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 <h1><img src="../../../../boost.png" align="middle" />Symmetric Matrix</h1>
 <div class="toc" id="toc"></div>
 <h2><a name="symmetric_matrix"></a>Symmetric Matrix</h2>
 <h4>Description</h4>
 <p>The templated class <code>symmetric_matrix&lt;T, F1, F2,
 A&gt;</code> is the base container adaptor for symmetric matrices.
 For a <em>(n x n</em> )-dimensional symmetric matrix and <em>0
 &lt;= i &lt; n</em>, <em>0 &lt;= j &lt; n</em> holds
 <em>s</em><sub><em>i, j</em></sub> <em>= s</em><sub><em>j,
 i</em></sub>. The storage of symmetric matrices is packed.</p>
 <h4>Example</h4>
 <pre>
 #include &lt;boost/numeric/ublas/symmetric.hpp&gt;
 #include &lt;boost/numeric/ublas/io.hpp&gt;

 int main () {
     using namespace boost::numeric::ublas;
     symmetric_matrix&lt;double, lower&gt; ml (3, 3);
     for (unsigned i = 0; i &lt; ml.size1 (); ++ i)
         for (unsigned j = 0; j &lt;= i; ++ j)
             ml (i, j) = 3 * i + j;
     std::cout &lt;&lt; ml &lt;&lt; std::endl;
     symmetric_matrix&lt;double, upper&gt; mu (3, 3);
     for (unsigned i = 0; i &lt; mu.size1 (); ++ i)
         for (unsigned j = i; j &lt; mu.size2 (); ++ j)
             mu (i, j) = 3 * i + j;
     std::cout &lt;&lt; mu &lt;&lt; std::endl;
 }
 </pre>
 <h4>Definition</h4>
 <p>Defined in the header symmetric.hpp.</p>
 <h4>Template parameters</h4>
 <table border="1" summary="parameters">
 <tbody>
 <tr>
 <th>Parameter</th>
 <th>Description</th>
 <th>Default</th>
 </tr>
 <tr>
 <td><code>T</code></td>
 <td>The type of object stored in the matrix.</td>
 <td></td>
 </tr>
 <tr>
 <td><code>F1</code></td>
 <td>Functor describing the type of the symmetric matrix. <a name=
 "#symmetric_matrix_1">[1]</a></td>
 <td><code>lower</code></td>
 </tr>
 <tr>
 <td><code>F2</code></td>
 <td>Functor describing the storage organization. <a name=
 "#symmetric_matrix_2">[2]</a></td>
 <td><code>row_major</code></td>
 </tr>
 <tr>
 <td><code>A</code></td>
 <td>The type of the adapted array. <a name="#symmetric_matrix_3"
 >[3]</a></td>
 <td><code>unbounded_array&lt;T&gt;</code></td>
 </tr>
 </tbody>
 </table>
 <h4>Model of</h4>
 <p><a href="container_concept.htm#matrix">Matrix</a> .</p>
 <h4>Type requirements</h4>
 <p>None, except for those imposed by the requirements of <a href=
 "container_concept.htm#matrix">Matrix</a> .</p>
 <h4>Public base classes</h4>
 <p><code>matrix_container&lt;symmetric_matrix&lt;T, F1, F2, A&gt;
 &gt;</code></p>
 <h4>Members</h4>
 <table border="1" summary="members">
 <tbody>
 <tr>
 <th>Member</th>
 <th>Description</th>
 </tr>
 <tr>
 <td><code>symmetric_matrix (size_type size)</code></td>
 <td>Allocates an uninitialized <code>symmetric_matrix</code> that
 holds <code>size</code> rows of <code>size</code> elements.</td>
 </tr>
 <tr>
 <td><code>symmetric_matrix (const symmetric_matrix
 &amp;m)</code></td>
 <td>The copy constructor.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_matrix (const matrix_expression&lt;AE&gt;
 &amp;ae)</code></td>
 <td>The extended copy constructor.</td>
 </tr>
 <tr>
 <td><code>void resize (size_type size, bool preserve =
 true)</code></td>
 <td>Reallocates a <code>symmetric_matrix</code> to hold
 <code>size</code> rows of <code>size</code> elements. The existing
 elements of the <code>symmetric_matrix</code> are preseved when
 specified.</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 a <code>const</code> reference 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>symmetric_matrix &amp;operator = (const symmetric_matrix
 &amp;m)</code></td>
 <td>The assignment operator.</td>
 </tr>
 <tr>
 <td><code>symmetric_matrix &amp;assign_temporary (symmetric_matrix
 &amp;m)</code></td>
 <td>Assigns a temporary. May change the symmetric matrix
 <code>m</code> .</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
 &amp;ae)</code></td>
 <td>The extended assignment operator.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_matrix &amp;assign (const matrix_expression&lt;AE&gt;
 &amp;ae)</code></td>
 <td>Assigns a matrix expression to the symmetric matrix. Left and
 right hand side of the assignment should be independent.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_matrix &amp;operator += (const
 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 <td>A computed assignment operator. Adds the matrix expression to
 the symmetric matrix.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_matrix &amp;plus_assign (const
 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 <td>Adds a matrix expression to the symmetric matrix. Left and
 right hand side of the assignment should be independent.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_matrix &amp;operator -= (const
 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 <td>A computed assignment operator. Subtracts the matrix expression
 from the symmetric matrix.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_matrix &amp;minus_assign (const
 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 <td>Subtracts a matrix expression from the symmetric matrix. Left
 and right hand side of the assignment should be independent.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AT&gt;<br />
 symmetric_matrix &amp;operator *= (const AT &amp;at)</code></td>
 <td>A computed assignment operator. Multiplies the symmetric matrix
 with a scalar.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AT&gt;<br />
 symmetric_matrix &amp;operator /= (const AT &amp;at)</code></td>
 <td>A computed assignment operator. Divides the symmetric matrix
 through a scalar.</td>
 </tr>
 <tr>
 <td><code>void swap (symmetric_matrix &amp;m)</code></td>
 <td>Swaps the contents of the symmetric matrices.</td>
 </tr>
 <tr>
 <td><code>void insert (size_type i, size_type j, const_reference
 t)</code></td>
 <td>Inserts the value <code>t</code> at the <code>j</code>-th
 element of the <code>i</code>-th row.</td>
 </tr>
 <tr>
 <td><code>void erase (size_type i, size_type j)</code></td>
 <td>Erases the value at the <code>j</code>-th elemenst of the
 <code>i</code>-th row.</td>
 </tr>
 <tr>
 <td><code>void clear ()</code></td>
 <td>Clears the matrix.</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>symmetric_matrix</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>symmetric_matrix</code>.</td>
 </tr>
 <tr>
 <td><code>iterator1 begin1 ()</code></td>
 <td>Returns a <code>iterator1</code> pointing to the beginning of
 the <code>symmetric_matrix</code>.</td>
 </tr>
 <tr>
 <td><code>iterator1 end1 ()</code></td>
 <td>Returns a <code>iterator1</code> pointing to the end of the
 <code>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</code>.</td>
 </tr>
 <tr>
 <td><code>iterator2 begin2 ()</code></td>
 <td>Returns a <code>iterator2</code> pointing to the beginning of
 the <code>symmetric_matrix</code>.</td>
 </tr>
 <tr>
 <td><code>iterator2 end2 ()</code></td>
 <td>Returns a <code>iterator2</code> pointing to the end of the
 <code>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</code>.</td>
 </tr>
 <tr>
 <td><code>reverse_iterator2 rend2 ()</code></td>
 <td>Returns a <code>reverse_iterator2</code> pointing to the end of
 the reversed <code>symmetric_matrix</code>.</td>
 </tr>
 </tbody>
 </table>
 <h4>Notes</h4>
 <p><a name="symmetric_matrix_1">[1]</a>
 Supported parameters for the type of the symmetric matrix are
 <code>lower</code> and <code>upper</code>.</p>
 <p><a name="symmetric_matrix_2">[2]</a>
 Supported parameters for the storage organization are
 <code>row_major</code> and <code>column_major</code>.</p>
 <p><a name="symmetric_matrix_3">[3]</a>
 Supported parameters for the adapted array are
 <code>unbounded_array&lt;T&gt;</code> ,
 <code>bounded_array&lt;T&gt;</code> and
 <code>std::vector&lt;T&gt;</code> .</p>
 <h2><a name="symmetric_adaptor"></a>Symmetric Adaptor</h2>
 <h4>Description</h4>
 <p>The templated class <code>symmetric_adaptor&lt;M, F&gt;</code>
 is a symmetric matrix adaptor for other matrices.</p>
 <h4>Example</h4>
 <pre>
 #include &lt;boost/numeric/ublas/symmetric.hpp&gt;
 #include &lt;boost/numeric/ublas/io.hpp&gt;

 int main () {
     using namespace boost::numeric::ublas;
     matrix&lt;double&gt; m (3, 3);
     symmetric_adaptor&lt;matrix&lt;double&gt;, lower&gt; sal (m);
     for (unsigned i = 0; i &lt; sal.size1 (); ++ i)
         for (unsigned j = 0; j &lt;= i; ++ j)
             sal (i, j) = 3 * i + j;
     std::cout &lt;&lt; sal &lt;&lt; std::endl;
     symmetric_adaptor&lt;matrix&lt;double&gt;, upper&gt; sau (m);
     for (unsigned i = 0; i &lt; sau.size1 (); ++ i)
         for (unsigned j = i; j &lt; sau.size2 (); ++ j)
             sau (i, j) = 3 * i + j;
     std::cout &lt;&lt; sau &lt;&lt; std::endl;
 }
 </pre>
 <h4>Definition</h4>
 <p>Defined in the header symmetric.hpp.</p>
 <h4>Template parameters</h4>
 <table border="1" summary="parameters">
 <tbody>
 <tr>
 <th>Parameter</th>
 <th>Description</th>
 <th>Default</th>
 </tr>
 <tr>
 <td><code>M</code></td>
 <td>The type of the adapted matrix.</td>
 <td></td>
 </tr>
 <tr>
 <td><code>F</code></td>
 <td>Functor describing the type of the symmetric adaptor. <a href=
 "#symmetric_adaptor_1">[1]</a></td>
 <td><code>lower</code></td>
 </tr>
 </tbody>
 </table>
 <h4>Model of</h4>
 <p><a href="expression_concept.htm#matrix_expression">Matrix Expression</a>
 .</p>
 <h4>Type requirements</h4>
 <p>None, except for those imposed by the requirements of <a href=
 "expression_concept.htm#matrix_expression">Matrix Expression</a> .</p>
 <h4>Public base classes</h4>
 <p><code>matrix_expression&lt;symmetric_adaptor&lt;M, F&gt;
 &gt;</code></p>
 <h4>Members</h4>
 <table border="1" summary="members">
 <tbody>
 <tr>
 <th>Member</th>
 <th>Description</th>
 </tr>
 <tr>
 <td><code>symmetric_adaptor ()</code></td>
 <td>Constructs a <code>symmetric_adaptor</code> that holds zero
 rows of zero elements.</td>
 </tr>
 <tr>
 <td><code>symmetric_adaptor (matrix_type &amp;data)</code></td>
 <td>Constructs a <code>symmetric_adaptor</code> of a matrix.</td>
 </tr>
 <tr>
 <td><code>symmetric_adaptor (const symmetric_adaptor
 &amp;m)</code></td>
 <td>The copy constructor.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_adaptor (const matrix_expression&lt;AE&gt;
 &amp;ae)</code></td>
 <td>The extended copy constructor.</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 a <code>const</code> reference 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>symmetric_adaptor &amp;operator = (const
 symmetric_adaptor &amp;m)</code></td>
 <td>The assignment operator.</td>
 </tr>
 <tr>
 <td><code>symmetric_adaptor &amp;assign_temporary
 (symmetric_adaptor &amp;m)</code></td>
 <td>Assigns a temporary. May change the symmetric adaptor
 <code>m</code>.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_adaptor &amp;operator = (const
 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 <td>The extended assignment operator.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_adaptor &amp;assign (const matrix_expression&lt;AE&gt;
 &amp;ae)</code></td>
 <td>Assigns a matrix expression to the symmetric adaptor. Left and
 right hand side of the assignment should be independent.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_adaptor &amp;operator += (const
 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 <td>A computed assignment operator. Adds the matrix expression to
 the symmetric adaptor.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_adaptor &amp;plus_assign (const
 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 <td>Adds a matrix expression to the symmetric adaptor. Left and
 right hand side of the assignment should be independent.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_adaptor &amp;operator -= (const
 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 <td>A computed assignment operator. Subtracts the matrix expression
 from the symmetric adaptor.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AE&gt;<br />
 symmetric_adaptor &amp;minus_assign (const
 matrix_expression&lt;AE&gt; &amp;ae)</code></td>
 <td>Subtracts a matrix expression from the symmetric adaptor. Left
 and right hand side of the assignment should be independent.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AT&gt;<br />
 symmetric_adaptor &amp;operator *= (const AT &amp;at)</code></td>
 <td>A computed assignment operator. Multiplies the symmetric
 adaptor with a scalar.</td>
 </tr>
 <tr>
 <td><code>template&lt;class AT&gt;<br />
 symmetric_adaptor &amp;operator /= (const AT &amp;at)</code></td>
 <td>A computed assignment operator. Divides the symmetric adaptor
 through a scalar.</td>
 </tr>
 <tr>
 <td><code>void swap (symmetric_adaptor &amp;m)</code></td>
 <td>Swaps the contents of the symmetric adaptors.</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>symmetric_adaptor</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>symmetric_adaptor</code>.</td>
 </tr>
 <tr>
 <td><code>iterator1 begin1 ()</code></td>
 <td>Returns a <code>iterator1</code> pointing to the beginning of
 the <code>symmetric_adaptor</code>.</td>
 </tr>
 <tr>
 <td><code>iterator1 end1 ()</code></td>
 <td>Returns a <code>iterator1</code> pointing to the end of the
 <code>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</code>.</td>
 </tr>
 <tr>
 <td><code>iterator2 begin2 ()</code></td>
 <td>Returns a <code>iterator2</code> pointing to the beginning of
 the <code>symmetric_adaptor</code>.</td>
 </tr>
 <tr>
 <td><code>iterator2 end2 ()</code></td>
 <td>Returns a <code>iterator2</code> pointing to the end of the
 <code>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</code>.</td>
 </tr>
 <tr>
 <td><code>reverse_iterator2 rend2 ()</code></td>
 <td>Returns a <code>reverse_iterator2</code> pointing to the end of
 the reversed <code>symmetric_adaptor</code>.</td>
 </tr>
 </tbody>
 </table>
 <h4>Notes</h4>
 <p><a name="symmetric_adaptor_1">[1]</a>
 Supported parameters for the type of the symmetric adaptor are
 <code>lower</code> and <code>upper</code>.</p>
 <hr />
 <p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
    Use, modification and distribution are subject to the
    Boost Software License, Version 1.0.
    (See accompanying file LICENSE_1_0.txt
    or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
       http://www.boost.org/LICENSE_1_0.txt
    </a>).
 </p>
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	<h1><img src="../../../../boost.png" align="middle" />Symmetric Matrix</h1>
	<div class="toc" id="toc"></div>
	<h2><a name="symmetric_matrix"></a>Symmetric Matrix</h2>
	<h4>Description</h4>
	<p>The templated class <code>symmetric_matrix<T, F1, F2,
	A></code> is the base container adaptor for symmetric matrices.
	For a <em>(n x n</em> )-dimensional symmetric matrix and <em>0
	<= i < n</em>, <em>0 <= j < n</em> holds
	<em>s</em><sub><em>i, j</em></sub> <em>= s</em><sub><em>j,
	i</em></sub>. The storage of symmetric matrices is packed.</p>
	<h4>Example</h4>
	<pre>
	#include <boost/numeric/ublas/symmetric.hpp>
	#include <boost/numeric/ublas/io.hpp>

	int main () {
	using namespace boost::numeric::ublas;
	symmetric_matrix<double, lower> ml (3, 3);
	for (unsigned i = 0; i < ml.size1 (); ++ i)
	for (unsigned j = 0; j <= i; ++ j)
	ml (i, j) = 3 * i + j;
	std::cout << ml << std::endl;
	symmetric_matrix<double, upper> mu (3, 3);
	for (unsigned i = 0; i < mu.size1 (); ++ i)
	for (unsigned j = i; j < mu.size2 (); ++ j)
	mu (i, j) = 3 * i + j;
	std::cout << mu << std::endl;
	}
	</pre>
	<h4>Definition</h4>
	<p>Defined in the header symmetric.hpp.</p>
	<h4>Template parameters</h4>
	<table border="1" summary="parameters">
	<tbody>
	<tr>
	<th>Parameter</th>
	<th>Description</th>
	<th>Default</th>
	</tr>
	<tr>
	<td><code>T</code></td>
	<td>The type of object stored in the matrix.</td>
	<td></td>
	</tr>
	<tr>
	<td><code>F1</code></td>
	<td>Functor describing the type of the symmetric matrix. <a name=
	"#symmetric_matrix_1">[1]</a></td>
	<td><code>lower</code></td>
	</tr>
	<tr>
	<td><code>F2</code></td>
	<td>Functor describing the storage organization. <a name=
	"#symmetric_matrix_2">[2]</a></td>
	<td><code>row_major</code></td>
	</tr>
	<tr>
	<td><code>A</code></td>
	<td>The type of the adapted array. <a name="#symmetric_matrix_3"
	>[3]</a></td>
	<td><code>unbounded_array<T></code></td>
	</tr>
	</tbody>
	</table>
	<h4>Model of</h4>
	<p><a href="container_concept.htm#matrix">Matrix</a> .</p>
	<h4>Type requirements</h4>
	<p>None, except for those imposed by the requirements of <a href=
	"container_concept.htm#matrix">Matrix</a> .</p>
	<h4>Public base classes</h4>
	<p><code>matrix_container<symmetric_matrix<T, F1, F2, A>
	></code></p>
	<h4>Members</h4>
	<table border="1" summary="members">
	<tbody>
	<tr>
	<th>Member</th>
	<th>Description</th>
	</tr>
	<tr>
	<td><code>symmetric_matrix (size_type size)</code></td>
	<td>Allocates an uninitialized <code>symmetric_matrix</code> that
	holds <code>size</code> rows of <code>size</code> elements.</td>
	</tr>
	<tr>
	<td><code>symmetric_matrix (const symmetric_matrix
	&m)</code></td>
	<td>The copy constructor.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_matrix (const matrix_expression<AE>
	&ae)</code></td>
	<td>The extended copy constructor.</td>
	</tr>
	<tr>
	<td><code>void resize (size_type size, bool preserve =
	true)</code></td>
	<td>Reallocates a <code>symmetric_matrix</code> to hold
	<code>size</code> rows of <code>size</code> elements. The existing
	elements of the <code>symmetric_matrix</code> are preseved when
	specified.</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 a <code>const</code> reference 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>symmetric_matrix &operator = (const symmetric_matrix
	&m)</code></td>
	<td>The assignment operator.</td>
	</tr>
	<tr>
	<td><code>symmetric_matrix &assign_temporary (symmetric_matrix
	&m)</code></td>
	<td>Assigns a temporary. May change the symmetric matrix
	<code>m</code> .</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_matrix &operator = (const matrix_expression<AE>
	&ae)</code></td>
	<td>The extended assignment operator.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_matrix &assign (const matrix_expression<AE>
	&ae)</code></td>
	<td>Assigns a matrix expression to the symmetric matrix. Left and
	right hand side of the assignment should be independent.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_matrix &operator += (const
	matrix_expression<AE> &ae)</code></td>
	<td>A computed assignment operator. Adds the matrix expression to
	the symmetric matrix.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_matrix &plus_assign (const
	matrix_expression<AE> &ae)</code></td>
	<td>Adds a matrix expression to the symmetric matrix. Left and
	right hand side of the assignment should be independent.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_matrix &operator -= (const
	matrix_expression<AE> &ae)</code></td>
	<td>A computed assignment operator. Subtracts the matrix expression
	from the symmetric matrix.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_matrix &minus_assign (const
	matrix_expression<AE> &ae)</code></td>
	<td>Subtracts a matrix expression from the symmetric matrix. Left
	and right hand side of the assignment should be independent.</td>
	</tr>
	<tr>
	<td><code>template<class AT><br />
	symmetric_matrix &operator *= (const AT &at)</code></td>
	<td>A computed assignment operator. Multiplies the symmetric matrix
	with a scalar.</td>
	</tr>
	<tr>
	<td><code>template<class AT><br />
	symmetric_matrix &operator /= (const AT &at)</code></td>
	<td>A computed assignment operator. Divides the symmetric matrix
	through a scalar.</td>
	</tr>
	<tr>
	<td><code>void swap (symmetric_matrix &m)</code></td>
	<td>Swaps the contents of the symmetric matrices.</td>
	</tr>
	<tr>
	<td><code>void insert (size_type i, size_type j, const_reference
	t)</code></td>
	<td>Inserts the value <code>t</code> at the <code>j</code>-th
	element of the <code>i</code>-th row.</td>
	</tr>
	<tr>
	<td><code>void erase (size_type i, size_type j)</code></td>
	<td>Erases the value at the <code>j</code>-th elemenst of the
	<code>i</code>-th row.</td>
	</tr>
	<tr>
	<td><code>void clear ()</code></td>
	<td>Clears the matrix.</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>symmetric_matrix</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>symmetric_matrix</code>.</td>
	</tr>
	<tr>
	<td><code>iterator1 begin1 ()</code></td>
	<td>Returns a <code>iterator1</code> pointing to the beginning of
	the <code>symmetric_matrix</code>.</td>
	</tr>
	<tr>
	<td><code>iterator1 end1 ()</code></td>
	<td>Returns a <code>iterator1</code> pointing to the end of the
	<code>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</code>.</td>
	</tr>
	<tr>
	<td><code>iterator2 begin2 ()</code></td>
	<td>Returns a <code>iterator2</code> pointing to the beginning of
	the <code>symmetric_matrix</code>.</td>
	</tr>
	<tr>
	<td><code>iterator2 end2 ()</code></td>
	<td>Returns a <code>iterator2</code> pointing to the end of the
	<code>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</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>symmetric_matrix</code>.</td>
	</tr>
	<tr>
	<td><code>reverse_iterator2 rend2 ()</code></td>
	<td>Returns a <code>reverse_iterator2</code> pointing to the end of
	the reversed <code>symmetric_matrix</code>.</td>
	</tr>
	</tbody>
	</table>
	<h4>Notes</h4>
	<p><a name="symmetric_matrix_1">[1]</a>
	Supported parameters for the type of the symmetric matrix are
	<code>lower</code> and <code>upper</code>.</p>
	<p><a name="symmetric_matrix_2">[2]</a>
	Supported parameters for the storage organization are
	<code>row_major</code> and <code>column_major</code>.</p>
	<p><a name="symmetric_matrix_3">[3]</a>
	Supported parameters for the adapted array are
	<code>unbounded_array<T></code> ,
	<code>bounded_array<T></code> and
	<code>std::vector<T></code> .</p>
	<h2><a name="symmetric_adaptor"></a>Symmetric Adaptor</h2>
	<h4>Description</h4>
	<p>The templated class <code>symmetric_adaptor<M, F></code>
	is a symmetric matrix adaptor for other matrices.</p>
	<h4>Example</h4>
	<pre>
	#include <boost/numeric/ublas/symmetric.hpp>
	#include <boost/numeric/ublas/io.hpp>

	int main () {
	using namespace boost::numeric::ublas;
	matrix<double> m (3, 3);
	symmetric_adaptor<matrix<double>, lower> sal (m);
	for (unsigned i = 0; i < sal.size1 (); ++ i)
	for (unsigned j = 0; j <= i; ++ j)
	sal (i, j) = 3 * i + j;
	std::cout << sal << std::endl;
	symmetric_adaptor<matrix<double>, upper> sau (m);
	for (unsigned i = 0; i < sau.size1 (); ++ i)
	for (unsigned j = i; j < sau.size2 (); ++ j)
	sau (i, j) = 3 * i + j;
	std::cout << sau << std::endl;
	}
	</pre>
	<h4>Definition</h4>
	<p>Defined in the header symmetric.hpp.</p>
	<h4>Template parameters</h4>
	<table border="1" summary="parameters">
	<tbody>
	<tr>
	<th>Parameter</th>
	<th>Description</th>
	<th>Default</th>
	</tr>
	<tr>
	<td><code>M</code></td>
	<td>The type of the adapted matrix.</td>
	<td></td>
	</tr>
	<tr>
	<td><code>F</code></td>
	<td>Functor describing the type of the symmetric adaptor. <a href=
	"#symmetric_adaptor_1">[1]</a></td>
	<td><code>lower</code></td>
	</tr>
	</tbody>
	</table>
	<h4>Model of</h4>
	<p><a href="expression_concept.htm#matrix_expression">Matrix Expression</a>
	.</p>
	<h4>Type requirements</h4>
	<p>None, except for those imposed by the requirements of <a href=
	"expression_concept.htm#matrix_expression">Matrix Expression</a> .</p>
	<h4>Public base classes</h4>
	<p><code>matrix_expression<symmetric_adaptor<M, F>
	></code></p>
	<h4>Members</h4>
	<table border="1" summary="members">
	<tbody>
	<tr>
	<th>Member</th>
	<th>Description</th>
	</tr>
	<tr>
	<td><code>symmetric_adaptor ()</code></td>
	<td>Constructs a <code>symmetric_adaptor</code> that holds zero
	rows of zero elements.</td>
	</tr>
	<tr>
	<td><code>symmetric_adaptor (matrix_type &data)</code></td>
	<td>Constructs a <code>symmetric_adaptor</code> of a matrix.</td>
	</tr>
	<tr>
	<td><code>symmetric_adaptor (const symmetric_adaptor
	&m)</code></td>
	<td>The copy constructor.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_adaptor (const matrix_expression<AE>
	&ae)</code></td>
	<td>The extended copy constructor.</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 a <code>const</code> reference 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>symmetric_adaptor &operator = (const
	symmetric_adaptor &m)</code></td>
	<td>The assignment operator.</td>
	</tr>
	<tr>
	<td><code>symmetric_adaptor &assign_temporary
	(symmetric_adaptor &m)</code></td>
	<td>Assigns a temporary. May change the symmetric adaptor
	<code>m</code>.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_adaptor &operator = (const
	matrix_expression<AE> &ae)</code></td>
	<td>The extended assignment operator.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_adaptor &assign (const matrix_expression<AE>
	&ae)</code></td>
	<td>Assigns a matrix expression to the symmetric adaptor. Left and
	right hand side of the assignment should be independent.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_adaptor &operator += (const
	matrix_expression<AE> &ae)</code></td>
	<td>A computed assignment operator. Adds the matrix expression to
	the symmetric adaptor.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_adaptor &plus_assign (const
	matrix_expression<AE> &ae)</code></td>
	<td>Adds a matrix expression to the symmetric adaptor. Left and
	right hand side of the assignment should be independent.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_adaptor &operator -= (const
	matrix_expression<AE> &ae)</code></td>
	<td>A computed assignment operator. Subtracts the matrix expression
	from the symmetric adaptor.</td>
	</tr>
	<tr>
	<td><code>template<class AE><br />
	symmetric_adaptor &minus_assign (const
	matrix_expression<AE> &ae)</code></td>
	<td>Subtracts a matrix expression from the symmetric adaptor. Left
	and right hand side of the assignment should be independent.</td>
	</tr>
	<tr>
	<td><code>template<class AT><br />
	symmetric_adaptor &operator *= (const AT &at)</code></td>
	<td>A computed assignment operator. Multiplies the symmetric
	adaptor with a scalar.</td>
	</tr>
	<tr>
	<td><code>template<class AT><br />
	symmetric_adaptor &operator /= (const AT &at)</code></td>
	<td>A computed assignment operator. Divides the symmetric adaptor
	through a scalar.</td>
	</tr>
	<tr>
	<td><code>void swap (symmetric_adaptor &m)</code></td>
	<td>Swaps the contents of the symmetric adaptors.</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>symmetric_adaptor</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>symmetric_adaptor</code>.</td>
	</tr>
	<tr>
	<td><code>iterator1 begin1 ()</code></td>
	<td>Returns a <code>iterator1</code> pointing to the beginning of
	the <code>symmetric_adaptor</code>.</td>
	</tr>
	<tr>
	<td><code>iterator1 end1 ()</code></td>
	<td>Returns a <code>iterator1</code> pointing to the end of the
	<code>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</code>.</td>
	</tr>
	<tr>
	<td><code>iterator2 begin2 ()</code></td>
	<td>Returns a <code>iterator2</code> pointing to the beginning of
	the <code>symmetric_adaptor</code>.</td>
	</tr>
	<tr>
	<td><code>iterator2 end2 ()</code></td>
	<td>Returns a <code>iterator2</code> pointing to the end of the
	<code>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</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>symmetric_adaptor</code>.</td>
	</tr>
	<tr>
	<td><code>reverse_iterator2 rend2 ()</code></td>
	<td>Returns a <code>reverse_iterator2</code> pointing to the end of
	the reversed <code>symmetric_adaptor</code>.</td>
	</tr>
	</tbody>
	</table>
	<h4>Notes</h4>
	<p><a name="symmetric_adaptor_1">[1]</a>
	Supported parameters for the type of the symmetric adaptor are
	<code>lower</code> and <code>upper</code>.</p>
	<hr />
	<p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br />
	Use, modification and distribution are subject to the
	Boost Software License, Version 1.0.
	(See accompanying file LICENSE_1_0.txt
	or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
	http://www.boost.org/LICENSE_1_0.txt
	</a>).
	</p>
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