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605 lines
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605 lines
48 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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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>Banded 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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Banded Matrix</h1>
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<h2><a name="banded_matrix"></a>
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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 the base
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container adaptor for banded matrices. For a <em>(m x n</em>)-dimensional
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banded matrix with <em>l</em> lower and <em>u</em> upper diagonals and <em>
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0 <= i < m</em>,<em> 0 <= j < n</em> holds <em>b</em><sub><em>
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i, j</em></sub><em> = 0</em>, if <em>i > j + l</em> or <em>i < j -
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u</em>. The storage of banded matrices is packed.</p>
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<h4>Example</h4>
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<pre>#include <boost/numeric/ublas/banded.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> banded_matrix<double> m (3, 3, 1, 1);<br> for (signed i = 0; i < signed (m.size1 ()); ++ i)<br> for (signed j = std::max (i - 1, 0); j < std::min (i + 2, signed (m.size2 ())); ++ j)<br> m (i, j) = 3 * i + j;<br> std::cout << m << std::endl;<br>}<br></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">
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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="#banded_matrix_1">
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[1]</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="#banded_matrix_2">[2]</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<banded_matrix<T, F, A> ></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>banded_matrix ()</code> </td>
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<td>Allocates an uninitialized <code>banded_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>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>
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that holds <code>(lower + 1 + upper)</code> diagonals around the
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main diagonal of a matrix with <code>size1</code> rows of <code>size2</code>
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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> &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,
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size_type lower = 0, size_type upper = 0)</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
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a matrix with <code>size1</code> rows of <code>size2</code> elements.
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The content of the <code>banded_matrix</code> 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>size_type lower () const</code></td>
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<td>Returns the number of diagonals below the main diagonal.
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</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.
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</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>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 <code>m</code>
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.</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
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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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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
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to 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
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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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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
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expression 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.
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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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banded_matrix &operator *= (const AT &at)</code></td>
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<td>A computed assignment operator. Multiplies the banded
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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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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
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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>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
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end of 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
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of 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
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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 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
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end of 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
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of 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
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of the <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
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to the 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
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to the 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
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the 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
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the 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>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>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
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to the 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
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the 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
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the end of 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">[1]</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="#banded_matrix_2">[2]</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 banded matrix class<br> template<class T, class F, class A><br> class banded_matrix:<br> public matrix_expression<banded_matrix<T, F, 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 F functor_type;<br> typedef A array_type;<br> typedef const A const_array_type;<br> typedef const banded_matrix<T, F, A> const_self_type;<br> typedef banded_matrix<T, F, 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 F::orientation_category orientation_category;<br><br> // Construction and destruction<br> banded_matrix ();<br> banded_matrix (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0);<br> banded_matrix (const banded_matrix &m);<br> template<class AE><br> banded_matrix (const matrix_expression<AE> &ae, size_type lower = 0, size_type upper = 0);<br><br> // Accessors<br> size_type size1 () const;<br> size_type size2 () const;<br> size_type lower () const;<br> size_type upper () const;<br> const_array_type &data () const;<br> array_type &data ();<br><br> // Resizing<br> void resize (size_type size1, size_type size2, size_type lower = 0, size_type upper = 0);<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> banded_matrix &operator = (const banded_matrix &m);<br> banded_matrix &assign_temporary (banded_matrix &m);<br> template<class AE><br> banded_matrix &operator = (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_matrix &reset (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_matrix &assign (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_matrix& operator += (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_matrix &plus_assign (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_matrix& operator -= (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_matrix &minus_assign (const matrix_expression<AE> &ae);<br> template<class AT><br> banded_matrix& operator *= (const AT &at);<br> template<class AT><br> banded_matrix& operator /= (const AT &at);<br><br> // Swapping<br> void swap (banded_matrix &m);<br> friend void swap (banded_matrix &m1, banded_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 find1 (int rank, size_type i, size_type j) const;<br> iterator1 find1 (int rank, size_type i, size_type j);<br> const_iterator2 find2 (int rank, size_type i, size_type j) const;<br> iterator2 find2 (int rank, size_type i, size_type j);<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<banded_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 banded_matrix::difference_type difference_type;<br> typedef typename banded_matrix::value_type value_type;<br> typedef typename banded_matrix::const_reference reference;<br> typedef typename banded_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 banded_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<banded_matrix>,<br> public random_access_iterator_base<iterator1, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename banded_matrix::difference_type difference_type;<br> typedef typename banded_matrix::value_type value_type;<br> typedef typename banded_matrix::reference reference;<br> typedef typename banded_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 (banded_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<banded_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 banded_matrix::difference_type difference_type;<br> typedef typename banded_matrix::value_type value_type;<br> typedef typename banded_matrix::const_reference reference;<br> typedef typename banded_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 banded_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<banded_matrix>,<br> public random_access_iterator_base<iterator2, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename banded_matrix::difference_type difference_type;<br> typedef typename banded_matrix::value_type value_type;<br> typedef typename banded_matrix::reference reference;<br> typedef typename banded_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 (banded_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> iterat
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or1 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="banded_adaptor"></a>
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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 banded matrix
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adaptor for other matrices.</p>
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<h4>Example</h4>
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<pre>#include <boost/numeric/ublas/banded.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> banded_adaptor<matrix<double> > ba (m, 1, 1);<br> for (signed i = 0; i < signed (ba.size1 ()); ++ i)<br> for (signed j = std::max (i - 1, 0); j < std::min (i + 2, signed (ba.size2 ())); ++ j)<br> ba (i, j) = 3 * i + j;<br> std::cout << ba << std::endl;<br>}<br></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">
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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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</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<banded_adaptor<M> ></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>banded_adaptor ()</code> </td>
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<td>Constructs a <code>banded_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>banded_adaptor (matrix_type &data, size_type
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lower = 0, size_type upper = 0)</code></td>
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<td>Constructs a <code>banded_adaptor</code> that holds <code>(lower
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+ 1 + upper)</code> diagonals around the main diagonal of
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a matrix.</td>
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</tr>
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<tr>
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<td><code>banded_adaptor (const banded_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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banded_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>size_type lower () const</code></td>
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<td>Returns the number of diagonals below the main diagonal.
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</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.
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</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>banded_adaptor &operator = (const banded_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>banded_adaptor &assign_temporary (banded_adaptor
|
|
&m)</code></td>
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<td>Assigns a temporary. May change the banded adaptor <code>m</code>
|
|
.</td>
|
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</tr>
|
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<tr>
|
|
<td><code>template<class AE><br>
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banded_adaptor &operator = (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>The extended assignment operator.</td>
|
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</tr>
|
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<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>
|
|
|
|
<h4>Interface</h4>
|
|
|
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<pre><code> // Banded matrix adaptor class<br> template<class M><br> class banded_adaptor:<br> public matrix_expression<banded_adaptor<M> > {<br> public:<br> typedef const M const_matrix_type;<br> typedef M matrix_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 banded_adaptor<M> const_self_type;<br> typedef banded_adaptor<M> 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 M::orientation_category orientation_category;<br><br> // Construction and destruction<br> banded_adaptor ();<br> banded_adaptor (matrix_type &data, size_type lower = 0, size_type upper = 0);<br> banded_adaptor (const banded_adaptor &m);<br><br> // Accessors<br> size_type size1 () const;<br> size_type size2 () const;<br> size_type lower () const;<br> size_type upper () const;<br> const_matrix_type &data () const;<br> matrix_type &data ();<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> banded_adaptor &operator = (const banded_adaptor &m);<br> banded_adaptor &assign_temporary (banded_adaptor &m);<br> template<class AE><br> banded_adaptor &operator = (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_adaptor &assign (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_adaptor& operator += (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_adaptor &plus_assign (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_adaptor& operator -= (const matrix_expression<AE> &ae);<br> template<class AE><br> banded_adaptor &minus_assign (const matrix_expression<AE> &ae);<br> template<class AT><br> banded_adaptor& operator *= (const AT &at);<br> template<class AT><br> banded_adaptor& operator /= (const AT &at);<br><br> // Swapping<br> void swap (banded_adaptor &m);<br> friend void swap (banded_adaptor &m1, banded_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 find1 (int rank, size_type i, size_type j) const;<br> iterator1 find1 (int rank, size_type i, size_type j);<br> const_iterator2 find2 (int rank, size_type i, size_type j) const;<br> iterator2 find2 (int rank, size_type i, size_type j);<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<banded_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 banded_adaptor::difference_type difference_type;<br> typedef typename banded_adaptor::value_type value_type;<br> typedef typename banded_adaptor::const_reference reference;<br> typedef typename banded_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 banded_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<banded_adaptor>,<br> public random_access_iterator_base<iterator1, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename banded_adaptor::difference_type difference_type;<br> typedef typename banded_adaptor::value_type value_type;<br> typedef typename banded_adaptor::reference reference;<br> typedef typename banded_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 (banded_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<banded_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 banded_adaptor::difference_type difference_type;<br> typedef typename banded_adaptor::value_type value_type;<br> typedef typename banded_adaptor::const_reference reference;<br> typedef typename banded_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 banded_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<banded_adaptor>,<br> public random_access_iterator_base<iterator2, value_type> {<br> public:<br> typedef packed_random_access_iterator_tag iterator_category;<br> typedef typename banded_adaptor::difference_type difference_type;<br> typedef typename banded_adaptor::value_type value_type;<br> typedef typename banded_adaptor::reference reference;<br> typedef typename banded_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 (banded_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 () 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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