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1209 lines
45 KiB
HTML
1209 lines
45 KiB
HTML
<html>
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<head>
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<meta http-equiv="Content-Type"
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content="text/html; charset=iso-8859-1">
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<meta name="GENERATOR" content="Microsoft FrontPage Express 2.0">
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<title>Hermitian Matrix</title>
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</head>
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<body bgcolor="#FFFFFF">
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<h1><img src="c++boost.gif" alt="c++boost.gif" align="center"
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width="277" height="86">Hermitian Matrix</h1>
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<h2><a name="hermitian_matrix"></a>Hermitian Matrix</h2>
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<h4>Description</h4>
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<p>The templated class <code>hermitian_matrix<T, F1, F2, A>
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</code>is the base container adaptor for hermitian matrices. For
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a <em>(n x n</em>)-dimensional hermitian matrix and <em>0 <= i
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< n</em>,<em> 0 <= j < n</em> holds <em>h</em><sub><em>i,
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j</em></sub><em> = h</em><sub><em>j, i</em></sub><sup><em>-</em></sup>.
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The storage of hermitian matrices is packed.</p>
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<h4>Example</h4>
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<pre>int main () {
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using namespace boost::numeric::ublas;
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hermitian_matrix<std::complex<double>, lower> ml (3, 3);
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for (int i = 0; i < ml.size1 (); ++ i)
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for (int j = 0; j <= i; ++ j)
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ml (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
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std::cout << ml << std::endl;
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hermitian_matrix<std::complex<double>, upper> mu (3, 3);
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for (int i = 0; i < m.size1 (); ++ i)
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for (int j = i; j < m.size2 (); ++ j)
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mu (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
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std::cout << mu << std::endl;
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}</pre>
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<h4>Definition</h4>
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<p>Defined in the header hermitian.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1">
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<tr>
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<th>Parameter </th>
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<th>Description </th>
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<th>Default </th>
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</tr>
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<tr>
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<td><code>T</code> </td>
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<td>The type of object stored in the matrix. </td>
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<td> </td>
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</tr>
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<tr>
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<td><code>F1</code></td>
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<td>Functor describing the type of the hermitian matrix. <a
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href="#hermitian_matrix_1">[1]</a></td>
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<td><code>lower</code></td>
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</tr>
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<tr>
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<td><code>F2</code></td>
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<td>Functor describing the storage organization. <a
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href="#hermitian_matrix_2">[2]</a></td>
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<td><code>row_major</code></td>
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</tr>
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<tr>
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<td><code>A</code></td>
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<td>The type of the adapted array. <a
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href="#hermitian_matrix_3">[3]</a></td>
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<td><code>unbounded_array<T></code></td>
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</tr>
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</table>
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<h4>Model of</h4>
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<p><a href="container.htm#matrix">Matrix</a>. </p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a
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href="container.htm#matrix">Matrix</a>.</p>
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<h4>Public base classes</h4>
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<p><code>matrix_expression<hermitian_matrix<T, F1, F2,
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A> ></code> </p>
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<h4>Members</h4>
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<table border="1">
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<tr>
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<th>Member </th>
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<th>Description </th>
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</tr>
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<tr>
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<td><code>hermitian_matrix ()</code> </td>
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<td>Allocates an uninitialized <code>hermitian_matrix</code>
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that holds zero rows of zero elements.</td>
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</tr>
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<tr>
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<td><code>hermitian_matrix (size_type size)</code></td>
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<td>Allocates an uninitialized <code>hermitian_matrix</code>
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that holds <code>size</code> rows of <code>size</code>
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elements.</td>
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</tr>
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<tr>
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<td><code>hermitian_matrix (const hermitian_matrix
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&m)</code></td>
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<td>The copy constructor.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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hermitian_matrix (const matrix_expression<AE>
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&ae)</code></td>
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<td>The extended copy constructor.</td>
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</tr>
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<tr>
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<td><code>void resize (size_type size)</code></td>
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<td>Reallocates a <code>hermitian_matrix </code>to hold <code>size</code>
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rows of <code>size</code> elements. The content of the <code>hermitian_matrix</code>
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is not preserved.</td>
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</tr>
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<tr>
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<td><code>size_type size1 () const</code></td>
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<td>Returns the number of rows. </td>
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</tr>
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<tr>
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<td><code>size_type size2 () const</code></td>
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<td>Returns the number of columns. </td>
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</tr>
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<tr>
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<td><code>const_reference operator () (size_type i,
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size_type j) const</code></td>
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<td>Returns a <code>const</code> reference of the <code>j</code>-th
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element in the <code>i</code>-th row. </td>
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</tr>
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<tr>
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<td><code>reference operator () (size_type i, size_type
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j)</code></td>
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<td>Returns a reference of the <code>j</code>-th element
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in the <code>i</code>-th row. </td>
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</tr>
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<tr>
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<td><code>hermitian_matrix &operator = (const
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hermitian_matrix &m)</code></td>
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<td>The assignment operator.</td>
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</tr>
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<tr>
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<td><code>hermitian_matrix &assign_temporary
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(hermitian_matrix &m)</code></td>
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<td>Assigns a temporary. May change the hermitian matrix <code>m</code>.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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hermitian_matrix &operator = (const
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matrix_expression<AE> &ae)</code></td>
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<td>The extended assignment operator.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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hermitian_matrix &assign (const
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matrix_expression<AE> &ae)</code></td>
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<td>Assigns a matrix expression to the hermitian matrix.
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Left and right hand side of the assignment should be
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independent.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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hermitian_matrix &operator += (const
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matrix_expression<AE> &ae)</code></td>
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<td>A computed assignment operator. Adds the matrix
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expression to the hermitian matrix.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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hermitian_matrix &plus_assign (const
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matrix_expression<AE> &ae)</code></td>
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<td>Adds a matrix expression to the hermitian matrix.
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Left and right hand side of the assignment should be
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independent.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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hermitian_matrix &operator -= (const
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matrix_expression<AE> &ae)</code></td>
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<td>A computed assignment operator. Subtracts the matrix
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expression from the hermitian matrix.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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hermitian_matrix &minus_assign (const
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matrix_expression<AE> &ae)</code></td>
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<td>Subtracts a matrix expression from the hermitian
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matrix. Left and right hand side of the assignment should
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be independent.</td>
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</tr>
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<tr>
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<td><code>template<class AT><br>
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hermitian_matrix &operator *= (const AT &at)</code></td>
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<td>A computed assignment operator. Multiplies the
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hermitian matrix with a scalar.</td>
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</tr>
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<tr>
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<td><code>template<class AT><br>
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hermitian_matrix &operator /= (const AT &at)</code></td>
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<td>A computed assignment operator. Divides the hermitian
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matrix through a scalar.</td>
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</tr>
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<tr>
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<td><code>void swap (hermitian_matrix &m)</code></td>
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<td>Swaps the contents of the hermitian matrices. </td>
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</tr>
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<tr>
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<td><code>void insert (size_type i, size_type j,
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const_reference t)</code></td>
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<td>Inserts the value <code>t</code> at the <code>j</code>-th
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element of the <code>i</code>-th row.</td>
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</tr>
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<tr>
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<td><code>void erase (size_type i, size_type j)</code></td>
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<td>Erases the value at the <code>j</code>-th elemenst of
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the <code>i</code>-th row.</td>
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</tr>
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<tr>
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<td><code>void clear ()</code></td>
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<td>Clears the matrix.</td>
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</tr>
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<tr>
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<td><code>const_iterator1 begin1 () const</code></td>
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<td>Returns a <code>const_iterator1</code> pointing to
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the beginning of the <code>hermitian_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>const_iterator1 end1 () const</code></td>
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<td>Returns a <code>const_iterator1</code> pointing to
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the end of the <code>hermitian_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>iterator1 begin1 () </code></td>
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<td>Returns a <code>iterator1</code> pointing to the
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beginning of the <code>hermitian_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>iterator1 end1 () </code></td>
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<td>Returns a <code>iterator1</code> pointing to the end
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of the <code>hermitian_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>const_iterator2 begin2 () const</code></td>
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<td>Returns a <code>const_iterator2</code> pointing to
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the beginning of the <code>hermitian_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>const_iterator2 end2 () const</code></td>
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<td>Returns a <code>const_iterator2</code> pointing to
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the end of the <code>hermitian_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>iterator2 begin2 () </code></td>
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<td>Returns a <code>iterator2</code> pointing to the
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beginning of the <code>hermitian_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>iterator2 end2 () </code></td>
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<td>Returns a <code>iterator2</code> pointing to the end
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of the <code>hermitian_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code>
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pointing to the beginning of the reversed <code>hermitian_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator1 rend1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code>
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pointing to the end of the reversed <code>hermitian_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>reverse_iterator1 rbegin1 () </code></td>
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<td>Returns a <code>reverse_iterator1</code> pointing to
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the beginning of the reversed <code>hermitian_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>reverse_iterator1 rend1 () </code></td>
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<td>Returns a <code>reverse_iterator1</code> pointing to
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the end of the reversed <code>hermitian_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</code>
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pointing to the beginning of the reversed <code>hermitian_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator2 rend2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</code>
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pointing to the end of the reversed <code>hermitian_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>reverse_iterator2 rbegin2 () </code></td>
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<td>Returns a <code>reverse_iterator2</code> pointing to
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the beginning of the reversed <code>hermitian_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>reverse_iterator2 rend2 () </code></td>
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<td>Returns a <code>reverse_iterator2</code> pointing to
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the end of the reversed <code>hermitian_matrix</code>. </td>
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</tr>
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</table>
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<h4>Notes</h4>
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<p><a name="#hermitian_matrix_1">[1]</a> Supported parameters for
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the type of the hermitian matrix are <code>lower</code> and <code>upper</code>.</p>
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<p><a name="#hermitian_matrix_2">[2]</a> Supported parameters for
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the storage organization are <code>row_major</code> and <code>column_major</code>.</p>
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<p><a name="#hermitian_matrix_3">[3]</a> Supported parameters for
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the adapted array are <code>unbounded_array<T></code>, <code>bounded_array<T></code>
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and <code>std::vector<T></code>. </p>
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<h4>Interface</h4>
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<pre><code> // Array based hermitian matrix class
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template<class T, class F1, class F2, class A>
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class hermitian_matrix:
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public matrix_expression<hermitian_matrix<T, F1, F2, A> > {
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public:
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typedef std::size_t size_type;
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typedef std::ptrdiff_t difference_type;
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typedef T value_type;
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typedef const T const_reference;
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typedef T &reference;
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typedef const T *const_pointer;
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typedef T *pointer;
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typedef F1 functor1_type;
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typedef F2 functor2_type;
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typedef A array_type;
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typedef const A const_array_type;
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typedef const hermitian_matrix<T, F1, F2, A> const_self_type;
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typedef hermitian_matrix<T, F1, F2, A> self_type;
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typedef const matrix_const_reference<const_self_type> const_closure_type;
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typedef matrix_reference<self_type> closure_type;
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typedef packed_tag storage_category;
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typedef typename F1::packed_category packed_category;
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typedef typename F2::orientation_category orientation_category;
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// Construction and destruction
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hermitian_matrix ();
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hermitian_matrix (size_type size);
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hermitian_matrix (size_type size1, size_type size2);
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hermitian_matrix (const hermitian_matrix &m);
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template<class AE>
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hermitian_matrix (const matrix_expression<AE> &ae);
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// Accessors
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size_type size1 () const;
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size_type size2 () const;
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const_array_type &data () const;
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array_type &data ();
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// Resizing
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void resize (size_type size);
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void resize (size_type size1, size_type size2);
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|
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// Element access
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const_reference operator () (size_type i, size_type j) const;
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reference operator () (size_type i, size_type j);
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|
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// Assignment
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hermitian_matrix &operator = (const hermitian_matrix &m);
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hermitian_matrix &assign_temporary (hermitian_matrix &m);
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template<class AE>
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hermitian_matrix &operator = (const matrix_expression<AE> &ae);
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template<class AE>
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hermitian_matrix &reset (const matrix_expression<AE> &ae);
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template<class AE>
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hermitian_matrix &assign (const matrix_expression<AE> &ae);
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template<class AE>
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hermitian_matrix& operator += (const matrix_expression<AE> &ae);
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template<class AE>
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hermitian_matrix &plus_assign (const matrix_expression<AE> &ae);
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template<class AE>
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hermitian_matrix& operator -= (const matrix_expression<AE> &ae);
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template<class AE>
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hermitian_matrix &minus_assign (const matrix_expression<AE> &ae);
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template<class AT>
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hermitian_matrix& operator *= (const AT &at);
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template<class AT>
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hermitian_matrix& operator /= (const AT &at);
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// Swapping
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void swap (hermitian_matrix &m);
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friend void swap (hermitian_matrix &m1, hermitian_matrix &m2);
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// Element insertion and erasure
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void insert (size_type i, size_type j, const_reference t);
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void erase (size_type i, size_type j);
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void clear ();
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class const_iterator1;
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class iterator1;
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class const_iterator2;
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class iterator2;
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typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
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typedef reverse_iterator_base1<iterator1> reverse_iterator1;
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typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
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typedef reverse_iterator_base2<iterator2> reverse_iterator2;
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|
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// Element lookup
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const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
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iterator1 find_first1 (int rank, size_type i, size_type j);
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const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
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iterator1 find_last1 (int rank, size_type i, size_type j);
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const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
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iterator2 find_first2 (int rank, size_type i, size_type j);
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const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
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iterator2 find_last2 (int rank, size_type i, size_type j);
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|
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// Iterators simply are indices.
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class const_iterator1:
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public container_const_reference<hermitian_matrix>,
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public random_access_iterator_base<const_iterator1, value_type> {
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||
public:
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typedef packed_random_access_iterator_tag iterator_category;
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||
typedef typename hermitian_matrix::difference_type difference_type;
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||
typedef typename hermitian_matrix::value_type value_type;
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||
typedef typename hermitian_matrix::const_reference reference;
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typedef typename hermitian_matrix::const_pointer pointer;
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typedef const_iterator2 dual_iterator_type;
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typedef const_reverse_iterator2 dual_reverse_iterator_type;
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|
||
// Construction and destruction
|
||
const_iterator1 ();
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||
const_iterator1 (const hermitian_matrix &m, size_type it1, size_type it2);
|
||
const_iterator1 (const iterator1 &it);
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// Arithmetic
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||
const_iterator1 &operator ++ ();
|
||
const_iterator1 &operator -- ();
|
||
const_iterator1 &operator += (difference_type n);
|
||
const_iterator1 &operator -= (difference_type n);
|
||
difference_type operator - (const const_iterator1 &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
const_iterator2 begin () const;
|
||
const_iterator2 end () const;
|
||
const_reverse_iterator2 rbegin () const;
|
||
const_reverse_iterator2 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
const_iterator1 &operator = (const const_iterator1 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator1 &it) const;
|
||
bool operator < (const const_iterator1 &it) const;
|
||
};
|
||
|
||
const_iterator1 begin1 () const;
|
||
const_iterator1 end1 () const;
|
||
|
||
class iterator1:
|
||
public container_reference<hermitian_matrix>,
|
||
public random_access_iterator_base<iterator1, value_type> {
|
||
public:
|
||
typedef packed_random_access_iterator_tag iterator_category;
|
||
typedef typename hermitian_matrix::difference_type difference_type;
|
||
typedef typename hermitian_matrix::value_type value_type;
|
||
typedef typename hermitian_matrix::reference reference;
|
||
typedef typename hermitian_matrix::pointer pointer;
|
||
typedef iterator2 dual_iterator_type;
|
||
typedef reverse_iterator2 dual_reverse_iterator_type;
|
||
|
||
// Construction and destruction
|
||
iterator1 ();
|
||
iterator1 (hermitian_matrix &m, size_type it1, size_type it2);
|
||
|
||
// Arithmetic
|
||
iterator1 &operator ++ ();
|
||
iterator1 &operator -- ();
|
||
iterator1 &operator += (difference_type n);
|
||
iterator1 &operator -= (difference_type n);
|
||
difference_type operator - (const iterator1 &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
iterator2 begin () const;
|
||
iterator2 end () const;
|
||
reverse_iterator2 rbegin () const;
|
||
reverse_iterator2 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
iterator1 &operator = (const iterator1 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const iterator1 &it) const;
|
||
bool operator < (const iterator1 &it) const;
|
||
};
|
||
|
||
iterator1 begin1 ();
|
||
iterator1 end1 ();
|
||
|
||
class const_iterator2:
|
||
public container_const_reference<hermitian_matrix>,
|
||
public random_access_iterator_base<const_iterator2, value_type> {
|
||
public:
|
||
typedef packed_random_access_iterator_tag iterator_category;
|
||
typedef typename hermitian_matrix::difference_type difference_type;
|
||
typedef typename hermitian_matrix::value_type value_type;
|
||
typedef typename hermitian_matrix::const_reference reference;
|
||
typedef typename hermitian_matrix::const_pointer pointer;
|
||
typedef const_iterator1 dual_iterator_type;
|
||
typedef const_reverse_iterator1 dual_reverse_iterator_type;
|
||
|
||
// Construction and destruction
|
||
const_iterator2 ();
|
||
const_iterator2 (const hermitian_matrix &m, size_type it1, size_type it2);
|
||
const_iterator2 (const iterator2 &it);
|
||
|
||
// Arithmetic
|
||
const_iterator2 &operator ++ ();
|
||
const_iterator2 &operator -- ();
|
||
const_iterator2 &operator += (difference_type n);
|
||
const_iterator2 &operator -= (difference_type n);
|
||
difference_type operator - (const const_iterator2 &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
const_iterator1 begin () const;
|
||
const_iterator1 end () const;
|
||
const_reverse_iterator1 rbegin () const;
|
||
const_reverse_iterator1 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
const_iterator2 &operator = (const const_iterator2 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator2 &it) const;
|
||
bool operator < (const const_iterator2 &it) const;
|
||
};
|
||
|
||
const_iterator2 begin2 () const;
|
||
const_iterator2 end2 () const;
|
||
|
||
class iterator2:
|
||
public container_reference<hermitian_matrix>,
|
||
public random_access_iterator_base<iterator2, value_type> {
|
||
public:
|
||
typedef packed_random_access_iterator_tag iterator_category;
|
||
typedef typename hermitian_matrix::difference_type difference_type;
|
||
typedef typename hermitian_matrix::value_type value_type;
|
||
typedef typename hermitian_matrix::reference reference;
|
||
typedef typename hermitian_matrix::pointer pointer;
|
||
typedef iterator1 dual_iterator_type;
|
||
typedef reverse_iterator1 dual_reverse_iterator_type;
|
||
|
||
// Construction and destruction
|
||
iterator2 ();
|
||
iterator2 (hermitian_matrix &m, size_type it1, size_type it2);
|
||
|
||
// Arithmetic
|
||
iterator2 &operator ++ ();
|
||
iterator2 &operator -- ();
|
||
iterator2 &operator += (difference_type n);
|
||
iterator2 &operator -= (difference_type n);
|
||
difference_type operator - (const iterator2 &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
iterator1 begin () const;
|
||
iterator1 end () const;
|
||
reverse_iterator1 rbegin () const;
|
||
reverse_iterator1 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
iterator2 &operator = (const iterator2 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const iterator2 &it) const;
|
||
bool operator < (const iterator2 &it) const;
|
||
};
|
||
|
||
iterator2 begin2 ();
|
||
iterator2 end2 ();
|
||
|
||
// Reverse iterators
|
||
|
||
const_reverse_iterator1 rbegin1 () const;
|
||
const_reverse_iterator1 rend1 () const;
|
||
|
||
reverse_iterator1 rbegin1 ();
|
||
reverse_iterator1 rend1 ();
|
||
|
||
const_reverse_iterator2 rbegin2 () const;
|
||
const_reverse_iterator2 rend2 () const;
|
||
|
||
reverse_iterator2 rbegin2 ();
|
||
reverse_iterator2 rend2 ();
|
||
};</code></pre>
|
||
|
||
<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>int main () {
|
||
using namespace boost::numeric::ublas;
|
||
matrix<std::complex<double> > m (3, 3);
|
||
hermitian_adaptor<matrix<std::complex<double> >, lower> hal (m);
|
||
for (int i = 0; i < hal.size1 (); ++ i)
|
||
for (int j = 0; j <= i; ++ j)
|
||
hal (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
|
||
std::cout << hal << std::endl;
|
||
hermitian_adaptor<matrix<std::complex<double> >, upper> hau (m);
|
||
for (int i = 0; i < hau.size1 (); ++ i)
|
||
for (int j = i; j < hau.size2 (); ++ j)
|
||
hau (i, j) = std::complex<double> (3 * i + j, 3 * i + j);
|
||
std::cout << sau << std::endl;
|
||
}</pre>
|
||
|
||
<h4>Definition</h4>
|
||
|
||
<p>Defined in the header hermitian.hpp.</p>
|
||
|
||
<h4>Template parameters</h4>
|
||
|
||
<table border="1">
|
||
<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>
|
||
</table>
|
||
|
||
<h4>Model of</h4>
|
||
|
||
<p><a href="expression.htm#matrix_expression">Matrix Expression</a>.
|
||
</p>
|
||
|
||
<h4>Type requirements</h4>
|
||
|
||
<p>None, except for those imposed by the requirements of <a
|
||
href="expression.htm#matrix_expression">Matrix Expression</a>.</p>
|
||
|
||
<h4>Public base classes</h4>
|
||
|
||
<p><code>matrix_expression<hermitian_adaptor<M, F> ></code>
|
||
</p>
|
||
|
||
<h4>Members</h4>
|
||
|
||
<table border="1">
|
||
<tr>
|
||
<th>Member </th>
|
||
<th>Description </th>
|
||
</tr>
|
||
<tr>
|
||
<td><code>hermitian_adaptor ()</code> </td>
|
||
<td>Constructs a <code>hermitian_adaptor</code> that
|
||
holds zero rows of zero elements.</td>
|
||
</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>
|
||
</table>
|
||
|
||
<h4>Notes</h4>
|
||
|
||
<p><a name="#hermitian_adaptor_1">[1]</a> Supported parameters
|
||
for the type of the hermitian adaptor are <code>lower</code> and <code>upper</code>.</p>
|
||
|
||
<h4>Interface</h4>
|
||
|
||
<pre><code> // Hermitian matrix adaptor class
|
||
template<class M, class F>
|
||
class hermitian_adaptor:
|
||
public matrix_expression<hermitian_adaptor<M, F> > {
|
||
public:
|
||
typedef const M const_matrix_type;
|
||
typedef M matrix_type;
|
||
typedef F functor_type;
|
||
typedef typename M::size_type size_type;
|
||
typedef typename M::difference_type difference_type;
|
||
typedef typename M::value_type value_type;
|
||
typedef typename M::value_type const_reference;
|
||
typedef typename M::reference reference;
|
||
typedef typename M::const_pointer const_pointer;
|
||
typedef typename M::pointer pointer;
|
||
typedef const hermitian_adaptor<M, F> const_self_type;
|
||
typedef hermitian_adaptor<M, F> self_type;
|
||
typedef const matrix_const_reference<const_self_type> const_closure_type;
|
||
typedef matrix_reference<self_type> closure_type;
|
||
typedef typename storage_restrict_traits<typename M::storage_category,
|
||
packed_proxy_tag>::storage_category storage_category;
|
||
typedef typename F::packed_category packed_category;
|
||
typedef typename M::orientation_category orientation_category;
|
||
|
||
// Construction and destruction
|
||
hermitian_adaptor ();
|
||
hermitian_adaptor (matrix_type &data);
|
||
hermitian_adaptor (const hermitian_adaptor &m);
|
||
|
||
// Accessors
|
||
size_type size1 () const;
|
||
size_type size2 () const;
|
||
const_matrix_type &data () const;
|
||
matrix_type &data ();
|
||
|
||
// Element access
|
||
const_reference operator () (size_type i, size_type j) const;
|
||
reference operator () (size_type i, size_type j);
|
||
|
||
// Assignment
|
||
hermitian_adaptor &operator = (const hermitian_adaptor &m);
|
||
hermitian_adaptor &assign_temporary (hermitian_adaptor &m);
|
||
template<class AE>
|
||
hermitian_adaptor &operator = (const matrix_expression<AE> &ae);
|
||
template<class AE>
|
||
hermitian_adaptor &assign (const matrix_expression<AE> &ae);
|
||
template<class AE>
|
||
hermitian_adaptor& operator += (const matrix_expression<AE> &ae);
|
||
template<class AE>
|
||
hermitian_adaptor &plus_assign (const matrix_expression<AE> &ae);
|
||
template<class AE>
|
||
hermitian_adaptor& operator -= (const matrix_expression<AE> &ae);
|
||
template<class AE>
|
||
hermitian_adaptor &minus_assign (const matrix_expression<AE> &ae);
|
||
template<class AT>
|
||
hermitian_adaptor& operator *= (const AT &at);
|
||
template<class AT>
|
||
hermitian_adaptor& operator /= (const AT &at);
|
||
|
||
// Swapping
|
||
void swap (hermitian_adaptor &m);
|
||
friend void swap (hermitian_adaptor &m1, hermitian_adaptor &m2);
|
||
|
||
class const_iterator1;
|
||
class iterator1;
|
||
class const_iterator2;
|
||
class iterator2;
|
||
typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
|
||
typedef reverse_iterator_base1<iterator1> reverse_iterator1;
|
||
typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
|
||
typedef reverse_iterator_base2<iterator2> reverse_iterator2;
|
||
|
||
// Element lookup
|
||
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
|
||
iterator1 find_first1 (int rank, size_type i, size_type j);
|
||
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
|
||
iterator1 find_last1 (int rank, size_type i, size_type j);
|
||
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
|
||
iterator2 find_first2 (int rank, size_type i, size_type j);
|
||
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
|
||
iterator2 find_last2 (int rank, size_type i, size_type j);
|
||
|
||
// Iterators simply are indices.
|
||
|
||
class const_iterator1:
|
||
public container_const_reference<hermitian_adaptor>,
|
||
public random_access_iterator_base<const_iterator1, value_type> {
|
||
public:
|
||
typedef packed_random_access_iterator_tag iterator_category;
|
||
typedef typename hermitian_adaptor::difference_type difference_type;
|
||
typedef typename hermitian_adaptor::value_type value_type;
|
||
typedef typename hermitian_adaptor::const_reference reference;
|
||
typedef typename hermitian_adaptor::const_pointer pointer;
|
||
typedef const_iterator2 dual_iterator_type;
|
||
typedef const_reverse_iterator2 dual_reverse_iterator_type;
|
||
|
||
// Construction and destruction
|
||
const_iterator1 ();
|
||
const_iterator1 (const hermitian_adaptor &m, size_type it1, size_type it2);
|
||
const_iterator1 (const iterator1 &it);
|
||
|
||
// Arithmetic
|
||
const_iterator1 &operator ++ ();
|
||
const_iterator1 &operator -- ();
|
||
const_iterator1 &operator += (difference_type n);
|
||
const_iterator1 &operator -= (difference_type n);
|
||
difference_type operator - (const const_iterator1 &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
const_iterator2 begin () const;
|
||
const_iterator2 end () const;
|
||
const_reverse_iterator2 rbegin () const;
|
||
const_reverse_iterator2 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
const_iterator1 &operator = (const const_iterator1 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator1 &it) const;
|
||
bool operator < (const const_iterator1 &it) const;
|
||
};
|
||
|
||
const_iterator1 begin1 () const;
|
||
const_iterator1 end1 () const;
|
||
|
||
class iterator1:
|
||
public container_reference<hermitian_adaptor>,
|
||
public random_access_iterator_base<iterator1, value_type> {
|
||
public:
|
||
typedef packed_random_access_iterator_tag iterator_category;
|
||
typedef typename hermitian_adaptor::difference_type difference_type;
|
||
typedef typename hermitian_adaptor::value_type value_type;
|
||
typedef typename hermitian_adaptor::reference reference;
|
||
typedef typename hermitian_adaptor::pointer pointer;
|
||
typedef iterator2 dual_iterator_type;
|
||
typedef reverse_iterator2 dual_reverse_iterator_type;
|
||
|
||
// Construction and destruction
|
||
iterator1 ();
|
||
iterator1 (hermitian_adaptor &m, size_type it1, size_type it2);
|
||
|
||
// Arithmetic
|
||
iterator1 &operator ++ ();
|
||
iterator1 &operator -- ();
|
||
iterator1 &operator += (difference_type n);
|
||
iterator1 &operator -= (difference_type n);
|
||
difference_type operator - (const iterator1 &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
iterator2 begin () const;
|
||
iterator2 end () const;
|
||
reverse_iterator2 rbegin () const;
|
||
reverse_iterator2 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
iterator1 &operator = (const iterator1 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const iterator1 &it) const;
|
||
bool operator < (const iterator1 &it) const;
|
||
};
|
||
|
||
iterator1 begin1 ();
|
||
iterator1 end1 ();
|
||
|
||
class const_iterator2:
|
||
public container_const_reference<hermitian_adaptor>,
|
||
public random_access_iterator_base<const_iterator2, value_type> {
|
||
public:
|
||
typedef packed_random_access_iterator_tag iterator_category;
|
||
typedef typename hermitian_adaptor::difference_type difference_type;
|
||
typedef typename hermitian_adaptor::value_type value_type;
|
||
typedef typename hermitian_adaptor::const_reference reference;
|
||
typedef typename hermitian_adaptor::const_pointer pointer;
|
||
typedef const_iterator1 dual_iterator_type;
|
||
typedef const_reverse_iterator1 dual_reverse_iterator_type;
|
||
|
||
// Construction and destruction
|
||
const_iterator2 ();
|
||
const_iterator2 (const hermitian_adaptor &m, size_type it1, size_type it2);
|
||
const_iterator2 (const iterator2 &it);
|
||
|
||
// Arithmetic
|
||
const_iterator2 &operator ++ ();
|
||
const_iterator2 &operator -- ();
|
||
const_iterator2 &operator += (difference_type n);
|
||
const_iterator2 &operator -= (difference_type n);
|
||
difference_type operator - (const const_iterator2 &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
const_iterator1 begin () const;
|
||
const_iterator1 end () const;
|
||
const_reverse_iterator1 rbegin () const;
|
||
const_reverse_iterator1 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
const_iterator2 &operator = (const const_iterator2 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator2 &it) const;
|
||
bool operator < (const const_iterator2 &it) const;
|
||
};
|
||
|
||
const_iterator2 begin2 () const;
|
||
const_iterator2 end2 () const;
|
||
|
||
class iterator2:
|
||
public container_reference<hermitian_adaptor>,
|
||
public random_access_iterator_base<iterator2, value_type> {
|
||
public:
|
||
typedef packed_random_access_iterator_tag iterator_category;
|
||
typedef typename hermitian_adaptor::difference_type difference_type;
|
||
typedef typename hermitian_adaptor::value_type value_type;
|
||
typedef typename hermitian_adaptor::reference reference;
|
||
typedef typename hermitian_adaptor::pointer pointer;
|
||
typedef iterator1 dual_iterator_type;
|
||
typedef reverse_iterator1 dual_reverse_iterator_type;
|
||
|
||
// Construction and destruction
|
||
iterator2 ();
|
||
iterator2 (hermitian_adaptor &m, size_type it1, size_type it2);
|
||
|
||
// Arithmetic
|
||
iterator2 &operator ++ ();
|
||
iterator2 &operator -- ();
|
||
iterator2 &operator += (difference_type n);
|
||
iterator2 &operator -= (difference_type n);
|
||
difference_type operator - (const iterator2 &it) const;
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
iterator1 begin () const;
|
||
iterator1 end () const;
|
||
reverse_iterator1 rbegin () const;
|
||
reverse_iterator1 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
iterator2 &operator = (const iterator2 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const iterator2 &it) const;
|
||
bool operator <(const iterator2 &it) const;
|
||
};
|
||
|
||
iterator2 begin2 ();
|
||
iterator2 end2 ();
|
||
|
||
// Reverse iterators
|
||
|
||
const_reverse_iterator1 rbegin1 () const;
|
||
const_reverse_iterator1 rend1 () const;
|
||
|
||
reverse_iterator1 rbegin1 ();
|
||
reverse_iterator1 rend1 ();
|
||
|
||
const_reverse_iterator2 rbegin2 () const;
|
||
const_reverse_iterator2 rend2 () const;
|
||
|
||
reverse_iterator2 rbegin2 ();
|
||
reverse_iterator2 rend2 ();
|
||
};</code></pre>
|
||
|
||
<hr>
|
||
|
||
<p>Copyright (<28>) 2000-2002 Joerg Walter, Mathias Koch <br>
|
||
Permission to copy, use, modify, sell and distribute this
|
||
document is granted provided this copyright notice appears in all
|
||
copies. This document is provided ``as is'' without express or
|
||
implied warranty, and with no claim as to its suitability for any
|
||
purpose.</p>
|
||
|
||
<p>Last revised: 8/3/2002</p>
|
||
</body>
|
||
</html>
|