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| <title>Sparse Matrix</title> |
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| <h1><img src="../../../../boost.png" align="middle" />Sparse Matricies</h1> |
| <div class="toc" id="toc"></div> |
| <h2><a name="mapped_matrix"></a>Mapped Matrix</h2> |
| <h4>Description</h4> |
| <p>The templated class <code>mapped_matrix<T, F, A></code> is |
| the base container adaptor for sparse matricies using element maps. |
| For a <em>(m xn</em>)-dimensional sparse 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 associative |
| container, 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>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>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> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| mapped_matrix<double> m (3, 3, 3 * 3); |
| for (unsigned i = 0; i < m.size1 (); ++ i) |
| for (unsigned j = 0; j < m.size2 (); ++ j) |
| m (i, j) = 3 * i + j; |
| std::cout << m << std::endl; |
| } |
| </pre> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_sparse.hpp.</p> |
| <h4>Template parameters</h4> |
| <table border="1" summary="parameters"> |
| <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 mapped matrix.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>F</code></td> |
| <td>Functor describing the storage organization. <a href= |
| "#mapped_matrix_1">[1]</a></td> |
| <td><code>row_major</code></td> |
| </tr> |
| <tr> |
| <td><code>A</code></td> |
| <td>The type of the adapted array. <a href= |
| "#mapped_matrix_2">[2]</a></td> |
| <td><code>map_std<std::size_t, T></code></td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Model of</h4> |
| <p><a href="container_concept.htm#matrix">Matrix</a> .</p> |
| <h4>Type requirements</h4> |
| <p>None, except for those imposed by the requirements of <a href= |
| "container_concept.htm#matrix">Matrix</a> .</p> |
| <h4>Public base classes</h4> |
| <p><code>matrix_container<mapped_matrix<T, F, A> |
| ></code></p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>mapped_matrix ()</code></td> |
| <td>Allocates a <code>mapped_matrix</code> that holds at most zero |
| rows of zero elements.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_matrix (size_type size1, size_type2, size_type non_zeros = 0)</code></td> |
| <td>Allocates a <code>mapped_matrix</code> that holds at most |
| <code>size1</code> rows of <code>size2</code> elements.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_matrix (const mapped_matrix &m)</code></td> |
| <td>The copy constructor.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| mapped_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, bool preserve = true)</code></td> |
| <td>Reallocates a <code>mapped_matrix</code> to hold at most |
| <code>size1</code> rows of <code>size2</code> elements. The |
| existing elements of the <code>mapped_matrix</code> are preseved |
| when specified.</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>mapped_matrix &operator = (const mapped_matrix |
| &m)</code></td> |
| <td>The assignment operator.</td> |
| </tr> |
| <tr> |
| <td><code>mapped_matrix &assign_temporary (mapped_matrix |
| &m)</code></td> |
| <td>Assigns a temporary. May change the mapped matrix |
| <code>m</code> .</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| mapped_matrix &operator = (const matrix_expression<AE> |
| &ae)</code></td> |
| <td>The extended assignment operator.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| mapped_matrix &assign (const matrix_expression<AE> |
| &ae)</code></td> |
| <td>Assigns a matrix expression to the mapped matrix. Left and |
| right hand side of the assignment should be independent.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| mapped_matrix &operator += (const matrix_expression<AE> |
| &ae)</code></td> |
| <td>A computed assignment operator. Adds the matrix expression to |
| the mapped matrix.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| mapped_matrix &plus_assign (const matrix_expression<AE> |
| &ae)</code></td> |
| <td>Adds a matrix expression to the mapped matrix. Left and right |
| hand side of the assignment should be independent.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| mapped_matrix &operator -= (const matrix_expression<AE> |
| &ae)</code></td> |
| <td>A computed assignment operator. Subtracts the matrix expression |
| from the mapped matrix.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| mapped_matrix &minus_assign (const matrix_expression<AE> |
| &ae)</code></td> |
| <td>Subtracts a matrix expression from the mapped matrix. Left and |
| right hand side of the assignment should be independent.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AT><br /> |
| mapped_matrix &operator *= (const AT &at)</code></td> |
| <td>A computed assignment operator. Multiplies the mapped matrix |
| with a scalar.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AT><br /> |
| mapped_matrix &operator /= (const AT &at)</code></td> |
| <td>A computed assignment operator. Divides the mapped matrix |
| through a scalar.</td> |
| </tr> |
| <tr> |
| <td><code>void swap (mapped_matrix &m)</code></td> |
| <td>Swaps the contents of the mapped matrices.</td> |
| </tr> |
| <tr> |
| <td><code>true_refrence insert_element (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. Duplicates elements are not allowed.</td> |
| </tr> |
| <tr> |
| <td><code>void erase_element (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 mapped 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>mapped_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>mapped_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator1 begin1 ()</code></td> |
| <td>Returns a <code>iterator1</code> pointing to the beginning of |
| the <code>mapped_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator1 end1 ()</code></td> |
| <td>Returns a <code>iterator1</code> pointing to the end of the |
| <code>mapped_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>mapped_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>mapped_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator2 begin2 ()</code></td> |
| <td>Returns a <code>iterator2</code> pointing to the beginning of |
| the <code>mapped_matrix</code>.</td> |
| </tr> |
| <tr> |
| <td><code>iterator2 end2 ()</code></td> |
| <td>Returns a <code>iterator2</code> pointing to the end of the |
| <code>mapped_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>mapped_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>mapped_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>mapped_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>mapped_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>mapped_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>mapped_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>mapped_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>mapped_matrix</code>.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Notes</h4> |
| <p><a name="mapped_matrix_1">[1]</a> Supported |
| parameters for the storage organization are <code>row_major</code> |
| and <code>column_major</code>.</p> |
| <p><a name="mapped_matrix_2">[2]</a> Supported |
| parameters for the adapted array are |
| <code>map_array<std::size_t, T></code> and |
| <code>map_std<std::size_t, T></code>. The latter is |
| equivalent to <code>std::map<std::size_t, T></code>.</p> |
| <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>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>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> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| compressed_matrix<double> m (3, 3, 3 * 3); |
| for (unsigned i = 0; i < m.size1 (); ++ i) |
| for (unsigned j = 0; j < m.size2 (); ++ j) |
| m (i, j) = 3 * i + j; |
| std::cout << m << std::endl; |
| } |
| </pre> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_sparse.hpp.</p> |
| <h4>Template parameters</h4> |
| <table border="1" summary="parameters"> |
| <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_concept.htm#matrix">Matrix</a> .</p> |
| <h4>Type requirements</h4> |
| <p>None, except for those imposed by the requirements of <a href= |
| "container_concept.htm#matrix">Matrix</a> .</p> |
| <h4>Public base classes</h4> |
| <p><code>matrix_container<compressed_matrix<T, F, IB, IA, |
| TA> ></code></p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <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 = 0)</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, bool preserve = true)</code></td> |
| <td>Reallocates a <code>compressed_matrix</code> to hold at most |
| <code>size1</code> rows of <code>size2</code> elements. The |
| existing elements of the <code>compressed_matrix</code> are |
| preseved when specified.</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>true_reference insert_element (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. Duplicates elements are not allowed.</td> |
| </tr> |
| <tr> |
| <td><code>void erase_element (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> |
| <h2><a name="coordinate_matrix"></a>Coordinate Matrix</h2> |
| <h4>Description</h4> |
| <p>The templated class <code>coordinate_matrix<T, F, IB, IA, |
| TA></code> is the base container adaptor for compressed |
| matrices. For a <em>(m x n</em> )-dimensional sorted coordinate |
| 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>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>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> |
| #include <boost/numeric/ublas/io.hpp> |
| |
| int main () { |
| using namespace boost::numeric::ublas; |
| coordinate_matrix<double> m (3, 3, 3 * 3); |
| for (unsigned i = 0; i < m.size1 (); ++ i) |
| for (unsigned j = 0; j < m.size2 (); ++ j) |
| m (i, j) = 3 * i + j; |
| std::cout << m << std::endl; |
| } |
| </pre> |
| <h4>Definition</h4> |
| <p>Defined in the header matrix_sparse.hpp.</p> |
| <h4>Template parameters</h4> |
| <table border="1" summary="parameters"> |
| <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 coordinate matrix.</td> |
| <td></td> |
| </tr> |
| <tr> |
| <td><code>F</code></td> |
| <td>Functor describing the storage organization. <a href= |
| "#coordinate_matrix_1">[1]</a></td> |
| <td><code>row_major</code></td> |
| </tr> |
| <tr> |
| <td><code>IB</code></td> |
| <td>The index base of the coordinate vector. <a href= |
| "#coordinate_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= |
| "#coordinate_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= |
| "#coordinate_matrix_3">[3]</a></td> |
| <td><code>unbounded_array<T></code></td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Model of</h4> |
| <p><a href="container_concept.htm#matrix">Matrix</a> .</p> |
| <h4>Type requirements</h4> |
| <p>None, except for those imposed by the requirements of <a href= |
| "container_concept.htm#matrix">Matrix</a> .</p> |
| <h4>Public base classes</h4> |
| <p><code>matrix_container<coordinate_matrix<T, F, IB, IA, |
| TA> ></code></p> |
| <h4>Members</h4> |
| <table border="1" summary="members"> |
| <tbody> |
| <tr> |
| <th>Member</th> |
| <th>Description</th> |
| </tr> |
| <tr> |
| <td><code>coordinate_matrix ()</code></td> |
| <td>Allocates a <code>coordinate_matrix</code> that holds at most |
| zero rows of zero elements.</td> |
| </tr> |
| <tr> |
| <td><code>coordinate_matrix (size_type size1, size_type2, size_type non_zeros = 0)</code></td> |
| <td>Allocates a <code>coordinate_matrix</code> that holds at most |
| <code>size1</code> rows of <code>size2</code> elements.</td> |
| </tr> |
| <tr> |
| <td><code>coordinate_matrix (const coordinate_matrix |
| &m)</code></td> |
| <td>The copy constructor.</td> |
| </tr> |
| <tr> |
| <td><code>template<class AE><br /> |
| 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, bool preserve = true)</code></td> |
| <td>Reallocates a <code>coordinate_matrix</code> to hold at most |
| <code>size1</code> rows of <code>size2</code> elements. The |
| existing elements of the <code>coordinate_matrix</code> are |
| preseved when specified.</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>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>true_reference insert_element (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. Duplicates elements are not allowed.</td> |
| </tr> |
| <tr> |
| <td><code>void append_element (size_type i, size_type j, const_reference t)</code></td> |
| <td>Appends the value <code>t</code> at the <code>j</code>-th element of the <code>i</code>-th row. |
| Duplicate elements can be appended to a <code>coordinate_matrix</code>. They are merged into a single |
| arithmetically summed element by the <code>sort</code> function.</td> |
| </tr> |
| <tr> |
| <td><code>void erase_element (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> |
| <tr> |
| <td><code>iterator2 end2 ()</code></td> |
| <td>Returns a <code>iterator2</code> pointing to the end of the |
| <code>coordinate_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>coordinate_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>coordinate_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>coordinate_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>coordinate_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>coordinate_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>coordinate_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>coordinate_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>coordinate_matrix</code>.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h4>Notes</h4> |
| <p><a name="coordinate_matrix_1">[1]</a> |
| Supported parameters for the storage organization are |
| <code>row_major</code> and <code>column_major</code>.</p> |
| <p><a name="coordinate_matrix_2">[2]</a> |
| Supported parameters for the index base are <code>0</code> and |
| <code>1</code> at least.</p> |
| <p><a name="coordinate_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> |
| <hr /> |
| <p>Copyright (©) 2000-2002 Joerg Walter, Mathias Koch<br /> |
| Use, modification and distribution are subject to the |
| Boost Software License, Version 1.0. |
| (See accompanying file LICENSE_1_0.txt |
| or copy at <a href="http://www.boost.org/LICENSE_1_0.txt"> |
| http://www.boost.org/LICENSE_1_0.txt |
| </a>). |
| </p> |
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