1 () const</code></td>
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||
<td>Returns the number of rows. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>size_type size2 () const</code></td>
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||
<td>Returns the number of columns. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reference operator () (size_type i,
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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>
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||
<tr>
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||
<td><code>reference operator () (size_type i, size_type
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j)</code></td>
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||
<td>Returns a reference of the <code>j</code>-th element
|
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in the<code> i</code>-th row. </td>
|
||
</tr>
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||
<tr>
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||
<td><code>const_iterator1 begin1 () const</code></td>
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<td>Returns a <code>const_iterator1</code> pointing to
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||
the beginning of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator1 end1 () const</code></td>
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<td>Returns a <code>const_iterator1</code> pointing to
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||
the end of the expression. </td>
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||
</tr>
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||
<tr>
|
||
<td><code>iterator1 begin1 () </code></td>
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<td>Returns a <code>iterator1</code> pointing to the
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beginning of the expression. </td>
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||
</tr>
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||
<tr>
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||
<td><code>iterator1 end1 () </code></td>
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<td>Returns a <code>iterator1</code> pointing to the end
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||
of the expression. </td>
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||
</tr>
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||
<tr>
|
||
<td><code>const_iterator2 begin2 () const</code></td>
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||
<td>Returns a <code>const_iterator2</code> pointing to
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||
the beginning of the expression. </td>
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||
</tr>
|
||
<tr>
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||
<td><code>const_iterator2 end2 () const</code></td>
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<td>Returns a <code>const_iterator2</code> pointing to
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the end of the expression. </td>
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</tr>
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<tr>
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<td><code>iterator2 begin2 () </code></td>
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<td>Returns a <code>iterator2</code> pointing to the
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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>iterator2 end2 () </code></td>
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<td>Returns a <code>iterator2</code> pointing to the end
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||
of the expression. </td>
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||
</tr>
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||
<tr>
|
||
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code>
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||
pointing to the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
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||
<td><code>const_reverse_iterator1 rend1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code>
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||
pointing to the end of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>reverse_iterator1 rbegin1 () </code></td>
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||
<td>Returns a <code>reverse_iterator1</code> pointing to
|
||
the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>reverse_iterator1 rend1 () </code></td>
|
||
<td>Returns a <code>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>
|
||
<tr>
|
||
<td><code>reverse_iterator2 rbegin2 () </code></td>
|
||
<td>Returns a <code>reverse_iterator2</code> pointing to
|
||
the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>reverse_iterator2 rend2 () </code></td>
|
||
<td>Returns a <code>reverse_iterator2</code> pointing to
|
||
the end of the reversed expression. </td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> template<class E>
|
||
class matrix_reference:
|
||
public matrix_expression<matrix_reference<E> > {
|
||
public:
|
||
typedef E expression_type;
|
||
typedef typename E::size_type size_type;
|
||
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;
|
||
typedef typename E::const_pointer const_pointer;
|
||
typedef typename E::pointer pointer;
|
||
typedef typename E::orientation_category orientation_category;
|
||
typedef typename E::const_iterator1 const_iterator1_type;
|
||
typedef typename E::iterator1 iterator1_type;
|
||
typedef typename E::const_iterator2 const_iterator2_type;
|
||
typedef typename E::iterator2 iterator2_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
matrix_reference ();
|
||
matrix_reference (expression_type &e);
|
||
|
||
// Accessors
|
||
size_type size1 () const;
|
||
size_type size2 () const;
|
||
const expression_type &expression () const;
|
||
expression_type &expression ();
|
||
|
||
// Resizing
|
||
void resize (size_type size1, size_type size2);
|
||
|
||
// Element access
|
||
const_reference operator () (size_type i, size_type j) const;
|
||
reference operator () (size_type i, size_type j);
|
||
|
||
typedef const_iterator1_type const_iterator1;
|
||
typedef iterator1_type iterator1;
|
||
typedef const_iterator2_type const_iterator2;
|
||
typedef iterator2_type iterator2;
|
||
|
||
// Element lookup
|
||
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
|
||
iterator1 find_first1 (int rank, size_type i, size_type j);
|
||
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
|
||
iterator1 find_last1 (int rank, size_type i, size_type j);
|
||
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
|
||
iterator2 find_first2 (int rank, size_type i, size_type j);
|
||
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
|
||
iterator2 find_last2 (int rank, size_type i, size_type j);
|
||
|
||
// Iterators are the iterators of the referenced expression.
|
||
|
||
const_iterator1 begin1 () const;
|
||
const_iterator1 end1 () const;
|
||
|
||
iterator1 begin1 ();
|
||
iterator1 end1 ();
|
||
|
||
const_iterator2 begin2 () const;
|
||
const_iterator2 end2 () const;
|
||
|
||
iterator2 begin2 ();
|
||
iterator2 end2 ();
|
||
|
||
// Reverse iterators
|
||
|
||
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
|
||
|
||
const_reverse_iterator1 rbegin1 () const;
|
||
const_reverse_iterator1 rend1 () const;
|
||
|
||
typedef reverse_iterator_base1<iterator1> reverse_iterator1;
|
||
|
||
reverse_iterator1 rbegin1 ();
|
||
reverse_iterator1 rend1 ();
|
||
|
||
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
|
||
|
||
const_reverse_iterator2 rbegin2 () const;
|
||
const_reverse_iterator2 rend2 () const;
|
||
|
||
typedef reverse_iterator_base2<iterator2> reverse_iterator2;
|
||
|
||
reverse_iterator2 rbegin2 ();
|
||
reverse_iterator2 rend2 ();
|
||
};</code></pre>
|
||
|
||
<h2><a name="matrix_operations"></a>Matrix Operations</h2>
|
||
|
||
<h3>Unary Operation Description</h3>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p>The templated classes <code>matrix_unary1<E, F> </code>and
|
||
<code>matrix_unary2<E, F> </code>describe unary matrix
|
||
operations.</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>E</code> </td>
|
||
<td>The type of the matrix expression. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>F</code></td>
|
||
<td>The type of the operation.</td>
|
||
<td> </td>
|
||
</tr>
|
||
</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<matrix_unary1<E, F> > </code>and<code>
|
||
matrix_expression<matrix_unary2<E, F> > </code>resp.</p>
|
||
|
||
<h4>Members</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Member </th>
|
||
<th>Description </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>matrix_unary1 (const expression_type &e)</code>
|
||
</td>
|
||
<td>Constructs a description of the expression.</td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>matrix_unary2 (const expression_type &e)</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 E, class F>
|
||
class matrix_unary1:
|
||
public matrix_expression<matrix_unary1<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 matrix_unary1<E, F> const_closure_type;
|
||
typedef typename E::orientation_category orientation_category;
|
||
typedef typename E::const_iterator1 const_iterator1_type;
|
||
typedef typename E::const_iterator2 const_iterator2_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
matrix_unary1 ();
|
||
matrix_unary1 (const expression_type &e);
|
||
|
||
// Accessors
|
||
size_type size1 () const;
|
||
size_type size2 () const;
|
||
const expression_type &expression () 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;
|
||
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
|
||
typedef reverse_iterator_base2<const_iterator2> const_reverse_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 expression
|
||
// with the unary functor.
|
||
|
||
class const_iterator1:
|
||
public container_const_reference<matrix_unary1>,
|
||
public random_access_iterator_base<const_iterator1, value_type> {
|
||
public:
|
||
typedef typename E::const_iterator1::iterator_category iterator_category;
|
||
typedef typename matrix_unary1::difference_type difference_type;
|
||
typedef typename matrix_unary1::value_type value_type;
|
||
typedef typename matrix_unary1::const_reference reference;
|
||
typedef typename matrix_unary1::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 matrix_unary1 &mu, const const_iterator1_type &it);
|
||
|
||
// 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<matrix_unary1>,
|
||
public random_access_iterator_base<const_iterator2, value_type> {
|
||
public:
|
||
typedef typename E::const_iterator2::iterator_category iterator_category;
|
||
typedef typename matrix_unary1::difference_type difference_type;
|
||
typedef typename matrix_unary1::value_type value_type;
|
||
typedef typename matrix_unary1::const_reference reference;
|
||
typedef typename matrix_unary1::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 matrix_unary1 &mu, const const_iterator2_type &it);
|
||
|
||
// 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;
|
||
};
|
||
|
||
template<class E, class F>
|
||
class matrix_unary2:
|
||
public matrix_expression<matrix_unary2<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 matrix_unary2<E, F> const_closure_type;
|
||
typedef typename E::orientation_category orientation_category;
|
||
typedef typename E::const_iterator1 const_iterator2_type;
|
||
typedef typename E::const_iterator2 const_iterator1_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
matrix_unary2 ();
|
||
matrix_unary2 (const expression_type &e);
|
||
|
||
// Accessors
|
||
size_type size1 () const;
|
||
size_type size2 () const;
|
||
const expression_type &expression () 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;
|
||
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
|
||
typedef reverse_iterator_base2<const_iterator2> const_reverse_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 expression
|
||
// with the unary functor.
|
||
|
||
class const_iterator1:
|
||
public container_const_reference<matrix_unary2>,
|
||
public random_access_iterator_base<const_iterator1, value_type> {
|
||
public:
|
||
typedef typename E::const_iterator2::iterator_category iterator_category;
|
||
typedef typename matrix_unary2::difference_type difference_type;
|
||
typedef typename matrix_unary2::value_type value_type;
|
||
typedef typename matrix_unary2::const_reference reference;
|
||
typedef typename matrix_unary2::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 matrix_unary2 &mu, const const_iterator1_type &it);
|
||
|
||
// 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<matrix_unary2>,
|
||
public random_access_iterator_base<const_iterator2, value_type> {
|
||
public:
|
||
typedef typename E::const_iterator1::iterator_category iterator_category;
|
||
typedef typename matrix_unary2::difference_type difference_type;
|
||
typedef typename matrix_unary2::value_type value_type;
|
||
typedef typename matrix_unary2::const_reference reference;
|
||
typedef typename matrix_unary2::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 matrix_unary2 &mu, const const_iterator2_type &it);
|
||
|
||
// 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>Unary Operations</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class E, class F>
|
||
struct matrix_unary1_traits {
|
||
typedef matrix_unary1<typename E::const_closure_type, F> expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
// (- m) [i] [j] = - m [i] [j]
|
||
template<class E>
|
||
typename matrix_unary1_traits<E, scalar_negate<typename E::value_type> >::result_type
|
||
operator - (const matrix_expression<E> &e);
|
||
|
||
// (conj m) [i] [j] = conj (m [i] [j])
|
||
template<class E>
|
||
typename matrix_unary1_traits<E, scalar_conj<typename E::value_type> >::result_type
|
||
conj (const matrix_expression<E> &e);
|
||
|
||
// (real m) [i] [j] = real (m [i] [j])
|
||
template<class E>
|
||
typename matrix_unary1_traits<E, scalar_real<typename E::value_type> >::result_type
|
||
real (const matrix_expression<E> &e);
|
||
|
||
// (imag m) [i] [j] = imag (m [i] [j])
|
||
template<class E>
|
||
typename matrix_unary1_traits<E, scalar_imag<typename E::value_type> >::result_type
|
||
imag (const matrix_expression<E> &e);
|
||
|
||
template<class E, class F>
|
||
struct matrix_unary2_traits {
|
||
typedef matrix_unary2<typename E::const_closure_type, F> expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
// (trans m) [i] [j] = m [j] [i]
|
||
template<class E>
|
||
typename matrix_unary2_traits<E, scalar_identity<typename E::value_type> >::result_type
|
||
trans (const matrix_expression<E> &e);
|
||
|
||
// (herm m) [i] [j] = conj (m [j] [i])
|
||
template<class E>
|
||
typename matrix_unary2_traits<E, scalar_conj<typename E::value_type> >::result_type
|
||
herm (const matrix_expression<E> &e);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>operator -</code> computes the additive inverse of a
|
||
matrix expression. <code>conj </code>computes the complex
|
||
conjugate of a matrix expression.<code> real</code> and <code>imag</code>
|
||
compute the real and imaginary parts of a matrix expression. <code>trans
|
||
</code>computes the transpose of a matrix expression. <code>herm </code>computes
|
||
the hermitian, i.e. the complex conjugate of the transpose of a
|
||
matrix expression.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<li><code>E</code> is a model of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a>.</li>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<p>None.</p>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Quadratic depending from the size of the matrix expression.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
matrix<std::complex<double> > m (3, 3);
|
||
for (int i = 0; i < m.size1 (); ++ i)
|
||
for (int j = 0; j < m.size2 (); ++ j)
|
||
m (i, j) = std::complex (3 * i + j, 3 * i + j);
|
||
|
||
std::cout << - m << std::endl;
|
||
std::cout << conj (m) << std::endl;
|
||
std::cout << real (m) << std::endl;
|
||
std::cout << imag (m) << std::endl;
|
||
std::cout << trans (m) << std::endl;
|
||
std::cout << herm (m) << std::endl;
|
||
}</pre>
|
||
|
||
<h3>Binary Operation Description</h3>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p>The templated class <code>matrix_binary<E1, E2, F> </code>describes
|
||
a binary matrix operation.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Template parameters</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Parameter </th>
|
||
<th>Description </th>
|
||
<th>Default </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>E1</code> </td>
|
||
<td>The type of the first matrix expression. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>E2</code></td>
|
||
<td>The type of the second matrix expression. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>F</code></td>
|
||
<td>The type of the operation.</td>
|
||
<td> </td>
|
||
</tr>
|
||
</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<matrix_binary<E1, E2, F> ></code>.</p>
|
||
|
||
<h4>Members</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Member </th>
|
||
<th>Description </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>matrix_binary (const expression1_type &e1,
|
||
const expression2_type &e2)</code> </td>
|
||
<td>Constructs a description of the expression.</td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>size_type size1 () const</code></td>
|
||
<td>Returns the number of rows. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>size_type size2 () const</code></td>
|
||
<td>Returns the number of columns. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reference operator () (size_type i,
|
||
size_type j) const</code></td>
|
||
<td>Returns the value of the <code>j</code>-th element in
|
||
the<code> i</code>-th row. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator1 begin1 () const</code></td>
|
||
<td>Returns a <code>const_iterator1</code> pointing to
|
||
the beginning of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator1 end1 () const</code></td>
|
||
<td>Returns a <code>const_iterator1</code> pointing to
|
||
the end of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator2 begin2 () const</code></td>
|
||
<td>Returns a <code>const_iterator2</code> pointing to
|
||
the beginning of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator2 end2 () const</code></td>
|
||
<td>Returns a <code>const_iterator2</code> pointing to
|
||
the end of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator1</code>
|
||
pointing to the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator1 rend1 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator1</code>
|
||
pointing to the end of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator2</code>
|
||
pointing to the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator2 rend2 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator2</code>
|
||
pointing to the end of the reversed expression.</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
class matrix_binary:
|
||
public matrix_expression<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 matrix_binary<E1, E2, F> const_closure_type;
|
||
typedef unknown_orientation_tag orientation_category;
|
||
typedef typename E1::const_iterator1 const_iterator11_type;
|
||
typedef typename E1::const_iterator2 const_iterator12_type;
|
||
typedef typename E2::const_iterator1 const_iterator21_type;
|
||
typedef typename E2::const_iterator2 const_iterator22_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
matrix_binary ();
|
||
matrix_binary (const E1 &e1, const E2 &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;
|
||
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
|
||
typedef reverse_iterator_base2<const_iterator2> const_reverse_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 expression
|
||
// with the binary functor.
|
||
|
||
class const_iterator1:
|
||
public container_const_reference<matrix_binary>,
|
||
public random_access_iterator_base<const_iterator1, value_type> {
|
||
public:
|
||
typedef typename restrict_traits<typename E1::const_iterator1::iterator_category,
|
||
typename E2::const_iterator1::iterator_category>::iterator_category iterator_category;
|
||
typedef typename matrix_binary::difference_type difference_type;
|
||
typedef typename matrix_binary::value_type value_type;
|
||
typedef typename matrix_binary::const_reference reference;
|
||
typedef typename 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 matrix_binary &mb, size_type i, size_type j,
|
||
const const_iterator11_type &it1, const const_iterator11_type &it1_end,
|
||
const const_iterator21_type &it2, const const_iterator21_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_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<matrix_binary>,
|
||
public random_access_iterator_base<const_iterator2, value_type> {
|
||
public:
|
||
typedef typename restrict_traits<typename E1::const_iterator2::iterator_category,
|
||
typename E2::const_iterator2::iterator_category>::iterator_category iterator_category;
|
||
typedef typename matrix_binary::difference_type difference_type;
|
||
typedef typename matrix_binary::value_type value_type;
|
||
typedef typename matrix_binary::const_reference reference;
|
||
typedef typename 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 matrix_binary &mb, size_type i, size_type j,
|
||
const const_iterator12_type &it1, const const_iterator12_type &it1_end,
|
||
const const_iterator22_type &it2, const const_iterator22_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_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 Operations</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
struct matrix_binary_traits {
|
||
typedef matrix_binary<typename E1::const_closure_type,
|
||
typename E2::const_closure_type, F> expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
// (m1 + m2) [i] [j] = m1 [i] [j] + m2 [i] [j]
|
||
template<class E1, class E2>
|
||
typename matrix_binary_traits<E1, E2, scalar_plus<typename E1::value_type,
|
||
typename E2::value_type> >::result_type
|
||
operator + (const matrix_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2);
|
||
|
||
// (m1 - m2) [i] [j] = m1 [i] [j] - m2 [i] [j]
|
||
template<class E1, class E2>
|
||
typename matrix_binary_traits<E1, E2, scalar_minus<typename E1::value_type,
|
||
typename E2::value_type> >::result_type
|
||
operator - (const matrix_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>operator +</code> computes the sum of two matrix
|
||
expressions. <code>operator - </code>computes the difference of
|
||
two matrix expressions.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<li><code>E1</code> is a model of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a>.
|
||
</li>
|
||
<li><code>E2</code> is a model of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a>.
|
||
</li>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<dir>
|
||
<li><code>e1 ().size1 () == e2 ().size1 ()</code> </li>
|
||
<li><code>e1 ().size2 () == e2 ().size2 ()</code></li>
|
||
</dir>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Quadratic depending from the size of the matrix expressions.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
matrix<double > m1 (3, 3), m (3, 3);
|
||
for (int i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i)
|
||
for (int j = 0; j < std::min (m1.size2 (), m2.size2 ()); ++ j)
|
||
m1 (i, j) = m2 (i, j) = 3 * i + j;
|
||
|
||
std::cout << m1 + m2 << std::endl;
|
||
std::cout << m1 - m2 << std::endl;
|
||
}</pre>
|
||
|
||
<h3>Scalar Matrix Operation Description</h3>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p>The templated classes <code>matrix_binary_scalar1<E1, E2,
|
||
F> </code>and <code>matrix_binary_scalar2<E1, E2, F></code>
|
||
describe binary operations between a scalar and a matrix.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Template parameters</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Parameter </th>
|
||
<th>Description </th>
|
||
<th>Default </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>E1/E2</code> </td>
|
||
<td>The type of the scalar expression. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>E2/E1</code></td>
|
||
<td>The type of the matrix expression. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>F</code></td>
|
||
<td>The type of the operation.</td>
|
||
<td> </td>
|
||
</tr>
|
||
</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<matrix_binary_scalar1<E1, E2,
|
||
F> ></code> and<code>
|
||
matrix_expression<matrix_binary_scalar2<E1, E2, F> > </code>resp.</p>
|
||
|
||
<h4>Members</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Member </th>
|
||
<th>Description </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>matrix_binary_scalar1 (const expression1_type
|
||
&e1, const expression2_type &e2)</code> </td>
|
||
<td>Constructs a description of the expression.</td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>matrix_binary_scalar1 (const expression1_type
|
||
&e1, const expression2_type &e2)</code> </td>
|
||
<td>Constructs a description of the expression.</td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>size_type size1 () const</code></td>
|
||
<td>Returns the number of rows. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>size_type size2 () const</code></td>
|
||
<td>Returns the number of columns. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reference operator () (size_type i,
|
||
size_type j) const</code></td>
|
||
<td>Returns the value of the <code>j</code>-th element in
|
||
the<code> i</code>-th row. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator1 begin1 () const</code></td>
|
||
<td>Returns a <code>const_iterator1</code> pointing to
|
||
the beginning of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator1 end1 () const</code></td>
|
||
<td>Returns a <code>const_iterator1</code> pointing to
|
||
the end of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator2 begin2 () const</code></td>
|
||
<td>Returns a <code>const_iterator2</code> pointing to
|
||
the beginning of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator2 end2 () const</code></td>
|
||
<td>Returns a <code>const_iterator2</code> pointing to
|
||
the end of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator1</code>
|
||
pointing to the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator1 rend1 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator1</code>
|
||
pointing to the end of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator2</code>
|
||
pointing to the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator2 rend2 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator2</code>
|
||
pointing to the end of the reversed expression. </td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
class matrix_binary_scalar1:
|
||
public matrix_expression<matrix_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 matrix_binary_scalar1<E1, E2, F> const_closure_type;
|
||
typedef typename E2::orientation_category orientation_category;
|
||
typedef typename E1::value_type const_iterator1_type;
|
||
typedef typename E2::const_iterator1 const_iterator21_type;
|
||
typedef typename E2::const_iterator2 const_iterator22_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
matrix_binary_scalar1 ();
|
||
matrix_binary_scalar1 (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;
|
||
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
|
||
typedef reverse_iterator_base2<const_iterator2> const_reverse_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 expression
|
||
// with the binary functor.
|
||
|
||
class const_iterator1:
|
||
public container_const_reference<matrix_binary_scalar1>,
|
||
public random_access_iterator_base<const_iterator1, value_type> {
|
||
public:
|
||
typedef typename E2::const_iterator1::iterator_category iterator_category;
|
||
typedef typename matrix_binary_scalar1::difference_type difference_type;
|
||
typedef typename matrix_binary_scalar1::value_type value_type;
|
||
typedef typename matrix_binary_scalar1::const_reference reference;
|
||
typedef typename matrix_binary_scalar1::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 matrix_binary_scalar1 &mbs, const const_iterator1_type &it1, const const_iterator21_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<matrix_binary_scalar1>,
|
||
public random_access_iterator_base<const_iterator2, value_type> {
|
||
public:
|
||
typedef typename E2::const_iterator2::iterator_category iterator_category;
|
||
typedef typename matrix_binary_scalar1::difference_type difference_type;
|
||
typedef typename matrix_binary_scalar1::value_type value_type;
|
||
typedef typename matrix_binary_scalar1::const_reference reference;
|
||
typedef typename matrix_binary_scalar1::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 matrix_binary_scalar1 &mbs, const const_iterator1_type &it1, const const_iterator22_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;
|
||
};
|
||
|
||
template<class E1, class E2, class F>
|
||
class matrix_binary_scalar2:
|
||
public matrix_expression<matrix_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 matrix_binary_scalar2<E1, E2, F> const_closure_type;
|
||
typedef typename E1::orientation_category orientation_category;
|
||
typedef typename E1::const_iterator1 const_iterator11_type;
|
||
typedef typename E1::const_iterator2 const_iterator12_type;
|
||
typedef typename E2::value_type const_iterator2_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
matrix_binary_scalar2 ();
|
||
matrix_binary_scalar2 (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;
|
||
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
|
||
typedef reverse_iterator_base2<const_iterator2> const_reverse_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 expression
|
||
// with the binary functor.
|
||
|
||
class const_iterator1:
|
||
public container_const_reference<matrix_binary_scalar2>,
|
||
public random_access_iterator_base<const_iterator1, value_type> {
|
||
public:
|
||
typedef typename E1::const_iterator1::iterator_category iterator_category;
|
||
typedef typename matrix_binary_scalar2::difference_type difference_type;
|
||
typedef typename matrix_binary_scalar2::value_type value_type;
|
||
typedef typename matrix_binary_scalar2::const_reference reference;
|
||
typedef typename matrix_binary_scalar2::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 matrix_binary_scalar2 &mbs, const const_iterator11_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<matrix_binary_scalar2>,
|
||
public random_access_iterator_base<const_iterator2, value_type> {
|
||
public:
|
||
typedef typename E1::const_iterator2::iterator_category iterator_category;
|
||
typedef typename matrix_binary_scalar2::difference_type difference_type;
|
||
typedef typename matrix_binary_scalar2::value_type value_type;
|
||
typedef typename matrix_binary_scalar2::const_reference reference;
|
||
typedef typename matrix_binary_scalar2::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 matrix_binary_scalar2 &mbs, const const_iterator12_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>Scalar Matrix Operations </h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class T1, class E2, class F>
|
||
struct matrix_binary_scalar1_traits {
|
||
typedef matrix_binary_scalar1<scalar_const_reference<T1>,
|
||
typename E2::const_closure_type, F> expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
// (t * m) [i] [j] = t * m [i] [j]
|
||
template<class T1, class E2>
|
||
typename matrix_binary_scalar1_traits<T1, E2, scalar_multiplies<T1, typename E2::value_type> >::result_type
|
||
operator * (const T1 &e1,
|
||
const matrix_expression<E2> &e2);
|
||
|
||
template<class E1, class T2, class F>
|
||
struct matrix_binary_scalar2_traits {
|
||
typedef matrix_binary_scalar2<typename E1::const_closure_type,
|
||
scalar_const_reference<T2>, F> expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
// (m * t) [i] [j] = m [i] [j] * t
|
||
template<class E1, class T2>
|
||
typename matrix_binary_scalar2_traits<E1, T2, scalar_multiplies<typename E1::value_type, T2> >::result_type
|
||
operator * (const matrix_expression<E1> &e1,
|
||
const T2 &e2);
|
||
|
||
// (m / t) [i] [j] = m [i] [j] / t
|
||
template<class E1, class T2>
|
||
typename matrix_binary_scalar2_traits<E1, T2, scalar_divides<typename E1::value_type, T2> >::result_type
|
||
operator / (const matrix_expression<E1> &e1,
|
||
const T2 &e2);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>operator *</code> computes the product of a scalar and a
|
||
matrix expression. <code>operator /</code> multiplies the matrix
|
||
with the reciprocal of the scalar. </p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<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#matrix_expression">Matrix Expression</a>.</li>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<p>None.</p>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Quadratic depending from the size of the matrix expression.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
matrix<double > m (3, 3);
|
||
for (int i = 0; i < m.size1 (); ++ i)
|
||
for (int j = 0; j < m.size2 (); ++ j)
|
||
m (i, j) = 3 * i + j;
|
||
|
||
std::cout << 2.0 * m << std::endl;
|
||
std::cout << m * 2.0 << std::endl;
|
||
}</pre>
|
||
|
||
<h2><a name="matrix_reductions"></a>Matrix Reductions</h2>
|
||
|
||
<h3>Operations</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class M>
|
||
matrix_row<M> row (M &data, std::size_t i);
|
||
|
||
template<class M>
|
||
matrix_column<M> column (M &data, std::size_t j);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>row</code> returns the the <code>i</code>-th row of a
|
||
matrix expression. <code>column </code>returns the the j-th row
|
||
of a matrix expression. </p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_proxy.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<li><code>E</code> is a model of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a>.</li>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<dir>
|
||
<li><code>i < e ().size1 ()</code> </li>
|
||
<li><code>j < e ().size2 ()</code></li>
|
||
</dir>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Linear depending from the size of the matrix expression.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
matrix<double > m (3, 3);
|
||
for (int i = 0; i < m.size1 (); ++ i)
|
||
for (int j = 0; j < m.size2 (); ++ j)
|
||
m (i, j) = 3 * i + j;
|
||
|
||
for (int i = 0; i < m.size1 (); ++ i)
|
||
std::cout << row (m, i) << std::endl;
|
||
for (int j = 0; j < m.size2 (); ++ j)
|
||
std::cout << column (m, j) << std::endl;
|
||
}</pre>
|
||
|
||
<h2><a name="matrix_vector_operations"></a>Matrix Vector
|
||
Operations</h2>
|
||
|
||
<h3>Binary Operation Description</h3>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p>The templated classes <code>matrix_vector_binary1<E1, E2,
|
||
F> </code>and <code>matrix_vector_binary2<E1, E2, F> </code>describe
|
||
binary matrix vector operations.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Template parameters</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Parameter </th>
|
||
<th>Description </th>
|
||
<th>Default </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>E1</code> </td>
|
||
<td>The type of the matrix or vector expression. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>E2</code> </td>
|
||
<td>The type of the vector or matrix expression. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>F</code> </td>
|
||
<td>The type of the operation.</td>
|
||
<td> </td>
|
||
</tr>
|
||
</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<matrix_vector_binary1<E1, E2,
|
||
F> ></code> and <code>vector_expression<matrix_vector_binary2<E1,
|
||
E2, F> ></code> resp.</p>
|
||
|
||
<h4>Members</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Member </th>
|
||
<th>Description </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>matrix_vector_binary1 (const expression1_type
|
||
&e1, const expression2_type &e2)</code></td>
|
||
<td>Constructs a description of the expression.</td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>matrix_vector_binary2 (const expression1_type
|
||
&e1, const expression2_type &e2)</code></td>
|
||
<td>Constructs a description of the expression.</td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>size_type size () const</code></td>
|
||
<td>Returns the size of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reference operator () (size_type i) const</code></td>
|
||
<td>Returns the value of the <code>i</code>-th element. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator begin () const</code></td>
|
||
<td>Returns a <code>const_iterator</code> pointing to the
|
||
beginning of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator end () const</code></td>
|
||
<td>Returns a <code>const_iterator</code> pointing to the
|
||
end of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator rbegin () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator</code>
|
||
pointing to the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator rend () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator</code>
|
||
pointing to the end of the reversed expression. </td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
class matrix_vector_binary1:
|
||
public vector_expression<matrix_vector_binary1<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 matrix_vector_binary1<E1, E2, F> const_closure_type;
|
||
typedef typename E1::const_iterator1 const_iterator1_type;
|
||
typedef typename E2::const_iterator const_iterator2_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
matrix_vector_binary1 ();
|
||
matrix_vector_binary1 (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;
|
||
|
||
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 simply is a pointer.
|
||
|
||
class const_iterator:
|
||
public container_const_reference<matrix_vector_binary1>,
|
||
public random_access_iterator_base<const_iterator, value_type> {
|
||
public:
|
||
typedef typename restrict_traits<typename E1::const_iterator1::iterator_category,
|
||
typename E2::const_iterator::iterator_category>::iterator_category iterator_category;
|
||
typedef typename matrix_vector_binary1::difference_type difference_type;
|
||
typedef typename matrix_vector_binary1::value_type value_type;
|
||
typedef typename matrix_vector_binary1::const_reference reference;
|
||
typedef typename matrix_vector_binary1::const_pointer pointer;
|
||
|
||
// Construction and destruction
|
||
const_iterator ();
|
||
const_iterator (const matrix_vector_binary1 &mvb, const const_iterator1_type &it1);
|
||
|
||
// Dense random access specialization
|
||
value_type dereference (dense_random_access_iterator_tag) const;
|
||
|
||
// Packed bidirectional specialization
|
||
value_type dereference (packed_bidirectional_iterator_tag) const;
|
||
|
||
// Sparse bidirectional specialization
|
||
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;
|
||
};
|
||
|
||
template<class E1, class E2, class F>
|
||
class matrix_vector_binary2:
|
||
public vector_expression<matrix_vector_binary2<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 matrix_vector_binary2<E1, E2, F> const_closure_type;
|
||
typedef typename E1::const_iterator const_iterator1_type;
|
||
typedef typename E2::const_iterator2 const_iterator2_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
matrix_vector_binary2 ();
|
||
matrix_vector_binary2 (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 j) const;
|
||
|
||
class const_iterator;
|
||
typedef const_iterator iterator;
|
||
|
||
// Element lookup
|
||
const_iterator find_first (size_type j) const;
|
||
const_iterator find_last (size_type j) const;
|
||
|
||
// Iterator simply is a pointer.
|
||
|
||
class const_iterator:
|
||
public container_const_reference<matrix_vector_binary2>,
|
||
public random_access_iterator_base<const_iterator, value_type> {
|
||
public:
|
||
typedef typename restrict_traits<typename E1::const_iterator::iterator_category,
|
||
typename E2::const_iterator2::iterator_category>::iterator_category iterator_category;
|
||
typedef typename matrix_vector_binary2::difference_type difference_type;
|
||
typedef typename matrix_vector_binary2::value_type value_type;
|
||
typedef typename matrix_vector_binary2::const_reference reference;
|
||
typedef typename matrix_vector_binary2::const_pointer pointer;
|
||
|
||
// Construction and destruction
|
||
const_iterator ();
|
||
const_iterator (const matrix_vector_binary2 &mvb, const const_iterator2_type &it2);
|
||
|
||
// Dense random access specialization
|
||
value_type dereference (dense_random_access_iterator_tag) const;
|
||
|
||
// Packed bidirectional specialization
|
||
value_type dereference (packed_bidirectional_iterator_tag) const;
|
||
|
||
// Sparse bidirectional specialization
|
||
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 T1, class E1, class T2, class E2>
|
||
struct matrix_vector_binary1_traits {
|
||
typedef row_major_tag dispatch_category;
|
||
typedef typename promote_traits<T1, T2>::promote_type promote_type;
|
||
typedef matrix_vector_binary1<typename E1::const_closure_type,
|
||
typename E2::const_closure_type,
|
||
matrix_vector_prod1<T1, T2, promote_type> > expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
template<class E1, class E2>
|
||
typename matrix_vector_binary1_traits<typename E1::value_type, E1,
|
||
typename E2::value_type, E2>::result_type
|
||
prod (const matrix_expression<E1> &e1,
|
||
const vector_expression<E2> &e2,
|
||
row_major_tag);
|
||
|
||
// Dispatcher
|
||
template<class E1, class E2>
|
||
typename matrix_vector_binary1_traits<typename E1::value_type, E1,
|
||
typename E2::value_type, E2>::result_type
|
||
prod (const matrix_expression<E1> &e1,
|
||
const vector_expression<E2> &e2);
|
||
|
||
template<class E1, class E2>
|
||
typename matrix_vector_binary1_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
prec_prod (const matrix_expression<E1> &e1,
|
||
const vector_expression<E2> &e2,
|
||
row_major_tag);
|
||
|
||
// Dispatcher
|
||
template<class E1, class E2>
|
||
typename matrix_vector_binary1_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
prec_prod (const matrix_expression<E1> &e1,
|
||
const vector_expression<E2> &e2);
|
||
|
||
template<class V, class E1, class E2>
|
||
V
|
||
prod (const matrix_expression<E1> &e1,
|
||
const vector_expression<E2> &e2);
|
||
|
||
template<class V, class E1, class E2>
|
||
V
|
||
prec_prod (const matrix_expression<E1> &e1,
|
||
const vector_expression<E2> &e2);
|
||
|
||
template<class T1, class E1, class T2, class E2>
|
||
struct matrix_vector_binary2_traits {
|
||
typedef column_major_tag dispatch_category;
|
||
typedef typename promote_traits<T1, T2>::promote_type promote_type;
|
||
typedef matrix_vector_binary2<typename E1::const_closure_type,
|
||
typename E2::const_closure_type,
|
||
matrix_vector_prod2<T1, T2, promote_type> > expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
template<class E1, class E2>
|
||
typename matrix_vector_binary2_traits<typename E1::value_type, E1,
|
||
typename E2::value_type, E2>::result_type
|
||
prod (const vector_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2,
|
||
column_major_tag);
|
||
|
||
// Dispatcher
|
||
template<class E1, class E2>
|
||
typename matrix_vector_binary2_traits<typename E1::value_type, E1,
|
||
typename E2::value_type, E2>::result_type
|
||
prod (const vector_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2);
|
||
|
||
template<class E1, class E2>
|
||
typename matrix_vector_binary2_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
prec_prod (const vector_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2,
|
||
column_major_tag);
|
||
|
||
// Dispatcher
|
||
template<class E1, class E2>
|
||
typename matrix_vector_binary2_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
prec_prod (const vector_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2);
|
||
|
||
template<class V, class E1, class E2>
|
||
V
|
||
prod (const vector_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2);
|
||
|
||
template<class V, class E1, class E2>
|
||
V
|
||
prec_prod (const vector_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>prod</code> computes the product of the matrix and the
|
||
vector expression.<code> prec_prod</code> computes the double
|
||
precision product of the matrix and the vector expression.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<li><code>E1</code> is a model of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a> or
|
||
<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>
|
||
or <a href="expression.htm#matrix_expression">Matrix
|
||
Expression</a>.</li>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<dir>
|
||
<li><code>e1 ().size2 () == e2 ().size ()</code> </li>
|
||
<li><code>e1 ().size () == e2 ().size1 ()</code></li>
|
||
</dir>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Quadratic depending from the size of the matrix expression.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
matrix<double > m (3, 3), v (3);
|
||
for (int i = 0; i < std::min (m.size1 (), v.size ()); ++ i) {
|
||
for (int j = 0; j < m.size2 (); ++ j)
|
||
m (i, j) = 3 * i + j;
|
||
v (i) = i
|
||
}
|
||
|
||
std::cout << prod (m, v) << std::endl;
|
||
std::cout << prod (v, m) << std::endl;
|
||
}</pre>
|
||
|
||
<h3>Triangular Solver</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class E1, class E2>
|
||
struct matrix_vector_solve_traits {
|
||
typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type;
|
||
typedef vector<promote_type> result_type;
|
||
};
|
||
|
||
template<class E1, class E2>
|
||
void inplace_solve (const matrix_expression<E1> &e1,
|
||
E2 &e2,
|
||
lower_tag,
|
||
vector_tag);
|
||
template<class E1, class E2>
|
||
void inplace_solve (const matrix_expression<E1> &e1,
|
||
E2 &e2,
|
||
upper_tag,
|
||
vector_tag);
|
||
template<class E1, class E2>
|
||
void inplace_solve (const matrix_expression<E1> &e1,
|
||
E2 &e2,
|
||
unit_lower_tag,
|
||
vector_tag);
|
||
template<class E1, class E2>
|
||
void inplace_solve (const matrix_expression<E1> &e1,
|
||
E2 &e2,
|
||
unit_upper_tag,
|
||
vector_tag);
|
||
|
||
template<class E1, class E2, class C>
|
||
typename matrix_vector_solve_traits<E1, E2>::result_type
|
||
solve (const matrix_expression<E1> &e1,
|
||
const vector_expression<E2> &e2,
|
||
C);
|
||
|
||
template<class E1, class E2>
|
||
void inplace_solve (E1 &e1,
|
||
const matrix_expression<E2> &e2,
|
||
vector_tag,
|
||
lower_tag);
|
||
template<class E1, class E2>
|
||
void inplace_solve (E1 &e1,
|
||
const matrix_expression<E2> &e2,
|
||
vector_tag,
|
||
upper_tag);
|
||
template<class E1, class E2>
|
||
void inplace_solve (E1 &e1,
|
||
const matrix_expression<E2> &e2,
|
||
vector_tag,
|
||
unit_lower_tag);
|
||
template<class E1, class E2>
|
||
void inplace_solve (E1 &e1,
|
||
const matrix_expression<E2> &e2,
|
||
vector_tag,
|
||
unit_upper_tag);
|
||
|
||
template<class E1, class E2, class C>
|
||
typename matrix_vector_solve_traits<E1, E2>::result_type
|
||
solve (const vector_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2,
|
||
C);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>solve</code> solves a linear equation for lower or upper
|
||
(unit) triangular matrices.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header triangular.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<li><code>E1</code> is a model of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a>
|
||
or <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>
|
||
or <a href="expression.htm#matrix_expression">Matrix
|
||
Expression</a>.</li>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<dir>
|
||
<li><code>e1 ().size1 () == e1 ().size2 ()</code> </li>
|
||
<li><code>e1 ().size2 () == e2 ().size ()</code> </li>
|
||
<li><code>e1 ().size () == e2 ().size1 ()</code> </li>
|
||
<li><code>e2 ().size1 () == e2 ().size2 ()</code></li>
|
||
</dir>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Quadratic depending from the size of the matrix expression.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
matrix<double > m (3, 3), v (3);
|
||
for (int i = 0; i < std::min (m.size1 (), v.size ()); ++ i) {
|
||
for (int j = 0; j <= i; ++ j)
|
||
m (i, j) = 3 * i + j;
|
||
v (i) = i
|
||
}
|
||
|
||
std::cout << solve (m, v, lower_tag ()) << std::endl;
|
||
std::cout << solve (v, m, lower_tag ()) << std::endl;
|
||
}</pre>
|
||
|
||
<h2><a name="matrix_matrix_operations"></a>Matrix Matrix
|
||
Operations</h2>
|
||
|
||
<h3>Binary Operation Description</h3>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p>The templated class <code>matrix_matrix_binary<E1, E2,
|
||
F> </code>describes a binary matrix operation.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Template parameters</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Parameter </th>
|
||
<th>Description </th>
|
||
<th>Default </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>E1</code> </td>
|
||
<td>The type of the first matrix expression. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>E2</code></td>
|
||
<td>The type of the second matrix expression. </td>
|
||
<td> </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>F</code></td>
|
||
<td>The type of the operation.</td>
|
||
<td> </td>
|
||
</tr>
|
||
</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<matrix_matrix_binary<E1, E2,
|
||
F> ></code>.</p>
|
||
|
||
<h4>Members</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Member </th>
|
||
<th>Description </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>matrix_matrix_binary (const expression1_type
|
||
&e1, const expression2_type &e2)</code> </td>
|
||
<td>Constructs a description of the expression.</td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>size_type size1 () const</code></td>
|
||
<td>Returns the number of rows. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>size_type size2 () const</code></td>
|
||
<td>Returns the number of columns. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reference operator () (size_type i,
|
||
size_type j) const</code></td>
|
||
<td>Returns the value of the <code>j</code>-th element in
|
||
the<code> i</code>-th row. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator1 begin1 () const</code></td>
|
||
<td>Returns a <code>const_iterator1</code> pointing to
|
||
the beginning of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator1 end1 () const</code></td>
|
||
<td>Returns a <code>const_iterator1</code> pointing to
|
||
the end of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator2 begin2 () const</code></td>
|
||
<td>Returns a <code>const_iterator2</code> pointing to
|
||
the beginning of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_iterator2 end2 () const</code></td>
|
||
<td>Returns a <code>const_iterator2</code> pointing to
|
||
the end of the expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator1</code>
|
||
pointing to the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator1 rend1 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator1</code>
|
||
pointing to the end of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator2</code>
|
||
pointing to the beginning of the reversed expression. </td>
|
||
</tr>
|
||
<tr>
|
||
<td><code>const_reverse_iterator2 rend2 () const</code></td>
|
||
<td>Returns a <code>const_reverse_iterator2</code>
|
||
pointing to the end of the reversed expression. </td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> template<class E1, class E2, class F>
|
||
class matrix_matrix_binary:
|
||
public matrix_expression<matrix_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 matrix_matrix_binary<E1, E2, F> const_closure_type;
|
||
typedef unknown_orientation_tag orientation_category;
|
||
typedef typename E1::const_iterator1 const_iterator11_type;
|
||
typedef typename E1::const_iterator2 const_iterator12_type;
|
||
typedef typename E2::const_iterator1 const_iterator21_type;
|
||
typedef typename E2::const_iterator2 const_iterator22_type;
|
||
typedef unknown_storage_tag storage_category;
|
||
|
||
// Construction and destruction
|
||
matrix_matrix_binary ();
|
||
matrix_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;
|
||
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
|
||
typedef reverse_iterator_base2<const_iterator2> const_reverse_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 simply are pointers.
|
||
|
||
class const_iterator1:
|
||
public container_const_reference<matrix_matrix_binary>,
|
||
public random_access_iterator_base<const_iterator1, value_type> {
|
||
public:
|
||
typedef typename restrict_traits<typename E1::const_iterator1::iterator_category,
|
||
typename E2::const_iterator2::iterator_category>::iterator_category iterator_category;
|
||
typedef typename matrix_matrix_binary::difference_type difference_type;
|
||
typedef typename matrix_matrix_binary::value_type value_type;
|
||
typedef typename matrix_matrix_binary::const_reference reference;
|
||
typedef typename matrix_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 matrix_matrix_binary &mmb, const const_iterator11_type &it1, const const_iterator22_type &it2);
|
||
|
||
// Random access specialization
|
||
value_type dereference (dense_random_access_iterator_tag) const;
|
||
|
||
// Packed bidirectional specialization
|
||
value_type dereference (packed_bidirectional_iterator_tag) const;
|
||
|
||
// Sparse bidirectional specialization
|
||
value_type dereference (sparse_bidirectional_iterator_tag) const;
|
||
|
||
// 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<matrix_matrix_binary>,
|
||
public random_access_iterator_base<const_iterator2, value_type> {
|
||
public:
|
||
typedef typename restrict_traits<typename E1::const_iterator1::iterator_category,
|
||
typename E2::const_iterator2::iterator_category>::iterator_category iterator_category;
|
||
typedef typename matrix_matrix_binary::difference_type difference_type;
|
||
typedef typename matrix_matrix_binary::value_type value_type;
|
||
typedef typename matrix_matrix_binary::const_reference reference;
|
||
typedef typename matrix_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 matrix_matrix_binary &mmb, const const_iterator11_type &it1, const const_iterator22_type &it2);
|
||
|
||
// Random access specialization
|
||
value_type dereference (dense_random_access_iterator_tag) const;
|
||
|
||
// Packed bidirectional specialization
|
||
value_type dereference (packed_bidirectional_iterator_tag) const;
|
||
|
||
// Sparse bidirectional specialization
|
||
value_type dereference (sparse_bidirectional_iterator_tag) const;
|
||
|
||
// 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 Operations</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class T1, class E1, class T2, class E2>
|
||
struct matrix_matrix_binary_traits {
|
||
typedef unknown_orientation_tag dispatch_category;
|
||
typedef typename promote_traits<T1, T2>::promote_type promote_type;
|
||
typedef matrix_matrix_binary<typename E1::const_closure_type,
|
||
typename E2::const_closure_type,
|
||
matrix_matrix_prod<T1, T2, promote_type> > expression_type;
|
||
typedef expression_type result_type;
|
||
};
|
||
|
||
template<class E1, class E2>
|
||
typename matrix_matrix_binary_traits<typename E1::value_type, E1,
|
||
typename E2::value_type, E2>::result_type
|
||
prod (const matrix_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2,
|
||
unknown_orientation_tag);
|
||
|
||
// Dispatcher
|
||
template<class E1, class E2>
|
||
typename matrix_matrix_binary_traits<typename E1::value_type, E1,
|
||
typename E2::value_type, E2>::result_type
|
||
prod (const matrix_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2);
|
||
|
||
template<class E1, class E2>
|
||
typename matrix_matrix_binary_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
prec_prod (const matrix_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2,
|
||
unknown_orientation_tag);
|
||
|
||
// Dispatcher
|
||
template<class E1, class E2>
|
||
typename matrix_matrix_binary_traits<typename type_traits<typename E1::value_type>::precision_type, E1,
|
||
typename type_traits<typename E2::value_type>::precision_type, E2>::result_type
|
||
prec_prod (const matrix_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2);
|
||
|
||
template<class M, class E1, class E2>
|
||
M
|
||
prod (const matrix_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2);
|
||
|
||
template<class M, class E1, class E2>
|
||
M
|
||
prec_prod (const matrix_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>prod</code> computes the product of the matrix
|
||
expressions.<code> prec_prod</code> computes the double precision
|
||
product of the matrix expressions.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header matrix_expression.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<li><code>E1</code> is a model of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a>.
|
||
</li>
|
||
<li><code>E2</code> is a model of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a>.</li>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<dir>
|
||
<li><code>e1 ().size2 () == e2 ().size1 ()</code></li>
|
||
</dir>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Cubic depending from the size of the matrix expression.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
matrix<double > m1 (3, 3), m2 (3, 3);
|
||
for (int i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i)
|
||
for (int j = 0; j < std::min (m1.size2 (), m2.size2 ()); ++ j)
|
||
m1 (i, j) = m2 (i, j) = 3 * i + j;
|
||
|
||
std::cout << prod (m1, m2) << std::endl;
|
||
}</pre>
|
||
|
||
<h3>Triangular Solvers</h3>
|
||
|
||
<h4>Prototypes</h4>
|
||
|
||
<pre><code> template<class E1, class E2>
|
||
struct matrix_matrix_solve_traits {
|
||
typedef typename promote_traits<typename E1::value_type, typename E2::value_type>::promote_type promote_type;
|
||
typedef matrix<promote_type> result_type;
|
||
};
|
||
|
||
template<class E1, class E2>
|
||
void inplace_solve (const matrix_expression<E1> &e1,
|
||
E2 &e2,
|
||
lower_tag,
|
||
matrix_tag);
|
||
template<class E1, class E2>
|
||
void inplace_solve (const matrix_expression<E1> &e1,
|
||
E2 &e2,
|
||
upper_tag,
|
||
matrix_tag);
|
||
template<class E1, class E2>
|
||
void inplace_solve (const matrix_expression<E1> &e1,
|
||
E2 &e2,
|
||
unit_lower_tag,
|
||
matrix_tag);
|
||
template<class E1, class E2>
|
||
void inplace_solve (const matrix_expression<E1> &e1,
|
||
E2 &e2,
|
||
unit_upper_tag,
|
||
matrix_tag);
|
||
|
||
template<class E1, class E2, class C>
|
||
typename matrix_matrix_solve_traits<E1, E2>::result_type
|
||
solve (const matrix_expression<E1> &e1,
|
||
const matrix_expression<E2> &e2,
|
||
C);</code></pre>
|
||
|
||
<h4>Description</h4>
|
||
|
||
<p><code>solve</code> solves a linear equation for lower or upper
|
||
(unit) triangular matrices.</p>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header triangular.hpp.</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<dir>
|
||
<li><code>E1</code> is a model of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a>.
|
||
</li>
|
||
<li><code>E2</code> is a model of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a>.</li>
|
||
</dir>
|
||
|
||
<h4>Preconditions</h4>
|
||
|
||
<dir>
|
||
<li><code>e1 ().size1 () == e1 ().size2 ()</code> </li>
|
||
<li><code>e1 ().size2 () == e2 ().size1 ()</code></li>
|
||
</dir>
|
||
|
||
<h4>Complexity</h4>
|
||
|
||
<p>Cubic depending from the size of the matrix expressions.</p>
|
||
|
||
<h4>Examples</h4>
|
||
|
||
<pre>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
matrix<double > m1 (3, 3), m2 (3, 3);
|
||
for (int i = 0; i < std::min (m1.size1 (), m2.size1 ()); ++ i)
|
||
for (int j = 0; j <= i; ++ j)
|
||
m1 (i, j) = m2 (i, j) = 3 * i + j;
|
||
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||
std::cout << solve (m1, m2, lower_tag ()) << 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>
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