[ceph.git] / ceph / src / boost / libs / numeric / ublas / doc / hermitian.html

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
    "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta name="generator" content=
"HTML Tidy for Linux/x86 (vers 1st March 2004), see www.w3.org" />
<meta http-equiv="Content-Type" content=
"text/html; charset=us-ascii" />
<link rel="stylesheet" href="../../../../boost.css" type="text/css"/>
<link rel="stylesheet" href="ublas.css" type="text/css" />
<script type="text/javascript" src="js/jquery-1.3.2.min.js" async="async" ></script>
<script type="text/javascript" src="js/jquery.toc-gw.js" async="async" ></script>
<title>Hermitian Matrix</title>
</head>
<body>
<h1><img src="../../../../boost.png" align="middle" />Hermitian Matrix</h1>
<div class="toc" id="toc"></div>
<h2><a name="hermitian_matrix"></a>Hermitian Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>hermitian_matrix&lt;T, F1, F2,
A&gt;</code> is the base container adaptor for hermitian matrices.
For a <em>(n x n</em> )-dimensional hermitian matrix and <em>0
&lt;= i &lt; n</em>, <em>0 &lt;= j &lt; n</em> holds
<em>h</em><sub><em>i, j</em></sub> <em>= h</em><sub><em>j,
i</em></sub><sup><em>-</em></sup>. The storage of hermitian
matrices is packed.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/hermitian.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    hermitian_matrix&lt;std::complex&lt;double&gt;, 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) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
        ml (i, i) = std::complex&lt;double&gt; (4 * i, 0);
    }
    std::cout &lt;&lt; ml &lt;&lt; std::endl;
    hermitian_matrix&lt;std::complex&lt;double&gt;, upper&gt; mu (3, 3);
    for (unsigned i = 0; i &lt; mu.size1 (); ++ i) {
        mu (i, i) = std::complex&lt;double&gt; (4 * i, 0);
        for (unsigned j = i + 1; j &lt; mu.size2 (); ++ j)
            mu (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
    }
    std::cout &lt;&lt; mu &lt;&lt; std::endl;
}
</pre>
<h4>Definition</h4>
<p>Defined in the header hermitian.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 hermitian matrix. <a href=
"#hermitian_matrix_1">[1]</a></td>
<td><code>lower</code></td>
</tr>
<tr>
<td><code>F2</code></td>
<td>Functor describing the storage organization. <a href=
"#hermitian_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 href=
"#hermitian_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.html#matrix">Matrix</a> .</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"container_concept.html#matrix">Matrix</a> .</p>
<h4>Public base classes</h4>
<p><code>matrix_container&lt;hermitian_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>hermitian_matrix ()</code></td>
<td>Allocates an uninitialized <code>hermitian_matrix</code> that
holds zero rows of zero elements.</td>
</tr>
<tr>
<td><code>hermitian_matrix (size_type size)</code></td>
<td>Allocates an uninitialized <code>hermitian_matrix</code> that
holds <code>size</code> rows of <code>size</code> elements.</td>
</tr>
<tr>
<td><code>hermitian_matrix (const hermitian_matrix
&amp;m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_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>hermitian_matrix</code> to hold
<code>size</code> rows of <code>size</code> elements. The existing
elements of the <code>hermitian_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>hermitian_matrix &amp;operator = (const hermitian_matrix
&amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>hermitian_matrix &amp;assign_temporary (hermitian_matrix
&amp;m)</code></td>
<td>Assigns a temporary. May change the hermitian matrix
<code>m</code> .</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_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 />
hermitian_matrix &amp;assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a matrix expression to the hermitian matrix. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_matrix &amp;operator += (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression to
the hermitian matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_matrix &amp;plus_assign (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Adds a matrix expression to the hermitian matrix. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_matrix &amp;operator -= (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix expression
from the hermitian matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_matrix &amp;minus_assign (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Subtracts a matrix expression from the hermitian matrix. Left
and right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br />
hermitian_matrix &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the hermitian matrix
with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br />
hermitian_matrix &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the hermitian matrix
through a scalar.</td>
</tr>
<tr>
<td><code>void swap (hermitian_matrix &amp;m)</code></td>
<td>Swaps the contents of the hermitian 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>hermitian_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>hermitian_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator1 begin1 ()</code></td>
<td>Returns a <code>iterator1</code> pointing to the beginning of
the <code>hermitian_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator1 end1 ()</code></td>
<td>Returns a <code>iterator1</code> pointing to the end of the
<code>hermitian_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>hermitian_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>hermitian_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator2 begin2 ()</code></td>
<td>Returns a <code>iterator2</code> pointing to the beginning of
the <code>hermitian_matrix</code>.</td>
</tr>
<tr>
<td><code>iterator2 end2 ()</code></td>
<td>Returns a <code>iterator2</code> pointing to the end of the
<code>hermitian_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>hermitian_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>hermitian_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>hermitian_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>hermitian_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>hermitian_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>hermitian_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>hermitian_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>hermitian_matrix</code>.</td>
</tr>
</tbody>
</table>
<h4>Notes</h4>
<p><a name="hermitian_matrix_1" id="hermitian_matrix_1">[1]</a>
Supported parameters for the type of the hermitian matrix are
<code>lower</code> and <code>upper</code>.</p>
<p><a name="hermitian_matrix_2" id="hermitian_matrix_2">[2]</a>
Supported parameters for the storage organization are
<code>row_major</code> and <code>column_major</code>.</p>
<p><a name="hermitian_matrix_3" id="hermitian_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="hermitian_adaptor"></a>Hermitian Adaptor</h2>
<h4>Description</h4>
<p>The templated class <code>hermitian_adaptor&lt;M, F&gt;</code>
is a hermitian matrix adaptor for other matrices.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/hermitian.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;std::complex&lt;double&gt; &gt; m (3, 3);
    hermitian_adaptor&lt;matrix&lt;std::complex&lt;double&gt; &gt;, lower&gt; hal (m);
    for (unsigned i = 0; i &lt; hal.size1 (); ++ i) {
        for (unsigned j = 0; j &lt; i; ++ j)
            hal (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
        hal (i, i) = std::complex&lt;double&gt; (4 * i, 0);
    }
    std::cout &lt;&lt; hal &lt;&lt; std::endl;
    hermitian_adaptor&lt;matrix&lt;std::complex&lt;double&gt; &gt;, upper&gt; hau (m);
    for (unsigned i = 0; i &lt; hau.size1 (); ++ i) {
        hau (i, i) = std::complex&lt;double&gt; (4 * i, 0);
        for (unsigned j = i + 1; j &lt; hau.size2 (); ++ j)
            hau (i, j) = std::complex&lt;double&gt; (3 * i + j, 3 * i + j);
    }
    std::cout &lt;&lt; hau &lt;&lt; std::endl;
}
</pre>
<h4>Definition</h4>
<p>Defined in the header hermitian.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 hermitian adaptor. <a href=
"#hermitian_adaptor_1">[1]</a></td>
<td><code>lower</code></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
<h4>Public base classes</h4>
<p><code>matrix_expression&lt;hermitian_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>hermitian_adaptor (matrix_type &amp;data)</code></td>
<td>Constructs a <code>hermitian_adaptor</code> of a matrix.</td>
</tr>
<tr>
<td><code>hermitian_adaptor (const hermitian_adaptor
&amp;m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_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>hermitian_adaptor &amp;operator = (const
hermitian_adaptor &amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>hermitian_adaptor &amp;assign_temporary
(hermitian_adaptor &amp;m)</code></td>
<td>Assigns a temporary. May change the hermitian adaptor
<code>m</code>.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_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 />
hermitian_adaptor &amp;assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a matrix expression to the hermitian adaptor. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_adaptor &amp;operator += (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression to
the hermitian adaptor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_adaptor &amp;plus_assign (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Adds a matrix expression to the hermitian adaptor. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_adaptor &amp;operator -= (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix expression
from the hermitian adaptor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br />
hermitian_adaptor &amp;minus_assign (const
matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Subtracts a matrix expression from the hermitian adaptor. Left
and right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br />
hermitian_adaptor &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the hermitian
adaptor with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br />
hermitian_adaptor &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the hermitian adaptor
through a scalar.</td>
</tr>
<tr>
<td><code>void swap (hermitian_adaptor &amp;m)</code></td>
<td>Swaps the contents of the hermitian 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>hermitian_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>hermitian_adaptor</code>.</td>
</tr>
<tr>
<td><code>iterator1 begin1 ()</code></td>
<td>Returns a <code>iterator1</code> pointing to the beginning of
the <code>hermitian_adaptor</code>.</td>
</tr>
<tr>
<td><code>iterator1 end1 ()</code></td>
<td>Returns a <code>iterator1</code> pointing to the end of the
<code>hermitian_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>hermitian_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>hermitian_adaptor</code>.</td>
</tr>
<tr>
<td><code>iterator2 begin2 ()</code></td>
<td>Returns a <code>iterator2</code> pointing to the beginning of
the <code>hermitian_adaptor</code>.</td>
</tr>
<tr>
<td><code>iterator2 end2 ()</code></td>
<td>Returns a <code>iterator2</code> pointing to the end of the
<code>hermitian_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>hermitian_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>hermitian_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>hermitian_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>hermitian_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>hermitian_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>hermitian_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>hermitian_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>hermitian_adaptor</code>.</td>
</tr>
</tbody>
</table>
<h4>Notes</h4>
<p><a name="hermitian_adaptor_1" id="hermitian_adaptor_1">[1]</a>
Supported parameters for the type of the hermitian 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>
<script type="text/javascript">
(function($) {
    $('#toc').toc();
})(jQuery);
</script>
</body>
</html>