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1015 lines
76 KiB
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1015 lines
76 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>Sparse 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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Sparse Matrix</h1>
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<h2><a name="sparse_matrix"></a>
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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 the base
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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> the
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non-zero elements <em>m</em><sub><em>i, j</em></sub> are mapped via <em>(i
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x n + j)</em> for row major orientation or via <em>(i + j x m)</em> for column
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major orientation to consecutive elements of the associative container, i.e.
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for elements <em>k</em> = <em>m</em><sub><em>i</em></sub><sub><sub><em>1</em></sub></sub><sub><em>
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,j</em></sub><sub><sub><em>1</em></sub></sub><sub><em> </em></sub>and <em>
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k + 1 = m</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
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,j</em></sub><sub><sub><em>2</em></sub></sub><sub><em> </em></sub>of the
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container holds <em>i</em><sub><em>1</em></sub><em> < i</em><sub><em>2</em></sub>
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or <em>(i</em><sub><em>1</em></sub><em> = i</em><sub><em>2 </em></sub>and
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<em>j</em><sub><em>1</em></sub><em> < j</em><sub><em>2</em></sub><em>)</em>
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with row major orientation or <em>j</em><sub><em>1</em></sub><em> < j</em><sub><em>
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2</em></sub> or <em>(j</em><sub><em>1</em></sub><em> = j</em><sub><em>2 </em></sub>
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and <em>i</em><sub><em>1</em></sub><em> < i</em><sub><em>2</em></sub><em>
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)</em> with column major orientation.</p>
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<h4>Example</h4>
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<pre>#include <boost/numeric/ublas/matrix_sparse.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> sparse_matrix<double> m (3, 3, 3 * 3);<br> for (unsigned i = 0; i < m.size1 (); ++ i)<br> for (unsigned j = 0; j < m.size2 (); ++ j)<br> m (i, j) = 3 * i + j;<br> std::cout << m << std::endl;<br>}</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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<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 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">
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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="#sparse_matrix_2">[2]</a>
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</td>
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<td><code>map_array<std::size_t, 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<sparse_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>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, size_type
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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 matrix_expression<AE>
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&ae)</code></td>
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<td>The extended copy constructor.</td>
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</tr>
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<tr>
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<td><code>void resize (size_type size1, size_type size2,
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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. The
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content of the <code>sparse_matrix </code>is preserved.</td>
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</tr>
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<tr>
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<td><code>size_type size1 () const</code></td>
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<td>Returns the number of rows. </td>
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</tr>
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<tr>
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<td><code>size_type size2 () const</code></td>
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<td>Returns the number of columns. </td>
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</tr>
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<tr>
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<td><code>const_reference operator () (size_type i, size_type
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j) const</code></td>
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<td>Returns 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 sparse_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>sparse_matrix &assign_temporary (sparse_matrix
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&m)</code></td>
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<td>Assigns a temporary. May change the sparse 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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sparse_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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sparse_matrix &assign (const matrix_expression<AE>
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&ae)</code></td>
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<td>Assigns a matrix expression to the sparse 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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sparse_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 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 matrix_expression<AE>
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&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 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 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 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 matrix_expression<AE>
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&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 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 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 (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, 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 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 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>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>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 beginning
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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>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 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>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>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 beginning
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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>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> pointing
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to the beginning 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_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>sparse_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>sparse_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>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> pointing
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to the beginning 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 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>sparse_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>sparse_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>sparse_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="#sparse_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="#sparse_matrix_2">[2]</a>
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Supported parameters for the adapted array are <code>map_array<std::size_t,
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T></code> and <code>std::map<std::size_t, T></code>. </p>
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<h4>Interface</h4>
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<pre><code> // Array based sparse matrix class <br> template<class T, class F, class A><br> class sparse_matrix: <br> public matrix_expression<sparse_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 sparse_matrix<T, F, A> const_self_type;<br> typedef sparse_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 typename A::const_iterator const_iterator_type;<br> typedef typename A::iterator iterator_type;<br> typedef sparse_tag storage_category;<br> typedef typename F::orientation_category orientation_category;<br><br> // Construction and destruction<br> sparse_matrix ();<br> sparse_matrix (size_type size1, size_type size2, size_type non_zeros = 0); <br> sparse_matrix (const sparse_matrix &m);<br> template<class AE><br> sparse_matrix (const matrix_expression<AE> &ae, size_type non_zeros = 0);<br><br> // Accessors<br> size_type size1 () const;<br> size_type size2 () const;<br> size_type non_zeros () 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 non_zeros = 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> sparse_matrix &operator = (const sparse_matrix &m);<br> sparse_matrix &assign_temporary (sparse_matrix &m);<br> template<class AE><br> sparse_matrix &operator = (const matrix_expression<AE> &ae);<br> template<class AE><br> sparse_matrix &reset (const matrix_expression<AE> &ae);<br> template<class AE><br> sparse_matrix &assign (const matrix_expression<AE> &ae);<br> template<class AE><br> sparse_matrix& operator += (const matrix_expression<AE> &ae);<br> template<class AE><br> sparse_matrix &plus_assign (const matrix_expression<AE> &ae);<br> template<class AE><br> sparse_matrix& operator -= (const matrix_expression<AE> &ae);<br> template<class AE><br> sparse_matrix &minus_assign (const matrix_expression<AE> &ae);<br> template<class AT><br> sparse_matrix& operator *= (const AT &at);<br> template<class AT><br> sparse_matrix& operator /= (const AT &at);<br><br> // Swapping<br> void swap (sparse_matrix &m);<br> friend void swap (sparse_matrix &m1, sparse_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 pointers.<br><br> class const_iterator1:<br> public container_const_reference<sparse_matrix>,<br> public bidirectional_iterator_base<const_iterator1, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename sparse_matrix::difference_type difference_type;<br> typedef typename sparse_matrix::value_type value_type;<br> typedef typename sparse_matrix::const_reference reference;<br> typedef typename sparse_matrix::const_pointer pointer;<br> typedef const_iterator2 dual_iterator_type;<br> typedef const_reverse_iterator2 dual_reverse_iterator_type;<br> typedef typename functor_type::functor1_type functor1_type;<br><br> // Construction and destruction<br> const_iterator1 ();<br> const_iterator1 (const sparse_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);<br> const_iterator1 (const iterator1 &it);<br><br> // Arithmetic<br> const_iterator1 &operator ++ ();<br> const_iterator1 &operator -- ();<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> };<br><br> const_iterator1 begin1 () const;<br> const_iterator1 end1 () const;<br><br> class iterator1:<br> public container_reference<sparse_matrix>,<br> public bidirectional_iterator_base<iterator1, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename sparse_matrix::difference_type difference_type;<br> typedef typename sparse_matrix::value_type value_type;<br> typedef typename sparse_matrix::reference reference;<br> typedef typename sparse_matrix::pointer pointer;<br> typedef iterator2 dual_iterator_type;<br> typedef reverse_iterator2 dual_reverse_iterator_type;<br> typedef typename functor_type::functor1_type functor1_type;<br><br> // Construction and destruction<br> iterator1 ();<br> iterator1 (sparse_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);<br><br> // Arithmetic<br> iterator1 &operator ++ ();<br> iterator1 &operator -- ();<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> };<br><br> iterator1 begin1 ();<br> iterator1 end1 ();<br><br> class const_iterator2:<br> public container_const_reference<sparse_matrix>,<br> public bidirectional_iterator_base<const_iterator2, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename sparse_matrix::difference_type difference_type;<br> typedef typename sparse_matrix::value_type value_type;<br> typedef typename sparse_matrix::const_reference reference;<br> typedef typename sparse_matrix::const_pointer pointer;<br> typedef const_iterator1 dual_iterator_type;<br> typedef const_reverse_iterator1 dual_reverse_iterator_type;<br> typedef typename functor_type::functor2_type functor2_type;<br><br> // Construction and destruction<br> const_iterator2 ();<br> const_iterator2 (const sparse_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);<br> const_iterator2 (const iterator2 &it);<br><br> // Arithmetic<br> const_iterator2 &operator ++ ();<br> const_iterator2 &operator -- ();<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> };<br><br> const_iterator2 begin2 () const;<br> const_iterator2 end2 () const;<br><br> class iterator2:<br> public container_reference<sparse_matrix>,<br> public bidirectional_iterator_base<iterator2, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename sparse_matrix::difference_type difference_type;<br> typedef typename sparse_matrix::value_type value_type;<br> typedef typename sparse_matrix::reference reference;<br> typedef typename sparse_matrix::pointer pointer;<br> typedef iterator1 dual_iterator_type;<br> typedef reverse_iterator1 dual_reverse_iterator_type;<br> typedef typename functor_type::functor2_type functor2_type;<br><br> // Construction and destruction<br> iterator2 ();<br> iterator2 (sparse_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);<br><br> // Arithmetic<br> iterator2 &operator ++ ();<br> iterator2 &operator -- ();<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> };<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>
|
|
|
|
<h2><a name="compressed_matrix"></a>
|
|
Compressed Matrix</h2>
|
|
|
|
<h4>Description</h4>
|
|
|
|
<p>The templated class <code>compressed_matrix<T, F, IB, IA, TA> </code>
|
|
is the base container adaptor for compressed matrices. For a <em>(m x n</em>
|
|
)-dimensional compressed matrix and <em>0 <= i < m</em>,<em> 0 <=
|
|
j < n</em> the non-zero elements <em>m</em><sub><em>i, j</em></sub> are
|
|
mapped via <em>(i x n + j)</em> for row major orientation or via <em>(i +
|
|
j x m)</em> for column major orientation to consecutive elements of the index
|
|
and value containers, i.e. for elements <em>k</em> = <em>m</em><sub><em>i</em></sub><sub><sub><em>
|
|
1</em></sub></sub><sub><em>,j</em></sub><sub><sub><em>1</em></sub></sub><sub><em>
|
|
</em></sub>and <em>k + 1 = m</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
|
|
,j</em></sub><sub><sub><em>2</em></sub></sub><sub><em> </em></sub>of the
|
|
container holds <em>i</em><sub><em>1</em></sub><em> < i</em><sub><em>2</em></sub>
|
|
or <em>(i</em><sub><em>1</em></sub><em> = i</em><sub><em>2 </em></sub>and
|
|
<em>j</em><sub><em>1</em></sub><em> < j</em><sub><em>2</em></sub><em>)</em>
|
|
with row major orientation or <em>j</em><sub><em>1</em></sub><em> < j</em><sub><em>
|
|
2</em></sub> or <em>(j</em><sub><em>1</em></sub><em> = j</em><sub><em>2 </em></sub>
|
|
and <em>i</em><sub><em>1</em></sub><em> < i</em><sub><em>2</em></sub><em>
|
|
)</em> with column major orientation.</p>
|
|
|
|
<h4>Example</h4>
|
|
|
|
<pre>#include <boost/numeric/ublas/matrix_sparse.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> compressed_matrix<double> m (3, 3, 3 * 3);<br> for (unsigned i = 0; i < m.size1 (); ++ i)<br> for (unsigned j = 0; j < m.size2 (); ++ j)<br> m (i, j) = 3 * i + j;<br> std::cout << m << std::endl;<br>}<br></pre>
|
|
<h4>Definition</h4>
|
|
|
|
<p>Defined in the header matrix_sparse.hpp.</p>
|
|
|
|
<h4>Template parameters</h4>
|
|
|
|
<table border="1">
|
|
<tbody>
|
|
<tr>
|
|
<th>Parameter </th>
|
|
<th>Description </th>
|
|
<th>Default </th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>T</code> </td>
|
|
<td>The type of object stored in the compressed matrix. </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>F</code></td>
|
|
<td>Functor describing the storage organization. <a href="#compressed_matrix_1">
|
|
[1]</a>
|
|
</td>
|
|
<td><code>row_major</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>IB</code></td>
|
|
<td>The index base of the compressed vector. <a href="#compressed_matrix_2">
|
|
[2]</a>
|
|
</td>
|
|
<td><code>0</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>IA</code></td>
|
|
<td>The type of the adapted array for indices. <a href="#compressed_matrix_3">
|
|
[3]</a>
|
|
</td>
|
|
<td><code>unbounded_array<std::size_t></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>TA</code></td>
|
|
<td>The type of the adapted array for values. <a href="#compressed_matrix_3">
|
|
[3]</a>
|
|
</td>
|
|
<td><code>unbounded_array<T></code></td>
|
|
</tr>
|
|
|
|
</tbody>
|
|
</table>
|
|
|
|
<h4>Model of</h4>
|
|
|
|
<p><a href="container.htm#matrix">Matrix</a>
|
|
. </p>
|
|
|
|
<h4>Type requirements</h4>
|
|
|
|
<p>None, except for those imposed by the requirements of <a href="container.htm#matrix">
|
|
Matrix</a>
|
|
.</p>
|
|
|
|
<h4>Public base classes</h4>
|
|
|
|
<p><code>matrix_expression<compressed_matrix<T, F, IB, IA, TA> ></code>
|
|
</p>
|
|
|
|
<h4>Members</h4>
|
|
|
|
<table border="1">
|
|
<tbody>
|
|
<tr>
|
|
<th>Member </th>
|
|
<th>Description </th>
|
|
</tr>
|
|
<tr>
|
|
<td><code>compressed_matrix ()</code> </td>
|
|
<td>Allocates a <code>compressed_matrix </code>that holds
|
|
at most zero rows of zero elements.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>compressed_matrix (size_type size1, size_type2,
|
|
size_type non_zeros)</code></td>
|
|
<td>Allocates a <code>compressed_matrix </code>that holds
|
|
at most <code>size1 </code>rows of <code>size2 </code>elements.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>compressed_matrix (const compressed_matrix &m)</code></td>
|
|
<td>The copy constructor.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
compressed_matrix (size_type non_zeros, const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>The extended copy constructor.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void resize (size_type size1, size_type size2,
|
|
size_type non_zeros)</code></td>
|
|
<td>Reallocates a <code>compressed_matrix </code>to hold
|
|
at most <code>size1 </code>rows of <code>size2 </code>elements.
|
|
The content of the <code>compressed_matrix </code>is preserved.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size1 () const</code></td>
|
|
<td>Returns the number of rows. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size2 () const</code></td>
|
|
<td>Returns the number of columns. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reference operator () (size_type i, size_type
|
|
j) const</code></td>
|
|
<td>Returns the value of the <code>j</code>-th element in
|
|
the<code> i</code>-th row. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reference operator () (size_type i, size_type
|
|
j)</code></td>
|
|
<td>Returns a reference of the <code>j</code>-th element
|
|
in the<code> i</code>-th row. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>compressed_matrix &operator = (const compressed_matrix
|
|
&m)</code></td>
|
|
<td>The assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>compressed_matrix &assign_temporary (compressed_matrix
|
|
&m)</code></td>
|
|
<td>Assigns a temporary. May change the compressed matrix
|
|
<code>m</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
compressed_matrix &operator = (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>The extended assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
compressed_matrix &assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Assigns a matrix expression to the compressed matrix.
|
|
Left and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
compressed_matrix &operator += (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Adds the matrix expression
|
|
to the compressed matrix.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
compressed_matrix &plus_assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Adds a matrix expression to the compressed matrix. Left
|
|
and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
compressed_matrix &operator -= (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Subtracts the matrix
|
|
expression from the compressed matrix.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
compressed_matrix &minus_assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Subtracts a matrix expression from the compressed matrix.
|
|
Left and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
compressed_matrix &operator *= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Multiplies the compressed
|
|
matrix with a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
compressed_matrix &operator /= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Divides the compressed
|
|
matrix through a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void swap (compressed_matrix &m)</code></td>
|
|
<td>Swaps the contents of the compressed matrices. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void insert (size_type i, size_type j, const_reference
|
|
t)</code></td>
|
|
<td>Inserts the value <code>t</code> at the <code>j</code>-th
|
|
element of the <code>i</code>-th row.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void erase (size_type i, size_type j)</code></td>
|
|
<td>Erases the value at the <code>j</code>-th element of
|
|
the <code>i</code>-th row.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void clear ()</code></td>
|
|
<td>Clears the compressed matrix.</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>compressed_matrix</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>compressed_matrix</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 begin1 () </code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the beginning
|
|
of the <code>compressed_matrix</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 end1 () </code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the end
|
|
of the <code>compressed_matrix</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>compressed_matrix</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>compressed_matrix</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 begin2 () </code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the beginning
|
|
of the <code>compressed_matrix</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 end2 () </code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the end
|
|
of the <code>compressed_matrix</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>compressed_matrix</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>compressed_matrix</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>compressed_matrix</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>compressed_matrix</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>compressed_matrix</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>compressed_matrix</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>compressed_matrix</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>compressed_matrix</code>. </td>
|
|
</tr>
|
|
|
|
</tbody>
|
|
</table>
|
|
|
|
<h4>Notes</h4>
|
|
|
|
<p><a name="#compressed_matrix_1">[1]</a>
|
|
Supported parameters for the storage organization are <code>row_major</code>
|
|
and <code>column_major</code>.</p>
|
|
|
|
<p><a name="#compressed_matrix_2">[2]</a>
|
|
Supported parameters for the index base are <code>0 </code>and <code>1</code>
|
|
at least. </p>
|
|
|
|
<p><a name="#compressed_matrix_3">[3]</a>
|
|
Supported parameters for the adapted array are <code>unbounded_array<></code>
|
|
, <code>bounded_array<></code> and <code>std::vector<></code>
|
|
. </p>
|
|
|
|
<h4>Interface</h4>
|
|
|
|
<pre><code> // Array based sparse matrix class <br> template<class T, class F, std::size_t IB, class IA, class TA><br> class compressed_matrix: <br> public matrix_expression<compressed_matrix<T, F, IB, IA, TA> > {<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 IA index_array_type;<br> typedef TA value_array_type;<br> typedef const compressed_matrix<T, F, IB, IA, TA> const_self_type;<br> typedef compressed_matrix<T, F, IB, IA, TA> 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 A::const_iterator const_iterator_type;<br> typedef typename A::iterator iterator_type;<br> typedef sparse_tag storage_category;<br> typedef typename F::orientation_category orientation_category;<br><br> // Construction and destruction<br> compressed_matrix ();<br> compressed_matrix (size_type size1, size_type size2, size_type non_zeros = 0); <br> compressed_matrix (const compressed_matrix &m);<br> template<class AE><br> compressed_matrix (const matrix_expression<AE> &ae, size_type non_zeros = 0);<br><br> // Accessors<br> size_type size1 () const;<br> size_type size2 () const;<br> size_type non_zeros () const;<br> static size_type index_base ();<br> const index_array_type &index1_data () const;<br> index_array_type &index1_data ();<br> const index_array_type &index2_data () const;<br> index_array_type &index2_data ();<br> const value_array_type &value_data () const;<br> value_array_type &value_data ();<br><br> // Resizing<br> void resize (size_type size1, size_type size2, size_type non_zeros = 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> compressed_matrix &operator = (const compressed_matrix &m);<br> compressed_matrix &assign_temporary (compressed_matrix &m);<br> template<class AE><br> compressed_matrix &operator = (const matrix_expression<AE> &ae);<br> template<class AE><br> compressed_matrix &reset (const matrix_expression<AE> &ae);<br> template<class AE><br> compressed_matrix &assign (const matrix_expression<AE> &ae);<br> template<class AE><br> compressed_matrix& operator += (const matrix_expression<AE> &ae);<br> template<class AE><br> compressed_matrix &plus_assign (const matrix_expression<AE> &ae);<br> template<class AE><br> compressed_matrix& operator -= (const matrix_expression<AE> &ae);<br> template<class AE><br> compressed_matrix &minus_assign (const matrix_expression<AE> &ae);<br> template<class AT><br> compressed_matrix& operator *= (const AT &at);<br> template<class AT><br> compressed_matrix& operator /= (const AT &at);<br><br> // Swapping<br> void swap (compressed_matrix &m);<br> friend void swap (compressed_matrix &m1, compressed_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 pointers.<br><br> class const_iterator1:<br> public container_const_reference<compressed_matrix>,<br> public bidirectional_iterator_base<const_iterator1, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename compressed_matrix::difference_type difference_type;<br> typedef typename compressed_matrix::value_type value_type;<br> typedef typename compressed_matrix::const_reference reference;<br> typedef typename compressed_matrix::const_pointer pointer;<br> typedef const_iterator2 dual_iterator_type;<br> typedef const_reverse_iterator2 dual_reverse_iterator_type;<br> typedef typename functor_type::functor1_type functor1_type;<br><br> // Construction and destruction<br> const_iterator1 ();<br> const_iterator1 (const compressed_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);<br> const_iterator1 (const iterator1 &it);<br><br> // Arithmetic<br> const_iterator1 &operator ++ ();<br> const_iterator1 &operator -- ();<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> };<br><br> const_iterator1 begin1 () const;<br> const_iterator1 end1 () const;<br><br> class iterator1:<br> public container_reference<compressed_matrix>,<br> public bidirectional_iterator_base<iterator1, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename compressed_matrix::difference_type difference_type;<br> typedef typename compressed_matrix::value_type value_type;<br> typedef typename compressed_matrix::reference reference;<br> typedef typename compressed_matrix::pointer pointer;<br> typedef iterator2 dual_iterator_type;<br> typedef reverse_iterator2 dual_reverse_iterator_type;<br> typedef typename functor_type::functor1_type functor1_type;<br><br> // Construction and destruction<br> iterator1 ();<br> iterator1 (compressed_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);<br><br> // Arithmetic<br> iterator1 &operator ++ ();<br> iterator1 &operator -- ();<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> };<br><br> iterator1 begin1 ();<br> iterator1 end1 ();<br><br> class const_iterator2:<br> public container_const_reference<compressed_matrix>,<br> public bidirectional_iterator_base<const_iterator2, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename compressed_matrix::difference_type difference_type;<br> typedef typename compressed_matrix::value_type value_type;<br> typedef typename compressed_matrix::const_reference reference;<br> typedef typename compressed_matrix::const_pointer pointer;<br> typedef const_iterator1 dual_iterator_type;<br> typedef const_reverse_iterator1 dual_reverse_iterator_type;<br> typedef typename functor_type::functor2_type functor2_type;<br><br> // Construction and destruction<br> const_iterator2 ();<br> const_iterator2 (const compressed_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);<br> const_iterator2 (const iterator2 &it);<br><br> // Arithmetic<br> const_iterator2 &operator ++ ();<br> const_iterator2 &operator -- ();<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 &operato
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r = (const const_iterator2 &it);<br><br> // Comparison<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<compressed_matrix>,<br> public bidirectional_iterator_base<iterator2, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename compressed_matrix::difference_type difference_type;<br> typedef typename compressed_matrix::value_type value_type;<br> typedef typename compressed_matrix::reference reference;<br> typedef typename compressed_matrix::pointer pointer;<br> typedef iterator1 dual_iterator_type;<br> typedef reverse_iterator1 dual_reverse_iterator_type;<br> typedef typename functor_type::functor2_type functor2_type;<br><br> // Construction and destruction<br> iterator2 ();<br> iterator2 (compressed_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);<br><br> // Arithmetic<br> iterator2 &operator ++ ();<br> iterator2 &operator -- ();<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> };<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="coordinate_matrix"></a>
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Coordinate Matrix</h2>
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<h4>Description</h4>
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<p>The templated class <code>coordinate_matrix<T, F, IB, IA, TA> </code>
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is the base container adaptor for compressed matrices. For a <em>(m x n</em>
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)-dimensional sorted coordinate matrix and <em>0 <= i < m</em>,<em>
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0 <= j < n</em> the non-zero elements <em>m</em><sub><em>i, j</em></sub>
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are mapped via <em>(i x n + j)</em> for row major orientation or via <em>
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(i + j x m)</em> for column major orientation to consecutive elements of
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the index and value containers, i.e. for elements <em>k</em> = <em>m</em><sub><em>
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i</em></sub><sub><sub><em>1</em></sub></sub><sub><em>,j</em></sub><sub><sub><em>
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1</em></sub></sub><sub><em> </em></sub>and <em>k + 1 = m</em><sub><em>i</em></sub><sub><sub><em>
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2</em></sub></sub><sub><em>,j</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
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</em></sub>of the container holds <em>i</em><sub><em>1</em></sub><em> <
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i</em><sub><em>2</em></sub> or <em>(i</em><sub><em>1</em></sub><em> = i</em><sub><em>
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2 </em></sub>and <em>j</em><sub><em>1</em></sub><em> < j</em><sub><em>
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2</em></sub><em>)</em> with row major orientation or <em>j</em><sub><em>1</em></sub><em>
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< j</em><sub><em>2</em></sub> or <em>(j</em><sub><em>1</em></sub><em>
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= j</em><sub><em>2 </em></sub>and <em>i</em><sub><em>1</em></sub><em> <
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i</em><sub><em>2</em></sub><em>)</em> with column major orientation.</p>
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|
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<h4>Example</h4>
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<pre>#include <boost/numeric/ublas/matrix_sparse.hpp><br>#include <boost/numeric/ublas/io.hpp><br><br>int main () {<br> using namespace boost::numeric::ublas;<br> coordinate_matrix<double> m (3, 3, 3 * 3);<br> for (unsigned i = 0; i < m.size1 (); ++ i)<br> for (unsigned j = 0; j < 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 matrix_sparse.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 coordinate 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="#coordinate_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>IB</code></td>
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<td>The index base of the coordinate vector. <a href="#coordinate_matrix_2">
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[2]</a>
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</td>
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<td><code>0</code></td>
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</tr>
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<tr>
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<td><code>IA</code></td>
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<td>The type of the adapted array for indices. <a href="#coordinate_matrix_3">
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[3]</a>
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</td>
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<td><code>unbounded_array<std::size_t></code></td>
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</tr>
|
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<tr>
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<td><code>TA</code></td>
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<td>The type of the adapted array for values. <a href="#coordinate_matrix_3">
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[3]</a>
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</td>
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<td><code>unbounded_array<T></code></td>
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</tr>
|
|
|
|
</tbody>
|
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</table>
|
|
|
|
<h4>Model of</h4>
|
|
|
|
<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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|
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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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|
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<h4>Public base classes</h4>
|
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<p><code>matrix_expression<coordinate_matrix<T, F, IB, IA, TA> ></code>
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</p>
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|
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<h4>Members</h4>
|
|
|
|
<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>
|
|
<td><code>coordinate_matrix ()</code> </td>
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<td>Allocates a <code>coordinate_matrix </code>that holds
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at most zero rows of zero elements.</td>
|
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</tr>
|
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<tr>
|
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<td><code>coordinate_matrix (size_type size1, size_type2,
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|
size_type non_zeros)</code></td>
|
|
<td>Allocates a <code>coordinate_matrix </code>that holds
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at most <code>size1 </code>rows of <code>size2 </code>elements.</td>
|
|
</tr>
|
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<tr>
|
|
<td><code>coordinate_matrix (const coordinate_matrix &m)</code></td>
|
|
<td>The copy constructor.</td>
|
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</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
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|
coordinate_matrix (size_type non_zeros, const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>The extended copy constructor.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void resize (size_type size1, size_type size2,
|
|
size_type non_zeros)</code></td>
|
|
<td>Reallocates a <code>coordinate_matrix </code>to hold
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|
at most <code>size1 </code>rows of <code>size2 </code>elements.
|
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The content of the <code>coordinate_matrix </code>is preserved.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size1 () const</code></td>
|
|
<td>Returns the number of rows. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>size_type size2 () const</code></td>
|
|
<td>Returns the number of columns. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>const_reference operator () (size_type i, size_type
|
|
j) const</code></td>
|
|
<td>Returns the value of the <code>j</code>-th element in
|
|
the<code> i</code>-th row. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>reference operator () (size_type i, size_type
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|
j)</code></td>
|
|
<td>Returns a reference of the <code>j</code>-th element
|
|
in the<code> i</code>-th row. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>coordinate_matrix &operator = (const coordinate_matrix
|
|
&m)</code></td>
|
|
<td>The assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>coordinate_matrix &assign_temporary (coordinate_matrix
|
|
&m)</code></td>
|
|
<td>Assigns a temporary. May change the coordinate matrix
|
|
<code>m</code>.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
coordinate_matrix &operator = (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>The extended assignment operator.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
coordinate_matrix &assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Assigns a matrix expression to the coordinate matrix.
|
|
Left and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
coordinate_matrix &operator += (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Adds the matrix expression
|
|
to the coordinate matrix.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
coordinate_matrix &plus_assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Adds a matrix expression to the coordinate matrix. Left
|
|
and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
coordinate_matrix &operator -= (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>A computed assignment operator. Subtracts the matrix
|
|
expression from the coordinate matrix.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AE><br>
|
|
coordinate_matrix &minus_assign (const matrix_expression<AE>
|
|
&ae)</code></td>
|
|
<td>Subtracts a matrix expression from the coordinate matrix.
|
|
Left and right hand side of the assignment should be independent.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
coordinate_matrix &operator *= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Multiplies the coordinate
|
|
matrix with a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>template<class AT><br>
|
|
coordinate_matrix &operator /= (const AT &at)</code></td>
|
|
<td>A computed assignment operator. Divides the coordinate
|
|
matrix through a scalar.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void swap (coordinate_matrix &m)</code></td>
|
|
<td>Swaps the contents of the coordinate matrices. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void insert (size_type i, size_type j, const_reference
|
|
t)</code></td>
|
|
<td>Inserts the value <code>t</code> at the <code>j</code>-th
|
|
element of the <code>i</code>-th row.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void erase (size_type i, size_type j)</code></td>
|
|
<td>Erases the value at the <code>j</code>-th element of
|
|
the <code>i</code>-th row.</td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>void clear ()</code></td>
|
|
<td>Clears the coordinate matrix.</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>coordinate_matrix</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>coordinate_matrix</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 begin1 () </code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the beginning
|
|
of the <code>coordinate_matrix</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator1 end1 () </code></td>
|
|
<td>Returns a <code>iterator1</code> pointing to the end
|
|
of the <code>coordinate_matrix</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>coordinate_matrix</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>coordinate_matrix</code>. </td>
|
|
</tr>
|
|
<tr>
|
|
<td><code>iterator2 begin2 () </code></td>
|
|
<td>Returns a <code>iterator2</code> pointing to the beginning
|
|
of the <code>coordinate_matrix</code>. </td>
|
|
</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>coordinate_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>coordinate_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator1 rend1 () const</code></td>
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<td>Returns a <code>const_reverse_iterator1</code> pointing
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to the end of the reversed <code>coordinate_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>coordinate_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>coordinate_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>coordinate_matrix</code>.
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</td>
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</tr>
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<tr>
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<td><code>const_reverse_iterator2 rend2 () const</code></td>
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<td>Returns a <code>const_reverse_iterator2</code> pointing
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to the end of the reversed <code>coordinate_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>coordinate_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>coordinate_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="#coordinate_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="#coordinate_matrix_2">[2]</a>
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Supported parameters for the index base are <code>0 </code>and <code>1</code>
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at least. </p>
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<p><a name="#coordinate_matrix_3">[3]</a>
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Supported parameters for the adapted array are <code>unbounded_array<></code>
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, <code>bounded_array<></code> and <code>std::vector<></code>
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. </p>
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<h4>Interface</h4>
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<pre><code> // Array based sparse matrix class <br> template<class T, class F, std::size_t IB, class IA, class TA><br> class coordinate_matrix: <br> public matrix_expression<coordinate_matrix<T, F, IB, IA, TA> > {<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 IA index_array_type;<br> typedef TA value_array_type;<br> typedef const coordinate_matrix<T, F, IB, IA, TA> const_self_type;<br> typedef coordinate_matrix<T, F, IB, IA, TA> 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 A::const_iterator const_iterator_type;<br> typedef typename A::iterator iterator_type;<br> typedef sparse_tag storage_category;<br> typedef typename F::orientation_category orientation_category;<br><br> // Construction and destruction<br> coordinate_matrix ();<br> coordinate_matrix (size_type size1, size_type size2, size_type non_zeros = 0); <br> coordinate_matrix (const coordinate_matrix &m);<br> template<class AE><br> coordinate_matrix (const matrix_expression<AE> &ae, size_type non_zeros = 0);<br><br> // Accessors<br> size_type size1 () const;<br> size_type size2 () const;<br> size_type non_zeros () const;<br> static size_type index_base ();<br> const index_array_type &index1_data () const;<br> index_array_type &index1_data ();<br> const index_array_type &index2_data () const;<br> index_array_type &index2_data ();<br> const value_array_type &value_data () const;<br> value_array_type &value_data ();<br><br> // Resizing<br> void resize (size_type size1, size_type size2, size_type non_zeros = 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> coordinate_matrix &operator = (const coordinate_matrix &m);<br> coordinate_matrix &assign_temporary (coordinate_matrix &m);<br> template<class AE><br> coordinate_matrix &operator = (const matrix_expression<AE> &ae);<br> template<class AE><br> coordinate_matrix &reset (const matrix_expression<AE> &ae);<br> template<class AE><br> coordinate_matrix &assign (const matrix_expression<AE> &ae);<br> template<class AE><br> coordinate_matrix& operator += (const matrix_expression<AE> &ae);<br> template<class AE><br> coordinate_matrix &plus_assign (const matrix_expression<AE> &ae);<br> template<class AE><br> coordinate_matrix& operator -= (const matrix_expression<AE> &ae);<br> template<class AE><br> coordinate_matrix &minus_assign (const matrix_expression<AE> &ae);<br> template<class AT><br> coordinate_matrix& operator *= (const AT &at);<br> template<class AT><br> coordinate_matrix& operator /= (const AT &at);<br><br> // Swapping<br> void swap (coordinate_matrix &m);<br> friend void swap (coordinate_matrix &m1, coordinate_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 pointers.<br><br> class const_iterator1:<br> public container_const_reference<coordinate_matrix>,<br> public bidirectional_iterator_base<const_iterator1, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename coordinate_matrix::difference_type difference_type;<br> typedef typename coordinate_matrix::value_type value_type;<br> typedef typename coordinate_matrix::const_reference reference;<br> typedef typename coordinate_matrix::const_pointer pointer;<br> typedef const_iterator2 dual_iterator_type;<br> typedef const_reverse_iterator2 dual_reverse_iterator_type;<br> typedef typename functor_type::functor1_type functor1_type;<br><br> // Construction and destruction<br> const_iterator1 ();<br> const_iterator1 (const coordinate_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);<br> const_iterator1 (const iterator1 &it);<br><br> // Arithmetic<br> const_iterator1 &operator ++ ();<br> const_iterator1 &operator -- ();<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> };<br><br> const_iterator1 begin1 () const;<br> const_iterator1 end1 () const;<br><br> class iterator1:<br> public container_reference<coordinate_matrix>,<br> public bidirectional_iterator_base<iterator1, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename coordinate_matrix::difference_type difference_type;<br> typedef typename coordinate_matrix::value_type value_type;<br> typedef typename coordinate_matrix::reference reference;<br> typedef typename coordinate_matrix::pointer pointer;<br> typedef iterator2 dual_iterator_type;<br> typedef reverse_iterator2 dual_reverse_iterator_type;<br> typedef typename functor_type::functor1_type functor1_type;<br><br> // Construction and destruction<br> iterator1 ();<br> iterator1 (coordinate_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);<br><br> // Arithmetic<br> iterator1 &operator ++ ();<br> iterator1 &operator -- ();<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> };<br><br> iterator1 begin1 ();<
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br> iterator1 end1 ();<br><br> class const_iterator2:<br> public container_const_reference<coordinate_matrix>,<br> public bidirectional_iterator_base<const_iterator2, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename coordinate_matrix::difference_type difference_type;<br> typedef typename coordinate_matrix::value_type value_type;<br> typedef typename coordinate_matrix::const_reference reference;<br> typedef typename coordinate_matrix::const_pointer pointer;<br> typedef const_iterator1 dual_iterator_type;<br> typedef const_reverse_iterator1 dual_reverse_iterator_type;<br> typedef typename functor_type::functor2_type functor2_type;<br><br> // Construction and destruction<br> const_iterator2 ();<br> const_iterator2 (const coordinate_matrix &m, int rank, size_type i, size_type j, const const_iterator_type &it);<br> const_iterator2 (const iterator2 &it);<br><br> // Arithmetic<br> const_iterator2 &operator ++ ();<br> const_iterator2 &operator -- ();<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> };<br><br> const_iterator2 begin2 () const;<br> const_iterator2 end2 () const;<br><br> class iterator2:<br> public container_reference<coordinate_matrix>,<br> public bidirectional_iterator_base<iterator2, value_type> {<br> public:<br> typedef sparse_bidirectional_iterator_tag iterator_category;<br> typedef typename coordinate_matrix::difference_type difference_type;<br> typedef typename coordinate_matrix::value_type value_type;<br> typedef typename coordinate_matrix::reference reference;<br> typedef typename coordinate_matrix::pointer pointer;<br> typedef iterator1 dual_iterator_type;<br> typedef reverse_iterator1 dual_reverse_iterator_type;<br> typedef typename functor_type::functor2_type functor2_type;<br><br> // Construction and destruction<br> iterator2 ();<br> iterator2 (coordinate_matrix &m, int rank, size_type i, size_type j, const iterator_type &it);<br><br> // Arithmetic<br> iterator2 &operator ++ ();<br> iterator2 &operator -- ();<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> };<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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</body>
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</html>
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