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1414 lines
104 KiB
HTML
1414 lines
104 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<html>
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<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
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<meta name="GENERATOR" content="Microsoft FrontPage Express 2.0">
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<title>Matrix Proxies</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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Matrix Proxies</h1>
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<h2><a name="matrix_row"></a>
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Matrix Row</h2>
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<h4>Description</h4>
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<p>The templated class <code>matrix_row<M> </code>allows addressing
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a row of a matrix.</p>
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<h4>Example</h4>
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<pre>#include <boost/numeric/ublas/matrix.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> for (unsigned i = 0; i < m.size1 (); ++ i) {<br> matrix_row<matrix<double> > mr (m, i);<br> for (unsigned j = 0; j < mr.size (); ++ j)<br> mr (j) = 3 * i + j;<br> std::cout << mr << std::endl;<br> }<br>}</pre>
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<h4>Definition</h4>
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<p>Defined in the header matrix_proxy.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1">
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<tbody>
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<tr>
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<th>Parameter </th>
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<th>Description </th>
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<th>Default </th>
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</tr>
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<tr>
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<td><code>M</code> </td>
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<td>The type of matrix referenced. </td>
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<td> </td>
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</tr>
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</tbody>
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</table>
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<h4>Model of</h4>
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<p><a href="expression.htm#vector_expression">Vector Expression</a>
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. </p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a href="expression.htm#vector_expression">
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Vector Expression</a>
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.</p>
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<h4>Public base classes</h4>
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<p><code>vector_expression<matrix_row<M> ></code> </p>
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<h4>Members</h4>
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<table border="1">
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<tbody>
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<tr>
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<th>Member </th>
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<th>Description </th>
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</tr>
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<tr>
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<td><code>matrix_row (matrix_type &data, size_type i)</code></td>
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<td>Constructs a sub vector.</td>
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</tr>
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<tr>
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<td><code>size_type size () const</code></td>
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<td>Returns the size of the sub vector.</td>
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</tr>
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<tr>
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<td><code>const_reference operator () (size_type i) const</code></td>
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<td>Returns the value of the <code>i</code>-th element. </td>
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</tr>
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<tr>
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<td><code>reference operator () (size_type i)</code></td>
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<td>Returns a reference of the <code>i</code>-th element.
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</td>
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</tr>
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<tr>
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<td><code>matrix_row &operator = (const matrix_row &mr)</code></td>
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<td>The assignment operator.</td>
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</tr>
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<tr>
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<td><code>matrix_row &assign_temporary (matrix_row &mr)</code></td>
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<td>Assigns a temporary. May change the matrix row <code>mr</code>
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.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_row &operator = (const vector_expression<AE>
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&ae)</code></td>
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<td>The extended assignment operator.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_row &assign (const vector_expression<AE>
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&ae)</code></td>
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<td>Assigns a vector expression to the sub vector. Left
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and right hand side of the assignment should be independent.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_row &operator += (const vector_expression<AE>
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&ae)</code></td>
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<td>A computed assignment operator. Adds the vector expression
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to the sub vector.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_row &plus_assign (const vector_expression<AE>
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&ae)</code></td>
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<td>Adds a vector expression to the sub vector. Left and
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right hand side of the assignment should be independent.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_row &operator -= (const vector_expression<AE>
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&ae)</code></td>
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<td>A computed assignment operator. Subtracts the vector
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expression from the sub vector.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_row &minus_assign (const vector_expression<AE>
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&ae)</code></td>
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<td>Subtracts a vector expression from the sub vector. Left
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and right hand side of the assignment should be independent.</td>
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</tr>
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<tr>
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<td><code>template<class AT><br>
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matrix_row &operator *= (const AT &at)</code></td>
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<td>A computed assignment operator. Multiplies the sub vector
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with a scalar.</td>
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</tr>
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<tr>
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<td><code>template<class AT><br>
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matrix_row &operator /= (const AT &at)</code></td>
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<td>A computed assignment operator. Divides the sub vector
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through a scalar.</td>
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</tr>
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<tr>
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<td><code>void swap (matrix_row &mr)</code></td>
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<td>Swaps the contents of the sub vectors. </td>
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</tr>
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<tr>
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<td><code>const_iterator begin () const</code></td>
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<td>Returns a <code>const_iterator</code> pointing to the
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beginning of the <code>matrix_row</code>. </td>
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</tr>
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<tr>
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<td><code>const_iterator end () const</code></td>
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<td>Returns a <code>const_iterator</code> pointing to the
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end of the <code>matrix_row</code>. </td>
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</tr>
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<tr>
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<td><code>iterator begin () </code></td>
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<td>Returns a <code>iterator</code> pointing to the beginning
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of the <code>matrix_row</code>. </td>
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</tr>
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<tr>
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<td><code>iterator end () </code></td>
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<td>Returns a <code>iterator</code> pointing to the end
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of the <code>matrix_row</code>. </td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator rbegin () const</code></td>
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<td>Returns a <code>const_reverse_iterator</code> pointing
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to the beginning of the reversed <code>matrix_row</code>. </td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator rend () const</code></td>
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<td>Returns a <code>const_reverse_iterator</code> pointing
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to the end of the reversed <code>matrix_row</code>. </td>
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</tr>
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<tr>
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<td><code>reverse_iterator rbegin () </code></td>
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<td>Returns a <code>reverse_iterator</code> pointing to
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the beginning of the reversed <code>matrix_row</code>. </td>
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</tr>
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<tr>
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<td><code>reverse_iterator rend () </code></td>
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<td>Returns a <code>reverse_iterator</code> pointing to
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the end of the reversed <code>matrix_row</code>. </td>
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</tr>
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</tbody>
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</table>
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<h4>Interface</h4>
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<pre><code> // Matrix based row vector class<br> template<class M><br> class matrix_row:<br> public vector_expression<matrix_row<M> > {<br> public:<br> typedef const M const_matrix_type;<br> typedef M matrix_type;<br> typedef typename M::size_type size_type;<br> typedef typename M::difference_type difference_type;<br> typedef typename M::value_type value_type;<br> typedef typename M::const_reference const_reference;<br> typedef typename M::reference reference;<br> typedef typename M::const_pointer const_pointer;<br> typedef typename M::pointer pointer;<br> typedef const vector_const_reference<const matrix_row<matrix_type> > const_closure_type;<br> typedef vector_reference<matrix_row<matrix_type> > closure_type;<br> typedef typename M::const_iterator2 const_iterator_type;<br> typedef typename M::iterator2 iterator_type;<br> typedef typename storage_restrict_traits<typename M::storage_category,<br> dense_proxy_tag>::storage_category storage_category;<br><br> // Construction and destruction<br> matrix_row ();<br> matrix_row (matrix_type &data, size_type i);<br><br> // Accessors<br> size_type size () const;<br> const_matrix_type &data () const;<br> matrix_type &data ();<br><br><br> // Element access<br> const_reference operator () (size_type j) const;<br> reference operator () (size_type j);<br><br> const_reference operator [] (size_type j) const;<br> reference operator [] (size_type j);<br><br> // Assignment<br> matrix_row &operator = (const matrix_row &mr);<br> matrix_row &assign_temporary (matrix_row &mr);<br> template<class AE><br> matrix_row &operator = (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_row &assign (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_row &operator += (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_row &plus_assign (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_row &operator -= (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_row &minus_assign (const vector_expression<AE> &ae);<br> template<class AT><br> matrix_row &operator *= (const AT &at);<br> template<class AT><br> matrix_row &operator /= (const AT &at);<br><br> // Swapping<br> void swap (matrix_row &mr);<br> friend void swap (matrix_row &mr1, matrix_row &mr2);<br><br> class const_iterator;<br> class iterator;<br><br> // Element lookup<br> const_iterator find_first (size_type j) const;<br> iterator find_first (size_type j);<br> const_iterator find_last (size_type j) const;<br> iterator find_last (size_type j);<br><br> // Iterators simply are pointers.<br><br> class const_iterator:<br> public container_const_reference<matrix_row>,<br> public random_access_iterator_base<const_iterator, value_type> {<br> public:<br> typedef typename const_iterator_type::iterator_category iterator_category;<br> typedef typename const_iterator_type::difference_type difference_type;<br> typedef typename const_iterator_type::value_type value_type;<br> typedef typename const_iterator_type::reference reference;<br> typedef typename const_iterator_type::pointer pointer;<br><br> // Construction and destruction<br> const_iterator ();<br> const_iterator (const matrix_row &mr, const const_iterator_type &it);<br> const_iterator (const iterator &it);<br><br> // Arithmetic<br> const_iterator &operator ++ ();<br> const_iterator &operator -- ();<br> const_iterator &operator += (difference_type n);<br> const_iterator &operator -= (difference_type n);<br> difference_type operator - (const const_iterator &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> // Index<br> size_type index () const;<br><br> // Assignment <br> const_iterator &operator = (const const_iterator &it);<br><br> // Comparison<br> bool operator == (const const_iterator &it) const;<br> bool operator <(const const_iterator &it) const;<br> };<br><br> const_iterator begin () const;<br> const_iterator end () const;<br><br> class iterator:<br> public container_reference<matrix_row>,<br> public random_access_iterator_base<iterator, value_type> {<br> public:<br> typedef typename iterator_type::iterator_category iterator_category;<br> typedef typename iterator_type::difference_type difference_type;<br> typedef typename iterator_type::value_type value_type;<br> typedef typename iterator_type::reference reference;<br> typedef typename iterator_type::pointer pointer;<br><br> // Construction and destruction<br> iterator ();<br> iterator (matrix_row &mr, const iterator_type &it);<br><br> // Arithmetic<br> iterator &operator ++ ();<br> iterator &operator -- ();<br> iterator &operator += (difference_type n);<br> iterator &operator -= (difference_type n);<br> difference_type operator - (const iterator &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> // Index<br> size_type index () const;<br><br> // Assignment <br> iterator &operator = (const iterator &it);<br><br> // Comparison<br> bool operator == (const iterator &it) const;<br> bool operator <(const iterator &it) const;<br> };<br><br> iterator begin ();<br> iterator end ();<br><br> // Reverse iterator<br><br> typedef reverse_iterator_base<const_iterator> const_reverse_iterator;<br><br> const_reverse_iterator rbegin () const;<br> const_reverse_iterator rend () const;<br><br> typedef reverse_iterator_base<iterator> reverse_iterator;<br><br> reverse_iterator rbegin ();<br> reverse_iterator rend ();<br> };</code></pre>
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<h3>Projections</h3>
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<h4>Prototypes</h4>
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<pre><code> template<class M><br> matrix_row<M> row (M &data, std::size_t i);<br> template<class M><br> const matrix_row<const M> row (const M &data, std::size_t i);</code></pre>
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<h4>Description</h4>
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<p>The free <code>row</code> functions support the construction of matrix
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rows.</p>
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<h4>Definition</h4>
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<p>Defined in the header matrix_proxy.hpp.</p>
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<h4>Type requirements</h4>
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<dir> <li><code>M</code> is a model of <a href="expression.htm#matrix_expression">
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Matrix Expression</a>
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.</li>
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</dir>
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<h4>Preconditions</h4>
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<ul type="Disc">
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<li><code>i < data.size1 ()</code></li>
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</ul>
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<h4>Complexity</h4>
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<p>Linear depending from the size of the row.</p>
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<h4>Examples</h4>
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<pre>#include <boost/numeric/ublas/matrix.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> for (unsigned i = 0; i < m.size1 (); ++ i) {<br> for (unsigned j = 0; j < m.size2 (); ++ j)<br> row (m, i) (j) = 3 * i + j;<br> std::cout << row (m, i) << std::endl;<br> }<br>}<br></pre>
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<h2><a name="matrix_column"></a>
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Matrix Column</h2>
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<h4>Description</h4>
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<p>The templated class <code>matrix_column<M> </code>allows addressing
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a column of a matrix.</p>
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<h4>Example</h4>
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<pre>#include <boost/numeric/ublas/matrix.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> for (unsigned j = 0; j < m.size2 (); ++ j) {<br> matrix_column<matrix<double> > mc (m, j);<br> for (unsigned i = 0; i < mc.size (); ++ i)<br> mc (i) = 3 * i + j;<br> std::cout << mc << std::endl;<br> }<br>}<br></pre>
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<h4>Definition</h4>
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<p>Defined in the header matrix_proxy.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1">
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<tbody>
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<tr>
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<th>Parameter </th>
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<th>Description </th>
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<th>Default </th>
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</tr>
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<tr>
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<td><code>M</code> </td>
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<td>The type of matrix referenced. </td>
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<td> </td>
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</tr>
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</tbody>
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</table>
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<h4>Model of</h4>
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<p><a href="expression.htm#vector_expression">Vector Expression</a>
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. </p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a href="expression.htm#vector_expression">
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Vector Expression</a>
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.</p>
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<h4>Public base classes</h4>
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<p><code>vector_expression<matrix_column<M> ></code> </p>
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<h4>Members</h4>
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<table border="1">
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<tbody>
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<tr>
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<th>Member </th>
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<th>Description </th>
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</tr>
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<tr>
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<td><code>matrix_column (matrix_type &data, size_type
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j)</code></td>
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<td>Constructs a sub vector.</td>
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</tr>
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<tr>
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<td><code>size_type size () const</code></td>
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<td>Returns the size of the sub vector.</td>
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</tr>
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<tr>
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<td><code>const_reference operator () (size_type i) const</code></td>
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<td>Returns the value of the <code>i</code>-th element. </td>
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</tr>
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<tr>
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<td><code>reference operator () (size_type i)</code></td>
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<td>Returns a reference of the <code>i</code>-th element.
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</td>
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</tr>
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<tr>
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<td><code>matrix_column &operator = (const matrix_column
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&mc)</code></td>
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<td>The assignment operator.</td>
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</tr>
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<tr>
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<td><code>matrix_column &assign_temporary (matrix_column
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&mc)</code></td>
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<td>Assigns a temporary. May change the matrix column <code>mc</code>
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.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_column &operator = (const vector_expression<AE>
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&ae)</code></td>
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<td>The extended assignment operator.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_column &assign (const vector_expression<AE>
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&ae)</code></td>
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<td>Assigns a vector expression to the sub vector. Left
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and right hand side of the assignment should be independent.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_column &operator += (const vector_expression<AE>
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&ae)</code></td>
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<td>A computed assignment operator. Adds the vector expression
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to the sub vector.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_column &plus_assign (const vector_expression<AE>
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&ae)</code></td>
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<td>Adds a vector expression to the sub vector. Left and
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right hand side of the assignment should be independent.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_column &operator -= (const vector_expression<AE>
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&ae)</code></td>
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<td>A computed assignment operator. Subtracts the vector
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expression from the sub vector.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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matrix_column &minus_assign (const vector_expression<AE>
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&ae)</code></td>
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<td>Subtracts a vector expression from the sub vector. Left
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and right hand side of the assignment should be independent.</td>
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</tr>
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<tr>
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<td><code>template<class AT><br>
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matrix_column &operator *= (const AT &at)</code></td>
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<td>A computed assignment operator. Multiplies the sub vector
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with a scalar.</td>
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</tr>
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<tr>
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<td><code>template<class AT><br>
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matrix_column &operator /= (const AT &at)</code></td>
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<td>A computed assignment operator. Divides the sub vector
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through a scalar.</td>
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</tr>
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<tr>
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<td><code>void swap (matrix_column &mc)</code></td>
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<td>Swaps the contents of the sub vectors. </td>
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</tr>
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<tr>
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<td><code>const_iterator begin () const</code></td>
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<td>Returns a <code>const_iterator</code> pointing to the
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beginning of the <code>matrix_column</code>. </td>
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</tr>
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<tr>
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<td><code>const_iterator end () const</code></td>
|
|
<td>Returns a <code>const_iterator</code> pointing to the
|
|
end of the <code>matrix_column</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator begin () </code></td>
|
|
<td>Returns a <code>iterator</code> pointing to the beginning
|
|
of the <code>matrix_column</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator end () </code></td>
|
|
<td>Returns a <code>iterator</code> pointing to the end
|
|
of the <code>matrix_column</code>. </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 <code>matrix_column</code>. </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 <code>matrix_column</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator rbegin () </code></td>
|
|
<td>Returns a <code>reverse_iterator</code> pointing to
|
|
the beginning of the reversed <code>matrix_column</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator rend () </code></td>
|
|
<td>Returns a <code>reverse_iterator</code> pointing to
|
|
the end of the reversed <code>matrix_column</code>. </td>
|
|
</tr>
|
|
|
|
</tbody>
|
|
</table>
|
|
|
|
<h4>Interface</h4>
|
|
|
|
<pre><code> // Matrix based column vector class<br> template<class M><br> class matrix_column:<br> public vector_expression<matrix_column<M> > {<br> public: <br> typedef const M const_matrix_type;<br> typedef M matrix_type;<br> typedef typename M::size_type size_type;<br> typedef typename M::difference_type difference_type;<br> typedef typename M::value_type value_type;<br> typedef typename M::const_reference const_reference;<br> typedef typename M::reference reference;<br> typedef typename M::const_pointer const_pointer;<br> typedef typename M::pointer pointer;<br> typedef const vector_const_reference<const matrix_column<matrix_type> > const_closure_type;<br> typedef vector_reference<matrix_column<matrix_type> > closure_type;<br> typedef typename M::const_iterator1 const_iterator_type;<br> typedef typename M::iterator1 iterator_type;<br> typedef typename storage_restrict_traits<typename M::storage_category,<br> dense_proxy_tag>::storage_category storage_category;<br><br> // Construction and destruction<br> matrix_column ();<br> matrix_column (matrix_type &data, size_type j);<br><br> // Accessors<br> size_type size () const;<br> const_matrix_type &data () const;<br> matrix_type &data ();<br><br><br> // Element access<br> const_reference operator () (size_type i) const;<br> reference operator () (size_type i);<br><br> const_reference operator [] (size_type i) const;<br> reference operator [] (size_type i);<br><br> // Assignment<br> matrix_column &operator = (const matrix_column &mc);<br> matrix_column &assign_temporary (matrix_column &mc);<br> template<class AE><br> matrix_column &operator = (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_column &assign (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_column &operator += (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_column &plus_assign (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_column &operator -= (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_column &minus_assign (const vector_expression<AE> &ae);<br> template<class AT><br> matrix_column &operator *= (const AT &at);<br> template<class AT><br> matrix_column &operator /= (const AT &at);<br><br> // Swapping<br> void swap (matrix_column &mc);<br> friend void swap (matrix_column &mc1, matrix_column &mc2);<br><br> class const_iterator;<br> class iterator;<br><br> // Element lookup<br> const_iterator find_first (size_type i) const;<br> iterator find_first (size_type i);<br> const_iterator find_last (size_type i) const;<br> iterator find_last (size_type i);<br><br> // Iterators simply are pointers.<br><br> class const_iterator:<br> public container_const_reference<matrix_column>,<br> public random_access_iterator_base<const_iterator, value_type> {<br> public:<br> typedef typename const_iterator_type::iterator_category iterator_category;<br> typedef typename const_iterator_type::difference_type difference_type;<br> typedef typename const_iterator_type::value_type value_type;<br> typedef typename const_iterator_type::reference reference;<br> typedef typename const_iterator_type::pointer pointer;<br><br> // Construction and destruction<br> const_iterator ();<br> const_iterator (const matrix_column &mc, const const_iterator_type &it);<br> const_iterator (const iterator &it);<br><br> // Arithmetic<br> const_iterator &operator ++ ();<br> const_iterator &operator -- ();<br> const_iterator &operator += (difference_type n);<br> const_iterator &operator -= (difference_type n);<br> difference_type operator - (const const_iterator &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> // Index<br> size_type index () const;<br><br> // Assignment<br> const_iterator &operator = (const const_iterator &it);<br><br> // Comparison<br> bool operator == (const const_iterator &it) const;<br> bool operator <(const const_iterator &it) const;<br> };<br><br> const_iterator begin () const;<br> const_iterator end () const;<br><br> class iterator:<br> public container_reference<matrix_column>,<br> public random_access_iterator_base<iterator, value_type> {<br> public:<br> typedef typename iterator_type::iterator_category iterator_category;<br> typedef typename iterator_type::difference_type difference_type;<br> typedef typename iterator_type::value_type value_type;<br> typedef typename iterator_type::reference reference;<br> typedef typename iterator_type::pointer pointer;<br><br> // Construction and destruction<br> iterator ();<br> iterator (matrix_column &mc, const iterator_type &it);<br><br> // Arithmetic<br> iterator &operator ++ ();<br> iterator &operator -- ();<br> iterator &operator += (difference_type n);<br> iterator &operator -= (difference_type n);<br> difference_type operator - (const iterator &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> // Index<br> size_type index () const;<br><br> // Assignment <br> iterator &operator = (const iterator &it);<br><br> // Comparison<br> bool operator == (const iterator &it) const;<br> bool operator <(const iterator &it) const;<br> };<br><br> iterator begin ();<br> iterator end ();<br><br> // Reverse iterator<br><br> typedef reverse_iterator_base<const_iterator> const_reverse_iterator;<br><br> const_reverse_iterator rbegin () const;<br> const_reverse_iterator rend () const;<br><br> typedef reverse_iterator_base<iterator> reverse_iterator;<br><br> reverse_iterator rbegin ();<br> reverse_iterator rend ();<br> };</code></pre>
|
|
|
|
<h3>Projections</h3>
|
|
|
|
<h4>Prototypes</h4>
|
|
|
|
<pre><code> template<class M><br> matrix_column<M> column (M &data, std::size_t j);<br> template<class M><br> const matrix_column<const M> column (const M &data, std::size_t j);</code></pre>
|
|
|
|
<h4>Description</h4>
|
|
|
|
<p>The free <code>column</code> functions support the construction of matrix
|
|
columns.</p>
|
|
|
|
<h4>Definition</h4>
|
|
|
|
<p>Defined in the header matrix_proxy.hpp.</p>
|
|
|
|
<h4>Type requirements</h4>
|
|
|
|
<dir> <li><code>M</code> is a model of <a href="expression.htm#matrix_expression">
|
|
Matrix Expression</a>
|
|
.</li>
|
|
</dir>
|
|
|
|
<h4>Preconditions</h4>
|
|
|
|
<ul type="Disc">
|
|
<li><code>j < data.size2 ()</code></li>
|
|
|
|
</ul>
|
|
|
|
<h4>Complexity</h4>
|
|
|
|
<p>Linear depending from the size of the column.</p>
|
|
|
|
<h4>Examples</h4>
|
|
|
|
<pre>#include <boost/numeric/ublas/matrix.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> for (unsigned j = 0; j < m.size2 (); ++ j) {<br> for (unsigned i = 0; i < m.size1 (); ++ i)<br> column (m, j) (i) = 3 * i + j;<br> std::cout << column (m, j) << std::endl;<br> }<br>}<br></pre>
|
|
<h2><a name="vector_range"></a>
|
|
Vector Range</h2>
|
|
|
|
<h4>Description</h4>
|
|
|
|
<p>The templated class <code>matrix_vector_range<M> </code>allows addressing
|
|
a sub vector of a matrix.</p>
|
|
|
|
<h4>Example</h4>
|
|
|
|
<pre>#include <boost/numeric/ublas/matrix.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> for (unsigned i = 0; i < m.size1 (); ++ i)<br> for (unsigned j = 0; j < m.size2 (); ++ j)<br> m (i, j) = 3 * i + j;<br><br> matrix_vector_range<matrix<double> > mvr (m, range (0, 3), range (0, 3));<br> std::cout << mvr << std::endl;<br>}<br></pre>
|
|
<h4>Definition</h4>
|
|
|
|
<p>Defined in the header matrix_proxy.hpp.</p>
|
|
|
|
<h4>Template parameters</h4>
|
|
|
|
<table border="1">
|
|
<tbody>
|
|
<tr>
|
|
<th>Parameter </th>
|
|
<th>Description </th>
|
|
<th>Default </th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>M</code> </td>
|
|
<td>The type of matrix referenced. </td>
|
|
<td> </td>
|
|
</tr>
|
|
|
|
</tbody>
|
|
</table>
|
|
|
|
<h4>Model of</h4>
|
|
|
|
<p><a href="expression.htm#vector_expression">Vector Expression</a>
|
|
.</p>
|
|
|
|
<h4>Type requirements</h4>
|
|
|
|
<p>None, except for those imposed by the requirements of <a href="expression.htm#vector_expression">
|
|
Vector Expression</a>
|
|
.</p>
|
|
|
|
<h4>Public base classes</h4>
|
|
|
|
<p><code>vector_expression<matrix_vector_range<M> ></code> </p>
|
|
|
|
<h4>Members</h4>
|
|
|
|
<table border="1">
|
|
<tbody>
|
|
<tr>
|
|
<th>Member </th>
|
|
<th>Description </th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>matrix_vector_range (matrix_type &data,<br>
|
|
const range &r1, const range &r2)</code></td>
|
|
<td>Constructs a sub vector.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size () const</code></td>
|
|
<td>Returns the size of the sub vector.</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>reference operator () (size_type i)</code></td>
|
|
<td>Returns a reference of the <code>i</code>-th element.
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>matrix_vector_range &operator = (const matrix_vector_range
|
|
&mvr)</code></td>
|
|
<td>The assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>matrix_vector_range &assign_temporary (matrix_vector_range
|
|
&mvr)</code></td>
|
|
<td>Assigns a temporary. May change the matrix vector range
|
|
<code>mvr</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_vector_range &operator = (const vector_expression<AE>
|
|
&ae)</code></td>
|
|
<td>The extended assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_vector_range &assign (const vector_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Assigns a vector expression to the sub vector. Left
|
|
and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_vector_range &operator += (const vector_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Adds the vector expression
|
|
to the sub vector.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_vector_range &plus_assign (const vector_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Adds a vector expression to the sub vector. Left and
|
|
right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_vector_range &operator -= (const vector_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Subtracts the vector
|
|
expression from the sub vector.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_vector_range &minus_assign (const vector_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Subtracts a vector expression from the sub vector. Left
|
|
and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
matrix_vector_range &operator *= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Multiplies the sub vector
|
|
with a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
matrix_vector_range &operator /= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Divides the sub vector
|
|
through a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void swap (matrix_vector_range &mvr)</code></td>
|
|
<td>Swaps the contents of the sub vectors. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator begin () const</code></td>
|
|
<td>Returns a <code>const_iterator</code> pointing to the
|
|
beginning of the <code>matrix_vector_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator end () const</code></td>
|
|
<td>Returns a <code>const_iterator</code> pointing to the
|
|
end of the <code>matrix_vector_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator begin () </code></td>
|
|
<td>Returns a <code>iterator</code> pointing to the beginning
|
|
of the <code>matrix_vector_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator end () </code></td>
|
|
<td>Returns a <code>iterator</code> pointing to the end
|
|
of the <code>matrix_vector_range</code>. </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 <code>matrix_vector_range</code>. </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 <code>matrix_vector_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator rbegin () </code></td>
|
|
<td>Returns a <code>reverse_iterator</code> pointing to
|
|
the beginning of the reversed <code>matrix_vector_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator rend () </code></td>
|
|
<td>Returns a <code>reverse_iterator</code> pointing to
|
|
the end of the reversed <code>matrix_vector_range</code>. </td>
|
|
</tr>
|
|
|
|
</tbody>
|
|
</table>
|
|
|
|
<h4>Interface</h4>
|
|
|
|
<pre><code> // Matrix based vector range class<br> template<class M><br> class matrix_vector_range:<br> public vector_expression<matrix_vector_range<M> > {<br> public: <br> typedef const M const_matrix_type;<br> typedef M matrix_type;<br> typedef typename M::size_type size_type;<br> typedef typename M::difference_type difference_type;<br> typedef typename M::value_type value_type;<br> typedef typename M::const_reference const_reference;<br> typedef typename M::reference reference;<br> typedef typename M::const_pointer const_pointer;<br> typedef typename M::pointer pointer;<br> typedef const vector_const_reference<const matrix_vector_range<matrix_type> > const_closure_type;<br> typedef vector_reference<matrix_vector_range<matrix_type> > closure_type;<br> typedef range::const_iterator const_iterator1_type;<br> typedef range::const_iterator iterator1_type;<br> typedef range::const_iterator const_iterator2_type;<br> typedef range::const_iterator iterator2_type;<br> typedef typename storage_restrict_traits<typename M::storage_category,<br> dense_proxy_tag>::storage_category storage_category;<br><br> // Construction and destruction<br> matrix_vector_range ();<br> matrix_vector_range (matrix_type &data, const range &r1, const range &r2);<br><br> // Accessors<br> size_type size () const;<br> const_matrix_type &data () const;<br> matrix_type &data ();<br><br><br> // Element access<br> const_reference operator () (size_type i) const;<br> reference operator () (size_type i);<br><br> const_reference operator [] (size_type i) const;<br> reference operator [] (size_type i);<br><br> // Assignment<br> matrix_vector_range &operator = (const matrix_vector_range &mvr);<br> matrix_vector_range &assign_temporary (matrix_vector_range &mvr);<br> template<class AE><br> matrix_vector_range &operator = (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_vector_range &assign (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_vector_range &operator += (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_vector_range &plus_assign (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_vector_range &operator -= (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_vector_range &minus_assign (const vector_expression<AE> &ae);<br> template<class AT><br> matrix_vector_range &operator *= (const AT &at);<br> template<class AT><br> matrix_vector_range &operator /= (const AT &at);<br><br> // Swapping<br> void swap (matrix_vector_range &mvr);<br> friend void swap (matrix_vector_range &mvr1, matrix_vector_range &mvr2);<br><br> class const_iterator;<br> class iterator;<br><br> // Element lookup<br> const_iterator find_first (size_type i) const;<br> iterator find_first (size_type i);<br> const_iterator find_last (size_type i) const;<br> iterator find_last (size_type i);<br><br> // Iterators simply are indices.<br><br> class const_iterator:<br> public container_const_reference<matrix_vector_range>,<br> public random_access_iterator_base<const_iterator, value_type> {<br> public:<br> typedef typename restrict_traits<typename M::const_iterator1::iterator_category,<br> typename M::const_iterator2::iterator_category>::iterator_category iterator_category; <br> typedef typename matrix_vector_range::difference_type difference_type;<br> typedef typename matrix_vector_range::value_type value_type;<br> typedef typename matrix_vector_range::const_reference reference;<br> typedef typename matrix_vector_range::const_pointer pointer;<br><br> // Construction and destruction<br> const_iterator ();<br> const_iterator (const matrix_vector_range &mvr, const const_iterator1_type &it1, const const_iterator2_type &it2);<br> const_iterator (const iterator &it);<br><br> // Arithmetic<br> const_iterator &operator ++ ();<br> const_iterator &operator -- ();<br> const_iterator &operator += (difference_type n);<br> const_iterator &operator -= (difference_type n);<br> difference_type operator - (const const_iterator &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> // Index<br> size_type index () const;<br><br> // Assignment <br> const_iterator &operator = (const const_iterator &it);<br><br> // Comparison<br> bool operator == (const const_iterator &it) const;<br> bool operator <(const const_iterator &it) const;<br> };<br><br> const_iterator begin () const;<br> const_iterator end () const;<br><br> class iterator:<br> public container_reference<matrix_vector_range>,<br> public random_access_iterator_base<iterator, value_type> {<br> public:<br> typedef typename restrict_traits<typename M::iterator1::iterator_category,<br> typename M::iterator2::iterator_category>::iterator_category iterator_category; <br> typedef typename matrix_vector_range::difference_type difference_type;<br> typedef typename matrix_vector_range::value_type value_type;<br> typedef typename matrix_vector_range::reference reference;<br> typedef typename matrix_vector_range::pointer pointer;<br><br> // Construction and destruction<br> iterator ();<br> iterator (matrix_vector_range &mvr, const iterator1_type &it1, const iterator2_type &it2);<br><br> // Arithmetic<br> iterator &operator ++ ();<br> iterator &operator -- ();<br> iterator &operator += (difference_type n);<br> iterator &operator -= (difference_type n);<br> difference_type operator - (const iterator &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> // Index<br> size_type index () const;<br><br> // Assignment <br> iterator &operator = (const iterator &it);<br><br> // Comparison<br> bool operator == (const iterator &it) const;<br> bool operator <(const iterator &it) const;<br> };<br><br> iterator begin ();<br> iterator end ();<br><br> // Reverse iterator<br><br> typedef reverse_iterator_base<const_iterator> const_reverse_iterator;<br><br> const_reverse_iterator rbegin () const;<br> const_reverse_iterator rend () const;<br><br> typedef reverse_iterator_base<iterator> reverse_iterator;<br><br> reverse_iterator rbegin ();<br> reverse_iterator rend ();<br> };</code></pre>
|
|
|
|
<h2><a name="vector_slice"></a>
|
|
Vector Slice</h2>
|
|
|
|
<h4>Description</h4>
|
|
|
|
<p>The templated class <code>matrix_vector_slice<M> </code>allows addressing
|
|
a sliced sub vector of a matrix.</p>
|
|
|
|
<h4>Example</h4>
|
|
|
|
<pre>#include <boost/numeric/ublas/matrix.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> for (unsigned i = 0; i < m.size1 (); ++ i)<br> for (unsigned j = 0; j < m.size2 (); ++ j)<br> m (i, j) = 3 * i + j;<br><br> matrix_vector_slice<matrix<double> > mvs (m, slice (0, 1, 3), slice (0, 1, 3));<br> std::cout << mvs << std::endl;<br>}</pre>
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<h4>Definition</h4>
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|
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<p>Defined in the header matrix_proxy.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1">
|
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<tbody>
|
|
<tr>
|
|
<th>Parameter </th>
|
|
<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>M</code> </td>
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<td>The type of matrix referenced. </td>
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<td> </td>
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</tr>
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|
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</tbody>
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</table>
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|
|
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<h4>Model of</h4>
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|
<p><a href="expression.htm#vector_expression">Vector Expression</a>
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|
.</p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a href="expression.htm#vector_expression">
|
|
Vector Expression</a>
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.</p>
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|
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<h4>Public base classes</h4>
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<p><code>vector_expression<matrix_vector_slice<M> ></code> </p>
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<h4>Members</h4>
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<table border="1">
|
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<tbody>
|
|
<tr>
|
|
<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_vector_slice (matrix_type &data, <br>
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const slice &s1, const slice &s2)</code></td>
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<td>Constructs a sub vector.</td>
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</tr>
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<tr>
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<td><code>size_type size () const</code></td>
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<td>Returns the size of the sub vector.</td>
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</tr>
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<tr>
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|
<td><code>const_reference operator () (size_type i) const</code></td>
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<td>Returns the value of the <code>i</code>-th element. </td>
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</tr>
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<tr>
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|
<td><code>reference operator () (size_type i)</code></td>
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<td>Returns a reference of the <code>i</code>-th element.
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</td>
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</tr>
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<tr>
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<td><code>matrix_vector_slice &operator = (const matrix_vector_slice
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&mvs)</code></td>
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<td>The assignment operator.</td>
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</tr>
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<tr>
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<td><code>matrix_vector_slice &assign_temporary (matrix_vector_slice
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&mvs)</code></td>
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<td>Assigns a temporary. May change the matrix vector slice
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<code>vs</code>.</td>
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</tr>
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<tr>
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|
<td><code>template<class AE><br>
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matrix_vector_slice &operator = (const vector_expression<AE>
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&ae)</code></td>
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<td>The extended assignment operator.</td>
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</tr>
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<tr>
|
|
<td><code>template<class AE><br>
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matrix_vector_slice &assign (const vector_expression<AE>
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&ae)</code></td>
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<td>Assigns a vector expression to the sub vector. Left
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and right hand side of the assignment should be independent.</td>
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</tr>
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<tr>
|
|
<td><code>template<class AE><br>
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matrix_vector_slice &operator += (const vector_expression<AE>
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|
&ae)</code></td>
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<td>A computed assignment operator. Adds the vector expression
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to the sub vector.</td>
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</tr>
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<tr>
|
|
<td><code>template<class AE><br>
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matrix_vector_slice &plus_assign (const vector_expression<AE>
|
|
&ae)</code></td>
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|
<td>Adds a vector expression to the sub vector. Left and
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|
right hand side of the assignment should be independent.</td>
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</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
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|
matrix_vector_slice &operator -= (const vector_expression<AE>
|
|
&ae)</code></td>
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|
<td>A computed assignment operator. Subtracts the vector
|
|
expression from the sub vector.</td>
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|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_vector_slice &minus_assign (const vector_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Subtracts a vector expression from the sub vector. Left
|
|
and right hand side of the assignment should be independent.</td>
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|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
matrix_vector_slice &operator *= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Multiplies the sub vector
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|
with a scalar.</td>
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|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
matrix_vector_slice &operator /= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Divides the sub vector
|
|
through a scalar.</td>
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|
</tr>
|
|
<tr>
|
|
<td><code>void swap (matrix_vector_slice &mvs)</code></td>
|
|
<td>Swaps the contents of the sub vectors. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator begin () const</code></td>
|
|
<td>Returns a <code>const_iterator</code> pointing to the
|
|
beginning of the <code>matrix_vector_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator end () const</code></td>
|
|
<td>Returns a <code>const_iterator</code> pointing to the
|
|
end of the <code>matrix_vector_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator begin () </code></td>
|
|
<td>Returns a <code>iterator</code> pointing to the beginning
|
|
of the <code>matrix_vector_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator end () </code></td>
|
|
<td>Returns a <code>iterator</code> pointing to the end
|
|
of the <code>matrix_vector_slice</code>. </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 <code>matrix_vector_slice</code>.
|
|
</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 <code>matrix_vector_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator rbegin () </code></td>
|
|
<td>Returns a <code>reverse_iterator</code> pointing to
|
|
the beginning of the reversed <code>matrix_vector_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator rend () </code></td>
|
|
<td>Returns a <code>reverse_iterator</code> pointing to
|
|
the end of the reversed <code>matrix_vector_slice</code>. </td>
|
|
</tr>
|
|
|
|
</tbody>
|
|
</table>
|
|
|
|
<h4>Interface</h4>
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|
|
|
<pre><code> // Matrix based vector slice class<br> template<class M><br> class matrix_vector_slice:<br> public vector_expression<matrix_vector_slice<M> > {<br> public: <br> typedef const M const_matrix_type;<br> typedef M matrix_type;<br> typedef typename M::size_type size_type;<br> typedef typename M::difference_type difference_type;<br> typedef typename M::value_type value_type;<br> typedef typename M::const_reference const_reference;<br> typedef typename M::reference reference;<br> typedef typename M::const_pointer const_pointer;<br> typedef typename M::pointer pointer;<br> typedef const vector_const_reference<const matrix_vector_slice<matrix_type> > const_closure_type;<br> typedef vector_reference<matrix_vector_slice<matrix_type> > closure_type;<br> typedef slice::const_iterator const_iterator1_type;<br> typedef slice::const_iterator iterator1_type;<br> typedef slice::const_iterator const_iterator2_type;<br> typedef slice::const_iterator iterator2_type;<br> typedef typename storage_restrict_traits<typename M::storage_category,<br> dense_proxy_tag>::storage_category storage_category;<br><br> // Construction and destruction<br> matrix_vector_slice ();<br> matrix_vector_slice (matrix_type &data, const slice &s1, const slice &s2);<br><br> // Accessors<br> size_type size () const;<br> const_matrix_type &data () const;<br> matrix_type &data ();<br><br><br> // Element access<br> const_reference operator () (size_type i) const;<br> reference operator () (size_type i);<br><br> const_reference operator [] (size_type i) const;<br> reference operator [] (size_type i);<br><br> // Assignment<br> matrix_vector_slice &operator = (const matrix_vector_slice &mvs);<br> matrix_vector_slice &assign_temporary (matrix_vector_slice &mvs);<br> template<class AE><br> matrix_vector_slice &operator = (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_vector_slice &assign (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_vector_slice &operator += (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_vector_slice &plus_assign (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_vector_slice &operator -= (const vector_expression<AE> &ae);<br> template<class AE><br> matrix_vector_slice &minus_assign (const vector_expression<AE> &ae);<br> template<class AT><br> matrix_vector_slice &operator *= (const AT &at);<br> template<class AT><br> matrix_vector_slice &operator /= (const AT &at);<br><br> // Swapping<br> void swap (matrix_vector_slice &mvs);<br> friend void swap (matrix_vector_slice &mvs1, matrix_vector_slice &mvs2);<br><br> class const_iterator;<br> class iterator;<br><br> // Element lookup<br> const_iterator find_first (size_type i) const;<br> iterator find_first (size_type i);<br> const_iterator find_last (size_type i) const;<br> iterator find_last (size_type i);<br><br> // Iterators simply are indices.<br><br> class const_iterator:<br> public container_const_reference<matrix_vector_slice>,<br> public random_access_iterator_base<const_iterator, value_type> {<br> public:<br> typedef typename restrict_traits<typename M::const_iterator1::iterator_category,<br> typename M::const_iterator2::iterator_category>::iterator_category iterator_category; <br> typedef typename matrix_vector_slice::difference_type difference_type;<br> typedef typename matrix_vector_slice::value_type value_type;<br> typedef typename matrix_vector_slice::const_reference reference;<br> typedef typename matrix_vector_slice::const_pointer pointer;<br><br> // Construction and destruction<br> const_iterator ();<br> const_iterator (const matrix_vector_slice &mvs, const const_iterator1_type &it1, const const_iterator2_type &it2);<br> const_iterator (const iterator &it);<br><br> // Arithmetic<br> const_iterator &operator ++ ();<br> const_iterator &operator -- ();<br> const_iterator &operator += (difference_type n);<br> const_iterator &operator -= (difference_type n);<br> difference_type operator - (const const_iterator &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> // Index<br> size_type index () const;<br><br> // Assignment <br> const_iterator &operator = (const const_iterator &it);<br><br> // Comparison<br> bool operator == (const const_iterator &it) const;<br> bool operator <(const const_iterator &it) const;<br> };<br><br> const_iterator begin () const;<br> const_iterator end () const;<br><br> class iterator:<br> public container_reference<matrix_vector_slice>,<br> public random_access_iterator_base<iterator, value_type> {<br> public:<br> typedef typename restrict_traits<typename M::iterator1::iterator_category,<br> typename M::iterator2::iterator_category>::iterator_category iterator_category; <br> typedef typename matrix_vector_slice::difference_type difference_type;<br> typedef typename matrix_vector_slice::value_type value_type;<br> typedef typename matrix_vector_slice::reference reference;<br> typedef typename matrix_vector_slice::pointer pointer;<br><br> // Construction and destruction<br> iterator ();<br> iterator (matrix_vector_slice &mvs, const iterator1_type &it1, const iterator2_type &it2);<br><br> // Arithmetic<br> iterator &operator ++ ();<br> iterator &operator -- ();<br> iterator &operator += (difference_type n);<br> iterator &operator -= (difference_type n);<br> difference_type operator - (const iterator &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> // Index<br> size_type index () const;<br><br> // Assignment <br> iterator &operator = (const iterator &it);<br><br> // Comparison<br> bool operator == (const iterator &it) const;<br> bool operator <(const iterator &it) const;<br> };<br><br> iterator begin ();<br> iterator end ();<br><br> // Reverse iterator<br><br> typedef reverse_iterator_base<const_iterator> const_reverse_iterator;<br><br> const_reverse_iterator rbegin () const;<br> const_reverse_iterator rend () const;<br><br> typedef reverse_iterator_base<iterator> reverse_iterator;<br><br> reverse_iterator rbegin ();<br> reverse_iterator rend ();<br> };</code></pre>
|
|
|
|
<h2><a name="matrix_range"></a>
|
|
Matrix Range</h2>
|
|
|
|
<h4>Description</h4>
|
|
|
|
<p>The templated class <code>matrix_range<M> </code>allows addressing
|
|
a sub matrix of a matrix.</p>
|
|
|
|
<h4>Example</h4>
|
|
|
|
<pre>#include <boost/numeric/ublas/matrix.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> matrix_range<matrix<double> > mr (m, range (0, 3), range (0, 3));<br> for (unsigned i = 0; i < mr.size1 (); ++ i)<br> for (unsigned j = 0; j < mr.size2 (); ++ j)<br> mr (i, j) = 3 * i + j;<br> std::cout << mr << std::endl;<br>}<br></pre>
|
|
<h4>Definition</h4>
|
|
|
|
<p>Defined in the header matrix_proxy.hpp.</p>
|
|
|
|
<h4>Template parameters</h4>
|
|
|
|
<table border="1">
|
|
<tbody>
|
|
<tr>
|
|
<th>Parameter </th>
|
|
<th>Description </th>
|
|
<th>Default </th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>M</code> </td>
|
|
<td>The type of matrix referenced.</td>
|
|
<td> </td>
|
|
</tr>
|
|
|
|
</tbody>
|
|
</table>
|
|
|
|
<h4>Model of</h4>
|
|
|
|
<p><a href="expression.htm#matrix_expression">Matrix Expression</a>
|
|
. </p>
|
|
|
|
<h4>Type requirements</h4>
|
|
|
|
<p>None, except for those imposed by the requirements of <a href="expression.htm#matrix_expression">
|
|
Matrix Expression</a>
|
|
.</p>
|
|
|
|
<h4>Public base classes</h4>
|
|
|
|
<p><code>matrix_expression<matrix_range<M> ></code> </p>
|
|
|
|
<h4>Members</h4>
|
|
|
|
<table border="1">
|
|
<tbody>
|
|
<tr>
|
|
<th>Member </th>
|
|
<th>Description </th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>matrix_range (matrix_type &data,<br>
|
|
const range &r1, const range &r2)</code></td>
|
|
<td>Constructs a sub matrix.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type start1 () const</code></td>
|
|
<td>Returns the index of the first row.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size1 () const</code></td>
|
|
<td>Returns the number of rows. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type start2 () const</code></td>
|
|
<td>Returns the index of the first column.</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>reference operator () (size_type i, size_type
|
|
j)</code></td>
|
|
<td>Returns a reference of the <code>j</code>-th element
|
|
in the<code> i</code>-th row. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>matrix_range &operator = (const matrix_range
|
|
&mr)</code></td>
|
|
<td>The assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>matrix_range &assign_temporary (matrix_range
|
|
&mr)</code></td>
|
|
<td>Assigns a temporary. May change the matrix range <code>mr</code>
|
|
.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_range &operator = (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>The extended assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_range &assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Assigns a matrix expression to the sub matrix. Left
|
|
and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_range &operator += (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Adds the matrix expression
|
|
to the sub matrix.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_range &plus_assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Adds a matrix expression to the sub matrix. Left and
|
|
right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_range &operator -= (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Subtracts the matrix
|
|
expression from the sub matrix.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_range &minus_assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Subtracts a matrix expression from the sub matrix. Left
|
|
and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
matrix_range &operator *= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Multiplies the sub matrix
|
|
with a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
matrix_range &operator /= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Divides the sub matrix
|
|
through a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void swap (matrix_range &mr)</code></td>
|
|
<td>Swaps the contents of the sub matrices. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator1 begin1 () const</code></td>
|
|
<td>Returns a <code>const_iterator1</code> pointing to the
|
|
beginning of the <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator1 end1 () const</code></td>
|
|
<td>Returns a <code>const_iterator1</code> pointing to the
|
|
end of the <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 begin1 () </code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the beginning
|
|
of the <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 end1 () </code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the end
|
|
of the <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator2 begin2 () const</code></td>
|
|
<td>Returns a <code>const_iterator2</code> pointing to the
|
|
beginning of the <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator2 end2 () const</code></td>
|
|
<td>Returns a <code>const_iterator2</code> pointing to the
|
|
end of the <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 begin2 () </code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the beginning
|
|
of the <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 end2 () </code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the end
|
|
of the <code>matrix_range</code>. </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 <code>matrix_range</code>. </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 <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator1 rbegin1 () </code></td>
|
|
<td>Returns a <code>reverse_iterator1</code> pointing to
|
|
the beginning of the reversed <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator1 rend1 () </code></td>
|
|
<td>Returns a <code>reverse_iterator1</code> pointing to
|
|
the end of the reversed <code>matrix_range</code>. </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 <code>matrix_range</code>. </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 <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator2 rbegin2 () </code></td>
|
|
<td>Returns a <code>reverse_iterator2</code> pointing to
|
|
the beginning of the reversed <code>matrix_range</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator2 rend2 () </code></td>
|
|
<td>Returns a <code>reverse_iterator2</code> pointing to
|
|
the end of reversed the <code>matrix_range</code>. </td>
|
|
</tr>
|
|
|
|
</tbody>
|
|
</table>
|
|
|
|
<h4>Interface</h4>
|
|
|
|
<pre><code> // Matrix based range class<br> template<class M><br> class matrix_range:<br> public matrix_expression<matrix_range<M> > {<br> public: <br> typedef const M const_matrix_type;<br> typedef M matrix_type;<br> typedef typename M::size_type size_type;<br> typedef typename M::difference_type difference_type;<br> typedef typename M::value_type value_type;<br> typedef typename M::const_reference const_reference;<br> typedef typename M::reference reference;<br> typedef typename M::const_pointer const_pointer;<br> typedef typename M::pointer pointer;<br> typedef const matrix_const_reference<const matrix_range<matrix_type> > const_closure_type;<br> typedef matrix_reference<matrix_range<matrix_type> > closure_type;<br> typedef typename M::const_iterator1 const_iterator1_type;<br> typedef typename M::iterator1 iterator1_type;<br> typedef typename M::const_iterator2 const_iterator2_type;<br> typedef typename M::iterator2 iterator2_type;<br> typedef typename storage_restrict_traits<typename M::storage_category,<br> dense_proxy_tag>::storage_category storage_category;<br> typedef typename M::orientation_category orientation_category;<br><br> // Construction and destruction<br> matrix_range ();<br> matrix_range (matrix_type &data, const range &r1, const range &r2);<br><br> // Accessors<br> size_type start1 () const;<br> size_type size1 () const;<br> size_type start2() const;<br> size_type size2 () const;<br> const_matrix_type &data () const;<br> matrix_type &data ();<br><br><br> // Element access<br> const_reference operator () (size_type i, size_type j) const;<br> reference operator () (size_type i, size_type j);<br><br> matrix_range<matrix_type> project (const range &r1, const range &r2) const;<br><br> // Assignment<br> matrix_range &operator = (const matrix_range &mr);<br> matrix_range &assign_temporary (matrix_range &mr);<br> template<class AE><br> matrix_range &operator = (const matrix_expression<AE> &ae);<br> template<class AE><br> matrix_range &assign (const matrix_expression<AE> &ae);<br> template<class AE><br> matrix_range& operator += (const matrix_expression<AE> &ae);<br> template<class AE><br> matrix_range &plus_assign (const matrix_expression<AE> &ae);<br> template<class AE><br> matrix_range& operator -= (const matrix_expression<AE> &ae);<br> template<class AE><br> matrix_range &minus_assign (const matrix_expression<AE> &ae);<br> template<class AT><br> matrix_range& operator *= (const AT &at);<br> template<class AT><br> matrix_range& operator /= (const AT &at);<br><br> // Swapping<br> void swap (matrix_range &mr);<br> friend void swap (matrix_range &mr1, matrix_range &mr2);<br><br> class const_iterator1;<br> class iterator1;<br> class const_iterator2;<br> class iterator2;<br> typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;<br> typedef reverse_iterator_base1<iterator1> reverse_iterator1;<br> typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;<br> typedef reverse_iterator_base2<iterator2> reverse_iterator2;<br><br> // Element lookup<br> const_iterator1 find_first1 (int rank, size_type i, size_type j) const;<br> iterator1 find_first1 (int rank, size_type i, size_type j);<br> const_iterator1 find_last1 (int rank, size_type i, size_type j) const;<br> iterator1 find_last1 (int rank, size_type i, size_type j);<br> const_iterator2 find_first2 (int rank, size_type i, size_type j) const;<br> iterator2 find_first2 (int rank, size_type i, size_type j);<br> const_iterator2 find_last2 (int rank, size_type i, size_type j) const;<br> iterator2 find_last2 (int rank, size_type i, size_type j);<br><br> // Iterators simply are pointers.<br><br> class const_iterator1:<br> public container_const_reference<matrix_range>,<br> public random_access_iterator_base<const_iterator1, value_type> {<br> public:<br> typedef typename const_iterator1_type::iterator_category iterator_category;<br> typedef typename const_iterator1_type::difference_type difference_type;<br> typedef typename const_iterator1_type::value_type value_type;<br> typedef typename const_iterator1_type::reference reference;<br> typedef typename const_iterator1_type::pointer pointer;<br> typedef const_iterator2 dual_iterator_type;<br> typedef const_reverse_iterator2 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> const_iterator1 ();<br> const_iterator1 (const matrix_range &mr, const const_iterator1_type &it);<br> const_iterator1 (const iterator1 &it);<br><br> // Arithmetic<br> const_iterator1 &operator ++ ();<br> const_iterator1 &operator -- ();<br> const_iterator1 &operator += (difference_type n);<br> const_iterator1 &operator -= (difference_type n);<br> difference_type operator - (const const_iterator1 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> const_iterator2 begin () const;<br> const_iterator2 end () const;<br> const_reverse_iterator2 rbegin () const;<br> const_reverse_iterator2 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment <br> const_iterator1 &operator = (const const_iterator1 &it);<br><br> // Comparison<br> bool operator == (const const_iterator1 &it) const;<br> bool operator <(const const_iterator1 &it) const;<br> };<br><br> const_iterator1 begin1 () const;<br> const_iterator1 end1 () const;<br><br> class iterator1:<br> public container_reference<matrix_range>,<br> public random_access_iterator_base<iterator1, value_type> {<br> public:<br> typedef typename iterator1_type::iterator_category iterator_category;<br> typedef typename iterator1_type::difference_type difference_type;<br> typedef typename iterator1_type::value_type value_type;<br> typedef typename iterator1_type::reference reference;<br> typedef typename iterator1_type::pointer pointer;<br> typedef iterator2 dual_iterator_type;<br> typedef reverse_iterator2 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> iterator1 ();<br> iterator1 (matrix_range &mr, const iterator1_type &it);<br><br> // Arithmetic<br> iterator1 &operator ++ ();<br> iterator1 &operator -- ();<br> iterator1 &operator += (difference_type n);<br> iterator1 &operator -= (difference_type n);<br> difference_type operator - (const iterator1 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> iterator2 begin () const;<br> iterator2 end () const;<br> reverse_iterator2 rbegin () const;<br> reverse_iterator2 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment <br> iterator1 &operator = (const iterator1 &it);<br><br> // Comparison<br> bool operator == (const iterator1 &it) const;<br> bool operator <(const iterator1 &it) const;<br> };<br><br> iterator1 begin1 ();<br> iterator1 end1 ();<br><br> class const_iterator2:<br> public container_const_reference<matrix_range>,<br> public random_access_iterator_base<const_iterator2, value_type> {<br> public:<br> typedef typename const_iterator2_type::iterator_category iterator_category;<br> typedef typename const_iterator2_type::difference_type difference_type;<br> typedef typename const_iterator2_type::value_type value_type;<br> typedef typename const_iterator2_type::reference reference;<br> typedef typename const_iterator2_type::pointer pointer;<br> typedef const_iterator1 dual_iterator_type;<br> typedef const_reverse_iterator1 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> const_iterator2 ();<br> const_iterator2 (const matrix_range &mr, const const_iterator2_type &it);<br> const_iterator2 (const iterator2 &it);<br><br> // Arithmetic<br> const_iterator2 &operator ++ ();<br> const_iterator2 &operator -- ();<br> const_iterator2 &operator += (difference_type n);<br> const_iterator2 &operator -= (difference_type n);<br> difference_type operator - (const const_iterator2 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> const_iterator1 begin () const;<br> const_iterator1 end () const;<br> const_reverse_iterator1 rbegin () const;<br> const_reverse_iterator1 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment <br> const_iterator2 &operator = (const const_iterator2 &it);<br><br> // Comparison<br> bool operator == (const const_iterator2 &it) const;<br> bool operator <(const const_iterator2 &it) const;<br> };<br><br> const_iterator2 begin2 () const;<br> const_iterator2 end2 () const;<br><br> class iterator2:<br> public container_reference<matrix_range>,<br> public random_access_iterator_base<iterator2, value_type> {<br> public:<br> typedef typename iterator2_type::iterator_category iterator_category;<br> typedef typename iterator2_type::difference_type difference_type;<br> typedef typename iterator2_type::value_type value_type;<br> typedef typename iterator2_type::reference reference;<br> typedef typename iterator2_type::pointer pointer;<br> typedef iterator1 dual_iterator_type;<br> typedef reverse_iterator1 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> iterator2 ();<br> iterator2 (matrix_range &mr, const iterator2_type &it);<br><br> // Arithmetic<br> iterator2 &operator ++ ();<br> iterator2 &operator -- ();<br> iterator2 &operator += (difference_type n);<br> iterator2 &operator -= (difference_type n);<br> difference_type operator - (const iterator2 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> iterator1 begin () const;<br> iterator1 end () const;<br> reverse_iterator1 rbegin () const;<br> reverse_iterator1 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment <br> iterator2 &operator = (const iterator2 &it);<br><br> // Comparison<br> bool operator == (const iterator2 &it) const;<br> bool operator <(const iterator2 &it) const;<br> };<br><br> iterator2 begin2 ();<br> iterator2 end2 ();<br><br> // Reverse iterators<br><br> const_reverse_iterator1 rbegin1 () const;<br> const_reverse_iterator1 rend1 () const;<br><br> reverse_iterator1 rbegin1 ();<br> reverse_iterator1 rend1 ();<br><br> const_reverse_iterator2 rbegin2 () const;<br> const_reverse_iterator2 rend2 () const;<br><br> reverse_iterator2 rbegin2 ();<br> reverse_iterator2 rend2 ();<br> };</code></pre>
|
|
|
|
<h3>Projections</h3>
|
|
|
|
<h4>Prototypes</h4>
|
|
|
|
<pre><code> template<class M><br> matrix_range<M> project (M &data, const range &r1, const range &r2);<br> template<class M><br> const matrix_range<const M> project (const M &data, const range &r1, const range &r2);<br> template<class M><br> matrix_range<M> project (const matrix_range<M> &data, const range &r1, const range &r2);</code></pre>
|
|
|
|
<h4>Description</h4>
|
|
|
|
<p>The free <code>project</code> functions support the construction of matrix
|
|
ranges.</p>
|
|
|
|
<h4>Definition</h4>
|
|
|
|
<p>Defined in the header matrix_proxy.hpp.</p>
|
|
|
|
<h4>Type requirements</h4>
|
|
|
|
<dir> <li><code>M</code> is a model of <a href="expression.htm#matrix_expression">
|
|
Matrix Expression</a>
|
|
.</li>
|
|
</dir>
|
|
|
|
<h4>Preconditions</h4>
|
|
|
|
<ul type="Disc">
|
|
<li><code>r1.start () + r1.size () <= data.size1 ()</code> </li>
|
|
<li><code>r2.start () + r2.size () <= data.size2 ()</code> </li>
|
|
|
|
</ul>
|
|
|
|
<h4>Complexity</h4>
|
|
|
|
<p>Quadratic depending from the size of the ranges.</p>
|
|
|
|
<h4>Examples</h4>
|
|
|
|
<pre>#include <boost/numeric/ublas/matrix.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> for (unsigned i = 0; i < m.size1 (); ++ i)<br> for (unsigned j = 0; j < m.size2 (); ++ j)<br> project (m, range (0, 3), range (0, 3)) (i, j) = 3 * i + j;<br> std::cout << project (m, range (0, 3), range (0, 3)) << std::endl;<br>}<br></pre>
|
|
<h2><a name="matrix_slice"></a>
|
|
Matrix Slice</h2>
|
|
|
|
<h4>Description</h4>
|
|
|
|
<p>The templated class <code>matrix_slice<M> </code>allows addressing
|
|
a sliced sub matrix of a matrix.</p>
|
|
|
|
<h4>Example</h4>
|
|
|
|
<pre>#include <boost/numeric/ublas/matrix.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> matrix_slice<matrix<double> > ms (m, slice (0, 1, 3), slice (0, 1, 3));<br> for (unsigned i = 0; i < ms.size1 (); ++ i)<br> for (unsigned j = 0; j < ms.size2 (); ++ j)<br> ms (i, j) = 3 * i + j;<br> std::cout << ms << std::endl;<br>}<br></pre>
|
|
<h4>Definition</h4>
|
|
|
|
<p>Defined in the header matrix_proxy.hpp.</p>
|
|
|
|
<h4>Template parameters</h4>
|
|
|
|
<table border="1">
|
|
<tbody>
|
|
<tr>
|
|
<th>Parameter </th>
|
|
<th>Description </th>
|
|
<th>Default </th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>M</code> </td>
|
|
<td>The type of matrix referenced.</td>
|
|
<td> </td>
|
|
</tr>
|
|
|
|
</tbody>
|
|
</table>
|
|
|
|
<h4>Model of</h4>
|
|
|
|
<p><a href="expression.htm#matrix_expression">Matrix Expression</a>
|
|
.</p>
|
|
|
|
<h4>Type requirements</h4>
|
|
|
|
<p>None, except for those imposed by the requirements of <a href="expression.htm#matrix_expression">
|
|
Matrix Expression</a>
|
|
.</p>
|
|
|
|
<h4>Public base classes</h4>
|
|
|
|
<p><code>matrix_expression<matrix_slice<M> ></code> </p>
|
|
|
|
<h4>Members</h4>
|
|
|
|
<table border="1">
|
|
<tbody>
|
|
<tr>
|
|
<th>Member </th>
|
|
<th>Description </th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>matrix_slice (matrix_type &data,<br>
|
|
const slice &s1, const slice &s2)</code></td>
|
|
<td>Constructs a sub matrix.</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>reference operator () (size_type i, size_type
|
|
j)</code></td>
|
|
<td>Returns a reference of the <code>j</code>-th element
|
|
in the<code> i</code>-th row. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>matrix_slice &operator = (const matrix_slice
|
|
&ms)</code></td>
|
|
<td>The assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>matrix_slice &assign_temporary (matrix_slice
|
|
&ms)</code></td>
|
|
<td>Assigns a temporary. May change the matrix slice <code>ms</code>
|
|
.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_slice &operator = (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>The extended assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_slice &assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Assigns a matrix expression to the sub matrix. Left
|
|
and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_slice &operator += (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Adds the matrix expression
|
|
to the sub matrix.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_slice &plus_assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Adds a matrix expression to the sub matrix. Left and
|
|
right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_slice &operator -= (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Subtracts the matrix
|
|
expression from the sub matrix.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
matrix_slice &minus_assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Subtracts a matrix expression from the sub matrix. Left
|
|
and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
matrix_slice &operator *= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Multiplies the sub matrix
|
|
with a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
matrix_slice &operator /= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Multiplies the sub matrix
|
|
through a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void swap (matrix_slice &ms)</code></td>
|
|
<td>Swaps the contents of the sub matrices. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator1 begin1 () const</code></td>
|
|
<td>Returns a <code>const_iterator1</code> pointing to the
|
|
beginning of the <code>matrix_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator1 end1 () const</code></td>
|
|
<td>Returns a <code>const_iterator1</code> pointing to the
|
|
end of the <code>matrix_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 begin1 () </code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the beginning
|
|
of the <code>matrix_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 end1 () </code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the end
|
|
of the <code>matrix_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator2 begin2 () const</code></td>
|
|
<td>Returns a <code>const_iterator2</code> pointing to the
|
|
beginning of the <code>matrix_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_iterator2 end2 () const</code></td>
|
|
<td>Returns a <code>const_iterator2</code> pointing to the
|
|
end of the <code>matrix_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 begin2 () </code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the beginning
|
|
of the <code>matrix_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 end2 () </code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the end
|
|
of the <code>matrix_slice</code>. </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 <code>matrix_slice</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reverse_iterator1 rend1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code> pointing
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to the end of the reversed <code>matrix_slice</code>. </td>
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</tr>
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<tr>
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<td><code>reverse_iterator1 rbegin1 () </code></td>
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<td>Returns a <code>reverse_iterator1</code> pointing to
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the beginning of the reversed <code>matrix_slice</code>. </td>
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</tr>
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<tr>
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<td><code>reverse_iterator1 rend1 () </code></td>
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<td>Returns a <code>reverse_iterator1</code> pointing to
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the end of the reversed <code>matrix_slice</code>. </td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</code> pointing
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to the beginning of the reversed <code>matrix_slice</code>. </td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator2 rend2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</code> pointing
|
|
to the end of the reversed <code>matrix_slice</code>. </td>
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</tr>
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<tr>
|
|
<td><code>reverse_iterator2 rbegin2 () </code></td>
|
|
<td>Returns a <code>reverse_iterator2</code> pointing to
|
|
the beginning of the reversed <code>matrix_slice</code>. </td>
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</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator2 rend2 () </code></td>
|
|
<td>Returns a <code>reverse_iterator2</code> pointing to
|
|
the end of the reversed <code>matrix_slice</code>. </td>
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</tr>
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</tbody>
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</table>
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<h4>Interface</h4>
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<pre><code> // Matrix based slice class<br> template<class M><br> class matrix_slice:<br> public matrix_expression<matrix_slice<M> > {<br> public: <br> typedef const M const_matrix_type;<br> typedef M matrix_type;<br> typedef typename M::size_type size_type;<br> typedef typename M::difference_type difference_type;<br> typedef typename M::value_type value_type;<br> typedef typename M::const_reference const_reference;<br> typedef typename M::reference reference;<br> typedef typename M::const_pointer const_pointer;<br> typedef typename M::pointer pointer;<br> typedef const matrix_const_reference<const matrix_slice<matrix_type> > const_closure_type;<br> typedef matrix_reference<matrix_slice<matrix_type> > closure_type;<br> typedef slice::const_iterator const_iterator1_type;<br> typedef slice::const_iterator iterator1_type;<br> typedef slice::const_iterator const_iterator2_type;<br> typedef slice::const_iterator iterator2_type;<br> typedef typename storage_restrict_traits<typename M::storage_category,<br> dense_proxy_tag>::storage_category storage_category;<br> typedef typename M::orientation_category orientation_category;<br><br> // Construction and destruction<br> matrix_slice ();<br> matrix_slice (matrix_type &data, const slice &s1, const slice &s2);<br><br> // Accessors<br> size_type size1 () const;<br> size_type size2 () const;<br> const_matrix_type &data () const;<br> matrix_type &data ();<br><br> // Element access<br> const_reference operator () (size_type i, size_type j) const;<br> reference operator () (size_type i, size_type j);<br><br> matrix_slice<matrix_type> project (const range &r1, const range &r2) const;<br> matrix_slice<matrix_type> project (const slice &s1, const slice &s2) const;<br><br> // Assignment<br> matrix_slice &operator = (const matrix_slice &ms);<br> matrix_slice &assign_temporary (matrix_slice &ms);<br> template<class AE><br> matrix_slice &operator = (const matrix_expression<AE> &ae);<br> template<class AE><br> matrix_slice &assign (const matrix_expression<AE> &ae);<br> template<class AE><br> matrix_slice& operator += (const matrix_expression<AE> &ae);<br> template<class AE><br> matrix_slice &plus_assign (const matrix_expression<AE> &ae);<br> template<class AE><br> matrix_slice& operator -= (const matrix_expression<AE> &ae);<br> template<class AE><br> matrix_slice &minus_assign (const matrix_expression<AE> &ae);<br> template<class AT><br> matrix_slice& operator *= (const AT &at);<br> template<class AT><br> matrix_slice& operator /= (const AT &at);<br><br> // Swapping<br> void swap (matrix_slice &ms);<br> friend void swap (matrix_slice &ms1, matrix_slice &ms2);<br><br> class const_iterator1;<br> class iterator1;<br> class const_iterator2;<br> class iterator2;<br> typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;<br> typedef reverse_iterator_base1<iterator1> reverse_iterator1;<br> typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;<br> typedef reverse_iterator_base2<iterator2> reverse_iterator2;<br><br> // Element lookup<br> const_iterator1 find_first1 (int rank, size_type i, size_type j) const;<br> iterator1 find_first1 (int rank, size_type i, size_type j);<br> const_iterator1 find_last1 (int rank, size_type i, size_type j) const;<br> iterator1 find_last1 (int rank, size_type i, size_type j);<br> const_iterator2 find_first2 (int rank, size_type i, size_type j) const;<br> iterator2 find_first2 (int rank, size_type i, size_type j);<br> const_iterator2 find_last2 (int rank, size_type i, size_type j) const;<br> iterator2 find_last2 (int rank, size_type i, size_type j);<br><br> // Iterators simply are indices.<br><br> class const_iterator1:<br> public container_const_reference<matrix_slice>,<br> public random_access_iterator_base<const_iterator1, value_type> {<br> public:<br> typedef typename M::const_iterator1::iterator_category iterator_category;<br> typedef typename M::const_iterator1::difference_type difference_type;<br> typedef typename M::const_iterator1::value_type value_type;<br> typedef typename M::const_iterator1::reference reference;<br> typedef typename M::const_iterator1::pointer pointer;<br> typedef const_iterator2 dual_iterator_type;<br> typedef const_reverse_iterator2 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> const_iterator1 ();<br> const_iterator1 (const matrix_slice &ms, const const_iterator1_type &it1, const const_iterator2_type &it2);<br> const_iterator1 (const iterator1 &it);<br><br> // Arithmetic<br> const_iterator1 &operator ++ ();<br> const_iterator1 &operator -- ();<br> const_iterator1 &operator += (difference_type n);<br> const_iterator1 &operator -= (difference_type n);<br> difference_type operator - (const const_iterator1 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> const_iterator2 begin () const;<br> const_iterator2 end () const;<br> const_reverse_iterator2 rbegin () const;<br> const_reverse_iterator2 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> const_iterator1 &operator = (const const_iterator1 &it);<br><br> // Comparison<br> bool operator == (const const_iterator1 &it) const;<br> bool operator <(const const_iterator1 &it) const;<br> };<br><br> const_iterator1 begin1 () const;<br> const_iterator1 end1 () const;<br><br> class iterator1:<br> public container_reference<matrix_slice>,<br> public random_access_iterator_base<iterator1, value_type> {<br> public:<br> typedef typename M::iterator1::iterator_category iterator_category;<br> typedef typename M::iterator1::difference_type difference_type;<br> typedef typename M::iterator1::value_type value_type;<br> typedef typename M::iterator1::reference reference;<br> typedef typename M::iterator1::pointer pointer;<br> typedef iterator2 dual_iterator_type;<br> typedef reverse_iterator2 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> iterator1 ();<br> iterator1 (matrix_slice &ms, const iterator1_type &it1, const iterator2_type &it2);<br><br> // Arithmetic<br> iterator1 &operator ++ ();<br> iterator1 &operator -- ();<br> iterator1 &operator += (difference_type n);<br> iterator1 &operator -= (difference_type n);<br> difference_type operator - (const iterator1 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> iterator2 begin () const;<br> iterator2 end () const;<br> reverse_iterator2 rbegin () const;<br> reverse_iterator2 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> iterator1 &operator = (const iterator1 &it);<br><br> // Comparison<br> bool operator == (const iterator1 &it) const;<br> bool operator <(const iterator1 &it) const;<br> };<br><br> iterator1 begin1 ();<br> iterator1 end1 ();<br><br> class const_iterator2:<br> public container_const_reference<matrix_slice>,<br> public random_access_iterator_base<const_iterator2, value_type> {<br> public:<br> typedef typename M::const_iterator2::iterator_category iterator_category;<br> typedef typename M::const_iterator2::difference_type difference_type;<br> typedef typename M::const_iterator2::value_type value_type;<br> typedef typename M::const_iterator2::reference reference;<br> typedef typename M::const_iterator2::pointer pointer;<br> typedef const_iterator1 dual_iterator_type;<br> typedef const_reverse_iterator1 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> const_iterator2 ();<br> const_iterator2 (const matrix_slice &ms, const const_iterator1_type &it1, const const_iterator2_type &it2);<br> const_iterator2 (const iterator2 &it);<br><br> // Arithmetic<br> const_iterator2 &operator ++ ();<br> const_iterator2 &operator -- ();<br> const_iterator2 &operator += (difference_type n);<br> const_iterator2 &operator -= (difference_type n);<br> difference_type operator - (const const_iterator2 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> const_iterator1 begin () const;<br> const_iterator1 end () const;<br> const_reverse_iterator1 rbegin () const;<br> const_reverse_iterator1 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> const_iterator2 &operator = (const const_iterator2 &it);<br><br> // Comparison<br> bool operator == (const const_iterator2 &it) const;<br> bool operator <(const const_iterator2 &it) const;<br> };<br><br> const_iterator2 begin2 () const;<br> const_iterator2 end2 () const;<br><br> class iterator2:<br> public container_reference<matrix_slice>,<br> public random_access_iterator_base<iterator2, value_type> {<br> public:<br> typedef typename M::iterator2::iterator_category iterator_category;<br> typedef typename M::iterator2::difference_type difference_type;<br> typedef typename M::iterator2::value_type value_type;<br> typedef typename M::iterator2::reference reference;<br> typedef typename M::iterator2::pointer pointer;<br> typedef iterator1 dual_iterator_type;<br> typedef reverse_iterator1 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> iterator2 ();<br> iterator2 (matrix_slice &ms, const iterator1_type &it1, const iterator2_type &it2);<br><br> // Arithmetic<br> iterator2 &operator ++ ();<br> iterator2 &operator -- ();<br> iterator2 &operator += (difference_type n);<br> iterator2 &operator -= (difference_type n);<br> difference_type operator - (const iterator2 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> iterator1 begin () const;<br> iterator1 end () const;<br> reverse_iterator1 rbegin () const;<br> reverse_iterator1 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> iterator2 &operator = (const iterator2 &it);<br><br> // Comparison<br> bool operator == (const iterator2 &it) const;<br> bool operator <(const iterator2 &it) const;<br> };<br><br> iterator2 begin2 ();<br> iterator2 end2 ();<br><br> // Reverse iterators<br><br> const_reverse_iterator1 rbegin1 () const;<br> const_reverse_iterator1 rend1 () const;<br><br> reverse_iterator1 rbegin1 ();<br> reverse_iterator1 rend1 ();<br><br> const_reverse_iterator2 rbegin2 () const;<br> const_reverse_iterator2 rend2 () const;<br><br> reverse_iterator2 rbegin2 ();<br> reverse_iterator2 rend2 ();<br> };</code></pre>
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<h3>Projections</h3>
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<h4>Prototypes</h4>
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|
|
<pre><code> template<class M><br> matrix_slice<M> project (const matrix_slice<M> &data, const range &r1, const range &r2);<br> template<class M><br> matrix_slice<M> project (M &data, const slice &s1, const slice &s2);<br> template<class M><br> const matrix_slice<const M> project (const M &data, const slice &s1, const slice &s2);<br> template<class M><br> matrix_slice<M> project (const matrix_slice<M> &data, const slice &s1, const slice &s2);</code></pre>
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<h4>Description</h4>
|
|
|
|
<p>The free <code>project</code> functions support the construction of matrix
|
|
slices.</p>
|
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|
|
<h4>Definition</h4>
|
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|
|
<p>Defined in the header matrix_proxy.hpp.</p>
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<h4>Type requirements</h4>
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|
<dir> <li><code>M</code> is a model of <a href="expression.htm#matrix_expression">
|
|
Matrix Expression</a>
|
|
.</li>
|
|
</dir>
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<h4>Preconditions</h4>
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|
<ul type="Disc">
|
|
<li><code>s1.start () + s1.stride () * s1.size () <= data.size1 ()</code>
|
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</li>
|
|
<li><code>s2.start () + s2.stride () * s2.size () <= data.size2 ()</code>
|
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</li>
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|
|
</ul>
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<h4>Complexity</h4>
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<p>Quadratic depending from the size of the slices.</p>
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<h4>Examples</h4>
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|
<pre>#include <boost/numeric/ublas/matrix.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> for (unsigned i = 0; i < m.size1 (); ++ i)<br> for (unsigned j = 0; j < m.size2 (); ++ j)<br> project (m, slice (0, 1, 3), slice (0, 1, 3)) (i, j) = 3 * i + j;<br> std::cout << project (m, slice (0, 1, 3), slice (0, 1, 3)) << std::endl;<br>}<br></pre>
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<hr>
|
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<p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch <br>
|
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Permission to copy, use, modify, sell and distribute this document is granted
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provided this copyright notice appears in all copies. This document is provided
|
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``as is'' without express or implied warranty, and with no claim as to its
|
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suitability for any purpose.</p>
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<p>Last revised: 1/15/2003</p>
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</body>
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</html>
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