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603 lines
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603 lines
20 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml">
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<head>
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<meta name="generator" content=
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"HTML Tidy for Linux/x86 (vers 1st March 2004), see www.w3.org" />
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<meta http-equiv="Content-Type" content=
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"text/html; charset=us-ascii" />
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<link rel="stylesheet" href="../../../../boost.css" type="text/css"/>
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<link rel="stylesheet" href="ublas.css" type="text/css" />
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<script type="text/javascript" src="js/jquery-1.3.2.min.js" async="async" ></script>
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<script type="text/javascript" src="js/jquery.toc-gw.js" async="async" ></script>
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<title>Triangular Matrix</title>
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</head>
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<body>
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<h1><img src="../../../../boost.png" align="middle" />Triangular Matrix</h1>
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<div class="toc" id="toc"></div>
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<h2><a name="triangular_matrix"></a>Triangular Matrix</h2>
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<h4>Description</h4>
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<p>The templated class <code>triangular_matrix<T, F1, F2,
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A></code> is the base container adaptor for triangular matrices.
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For a <em>(n x n</em> )-dimensional lower triangular matrix and
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<em>0 <= i < n</em>,<em>0 <= j < n</em> holds
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<em>t</em><sub><em>i, j</em></sub> <em>= 0</em> , if <em>i >
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j</em>. If furthermore holds t<sub><em>i, i</em></sub><em>= 1</em>
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the matrix is called unit lower triangular. For a <em>(n x n</em>
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)-dimensional lower triangular matrix and <em>0 <= i <
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n</em>,<em>0 <= j < n</em> holds <em>t</em><sub><em>i,
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j</em></sub> <em>= 0</em> , if <em>i < j</em>. If furthermore
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holds t<sub><em>i, i</em></sub><em>= 1</em> the matrix is called
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unit lower triangular. The storage of triangular matrices is
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packed.</p>
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<h4>Example</h4>
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<pre>
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#include <boost/numeric/ublas/triangular.hpp>
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#include <boost/numeric/ublas/io.hpp>
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int main () {
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using namespace boost::numeric::ublas;
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triangular_matrix<double, lower> ml (3, 3);
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for (unsigned i = 0; i < ml.size1 (); ++ i)
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for (unsigned j = 0; j <= i; ++ j)
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ml (i, j) = 3 * i + j;
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std::cout << ml << std::endl;
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triangular_matrix<double, upper> mu (3, 3);
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for (unsigned i = 0; i < mu.size1 (); ++ i)
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for (unsigned j = i; j < mu.size2 (); ++ j)
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mu (i, j) = 3 * i + j;
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std::cout << mu << std::endl;
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}
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</pre>
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<p>Please read the <a href="samples/ex_triangular.cpp">full triangular example</a> for more details.</p>
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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" summary="parameters">
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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. <a href=
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"#triangular_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 href=
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"#triangular_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 href=
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"#triangular_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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</tbody>
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</table>
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<h4>Model of</h4>
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<p><a href="container_concept.html#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 href=
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"container_concept.html#matrix">Matrix</a> .</p>
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<h4>Public base classes</h4>
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<p><code>matrix_container<triangular_matrix<T, F1, F2, A>
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></code></p>
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<h4>Members</h4>
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<table border="1" summary="members">
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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> that
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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> that
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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
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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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triangular_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 size1, size_type size2, bool
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preserve = true)</code></td>
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<td>Reallocates a <code>triangular_matrix</code> to hold
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<code>size1</code> rows of <code>size2</code> elements. The
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existing elements of the <code>triangular_matrix</code> are
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preseved when specified.</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 j)
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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 in the
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<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
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triangular_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>triangular_matrix &assign_temporary
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(triangular_matrix &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
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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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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. Left and
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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
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matrix_expression<AE> &ae)</code></td>
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<td>A computed assignment operator. Adds the matrix expression to
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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
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matrix_expression<AE> &ae)</code></td>
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<td>Adds a matrix expression to the triangular matrix. Left and
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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
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matrix_expression<AE> &ae)</code></td>
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<td>A computed assignment operator. Subtracts the matrix expression
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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
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matrix_expression<AE> &ae)</code></td>
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<td>Subtracts a matrix expression from 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 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 matrix
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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 the
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<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 end of
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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 of
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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 of the
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<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 end of
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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 of
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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 of the
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<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 to the
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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>const_reverse_iterator1 rend1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code> pointing to the
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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 the
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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 the end of
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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 to the
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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>const_reverse_iterator2 rend2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</code> pointing to the
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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 the
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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 the end of
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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
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<code>lower</code> , <code>unit_lower</code>, <code>upper</code>
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and <code>unit_upper</code> .</p>
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<p><a name="triangular_matrix_2">[2]</a>
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Supported parameters for the storage organization are
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<code>row_major</code> 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
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<code>unbounded_array<T></code> ,
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<code>bounded_array<T></code> and
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<code>std::vector<T></code> .</p>
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<h2><a name="triangular_adaptor"></a>Triangular Adaptor</h2>
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<h4>Description</h4>
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<p>The templated class <code>triangular_adaptor<M, F></code>
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is a triangular matrix adaptor for other matrices.</p>
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<h4>Example</h4>
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<pre>
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#include <boost/numeric/ublas/triangular.hpp>
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#include <boost/numeric/ublas/io.hpp>
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int main () {
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using namespace boost::numeric::ublas;
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matrix<double> m (3, 3);
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triangular_adaptor<matrix<double>, lower> tal (m);
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for (unsigned i = 0; i < tal.size1 (); ++ i)
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for (unsigned j = 0; j <= i; ++ j)
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tal (i, j) = 3 * i + j;
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std::cout << tal << std::endl;
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triangular_adaptor<matrix<double>, upper> tau (m);
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for (unsigned i = 0; i < tau.size1 (); ++ i)
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for (unsigned j = i; j < tau.size2 (); ++ j)
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tau (i, j) = 3 * i + j;
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std::cout << tau << std::endl;
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}
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</pre>
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<p>Please read the <a href="samples/ex_triangular.cpp">full triangular example</a> for more details.</p>
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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" summary="parameters">
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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. <a href=
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"#triangular_adaptor_1">[1]</a></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_concept.html#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=
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"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
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<h4>Public base classes</h4>
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<p><code>matrix_expression<triangular_adaptor<M, F>
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></code></p>
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<h4>Members</h4>
|
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<table border="1" summary="members">
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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 (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
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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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triangular_adaptor (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>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 j)
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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 in the
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<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 &m)</code></td>
|
|
<td>The assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>triangular_adaptor &assign_temporary
|
|
(triangular_adaptor &m)</code></td>
|
|
<td>Assigns a temporary. May change the triangular adaptor
|
|
<code>m</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
triangular_adaptor &operator = (const
|
|
matrix_expression<AE> &ae)</code></td>
|
|
<td>The extended assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
triangular_adaptor &assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Assigns a matrix expression to the triangular adaptor. Left and
|
|
right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
triangular_adaptor &operator += (const
|
|
matrix_expression<AE> &ae)</code></td>
|
|
<td>A computed assignment operator. Adds the matrix expression to
|
|
the triangular adaptor.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
triangular_adaptor &plus_assign (const
|
|
matrix_expression<AE> &ae)</code></td>
|
|
<td>Adds a matrix expression to the triangular adaptor. Left and
|
|
right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
triangular_adaptor &operator -= (const
|
|
matrix_expression<AE> &ae)</code></td>
|
|
<td>A computed assignment operator. Subtracts the matrix expression
|
|
from the triangular adaptor.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
triangular_adaptor &minus_assign (const
|
|
matrix_expression<AE> &ae)</code></td>
|
|
<td>Subtracts a matrix expression from the triangular adaptor. Left
|
|
and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br />
|
|
triangular_adaptor &operator *= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Multiplies the triangular
|
|
adaptor with a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br />
|
|
triangular_adaptor &operator /= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Divides the triangular adaptor
|
|
through a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void swap (triangular_adaptor &m)</code></td>
|
|
<td>Swaps the contents of the triangular 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>triangular_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>triangular_adaptor</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 begin1 ()</code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the beginning of
|
|
the <code>triangular_adaptor</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 end1 ()</code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the end of the
|
|
<code>triangular_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>triangular_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>triangular_adaptor</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 begin2 ()</code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the beginning of
|
|
the <code>triangular_adaptor</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 end2 ()</code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the end of the
|
|
<code>triangular_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>triangular_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>triangular_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>triangular_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>triangular_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>triangular_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>triangular_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>triangular_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>triangular_adaptor</code>.</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<h4>Notes</h4>
|
|
<p><a name="triangular_adaptor_1">[1]</a>
|
|
Supported parameters for the type of the triangular adaptor are
|
|
<code>lower</code> , <code>unit_lower</code>, <code>upper</code>
|
|
and <code>unit_upper</code> .</p>
|
|
<hr />
|
|
<p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br />
|
|
Use, modification and distribution are subject to the
|
|
Boost Software License, Version 1.0.
|
|
(See accompanying file LICENSE_1_0.txt
|
|
or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
|
|
http://www.boost.org/LICENSE_1_0.txt
|
|
</a>).
|
|
</p>
|
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