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616 lines
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616 lines
48 KiB
HTML
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<meta http-equiv="Content-Type" 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>Triangular Matrix</title>
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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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Triangular Matrix</h1>
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<h2><a name="triangular_matrix"></a>
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Triangular Matrix</h2>
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<h4>Description</h4>
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<p>The templated class <code>triangular_matrix<T, F1, F2, A> </code>
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is the base container adaptor for triangular matrices. For a <em>(n x n</em>
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)-dimensional lower triangular matrix and <em>0 <= i < n</em>,<em>
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0 <= j < n</em> holds <em>t</em><sub><em>i, j</em></sub><em> = 0</em>
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, if <em>i > j</em>. If furthermore holds t<sub><em>i, i</em></sub><em>
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= 1</em> the matrix is called unit lower triangular. For a <em>(n x n</em>
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)-dimensional upper triangular matrix and <em>0 <= i < n</em>,<em>
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0 <= j < n</em> holds <em>t</em><sub><em>i, j</em></sub><em> = 0</em>
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, if <em>i < j</em>. If furthermore holds t<sub><em>i, i</em></sub><em>
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= 1</em> the matrix is called unit lower triangular. The storage of triangular
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matrices is packed.</p>
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<h4>Example</h4>
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<pre>#include <boost/numeric/ublas/triangular.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> triangular_matrix<double, lower> ml (3, 3);<br> for (unsigned i = 0; i < ml.size1 (); ++ i)<br> for (unsigned j = 0; j <= i; ++ j)<br> ml (i, j) = 3 * i + j;<br> std::cout << ml << std::endl;<br> triangular_matrix<double, upper> mu (3, 3);<br> for (unsigned i = 0; i < mu.size1 (); ++ i)<br> for (unsigned j = i; j < mu.size2 (); ++ j)<br> mu (i, j) = 3 * i + j;<br> std::cout << mu << std::endl;<br>}<br></pre>
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<h4>Definition</h4>
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<p>Defined in the header triangular.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1">
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<tbody>
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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 triangular matrix.
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<a href="#triangular_matrix_1">[1]</a>
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</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 href="#triangular_matrix_2">
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[2]</a>
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</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 href="#triangular_matrix_3">
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[3]</a>
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</td>
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<td><code>unbounded_array<T></code></td>
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</tr>
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</tbody>
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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>
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. </p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a href="container.htm#matrix">
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Matrix</a>
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.</p>
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<h4>Public base classes</h4>
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<p><code>matrix_expression<triangular_matrix<T, F1, F2, A> ></code>
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</p>
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<h4>Members</h4>
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<table border="1">
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<tbody>
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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>triangular_matrix ()</code> </td>
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<td>Allocates an uninitialized <code>triangular_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>triangular_matrix (size_type size1, size_type
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size2)</code></td>
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<td>Allocates an uninitialized <code>triangular_matrix</code>
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that holds <code>size1</code> rows of <code>size2</code> elements.</td>
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</tr>
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<tr>
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<td><code>triangular_matrix (const triangular_matrix &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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triangular_matrix (const matrix_expression<AE> &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 size1, size_type size2)</code></td>
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<td>Reallocates a <code>triangular_matrix </code>to hold <code>size1</code>
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rows of <code>size2</code> elements. The content of the <code>triangular_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, size_type
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j) const</code></td>
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<td>Returns a <code>const</code> reference of the <code>j</code>
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-th 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>triangular_matrix &operator = (const triangular_matrix
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&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>triangular_matrix &assign_temporary (triangular_matrix
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&m)</code></td>
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<td>Assigns a temporary. May change the triangular matrix
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<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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triangular_matrix &operator = (const matrix_expression<AE>
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&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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triangular_matrix &assign (const matrix_expression<AE>
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&ae)</code></td>
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<td>Assigns a matrix expression to the triangular matrix.
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Left and right hand side of the assignment should be 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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triangular_matrix &operator += (const matrix_expression<AE>
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&ae)</code></td>
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<td>A computed assignment operator. Adds the matrix expression
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to the triangular 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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triangular_matrix &plus_assign (const matrix_expression<AE>
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&ae)</code></td>
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<td>Adds a matrix expression to the triangular matrix. Left
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and right hand side of the assignment should be 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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triangular_matrix &operator -= (const matrix_expression<AE>
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&ae)</code></td>
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<td>A computed assignment operator. Subtracts the matrix
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expression from the triangular 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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triangular_matrix &minus_assign (const matrix_expression<AE>
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&ae)</code></td>
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<td>Subtracts a matrix expression from the triangular matrix.
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Left and right hand side of the assignment should 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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triangular_matrix &operator *= (const AT &at)</code></td>
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<td>A computed assignment operator. Multiplies the triangular
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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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triangular_matrix &operator /= (const AT &at)</code></td>
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<td>A computed assignment operator. Divides the triangular
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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 (triangular_matrix &m)</code></td>
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<td>Swaps the contents of the triangular 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, const_reference
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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 the
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beginning of the <code>triangular_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 the
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end of the <code>triangular_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 beginning
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of the <code>triangular_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>triangular_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 the
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beginning of the <code>triangular_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 the
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end of the <code>triangular_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 beginning
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of the <code>triangular_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>triangular_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> pointing
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to the beginning of the reversed <code>triangular_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> pointing
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to the end of the reversed <code>triangular_matrix</code>. </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>triangular_matrix</code>. </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>triangular_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> pointing
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to the beginning of the reversed <code>triangular_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> pointing
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to the end of the reversed <code>triangular_matrix</code>. </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>triangular_matrix</code>. </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>triangular_matrix</code>. </td>
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</tr>
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</tbody>
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</table>
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<h4>Notes</h4>
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<p><a name="#triangular_matrix_1">[1]</a>
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Supported parameters for the type of the triangular matrix are <code>lower</code>
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, <code>unit_lower</code>, <code>upper</code> and <code>unit_upper</code>
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.</p>
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<p><a name="#triangular_matrix_2">[2]</a>
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Supported parameters for the storage organization are <code>row_major</code>
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and <code>column_major</code>.</p>
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<p><a name="#triangular_matrix_3">[3]</a>
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Supported parameters for the adapted array are <code>unbounded_array<T></code>
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, <code>bounded_array<T></code> and <code>std::vector<T></code>
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. </p>
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<h4>Interface</h4>
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<pre><code> // Array based triangular matrix class<br> template<class T, class F1, class F2, class A><br> class triangular_matrix:<br> public matrix_expression<triangular_matrix<T, F1, F2, A> > {<br> public:<br> typedef std::size_t size_type;<br> typedef std::ptrdiff_t difference_type;<br> typedef T value_type;<br> typedef const T &const_reference;<br> typedef T &reference;<br> typedef const T *const_pointer;<br> typedef T *pointer;<br> typedef F1 functor1_type;<br> typedef F2 functor2_type;<br> typedef A array_type;<br> typedef const A const_array_type;<br> typedef const triangular_matrix<T, F1, F2, A> const_self_type;<br> typedef triangular_matrix<T, F1, F2, A> self_type;<br> typedef const matrix_const_reference<const_self_type> const_closure_type;<br> typedef matrix_reference<self_type> closure_type;<br> typedef packed_tag storage_category;<br> typedef typename F1::packed_category packed_category;<br> typedef typename F2::orientation_category orientation_category;<br><br> // Construction and destruction<br> triangular_matrix ();<br> triangular_matrix (size_type size1, size_type size2);<br> triangular_matrix (const triangular_matrix &m);<br> template<class AE><br> triangular_matrix (const matrix_expression<AE> &ae);<br><br> // Accessors<br> size_type size1 () const;<br> size_type size2 () const;<br> const_array_type &data () const;<br> array_type &data ();<br><br> // Resizing<br> void resize (size_type size1, size_type size2);<br><br> // Element access<br> const_reference operator () (size_type i, size_type j) const;<br> reference operator () (size_type i, size_type j);<br><br> // Assignment<br> triangular_matrix &operator = (const triangular_matrix &m);<br> triangular_matrix &assign_temporary (triangular_matrix &m);<br> template<class AE><br> triangular_matrix &operator = (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_matrix &reset (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_matrix &assign (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_matrix& operator += (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_matrix &plus_assign (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_matrix& operator -= (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_matrix &minus_assign (const matrix_expression<AE> &ae);<br> template<class AT><br> triangular_matrix& operator *= (const AT &at);<br> template<class AT><br> triangular_matrix& operator /= (const AT &at);<br><br> // Swapping<br> void swap (triangular_matrix &m);<br> friend void swap (triangular_matrix &m1, triangular_matrix &m2);<br><br> // Element insertion and erasure<br> void insert (size_type i, size_type j, const_reference t);<br> void erase (size_type i, size_type j);<br> void clear ();<br><br> class const_iterator1;<br> class iterator1;<br> class const_iterator2;<br> class iterator2;<br> typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;<br> typedef reverse_iterator_base1<iterator1> reverse_iterator1;<br> typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;<br> typedef reverse_iterator_base2<iterator2> reverse_iterator2;<br><br> // Element lookup<br> const_iterator1 find_first1 (int rank, size_type i, size_type j) const;<br> iterator1 find_first1 (int rank, size_type i, size_type j);<br> const_iterator1 find_last1 (int rank, size_type i, size_type j) const;<br> iterator1 find_last1 (int rank, size_type i, size_type j);<br> const_iterator2 find_first2 (int rank, size_type i, size_type j) const;<br> iterator2 find_first2 (int rank, size_type i, size_type j);<br> const_iterator2 find_last2 (int rank, size_type i, size_type j) const;<br> iterator2 find_last2 (int rank, size_type i, size_type j);<br><br> // Iterators simply are indices.<br><br> class const_iterator1:<br> public container_const_reference<triangular_matrix>,<br> public random_access_iterator_base<const_iterator1, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename triangular_matrix::difference_type difference_type;<br> typedef typename triangular_matrix::value_type value_type;<br> typedef typename triangular_matrix::const_reference reference;<br> typedef typename triangular_matrix::const_pointer pointer;<br> typedef const_iterator2 dual_iterator_type;<br> typedef const_reverse_iterator2 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> const_iterator1 ();<br> const_iterator1 (const triangular_matrix &m, size_type it1, size_type it2);<br> const_iterator1 (const iterator1 &it);<br><br> // Arithmetic<br> const_iterator1 &operator ++ ();<br> const_iterator1 &operator -- ();<br> const_iterator1 &operator += (difference_type n);<br> const_iterator1 &operator -= (difference_type n);<br> difference_type operator - (const const_iterator1 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> const_iterator2 begin () const;<br> const_iterator2 end () const;<br> const_reverse_iterator2 rbegin () const;<br> const_reverse_iterator2 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> const_iterator1 &operator = (const const_iterator1 &it);<br><br> // Comparison<br> bool operator == (const const_iterator1 &it) const;<br> bool operator <(const const_iterator1 &it) const;<br> };<br><br> const_iterator1 begin1 () const;<br> const_iterator1 end1 () const;<br><br> class iterator1:<br> public container_reference<triangular_matrix>,<br> public random_access_iterator_base<iterator1, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename triangular_matrix::difference_type difference_type;<br> typedef typename triangular_matrix::value_type value_type;<br> typedef typename triangular_matrix::reference reference;<br> typedef typename triangular_matrix::pointer pointer;<br> typedef iterator2 dual_iterator_type;<br> typedef reverse_iterator2 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> iterator1 ();<br> iterator1 (triangular_matrix &m, size_type it1, size_type it2);<br><br> // Arithmetic<br> iterator1 &operator ++ ();<br> iterator1 &operator -- ();<br> iterator1 &operator += (difference_type n);<br> iterator1 &operator -= (difference_type n);<br> difference_type operator - (const iterator1 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> iterator2 begin () const;<br> iterator2 end () const;<br> reverse_iterator2 rbegin () const;<br> reverse_iterator2 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> iterator1 &operator = (const iterator1 &it);<br><br> // Comparison<br> bool operator == (const iterator1 &it) const;<br> bool operator <(const iterator1 &it) const;<br> };<br><br> iterator1 begin1 ();<br> iterator1 end1 ();<br><br> class const_iterator2:<br> public container_const_reference<triangular_matrix>,<br> public random_access_iterator_base<const_iterator2, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename triangular_matrix::difference_type difference_type;<br> typedef typename triangular_matrix::value_type value_type;<br> typedef typename triangular_matrix::const_reference reference;<br> typedef typename triangular_matrix::const_pointer pointer;<br> typedef const_iterator1 dual_iterator_type;<br> typedef const_reverse_iterator1 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> const_iterator2 ();<br> const_iterator2 (const triangular_matrix &m, size_type it1, size_type it2);<br> const_iterator2 (const iterator2 &it);<br><br> // Arithmetic<br> const_iterator2 &operator ++ ();<br> const_iterator2 &operator -- ();<br> const_iterator2 &operator += (difference_type n);<br> const_iterator2 &operator -= (difference_type n);<br> difference_type operator - (const const_iterator2 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> const_iterator1 begin () const;<br> const_iterator1 end () const;<br> const_reverse_iterator1 rbegin () const;<br> const_reverse_iterator1 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> const_iterator2 &operator = (const const_iterator2 &it);<br><br> // Comparison<br> bool operator == (const const_iterator2 &it) const;<br> bool operator <(const const_iterator2 &it) const;<br> };<br><br> const_iterator2 begin2 () const;<br> const_iterator2 end2 () const;<br><br> class iterator2:<br> public container_reference<triangular_matrix>,<br> public random_access_iterator_base<iterator2, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename triangular_matrix::difference_type difference_type;<br> typedef typename triangular_matrix::value_type value_type;<br> typedef typename triangular_matrix::reference reference;<br> typedef typename triangular_matrix::pointer pointer;<br> typedef iterator1 dual_iterator_type;<br> typedef reverse_iterator1 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> iterator2 ();<br> iterator2 (triangu
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lar_matrix &m, size_type it1, size_type it2);<br><br> // Arithmetic<br> iterator2 &operator ++ ();<br> iterator2 &operator -- ();<br> iterator2 &operator += (difference_type n);<br> iterator2 &operator -= (difference_type n);<br> difference_type operator - (const iterator2 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> iterator1 begin () const;<br> iterator1 end () const;<br> reverse_iterator1 rbegin () const;<br> reverse_iterator1 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> iterator2 &operator = (const iterator2 &it);<br><br> // Comparison<br> bool operator == (const iterator2 &it) const;<br> bool operator <(const iterator2 &it) const;<br> };<br><br> iterator2 begin2 ();<br> iterator2 end2 ();<br><br> // Reverse iterators<br><br> const_reverse_iterator1 rbegin1 () const;<br> const_reverse_iterator1 rend1 () const;<br><br> reverse_iterator1 rbegin1 ();<br> reverse_iterator1 rend1 ();<br><br> const_reverse_iterator2 rbegin2 () const;<br> const_reverse_iterator2 rend2 () const;<br><br> reverse_iterator2 rbegin2 ();<br> reverse_iterator2 rend2 ();<br> };</code></pre>
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<h2><a name="triangular_adaptor"></a>
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Triangular Adaptor</h2>
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<h4>Description</h4>
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<p>The templated class <code>triangular_adaptor<M, F> </code>is a triangular
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matrix adaptor for other matrices.</p>
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<h4>Example</h4>
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<pre>#include <boost/numeric/ublas/triangular.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> matrix<double> m (3, 3);<br> triangular_adaptor<matrix<double>, lower> tal (m);<br> for (unsigned i = 0; i < tal.size1 (); ++ i)<br> for (unsigned j = 0; j <= i; ++ j)<br> tal (i, j) = 3 * i + j;<br> std::cout << tal << std::endl;<br> triangular_adaptor<matrix<double>, upper> tau (m);<br> for (unsigned i = 0; i < tau.size1 (); ++ i)<br> for (unsigned j = i; j < tau.size2 (); ++ j)<br> tau (i, j) = 3 * i + j;<br> std::cout << tau << std::endl;<br>}<br></pre>
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<h4>Definition</h4>
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<p>Defined in the header triangular.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1">
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<tbody>
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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>M</code></td>
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<td>The type of the adapted matrix.</td>
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<td> </td>
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</tr>
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<tr>
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<td><code>F</code></td>
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<td>Functor describing the type of the triangular adaptor.
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<a href="#triangular_adaptor_1">[1]</a>
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</td>
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<td><code>lower</code></td>
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</tr>
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</tbody>
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</table>
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<h4>Model of</h4>
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<p><a href="expression.htm#matrix_expression">Matrix Expression</a>
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. </p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a href="expression.htm#matrix_expression">
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Matrix Expression</a>
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.</p>
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<h4>Public base classes</h4>
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<p><code>matrix_expression<triangular_adaptor<M, F> ></code> </p>
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<h4>Members</h4>
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<table border="1">
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<tbody>
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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>triangular_adaptor ()</code> </td>
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<td>Constructs a <code>triangular_adaptor</code> that holds
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zero rows of zero elements.</td>
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</tr>
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<tr>
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<td><code>triangular_adaptor (matrix_type &data)</code></td>
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<td>Constructs a <code>triangular_adaptor</code> of a matrix.</td>
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</tr>
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<tr>
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<td><code>triangular_adaptor (const triangular_adaptor &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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triangular_adaptor (const matrix_expression<AE> &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>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, size_type
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j) const</code></td>
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<td>Returns a <code>const</code> reference of the <code>j</code>
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-th 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>triangular_adaptor &operator = (const triangular_adaptor
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&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>triangular_adaptor &assign_temporary (triangular_adaptor
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&m)</code></td>
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<td>Assigns a temporary. May change the triangular adaptor
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<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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triangular_adaptor &operator = (const matrix_expression<AE>
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&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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triangular_adaptor &assign (const matrix_expression<AE>
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&ae)</code></td>
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<td>Assigns a matrix expression to the triangular adaptor.
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Left and right hand side of the assignment should be 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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triangular_adaptor &operator += (const matrix_expression<AE>
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&ae)</code></td>
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<td>A computed assignment operator. Adds the matrix expression
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to the triangular adaptor.</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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triangular_adaptor &plus_assign (const matrix_expression<AE>
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&ae)</code></td>
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<td>Adds a matrix expression to the triangular adaptor.
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Left and right hand side of the assignment should be 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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triangular_adaptor &operator -= (const matrix_expression<AE>
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&ae)</code></td>
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<td>A computed assignment operator. Subtracts the matrix
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expression from the triangular adaptor.</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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triangular_adaptor &minus_assign (const matrix_expression<AE>
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&ae)</code></td>
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<td>Subtracts a matrix expression from the triangular adaptor.
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Left and right hand side of the assignment should 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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triangular_adaptor &operator *= (const AT &at)</code></td>
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<td>A computed assignment operator. Multiplies the triangular
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adaptor 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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triangular_adaptor &operator /= (const AT &at)</code></td>
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<td>A computed assignment operator. Divides the triangular
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adaptor through a scalar.</td>
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</tr>
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<tr>
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<td><code>void swap (triangular_adaptor &m)</code></td>
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<td>Swaps the contents of the triangular adaptors. </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 the
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beginning of the <code>triangular_adaptor</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 the
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end of the <code>triangular_adaptor</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 beginning
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of the <code>triangular_adaptor</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>triangular_adaptor</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 the
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beginning of the <code>triangular_adaptor</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 the
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end of the <code>triangular_adaptor</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 beginning
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of the <code>triangular_adaptor</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>triangular_adaptor</code>. </td>
|
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</tr>
|
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<tr>
|
|
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
|
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<td>Returns a <code>const_reverse_iterator1</code> pointing
|
|
to the beginning of the reversed <code>triangular_adaptor</code>.
|
|
</td>
|
|
</tr>
|
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<tr>
|
|
<td><code>const_reverse_iterator1 rend1 () const</code></td>
|
|
<td>Returns a <code>const_reverse_iterator1</code> pointing
|
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to the end of the reversed <code>triangular_adaptor</code>. </td>
|
|
</tr>
|
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<tr>
|
|
<td><code>reverse_iterator1 rbegin1 () </code></td>
|
|
<td>Returns a <code>reverse_iterator1</code> pointing to
|
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the beginning of the reversed <code>triangular_adaptor</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reverse_iterator1 rend1 () </code></td>
|
|
<td>Returns a <code>reverse_iterator1</code> pointing to
|
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the end of the reversed <code>triangular_adaptor</code>. </td>
|
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</tr>
|
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<tr>
|
|
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
|
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<td>Returns a <code>const_reverse_iterator2</code> pointing
|
|
to the beginning of the reversed <code>triangular_adaptor</code>.
|
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</td>
|
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</tr>
|
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<tr>
|
|
<td><code>const_reverse_iterator2 rend2 () const</code></td>
|
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<td>Returns a <code>const_reverse_iterator2</code> pointing
|
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to the end of the reversed <code>triangular_adaptor</code>. </td>
|
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</tr>
|
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<tr>
|
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<td><code>reverse_iterator2 rbegin2 () </code></td>
|
|
<td>Returns a <code>reverse_iterator2</code> pointing to
|
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the beginning of the reversed <code>triangular_adaptor</code>. </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>triangular_adaptor</code>. </td>
|
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</tr>
|
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|
|
</tbody>
|
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</table>
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<h4>Notes</h4>
|
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<p><a name="#triangular_adaptor_1">[1]</a>
|
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Supported parameters for the type of the triangular adaptor are <code>lower</code>
|
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, <code>unit_lower</code>, <code>upper</code> and <code>unit_upper</code>
|
|
.</p>
|
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|
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<h4>Interface</h4>
|
|
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<pre><code> // Triangular matrix adaptor class<br> template<class M, class F><br> class triangular_adaptor:<br> public matrix_expression<triangular_adaptor<M, F> > {<br> public:<br> typedef const M const_matrix_type;<br> typedef M matrix_type;<br> typedef F functor_type;<br> typedef typename M::size_type size_type;<br> typedef typename M::difference_type difference_type;<br> typedef typename M::value_type value_type;<br> typedef typename M::const_reference const_reference;<br> typedef typename M::reference reference;<br> typedef typename M::const_pointer const_pointer;<br> typedef typename M::pointer pointer;<br> typedef const triangular_adaptor<M, F> const_self_type;<br> typedef triangular_adaptor<M, F> self_type;<br> typedef const matrix_const_reference<const_self_type> const_closure_type;<br> typedef matrix_reference<self_type> closure_type;<br> typedef typename storage_restrict_traits<typename M::storage_category,<br> packed_proxy_tag>::storage_category storage_category;<br> typedef typename F::packed_category packed_category;<br> typedef typename M::orientation_category orientation_category;<br><br> // Construction and destruction<br> triangular_adaptor ();<br> triangular_adaptor (matrix_type &data);<br> triangular_adaptor (const triangular_adaptor &m);<br><br> // Accessors<br> size_type size1 () const;<br> size_type size2 () const;<br> const_matrix_type &data () const;<br> matrix_type &data ();<br><br><br> // Element access<br> const_reference operator () (size_type i, size_type j) const;<br> reference operator () (size_type i, size_type j);<br><br> // Assignment<br> triangular_adaptor &operator = (const triangular_adaptor &m);<br> triangular_adaptor &assign_temporary (triangular_adaptor &m);<br> template<class AE><br> triangular_adaptor &operator = (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_adaptor &assign (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_adaptor& operator += (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_adaptor &plus_assign (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_adaptor& operator -= (const matrix_expression<AE> &ae);<br> template<class AE><br> triangular_adaptor &minus_assign (const matrix_expression<AE> &ae);<br> template<class AT><br> triangular_adaptor& operator *= (const AT &at);<br> template<class AT><br> triangular_adaptor& operator /= (const AT &at);<br><br> // Swapping<br> void swap (triangular_adaptor &m);<br> friend void swap (triangular_adaptor &m1, triangular_adaptor &m2);<br><br> class const_iterator1;<br> class iterator1;<br> class const_iterator2;<br> class iterator2;<br> typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;<br> typedef reverse_iterator_base1<iterator1> reverse_iterator1;<br> typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;<br> typedef reverse_iterator_base2<iterator2> reverse_iterator2;<br><br> // Element lookup<br> const_iterator1 find_first1 (int rank, size_type i, size_type j) const;<br> iterator1 find_first1 (int rank, size_type i, size_type j);<br> const_iterator1 find_last1 (int rank, size_type i, size_type j) const;<br> iterator1 find_last1 (int rank, size_type i, size_type j);<br> const_iterator2 find_first2 (int rank, size_type i, size_type j) const;<br> iterator2 find_first2 (int rank, size_type i, size_type j);<br> const_iterator2 find_last2 (int rank, size_type i, size_type j) const;<br> iterator2 find_last2 (int rank, size_type i, size_type j);<br><br> // Iterators simply are indices.<br><br> class const_iterator1:<br> public container_const_reference<triangular_adaptor>,<br> public random_access_iterator_base<const_iterator1, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename triangular_adaptor::difference_type difference_type;<br> typedef typename triangular_adaptor::value_type value_type;<br> typedef typename triangular_adaptor::const_reference reference;<br> typedef typename triangular_adaptor::const_pointer pointer;<br> typedef const_iterator2 dual_iterator_type;<br> typedef const_reverse_iterator2 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> const_iterator1 ();<br> const_iterator1 (const triangular_adaptor &m, size_type it1, size_type it2);<br> const_iterator1 (const iterator1 &it);<br><br> // Arithmetic<br> const_iterator1 &operator ++ ();<br> const_iterator1 &operator -- ();<br> const_iterator1 &operator += (difference_type n);<br> const_iterator1 &operator -= (difference_type n);<br> difference_type operator - (const const_iterator1 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> const_iterator2 begin () const;<br> const_iterator2 end () const;<br> const_reverse_iterator2 rbegin () const;<br> const_reverse_iterator2 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> const_iterator1 &operator = (const const_iterator1 &it);<br><br> // Comparison<br> bool operator == (const const_iterator1 &it) const;<br> bool operator <(const const_iterator1 &it) const;<br> };<br><br> const_iterator1 begin1 () const;<br> const_iterator1 end1 () const;<br><br> class iterator1:<br> public container_reference<triangular_adaptor>,<br> public random_access_iterator_base<iterator1, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename triangular_adaptor::difference_type difference_type;<br> typedef typename triangular_adaptor::value_type value_type;<br> typedef typename triangular_adaptor::reference reference;<br> typedef typename triangular_adaptor::pointer pointer;<br> typedef iterator2 dual_iterator_type;<br> typedef reverse_iterator2 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> iterator1 ();<br> iterator1 (triangular_adaptor &m, size_type it1, size_type it2);<br><br> // Arithmetic<br> iterator1 &operator ++ ();<br> iterator1 &operator -- ();<br> iterator1 &operator += (difference_type n);<br> iterator1 &operator -= (difference_type n);<br> difference_type operator - (const iterator1 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> iterator2 begin () const;<br> iterator2 end () const;<br> reverse_iterator2 rbegin () const;<br> reverse_iterator2 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> iterator1 &operator = (const iterator1 &it);<br><br> // Comparison<br> bool operator == (const iterator1 &it) const;<br> bool operator <(const iterator1 &it) const;<br> };<br><br> iterator1 begin1 ();<br> iterator1 end1 ();<br><br> class const_iterator2:<br> public container_const_reference<triangular_adaptor>,<br> public random_access_iterator_base<const_iterator2, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename triangular_adaptor::difference_type difference_type;<br> typedef typename triangular_adaptor::value_type value_type;<br> typedef typename triangular_adaptor::const_reference reference;<br> typedef typename triangular_adaptor::const_pointer pointer;<br> typedef const_iterator1 dual_iterator_type;<br> typedef const_reverse_iterator1 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> const_iterator2 ();<br> const_iterator2 (const triangular_adaptor &m, size_type it1, size_type it2);<br> const_iterator2 (const iterator2 &it);<br><br> // Arithmetic<br> const_iterator2 &operator ++ ();<br> const_iterator2 &operator -- ();<br> const_iterator2 &operator += (difference_type n);<br> const_iterator2 &operator -= (difference_type n);<br> difference_type operator - (const const_iterator2 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> const_iterator1 begin () const;<br> const_iterator1 end () const;<br> const_reverse_iterator1 rbegin () const;<br> const_reverse_iterator1 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> const_iterator2 &operator = (const const_iterator2 &it);<br><br> // Comparison<br> bool operator == (const const_iterator2 &it) const;<br> bool operator <(const const_iterator2 &it) const;<br> };<br><br> const_iterator2 begin2 () const;<br> const_iterator2 end2 () const;<br><br> class iterator2:<br> public container_reference<triangular_adaptor>,<br> public random_access_iterator_base<iterator2, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename triangular_adaptor::difference_type difference_type;<br> typedef typename triangular_adaptor::value_type value_type;<br> typedef typename triangular_adaptor::reference reference;<br> typedef typename triangular_adaptor::pointer pointer;<br> typedef iterator1 dual_iterator_type;<br> typedef reverse_iterator1 dual_reverse_iterator_type;<br><br> // Construction and destruction<br> iterator2 ();<br> iterator2 (triangular_adaptor &m, size_type it1, size_type it2);<br><br> // Arithmetic<br> iterator2 &operator ++ ();<br> iterator2 &operator -- ();<br> iterator2 &operator += (difference_type n);<br> iterator2 &operator -= (difference_type n);<br> difference_type operator - (const iterator2 &it) const;<br><br> // Dereference<br> reference operator * () const;<br><br> iterator1 begin () const;<br> iterator1 end () const;<br> reverse_iterator1 rbegin () const;<br> reverse_iterator1 rend () const;<br><br> // Indices<br> size_type index1 () const;<br> size_type index2 () const;<br><br> // Assignment<br> iterator2 &operator = (const iterator2 &it);<br><br> // Comparison<br> bool operator == (const iterator2 &it) const;<br> bool operator <(const iterator2 &it) const;<br> };<br><br> iterator2 begin2 ();<br> iterator2 end2 ();<br><br> // Reverse iterators<br><br> const_reverse_iterator1 rbegin1 () const;<br> const_reverse_iterator1 rend1 () const;<br><br> reverse_iterator1 rbegin1 ();<br> reverse_iterator1 rend1 ();<br><br> const_reverse_iterator2 rbegin2 () const;<br> const_reverse_iterator2 rend2 ()
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const;<br><br> reverse_iterator2 rbegin2 ();<br> reverse_iterator2 rend2 ();<br> };</code></pre>
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<hr>
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<p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch <br>
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Permission to copy, use, modify, sell and distribute this document is granted
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provided this copyright notice appears in all copies. This document is provided
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``as is'' without express or implied warranty, and with no claim as to its
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suitability for any purpose.</p>
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<p>Last revised: 1/15/2003</p>
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