<!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 id="hermitian_matrix"><a name="hermitian_matrix" id="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.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<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 id="hermitian_adaptor"><a name="hermitian_adaptor" id="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.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<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>