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623 lines
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HTML
623 lines
23 KiB
HTML
<html>
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<head>
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<meta http-equiv="Content-Type"
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content="text/html; charset=iso-8859-1">
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<meta name="GENERATOR" content="Microsoft FrontPage Express 2.0">
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<title>Sparse Matrix</title>
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</head>
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<body bgcolor="#FFFFFF">
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<h1><img src="c++boost.gif" alt="c++boost.gif" align="center"
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width="277" height="86">Sparse Matrix</h1>
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<h2><a name="sparse_matrix"></a>Sparse Matrix</h2>
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<h4>Description</h4>
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<p>The templated class <code>sparse_matrix<T, F, A> </code>is
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the base container adaptor for sparse matrices. For a <em>(m x n</em>)-dimensional
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sparse matrix and <em>0 <= i < m</em>,<em> 0 <= j < n</em>
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every non-zero element <em>m</em><sub><em>i, j</em></sub> is
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mapped to the <em>(i x n + j)-</em>th element of the container
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for row major orientation or the <em>(i + j x m)-</em>th element
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of the container for column major orientation.</p>
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<h4>Example</h4>
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<pre>int main () {
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using namespace boost::numeric::ublas;
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sparse_matrix<double> m (3, 3, 3 * 3);
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for (int i = 0; i < m.size1 (); ++ i)
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for (int j = 0; j < 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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}</pre>
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<h4>Definition</h4>
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<p>Defined in the header matrix_sparse.hpp.</p>
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<h4>Template parameters</h4>
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<table border="1">
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<tr>
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<th>Parameter </th>
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<th>Description </th>
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<th>Default </th>
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</tr>
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<tr>
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<td><code>T</code> </td>
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<td>The type of object stored in the sparse 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="#sparse_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="#sparse_matrix_2">[2]</a></td>
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<td><code>map_array<std::size_t, T></code></td>
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</tr>
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</table>
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<h4>Model of</h4>
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<p><a href="container.htm#matrix">Matrix</a>. </p>
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<h4>Type requirements</h4>
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<p>None, except for those imposed by the requirements of <a
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href="container.htm#matrix">Matrix</a>.</p>
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<h4>Public base classes</h4>
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<p><code>matrix_expression<sparse_matrix<T, F, A> ></code>
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</p>
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<h4>Members</h4>
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<table border="1">
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<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>sparse_matrix ()</code> </td>
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<td>Allocates a <code>sparse_matrix </code>that holds at
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most zero rows of zero elements.</td>
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</tr>
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<tr>
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<td><code>sparse_matrix (size_type size1, size_type2,
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size_type non_zeros)</code></td>
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<td>Allocates a <code>sparse_matrix </code>that holds at
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most <code>size1 </code>rows of <code>size2 </code>elements.</td>
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</tr>
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<tr>
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<td><code>sparse_matrix (const sparse_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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sparse_matrix (size_type non_zeros, const
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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 non_zeros)</code></td>
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<td>Reallocates a <code>sparse_matrix </code>to hold at
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most <code>size1 </code>rows of <code>size2 </code>elements.
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The content of the <code>sparse_matrix </code>is
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preserved.</td>
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</tr>
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<tr>
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<td><code>size_type size1 () const</code></td>
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<td>Returns the number of rows. </td>
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</tr>
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<tr>
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<td><code>size_type size2 () const</code></td>
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<td>Returns the number of columns. </td>
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</tr>
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<tr>
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<td><code>const_reference operator () (size_type i,
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size_type j) const</code></td>
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<td>Returns the value of the <code>j</code>-th element in
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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>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>sparse_matrix &operator = (const
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sparse_matrix &m)</code></td>
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<td>The assignment operator.</td>
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</tr>
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<tr>
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<td><code>sparse_matrix &assign_temporary
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(sparse_matrix &m)</code></td>
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<td>Assigns a temporary. May change the sparse matrix <code>m</code>.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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sparse_matrix &operator = (const
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matrix_expression<AE> &ae)</code></td>
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<td>The extended assignment operator.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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sparse_matrix &assign (const
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matrix_expression<AE> &ae)</code></td>
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<td>Assigns a matrix expression to the sparse matrix.
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Left and right hand side of the assignment should be
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independent.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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sparse_matrix &operator += (const
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matrix_expression<AE> &ae)</code></td>
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<td>A computed assignment operator. Adds the matrix
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expression to the sparse 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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sparse_matrix &plus_assign (const
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matrix_expression<AE> &ae)</code></td>
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<td>Adds a matrix expression to the sparse matrix. Left
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and right hand side of the assignment should be
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independent.</td>
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</tr>
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<tr>
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<td><code>template<class AE><br>
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sparse_matrix &operator -= (const
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matrix_expression<AE> &ae)</code></td>
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<td>A computed assignment operator. Subtracts the matrix
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expression from the sparse 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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sparse_matrix &minus_assign (const
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matrix_expression<AE> &ae)</code></td>
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<td>Subtracts a matrix expression from the sparse matrix.
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Left and right hand side of the assignment should be
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independent.</td>
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</tr>
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<tr>
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<td><code>template<class AT><br>
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sparse_matrix &operator *= (const AT &at)</code></td>
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<td>A computed assignment operator. Multiplies the sparse
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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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sparse_matrix &operator /= (const AT &at)</code></td>
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<td>A computed assignment operator. Divides the sparse
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matrix through a scalar.</td>
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</tr>
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<tr>
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<td><code>void swap (sparse_matrix &m)</code></td>
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<td>Swaps the contents of the sparse matrices. </td>
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</tr>
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<tr>
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<td><code>void insert (size_type i, size_type j,
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const_reference t)</code></td>
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<td>Inserts the value <code>t</code> at the <code>j</code>-th
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element of the <code>i</code>-th row.</td>
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</tr>
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<tr>
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<td><code>void erase (size_type i, size_type j)</code></td>
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<td>Erases the value at the <code>j</code>-th element 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 sparse matrix.</td>
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</tr>
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<tr>
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<td><code>const_iterator1 begin1 () const</code></td>
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<td>Returns a <code>const_iterator1</code> pointing to
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the beginning of the <code>sparse_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>const_iterator1 end1 () const</code></td>
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<td>Returns a <code>const_iterator1</code> pointing to
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the end of the <code>sparse_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>iterator1 begin1 () </code></td>
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<td>Returns a <code>iterator1</code> pointing to the
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beginning of the <code>sparse_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>sparse_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>const_iterator2 begin2 () const</code></td>
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<td>Returns a <code>const_iterator2</code> pointing to
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the beginning of the <code>sparse_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>const_iterator2 end2 () const</code></td>
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<td>Returns a <code>const_iterator2</code> pointing to
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the end of the <code>sparse_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>iterator2 begin2 () </code></td>
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<td>Returns a <code>iterator2</code> pointing to the
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beginning of the <code>sparse_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>sparse_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code>
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pointing to the beginning of the reversed <code>sparse_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator1 rend1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code>
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pointing to the end of the reversed <code>sparse_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>reverse_iterator1 rbegin1 () </code></td>
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<td>Returns a <code>reverse_iterator1</code> pointing to
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the beginning of the reversed <code>sparse_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>reverse_iterator1 rend1 () </code></td>
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<td>Returns a <code>reverse_iterator1</code> pointing to
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the end of the reversed <code>sparse_matrix</code>. </td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</code>
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pointing to the beginning of the reversed <code>sparse_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator2 rend2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</code>
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pointing to the end of the reversed <code>sparse_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>reverse_iterator2 rbegin2 () </code></td>
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<td>Returns a <code>reverse_iterator2</code> pointing to
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the beginning of the reversed <code>sparse_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>reverse_iterator2 rend2 () </code></td>
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<td>Returns a <code>reverse_iterator2</code> pointing to
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the end of the reversed <code>sparse_matrix</code>. </td>
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</tr>
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</table>
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<h4>Notes</h4>
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<p><a name="#sparse_matrix_1">[1]</a> Supported parameters for the storage organization are
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<code>row_major</code> and <code>column_major</code>.</p>
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<p><a name="#sparse_matrix_2">[2]</a> Supported parameters for the adapted array are
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<code>map_array<std::size_t, T></code> and <code>std::map<std::size_t, T></code>.
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</p>
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<h4>Interface</h4>
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<pre><code> // Array based sparse matrix class
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template<class T, class F, class A>
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class sparse_matrix:
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public matrix_expression<sparse_matrix<T, F, A> > {
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public:
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typedef std::size_t size_type;
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typedef std::ptrdiff_t difference_type;
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typedef T value_type;
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typedef const T &const_reference;
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typedef T &reference;
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typedef const T *const_pointer;
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typedef T *pointer;
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typedef F functor_type;
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typedef A array_type;
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typedef const A const_array_type;
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typedef const sparse_matrix<T, F, A> const_self_type;
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typedef sparse_matrix<T, F, A> self_type;
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typedef const matrix_const_reference<const_self_type> const_closure_type;
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typedef matrix_reference<self_type> closure_type;
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typedef typename A::const_iterator const_iterator_type;
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typedef typename A::iterator iterator_type;
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typedef sparse_tag storage_category;
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typedef typename F::orientation_category orientation_category;
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// Construction and destruction
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sparse_matrix ();
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sparse_matrix (size_type size1, size_type size2, size_type non_zeros = 0);
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sparse_matrix (const sparse_matrix &m);
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template<class AE>
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sparse_matrix (const matrix_expression<AE> &ae, size_type non_zeros = 0);
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// Accessors
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size_type size1 () const;
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size_type size2 () const;
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size_type non_zeros () const;
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const_array_type &data () const;
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array_type &data ();
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// Resizing
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void resize (size_type size1, size_type size2, size_type non_zeros = 0);
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// Element access
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const_reference operator () (size_type i, size_type j) const;
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reference operator () (size_type i, size_type j);
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// Assignment
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sparse_matrix &operator = (const sparse_matrix &m);
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sparse_matrix &assign_temporary (sparse_matrix &m);
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template<class AE>
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sparse_matrix &operator = (const matrix_expression<AE> &ae);
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template<class AE>
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sparse_matrix &reset (const matrix_expression<AE> &ae);
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template<class AE>
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sparse_matrix &assign (const matrix_expression<AE> &ae);
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template<class AE>
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sparse_matrix& operator += (const matrix_expression<AE> &ae);
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template<class AE>
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sparse_matrix &plus_assign (const matrix_expression<AE> &ae);
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template<class AE>
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sparse_matrix& operator -= (const matrix_expression<AE> &ae);
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template<class AE>
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sparse_matrix &minus_assign (const matrix_expression<AE> &ae);
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template<class AT>
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sparse_matrix& operator *= (const AT &at);
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template<class AT>
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sparse_matrix& operator /= (const AT &at);
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|
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// Swapping
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void swap (sparse_matrix &m);
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friend void swap (sparse_matrix &m1, sparse_matrix &m2);
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|
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// Element insertion and erasure
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void insert (size_type i, size_type j, const_reference t);
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void erase (size_type i, size_type j);
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void clear ();
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|
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class const_iterator1;
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class iterator1;
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class const_iterator2;
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class iterator2;
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typedef reverse_iterator_base1<const_iterator1> const_reverse_iterator1;
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typedef reverse_iterator_base1<iterator1> reverse_iterator1;
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typedef reverse_iterator_base2<const_iterator2> const_reverse_iterator2;
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typedef reverse_iterator_base2<iterator2> reverse_iterator2;
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||
|
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// Element lookup
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const_iterator1 find1 (int rank, size_type i, size_type j) const;
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iterator1 find1 (int rank, size_type i, size_type j);
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const_iterator2 find2 (int rank, size_type i, size_type j) const;
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iterator2 find2 (int rank, size_type i, size_type j);
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const_iterator1 find_first1 (int rank, size_type i, size_type j) const;
|
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iterator1 find_first1 (int rank, size_type i, size_type j);
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const_iterator1 find_last1 (int rank, size_type i, size_type j) const;
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iterator1 find_last1 (int rank, size_type i, size_type j);
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const_iterator2 find_first2 (int rank, size_type i, size_type j) const;
|
||
iterator2 find_first2 (int rank, size_type i, size_type j);
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const_iterator2 find_last2 (int rank, size_type i, size_type j) const;
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iterator2 find_last2 (int rank, size_type i, size_type j);
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|
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// Iterators simply are pointers.
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||
|
||
class const_iterator1:
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||
public container_const_reference<sparse_matrix>,
|
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public bidirectional_iterator_base<const_iterator1, value_type> {
|
||
public:
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typedef sparse_bidirectional_iterator_tag iterator_category;
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typedef typename sparse_matrix::difference_type difference_type;
|
||
typedef typename sparse_matrix::value_type value_type;
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typedef typename sparse_matrix::const_reference reference;
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typedef typename sparse_matrix::const_pointer pointer;
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typedef const_iterator2 dual_iterator_type;
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typedef const_reverse_iterator2 dual_reverse_iterator_type;
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typedef typename functor_type::functor1_type functor1_type;
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|
||
// Construction and destruction
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||
const_iterator1 ();
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const_iterator1 (const sparse_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);
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const_iterator1 (const iterator1 &it);
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// Arithmetic
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||
const_iterator1 &operator ++ ();
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||
const_iterator1 &operator -- ();
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|
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// Dereference
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||
reference operator * () const;
|
||
|
||
const_iterator2 begin () const;
|
||
const_iterator2 end () const;
|
||
const_reverse_iterator2 rbegin () const;
|
||
const_reverse_iterator2 rend () const;
|
||
|
||
// Indices
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||
size_type index1 () const;
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||
size_type index2 () const;
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||
|
||
// Assignment
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||
const_iterator1 &operator = (const const_iterator1 &it);
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||
|
||
// Comparison
|
||
bool operator == (const const_iterator1 &it) const;
|
||
};
|
||
|
||
const_iterator1 begin1 () const;
|
||
const_iterator1 end1 () const;
|
||
|
||
class iterator1:
|
||
public container_reference<sparse_matrix>,
|
||
public bidirectional_iterator_base<iterator1, value_type> {
|
||
public:
|
||
typedef sparse_bidirectional_iterator_tag iterator_category;
|
||
typedef typename sparse_matrix::difference_type difference_type;
|
||
typedef typename sparse_matrix::value_type value_type;
|
||
typedef typename sparse_matrix::reference reference;
|
||
typedef typename sparse_matrix::pointer pointer;
|
||
typedef iterator2 dual_iterator_type;
|
||
typedef reverse_iterator2 dual_reverse_iterator_type;
|
||
typedef typename functor_type::functor1_type functor1_type;
|
||
|
||
// Construction and destruction
|
||
iterator1 ();
|
||
iterator1 (sparse_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);
|
||
|
||
// Arithmetic
|
||
iterator1 &operator ++ ();
|
||
iterator1 &operator -- ();
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
iterator2 begin () const;
|
||
iterator2 end () const;
|
||
reverse_iterator2 rbegin () const;
|
||
reverse_iterator2 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
iterator1 &operator = (const iterator1 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const iterator1 &it) const;
|
||
};
|
||
|
||
iterator1 begin1 ();
|
||
iterator1 end1 ();
|
||
|
||
class const_iterator2:
|
||
public container_const_reference<sparse_matrix>,
|
||
public bidirectional_iterator_base<const_iterator2, value_type> {
|
||
public:
|
||
typedef sparse_bidirectional_iterator_tag iterator_category;
|
||
typedef typename sparse_matrix::difference_type difference_type;
|
||
typedef typename sparse_matrix::value_type value_type;
|
||
typedef typename sparse_matrix::const_reference reference;
|
||
typedef typename sparse_matrix::const_pointer pointer;
|
||
typedef const_iterator1 dual_iterator_type;
|
||
typedef const_reverse_iterator1 dual_reverse_iterator_type;
|
||
typedef typename functor_type::functor2_type functor2_type;
|
||
|
||
// Construction and destruction
|
||
const_iterator2 ();
|
||
const_iterator2 (const sparse_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);
|
||
const_iterator2 (const iterator2 &it);
|
||
|
||
// Arithmetic
|
||
const_iterator2 &operator ++ ();
|
||
const_iterator2 &operator -- ();
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
const_iterator1 begin () const;
|
||
const_iterator1 end () const;
|
||
const_reverse_iterator1 rbegin () const;
|
||
const_reverse_iterator1 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
const_iterator2 &operator = (const const_iterator2 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const const_iterator2 &it) const;
|
||
};
|
||
|
||
const_iterator2 begin2 () const;
|
||
const_iterator2 end2 () const;
|
||
|
||
class iterator2:
|
||
public container_reference<sparse_matrix>,
|
||
public bidirectional_iterator_base<iterator2, value_type> {
|
||
public:
|
||
typedef sparse_bidirectional_iterator_tag iterator_category;
|
||
typedef typename sparse_matrix::difference_type difference_type;
|
||
typedef typename sparse_matrix::value_type value_type;
|
||
typedef typename sparse_matrix::reference reference;
|
||
typedef typename sparse_matrix::pointer pointer;
|
||
typedef iterator1 dual_iterator_type;
|
||
typedef reverse_iterator1 dual_reverse_iterator_type;
|
||
typedef typename functor_type::functor2_type functor2_type;
|
||
|
||
// Construction and destruction
|
||
iterator2 ();
|
||
iterator2 (sparse_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);
|
||
|
||
// Arithmetic
|
||
iterator2 &operator ++ ();
|
||
iterator2 &operator -- ();
|
||
|
||
// Dereference
|
||
reference operator * () const;
|
||
|
||
iterator1 begin () const;
|
||
iterator1 end () const;
|
||
reverse_iterator1 rbegin () const;
|
||
reverse_iterator1 rend () const;
|
||
|
||
// Indices
|
||
size_type index1 () const;
|
||
size_type index2 () const;
|
||
|
||
// Assignment
|
||
iterator2 &operator = (const iterator2 &it);
|
||
|
||
// Comparison
|
||
bool operator == (const iterator2 &it) const;
|
||
};
|
||
|
||
iterator2 begin2 ();
|
||
iterator2 end2 ();
|
||
|
||
// Reverse iterators
|
||
|
||
const_reverse_iterator1 rbegin1 () const;
|
||
const_reverse_iterator1 rend1 () const;
|
||
|
||
reverse_iterator1 rbegin1 ();
|
||
reverse_iterator1 rend1 ();
|
||
|
||
const_reverse_iterator2 rbegin2 () const;
|
||
const_reverse_iterator2 rend2 () const;
|
||
|
||
reverse_iterator2 rbegin2 ();
|
||
reverse_iterator2 rend2 ();
|
||
};</code></pre>
|
||
|
||
<hr>
|
||
|
||
<p>Copyright (<28>) 2000-2002 Joerg Walter, Mathias Koch <br>
|
||
Permission to copy, use, modify, sell and distribute this
|
||
document is granted provided this copyright notice appears in all
|
||
copies. This document is provided ``as is'' without express or
|
||
implied warranty, and with no claim as to its suitability for any
|
||
purpose.</p>
|
||
|
||
<p>Last revised: 8/3/2002</p>
|
||
</body>
|
||
</html>
|