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+<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<T, F1, F2,
+A></code> is the base container adaptor for hermitian matrices.
+For a <em>(n x n</em> )-dimensional hermitian matrix and <em>0
+<= i < n</em>, <em>0 <= j < 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 <boost/numeric/ublas/hermitian.hpp>
+#include <boost/numeric/ublas/io.hpp>
+
+int main () {
+ using namespace boost::numeric::ublas;
+ hermitian_matrix<std::complex<double>, lower> ml (3, 3);
+ for (unsigned i = 0; i < ml.size1 (); ++ i) {
+ for (unsigned j = 0; j < i; ++ j)
+ ml (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
+ ml (i, i) = std::complex<double> (4 * i, 0);
+ }
+ std::cout << ml << std::endl;
+ hermitian_matrix<std::complex<double>, upper> mu (3, 3);
+ for (unsigned i = 0; i < mu.size1 (); ++ i) {
+ mu (i, i) = std::complex<double> (4 * i, 0);
+ for (unsigned j = i + 1; j < mu.size2 (); ++ j)
+ mu (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
+ }
+ std::cout << mu << 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<T></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<hermitian_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>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
+&m)</code></td>
+<td>The copy constructor.</td>
+</tr>
+<tr>
+<td><code>template<class AE><br />
+hermitian_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>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 &operator = (const hermitian_matrix
+&m)</code></td>
+<td>The assignment operator.</td>
+</tr>
+<tr>
+<td><code>hermitian_matrix &assign_temporary (hermitian_matrix
+&m)</code></td>
+<td>Assigns a temporary. May change the hermitian matrix
+<code>m</code> .</td>
+</tr>
+<tr>
+<td><code>template<class AE><br />
+hermitian_matrix &operator = (const matrix_expression<AE>
+&ae)</code></td>
+<td>The extended assignment operator.</td>
+</tr>
+<tr>
+<td><code>template<class AE><br />
+hermitian_matrix &assign (const matrix_expression<AE>
+&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<class AE><br />
+hermitian_matrix &operator += (const
+matrix_expression<AE> &ae)</code></td>
+<td>A computed assignment operator. Adds the matrix expression to
+the hermitian matrix.</td>
+</tr>
+<tr>
+<td><code>template<class AE><br />
+hermitian_matrix &plus_assign (const
+matrix_expression<AE> &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<class AE><br />
+hermitian_matrix &operator -= (const
+matrix_expression<AE> &ae)</code></td>
+<td>A computed assignment operator. Subtracts the matrix expression
+from the hermitian matrix.</td>
+</tr>
+<tr>
+<td><code>template<class AE><br />
+hermitian_matrix &minus_assign (const
+matrix_expression<AE> &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<class AT><br />
+hermitian_matrix &operator *= (const AT &at)</code></td>
+<td>A computed assignment operator. Multiplies the hermitian matrix
+with a scalar.</td>
+</tr>
+<tr>
+<td><code>template<class AT><br />
+hermitian_matrix &operator /= (const AT &at)</code></td>
+<td>A computed assignment operator. Divides the hermitian matrix
+through a scalar.</td>
+</tr>
+<tr>
+<td><code>void swap (hermitian_matrix &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<T></code> ,
+<code>bounded_array<T></code> and
+<code>std::vector<T></code> .</p>
+<h2><a name="hermitian_adaptor"></a>Hermitian Adaptor</h2>
+<h4>Description</h4>
+<p>The templated class <code>hermitian_adaptor<M, F></code>
+is a hermitian matrix adaptor for other matrices.</p>
+<h4>Example</h4>
+<pre>
+#include <boost/numeric/ublas/hermitian.hpp>
+#include <boost/numeric/ublas/io.hpp>
+
+int main () {
+ using namespace boost::numeric::ublas;
+ matrix<std::complex<double> > m (3, 3);
+ hermitian_adaptor<matrix<std::complex<double> >, lower> hal (m);
+ for (unsigned i = 0; i < hal.size1 (); ++ i) {
+ for (unsigned j = 0; j < i; ++ j)
+ hal (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
+ hal (i, i) = std::complex<double> (4 * i, 0);
+ }
+ std::cout << hal << std::endl;
+ hermitian_adaptor<matrix<std::complex<double> >, upper> hau (m);
+ for (unsigned i = 0; i < hau.size1 (); ++ i) {
+ hau (i, i) = std::complex<double> (4 * i, 0);
+ for (unsigned j = i + 1; j < hau.size2 (); ++ j)
+ hau (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
+ }
+ std::cout << hau << 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<hermitian_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>hermitian_adaptor (matrix_type &data)</code></td>
+<td>Constructs a <code>hermitian_adaptor</code> of a matrix.</td>
+</tr>
+<tr>
+<td><code>hermitian_adaptor (const hermitian_adaptor
+&m)</code></td>
+<td>The copy constructor.</td>
+</tr>
+<tr>
+<td><code>template<class AE><br />
+hermitian_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>hermitian_adaptor &operator = (const
+hermitian_adaptor &m)</code></td>
+<td>The assignment operator.</td>
+</tr>
+<tr>
+<td><code>hermitian_adaptor &assign_temporary
+(hermitian_adaptor &m)</code></td>
+<td>Assigns a temporary. May change the hermitian adaptor
+<code>m</code>.</td>
+</tr>
+<tr>
+<td><code>template<class AE><br />
+hermitian_adaptor &operator = (const
+matrix_expression<AE> &ae)</code></td>
+<td>The extended assignment operator.</td>
+</tr>
+<tr>
+<td><code>template<class AE><br />
+hermitian_adaptor &assign (const matrix_expression<AE>
+&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<class AE><br />
+hermitian_adaptor &operator += (const
+matrix_expression<AE> &ae)</code></td>
+<td>A computed assignment operator. Adds the matrix expression to
+the hermitian adaptor.</td>
+</tr>
+<tr>
+<td><code>template<class AE><br />
+hermitian_adaptor &plus_assign (const
+matrix_expression<AE> &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<class AE><br />
+hermitian_adaptor &operator -= (const
+matrix_expression<AE> &ae)</code></td>
+<td>A computed assignment operator. Subtracts the matrix expression
+from the hermitian adaptor.</td>
+</tr>
+<tr>
+<td><code>template<class AE><br />
+hermitian_adaptor &minus_assign (const
+matrix_expression<AE> &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<class AT><br />
+hermitian_adaptor &operator *= (const AT &at)</code></td>
+<td>A computed assignment operator. Multiplies the hermitian
+adaptor with a scalar.</td>
+</tr>
+<tr>
+<td><code>template<class AT><br />
+hermitian_adaptor &operator /= (const AT &at)</code></td>
+<td>A computed assignment operator. Divides the hermitian adaptor
+through a scalar.</td>
+</tr>
+<tr>
+<td><code>void swap (hermitian_adaptor &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 (©) 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>