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19 KiB
HTML
581 lines
19 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C/utf-8XHTML 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>Banded Matrix</title>
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</head>
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<body>
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<h1><img src="../../../../boost.png" align="middle" />Banded Matrix</h1>
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<div class="toc" id="toc"></div>
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<h2><a name="banded_matrix"></a>Banded Matrix</h2>
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<h4>Description</h4>
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<p>The templated class <code>banded_matrix<T, F, A></code> is
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the base container adaptor for banded matrices. For a <em>(m x
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n</em>)-dimensional banded matrix with <em>l</em> lower and
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<em>u</em> upper diagonals and <em>0 <= i < m</em>, <em>0
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<= j < n</em> holds <em>b</em><sub><em>i, j</em></sub> <em>=
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0</em>, if <em>i > j + l</em> or <em>i < j - u</em>. The
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storage of banded matrices is packed.</p>
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<h4>Example</h4>
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<pre>
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#include <boost/numeric/ublas/banded.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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banded_matrix<double> m (3, 3, 1, 1);
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for (signed i = 0; i < signed (m.size1 ()); ++ i)
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for (signed j = std::max (i - 1, 0); j < std::min (i + 2, signed (m.size2 ())); ++ j)
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m (i, j) = 3 * i + j;
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std::cout << m << std::endl;
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}
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</pre>
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<h4>Definition</h4>
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<p>Defined in the header banded.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>F</code></td>
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<td>Functor describing the storage organization. <a href=
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"#banded_matrix_1">[1]</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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"#banded_matrix_2">[2]</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<banded_matrix<T, F, 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>banded_matrix ()</code></td>
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<td>Allocates an uninitialized <code>banded_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>banded_matrix (size_type size1, size_type size2,
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size_type lower = 0, size_type upper = 0)</code></td>
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<td>Allocates an uninitialized <code>banded_matrix</code> that
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holds <code>(lower + 1 + upper)</code> diagonals around the main
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diagonal of a matrix with <code>size1</code> rows of
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<code>size2</code> elements.</td>
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</tr>
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<tr>
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<td><code>banded_matrix (const banded_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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banded_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, size_type
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lower = 0, size_type upper = 0, bool preserve = true)</code></td>
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<td>Reallocates a <code>banded_matrix</code> to hold <code>(lower +
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1 + upper)</code> diagonals around the main diagonal of a matrix
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with <code>size1</code> rows of <code>size2</code> elements. The
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existing elements of the <code>banded_matrix</code> are preseved
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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>size_type lower () const</code></td>
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<td>Returns the number of diagonals below the main diagonal.</td>
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</tr>
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<tr>
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<td><code>size_type upper () const</code></td>
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<td>Returns the number of diagonals above the main diagonal.</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>banded_matrix &operator = (const banded_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>banded_matrix &assign_temporary (banded_matrix
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&m)</code></td>
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<td>Assigns a temporary. May change the banded 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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banded_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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banded_matrix &assign (const matrix_expression<AE>
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&ae)</code></td>
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<td>Assigns a matrix expression to the banded 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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banded_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 to
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the banded 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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banded_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 banded matrix. Left and right
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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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banded_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 expression
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from the banded 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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banded_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 banded 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 AT><br />
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banded_matrix &operator *= (const AT &at)</code></td>
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<td>A computed assignment operator. Multiplies the banded matrix
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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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banded_matrix &operator /= (const AT &at)</code></td>
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<td>A computed assignment operator. Divides the banded 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 (banded_matrix &m)</code></td>
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<td>Swaps the contents of the banded 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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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="banded_matrix_1" id="banded_matrix_1">[1]</a> Supported
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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="banded_matrix_2" id="banded_matrix_2">[2]</a> Supported
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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="banded_adaptor"></a>Banded Adaptor</h2>
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<h4>Description</h4>
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<p>The templated class <code>banded_adaptor<M></code> is a
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banded 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/banded.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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banded_adaptor<matrix<double> > ba (m, 1, 1);
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for (signed i = 0; i < signed (ba.size1 ()); ++ i)
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for (signed j = std::max (i - 1, 0); j < std::min (i + 2, signed (ba.size2 ())); ++ j)
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ba (i, j) = 3 * i + j;
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std::cout << ba << std::endl;
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}
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</pre>
|
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<h4>Definition</h4>
|
|
<p>Defined in the header banded.hpp.</p>
|
|
<h4>Template parameters</h4>
|
|
<table border="1" summary="parameters">
|
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<tbody>
|
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<tr>
|
|
<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>
|
|
</tbody>
|
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</table>
|
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<h4>Model of</h4>
|
|
<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
|
|
.</p>
|
|
<h4>Type requirements</h4>
|
|
<p>None, except for those imposed by the requirements of <a href=
|
|
"expression_concept.html#matrix_expression">Matrix Expression</a> .</p>
|
|
<h4>Public base classes</h4>
|
|
<p><code>matrix_expression<banded_adaptor<M>
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|
></code></p>
|
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<h4>Members</h4>
|
|
<table border="1" summary="members">
|
|
<tbody>
|
|
<tr>
|
|
<th>Member</th>
|
|
<th>Description</th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>banded_adaptor (matrix_type &data, size_type lower =
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0, size_type upper = 0)</code></td>
|
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<td>Constructs a <code>banded_adaptor</code> that holds
|
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<code>(lower + 1 + upper)</code> diagonals around the main diagonal
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|
of a matrix.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>banded_adaptor (const banded_adaptor &m)</code></td>
|
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<td>The copy constructor.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
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|
banded_adaptor (const matrix_expression<AE>
|
|
&ae)</code></td>
|
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<td>The extended copy constructor.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size1 () const</code></td>
|
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<td>Returns the number of rows.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size2 () const</code></td>
|
|
<td>Returns the number of columns.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type lower () const</code></td>
|
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<td>Returns the number of diagonals below the main diagonal.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type upper () const</code></td>
|
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<td>Returns the number of diagonals above the main diagonal.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reference operator () (size_type i, size_type j)
|
|
const</code></td>
|
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<td>Returns a <code>const</code> reference of the <code>j</code>
|
|
-th element in the <code>i</code>-th row.</td>
|
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</tr>
|
|
<tr>
|
|
<td><code>reference operator () (size_type i, size_type
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j)</code></td>
|
|
<td>Returns a reference of the <code>j</code>-th element in the
|
|
<code>i</code>-th row.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>banded_adaptor &operator = (const banded_adaptor
|
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&m)</code></td>
|
|
<td>The assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>banded_adaptor &assign_temporary (banded_adaptor
|
|
&m)</code></td>
|
|
<td>Assigns a temporary. May change the banded adaptor
|
|
<code>m</code> .</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
banded_adaptor &operator = (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>The extended assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
banded_adaptor &assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Assigns a matrix expression to the banded adaptor. Left and
|
|
right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
banded_adaptor &operator += (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Adds the matrix expression to
|
|
the banded adaptor.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
banded_adaptor &plus_assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Adds a matrix expression to the banded adaptor. Left and right
|
|
hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
banded_adaptor &operator -= (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Subtracts the matrix expression
|
|
from the banded adaptor.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br />
|
|
banded_adaptor &minus_assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Subtracts a matrix expression from the banded adaptor. Left and
|
|
right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br />
|
|
banded_adaptor &operator *= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Multiplies the banded adaptor
|
|
with a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br />
|
|
banded_adaptor &operator /= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Divides the banded adaptor
|
|
through a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void swap (banded_adaptor &m)</code></td>
|
|
<td>Swaps the contents of the banded 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>banded_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>banded_adaptor</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 begin1 ()</code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the beginning of
|
|
the <code>banded_adaptor</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 end1 ()</code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the end of the
|
|
<code>banded_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>banded_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>banded_adaptor</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 begin2 ()</code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the beginning of
|
|
the <code>banded_adaptor</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 end2 ()</code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the end of the
|
|
<code>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_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>banded_adaptor</code>.</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<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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