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<title>Sparse Matrix</title>
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<h1><img src="c++boost.gif" alt="c++boost.gif" align="Center">
Sparse Matrix</h1>
<h2><a name="sparse_matrix"></a>
Sparse Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>sparse_matrix&lt;T, F, A&gt; </code>is the base
container adaptor for sparse matrices. For a <em>(m x n</em>)-dimensional
sparse matrix and <em>0 &lt;= i &lt; m</em>,<em> 0 &lt;= j &lt; 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><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> &lt; 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> &lt; j</em><sub><em>2</em></sub><em>)</em>
with row major orientation or <em>j</em><sub><em>1</em></sub><em> &lt; 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> &lt; i</em><sub><em>2</em></sub><em>
)</em> with column major orientation.</p>
<h4>Example</h4>
<pre>#include &lt;boost/numeric/ublas/matrix_sparse.hpp&gt;<br>#include &lt;boost/numeric/ublas/io.hpp&gt;<br><br>int main () {<br> using namespace boost::numeric::ublas;<br> sparse_matrix&lt;double&gt; m (3, 3, 3 * 3);<br> for (unsigned i = 0; i &lt; m.size1 (); ++ i)<br> for (unsigned j = 0; j &lt; m.size2 (); ++ j)<br> m (i, j) = 3 * i + j;<br> std::cout &lt;&lt; m &lt;&lt; std::endl;<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 sparse matrix. </td>
<td>&nbsp;</td>
</tr>
<tr>
<td><code>F</code></td>
<td>Functor describing the storage organization. <a href="#sparse_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="#sparse_matrix_2">[2]</a>
</td>
<td><code>map_array&lt;std::size_t, T&gt;</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&lt;sparse_matrix&lt;T, F, A&gt; &gt;</code> </p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member </th>
<th>Description </th>
</tr>
<tr>
<td><code>sparse_matrix ()</code> </td>
<td>Allocates a <code>sparse_matrix </code>that holds at
most zero rows of zero elements.</td>
</tr>
<tr>
<td><code>sparse_matrix (size_type size1, size_type2, size_type
non_zeros)</code></td>
<td>Allocates a <code>sparse_matrix </code>that holds at
most <code>size1 </code>rows of <code>size2 </code>elements.</td>
</tr>
<tr>
<td><code>sparse_matrix (const sparse_matrix &amp;m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_matrix (size_type non_zeros, const matrix_expression&lt;AE&gt;
&amp;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>sparse_matrix </code>to hold at
most <code>size1 </code>rows of <code>size2 </code>elements. The
content of the <code>sparse_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>sparse_matrix &amp;operator = (const sparse_matrix
&amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>sparse_matrix &amp;assign_temporary (sparse_matrix
&amp;m)</code></td>
<td>Assigns a temporary. May change the sparse matrix <code>m</code>
.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_matrix &amp;assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a matrix expression to the sparse matrix. Left
and right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_matrix &amp;operator += (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression
to the sparse matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_matrix &amp;plus_assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Adds a matrix expression to the sparse matrix. Left
and right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_matrix &amp;operator -= (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix
expression from the sparse matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_matrix &amp;minus_assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Subtracts a matrix expression from the sparse matrix.
Left and right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
sparse_matrix &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the sparse
matrix with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
sparse_matrix &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the sparse matrix
through a scalar.</td>
</tr>
<tr>
<td><code>void swap (sparse_matrix &amp;m)</code></td>
<td>Swaps the contents of the sparse 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 sparse 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>sparse_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>sparse_matrix</code>. </td>
</tr>
<tr>
<td><code>iterator1 begin1 () </code></td>
<td>Returns a <code>iterator1</code> pointing to the beginning
of the <code>sparse_matrix</code>. </td>
</tr>
<tr>
<td><code>iterator1 end1 () </code></td>
<td>Returns a <code>iterator1</code> pointing to the end
of the <code>sparse_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>sparse_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>sparse_matrix</code>. </td>
</tr>
<tr>
<td><code>iterator2 begin2 () </code></td>
<td>Returns a <code>iterator2</code> pointing to the beginning
of the <code>sparse_matrix</code>. </td>
</tr>
<tr>
<td><code>iterator2 end2 () </code></td>
<td>Returns a <code>iterator2</code> pointing to the end
of the <code>sparse_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>sparse_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>sparse_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>sparse_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>sparse_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>sparse_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>sparse_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>sparse_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>sparse_matrix</code>. </td>
</tr>
</tbody>
</table>
<h4>Notes</h4>
<p><a name="#sparse_matrix_1">[1]</a>
Supported parameters for the storage organization are <code>row_major</code>
and <code>column_major</code>.</p>
<p><a name="#sparse_matrix_2">[2]</a>
Supported parameters for the adapted array are <code>map_array&lt;std::size_t,
T&gt;</code> and <code>std::map&lt;std::size_t, T&gt;</code>. </p>
<h4>Interface</h4>
<pre><code> // Array based sparse matrix class <br> template&lt;class T, class F, class A&gt;<br> class sparse_matrix: <br> public matrix_expression&lt;sparse_matrix&lt;T, F, A&gt; &gt; {<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 &amp;const_reference;<br> typedef T &amp;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&lt;T, F, A&gt; const_self_type;<br> typedef sparse_matrix&lt;T, F, A&gt; self_type;<br> typedef const matrix_const_reference&lt;const_self_type&gt; const_closure_type;<br> typedef matrix_reference&lt;self_type&gt; 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 &amp;m);<br> template&lt;class AE&gt;<br> sparse_matrix (const matrix_expression&lt;AE&gt; &amp;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 &amp;data () const;<br> array_type &amp;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 &amp;operator = (const sparse_matrix &amp;m);<br> sparse_matrix &amp;assign_temporary (sparse_matrix &amp;m);<br> template&lt;class AE&gt;<br> sparse_matrix &amp;operator = (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> sparse_matrix &amp;reset (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> sparse_matrix &amp;assign (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> sparse_matrix&amp; operator += (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> sparse_matrix &amp;plus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> sparse_matrix&amp; operator -= (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> sparse_matrix &amp;minus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AT&gt;<br> sparse_matrix&amp; operator *= (const AT &amp;at);<br> template&lt;class AT&gt;<br> sparse_matrix&amp; operator /= (const AT &amp;at);<br><br> // Swapping<br> void swap (sparse_matrix &amp;m);<br> friend void swap (sparse_matrix &amp;m1, sparse_matrix &amp;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&lt;const_iterator1&gt; const_reverse_iterator1;<br> typedef reverse_iterator_base1&lt;iterator1&gt; reverse_iterator1;<br> typedef reverse_iterator_base2&lt;const_iterator2&gt; const_reverse_iterator2;<br> typedef reverse_iterator_base2&lt;iterator2&gt; 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&lt;sparse_matrix&gt;,<br> public bidirectional_iterator_base&lt;const_iterator1, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const const_iterator_type &amp;it);<br> const_iterator1 (const iterator1 &amp;it);<br><br> // Arithmetic<br> const_iterator1 &amp;operator ++ ();<br> const_iterator1 &amp;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 &amp;operator = (const const_iterator1 &amp;it);<br><br> // Comparison<br> bool operator == (const const_iterator1 &amp;it) const;<br> };<br><br> const_iterator1 begin1 () const;<br> const_iterator1 end1 () const;<br><br> class iterator1:<br> public container_reference&lt;sparse_matrix&gt;,<br> public bidirectional_iterator_base&lt;iterator1, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const iterator_type &amp;it);<br><br> // Arithmetic<br> iterator1 &amp;operator ++ ();<br> iterator1 &amp;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 &amp;operator = (const iterator1 &amp;it);<br><br> // Comparison<br> bool operator == (const iterator1 &amp;it) const;<br> };<br><br> iterator1 begin1 ();<br> iterator1 end1 ();<br><br> class const_iterator2:<br> public container_const_reference&lt;sparse_matrix&gt;,<br> public bidirectional_iterator_base&lt;const_iterator2, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const const_iterator_type &amp;it);<br> const_iterator2 (const iterator2 &amp;it);<br><br> // Arithmetic<br> const_iterator2 &amp;operator ++ ();<br> const_iterator2 &amp;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 &amp;operator = (const const_iterator2 &amp;it);<br><br> // Comparison<br> bool operator == (const const_iterator2 &amp;it) const;<br> };<br><br> const_iterator2 begin2 () const;<br> const_iterator2 end2 () const;<br><br> class iterator2:<br> public container_reference&lt;sparse_matrix&gt;,<br> public bidirectional_iterator_base&lt;iterator2, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const iterator_type &amp;it);<br><br> // Arithmetic<br> iterator2 &amp;operator ++ ();<br> iterator2 &amp;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 &amp;operator = (const iterator2 &amp;it);<br><br> // Comparison<br> bool operator == (const iterator2 &amp;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&lt;T, F, IB, IA, TA&gt; </code>
is the base container adaptor for compressed matrices. For a <em>(m x n</em>
)-dimensional compressed matrix and <em>0 &lt;= i &lt; m</em>,<em> 0 &lt;=
j &lt; 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> &lt; 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> &lt; j</em><sub><em>2</em></sub><em>)</em>
with row major orientation or <em>j</em><sub><em>1</em></sub><em> &lt; 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> &lt; i</em><sub><em>2</em></sub><em>
)</em> with column major orientation.</p>
<h4>Example</h4>
<pre>#include &lt;boost/numeric/ublas/matrix_sparse.hpp&gt;<br>#include &lt;boost/numeric/ublas/io.hpp&gt;<br><br>int main () {<br> using namespace boost::numeric::ublas;<br> compressed_matrix&lt;double&gt; m (3, 3, 3 * 3);<br> for (unsigned i = 0; i &lt; m.size1 (); ++ i)<br> for (unsigned j = 0; j &lt; m.size2 (); ++ j)<br> m (i, j) = 3 * i + j;<br> std::cout &lt;&lt; m &lt;&lt; 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>&nbsp;</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&lt;std::size_t&gt;</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&lt;T&gt;</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&lt;compressed_matrix&lt;T, F, IB, IA, TA&gt; &gt;</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 &amp;m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_matrix (size_type non_zeros, const matrix_expression&lt;AE&gt;
&amp;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 &amp;operator = (const compressed_matrix
&amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>compressed_matrix &amp;assign_temporary (compressed_matrix
&amp;m)</code></td>
<td>Assigns a temporary. May change the compressed matrix
<code>m</code>.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_matrix &amp;assign (const matrix_expression&lt;AE&gt;
&amp;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&lt;class AE&gt;<br>
compressed_matrix &amp;operator += (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression
to the compressed matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_matrix &amp;plus_assign (const matrix_expression&lt;AE&gt;
&amp;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&lt;class AE&gt;<br>
compressed_matrix &amp;operator -= (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix
expression from the compressed matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_matrix &amp;minus_assign (const matrix_expression&lt;AE&gt;
&amp;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&lt;class AT&gt;<br>
compressed_matrix &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the compressed
matrix with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
compressed_matrix &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the compressed
matrix through a scalar.</td>
</tr>
<tr>
<td><code>void swap (compressed_matrix &amp;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&lt;&gt;</code>
, <code>bounded_array&lt;&gt;</code> and <code>std::vector&lt;&gt;</code>
. </p>
<h4>Interface</h4>
<pre><code> // Array based sparse matrix class <br> template&lt;class T, class F, std::size_t IB, class IA, class TA&gt;<br> class compressed_matrix: <br> public matrix_expression&lt;compressed_matrix&lt;T, F, IB, IA, TA&gt; &gt; {<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 &amp;const_reference;<br> typedef T &amp;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&lt;T, F, IB, IA, TA&gt; const_self_type;<br> typedef compressed_matrix&lt;T, F, IB, IA, TA&gt; self_type;<br> typedef const matrix_const_reference&lt;const_self_type&gt; const_closure_type;<br> typedef matrix_reference&lt;self_type&gt; 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 &amp;m);<br> template&lt;class AE&gt;<br> compressed_matrix (const matrix_expression&lt;AE&gt; &amp;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 &amp;index1_data () const;<br> index_array_type &amp;index1_data ();<br> const index_array_type &amp;index2_data () const;<br> index_array_type &amp;index2_data ();<br> const value_array_type &amp;value_data () const;<br> value_array_type &amp;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 &amp;operator = (const compressed_matrix &amp;m);<br> compressed_matrix &amp;assign_temporary (compressed_matrix &amp;m);<br> template&lt;class AE&gt;<br> compressed_matrix &amp;operator = (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> compressed_matrix &amp;reset (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> compressed_matrix &amp;assign (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> compressed_matrix&amp; operator += (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> compressed_matrix &amp;plus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> compressed_matrix&amp; operator -= (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> compressed_matrix &amp;minus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AT&gt;<br> compressed_matrix&amp; operator *= (const AT &amp;at);<br> template&lt;class AT&gt;<br> compressed_matrix&amp; operator /= (const AT &amp;at);<br><br> // Swapping<br> void swap (compressed_matrix &amp;m);<br> friend void swap (compressed_matrix &amp;m1, compressed_matrix &amp;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&lt;const_iterator1&gt; const_reverse_iterator1;<br> typedef reverse_iterator_base1&lt;iterator1&gt; reverse_iterator1;<br> typedef reverse_iterator_base2&lt;const_iterator2&gt; const_reverse_iterator2;<br> typedef reverse_iterator_base2&lt;iterator2&gt; 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&lt;compressed_matrix&gt;,<br> public bidirectional_iterator_base&lt;const_iterator1, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const const_iterator_type &amp;it);<br> const_iterator1 (const iterator1 &amp;it);<br><br> // Arithmetic<br> const_iterator1 &amp;operator ++ ();<br> const_iterator1 &amp;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 &amp;operator = (const const_iterator1 &amp;it);<br><br> // Comparison<br> bool operator == (const const_iterator1 &amp;it) const;<br> };<br><br> const_iterator1 begin1 () const;<br> const_iterator1 end1 () const;<br><br> class iterator1:<br> public container_reference&lt;compressed_matrix&gt;,<br> public bidirectional_iterator_base&lt;iterator1, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const iterator_type &amp;it);<br><br> // Arithmetic<br> iterator1 &amp;operator ++ ();<br> iterator1 &amp;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 &amp;operator = (const iterator1 &amp;it);<br><br> // Comparison<br> bool operator == (const iterator1 &amp;it) const;<br> };<br><br> iterator1 begin1 ();<br> iterator1 end1 ();<br><br> class const_iterator2:<br> public container_const_reference&lt;compressed_matrix&gt;,<br> public bidirectional_iterator_base&lt;const_iterator2, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const const_iterator_type &amp;it);<br> const_iterator2 (const iterator2 &amp;it);<br><br> // Arithmetic<br> const_iterator2 &amp;operator ++ ();<br> const_iterator2 &amp;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 &amp;operato
r = (const const_iterator2 &amp;it);<br><br> // Comparison<br> bool operator == (const const_iterator2 &amp;it) const;<br> };<br><br> const_iterator2 begin2 () const;<br> const_iterator2 end2 () const;<br><br> class iterator2:<br> public container_reference&lt;compressed_matrix&gt;,<br> public bidirectional_iterator_base&lt;iterator2, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const iterator_type &amp;it);<br><br> // Arithmetic<br> iterator2 &amp;operator ++ ();<br> iterator2 &amp;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 &amp;operator = (const iterator2 &amp;it);<br><br> // Comparison<br> bool operator == (const iterator2 &amp;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="coordinate_matrix"></a>
Coordinate Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>coordinate_matrix&lt;T, F, IB, IA, TA&gt; </code>
is the base container adaptor for compressed matrices. For a <em>(m x n</em>
)-dimensional sorted coordinate matrix and <em>0 &lt;= i &lt; m</em>,<em>
0 &lt;= j &lt; 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> &lt;
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> &lt; j</em><sub><em>
2</em></sub><em>)</em> with row major orientation or <em>j</em><sub><em>1</em></sub><em>
&lt; 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> &lt;
i</em><sub><em>2</em></sub><em>)</em> with column major orientation.</p>
<h4>Example</h4>
<pre>#include &lt;boost/numeric/ublas/matrix_sparse.hpp&gt;<br>#include &lt;boost/numeric/ublas/io.hpp&gt;<br><br>int main () {<br> using namespace boost::numeric::ublas;<br> coordinate_matrix&lt;double&gt; m (3, 3, 3 * 3);<br> for (unsigned i = 0; i &lt; m.size1 (); ++ i)<br> for (unsigned j = 0; j &lt; m.size2 (); ++ j)<br> m (i, j) = 3 * i + j;<br> std::cout &lt;&lt; m &lt;&lt; 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 coordinate matrix. </td>
<td>&nbsp;</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&lt;std::size_t&gt;</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&lt;T&gt;</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&lt;coordinate_matrix&lt;T, F, IB, IA, TA&gt; &gt;</code>
</p>
<h4>Members</h4>
<table border="1">
<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)</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 &amp;m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_matrix (size_type non_zeros, const matrix_expression&lt;AE&gt;
&amp;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
at most <code>size1 </code>rows of <code>size2 </code>elements.
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
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 &amp;operator = (const coordinate_matrix
&amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>coordinate_matrix &amp;assign_temporary (coordinate_matrix
&amp;m)</code></td>
<td>Assigns a temporary. May change the coordinate matrix
<code>m</code>.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_matrix &amp;operator = (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_matrix &amp;assign (const matrix_expression&lt;AE&gt;
&amp;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&lt;class AE&gt;<br>
coordinate_matrix &amp;operator += (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression
to the coordinate matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_matrix &amp;plus_assign (const matrix_expression&lt;AE&gt;
&amp;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&lt;class AE&gt;<br>
coordinate_matrix &amp;operator -= (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix
expression from the coordinate matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_matrix &amp;minus_assign (const matrix_expression&lt;AE&gt;
&amp;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&lt;class AT&gt;<br>
coordinate_matrix &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the coordinate
matrix with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
coordinate_matrix &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the coordinate
matrix through a scalar.</td>
</tr>
<tr>
<td><code>void swap (coordinate_matrix &amp;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>
<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&lt;&gt;</code>
, <code>bounded_array&lt;&gt;</code> and <code>std::vector&lt;&gt;</code>
. </p>
<h4>Interface</h4>
<pre><code> // Array based sparse matrix class <br> template&lt;class T, class F, std::size_t IB, class IA, class TA&gt;<br> class coordinate_matrix: <br> public matrix_expression&lt;coordinate_matrix&lt;T, F, IB, IA, TA&gt; &gt; {<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 &amp;const_reference;<br> typedef T &amp;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&lt;T, F, IB, IA, TA&gt; const_self_type;<br> typedef coordinate_matrix&lt;T, F, IB, IA, TA&gt; self_type;<br> typedef const matrix_const_reference&lt;const_self_type&gt; const_closure_type;<br> typedef matrix_reference&lt;self_type&gt; 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 &amp;m);<br> template&lt;class AE&gt;<br> coordinate_matrix (const matrix_expression&lt;AE&gt; &amp;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 &amp;index1_data () const;<br> index_array_type &amp;index1_data ();<br> const index_array_type &amp;index2_data () const;<br> index_array_type &amp;index2_data ();<br> const value_array_type &amp;value_data () const;<br> value_array_type &amp;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 &amp;operator = (const coordinate_matrix &amp;m);<br> coordinate_matrix &amp;assign_temporary (coordinate_matrix &amp;m);<br> template&lt;class AE&gt;<br> coordinate_matrix &amp;operator = (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> coordinate_matrix &amp;reset (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> coordinate_matrix &amp;assign (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> coordinate_matrix&amp; operator += (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> coordinate_matrix &amp;plus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> coordinate_matrix&amp; operator -= (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AE&gt;<br> coordinate_matrix &amp;minus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br> template&lt;class AT&gt;<br> coordinate_matrix&amp; operator *= (const AT &amp;at);<br> template&lt;class AT&gt;<br> coordinate_matrix&amp; operator /= (const AT &amp;at);<br><br> // Swapping<br> void swap (coordinate_matrix &amp;m);<br> friend void swap (coordinate_matrix &amp;m1, coordinate_matrix &amp;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&lt;const_iterator1&gt; const_reverse_iterator1;<br> typedef reverse_iterator_base1&lt;iterator1&gt; reverse_iterator1;<br> typedef reverse_iterator_base2&lt;const_iterator2&gt; const_reverse_iterator2;<br> typedef reverse_iterator_base2&lt;iterator2&gt; 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&lt;coordinate_matrix&gt;,<br> public bidirectional_iterator_base&lt;const_iterator1, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const const_iterator_type &amp;it);<br> const_iterator1 (const iterator1 &amp;it);<br><br> // Arithmetic<br> const_iterator1 &amp;operator ++ ();<br> const_iterator1 &amp;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 &amp;operator = (const const_iterator1 &amp;it);<br><br> // Comparison<br> bool operator == (const const_iterator1 &amp;it) const;<br> };<br><br> const_iterator1 begin1 () const;<br> const_iterator1 end1 () const;<br><br> class iterator1:<br> public container_reference&lt;coordinate_matrix&gt;,<br> public bidirectional_iterator_base&lt;iterator1, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const iterator_type &amp;it);<br><br> // Arithmetic<br> iterator1 &amp;operator ++ ();<br> iterator1 &amp;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 &amp;operator = (const iterator1 &amp;it);<br><br> // Comparison<br> bool operator == (const iterator1 &amp;it) const;<br> };<br><br> iterator1 begin1 ();<
br> iterator1 end1 ();<br><br> class const_iterator2:<br> public container_const_reference&lt;coordinate_matrix&gt;,<br> public bidirectional_iterator_base&lt;const_iterator2, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const const_iterator_type &amp;it);<br> const_iterator2 (const iterator2 &amp;it);<br><br> // Arithmetic<br> const_iterator2 &amp;operator ++ ();<br> const_iterator2 &amp;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 &amp;operator = (const const_iterator2 &amp;it);<br><br> // Comparison<br> bool operator == (const const_iterator2 &amp;it) const;<br> };<br><br> const_iterator2 begin2 () const;<br> const_iterator2 end2 () const;<br><br> class iterator2:<br> public container_reference&lt;coordinate_matrix&gt;,<br> public bidirectional_iterator_base&lt;iterator2, value_type&gt; {<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 &amp;m, int rank, size_type i, size_type j, const iterator_type &amp;it);<br><br> // Arithmetic<br> iterator2 &amp;operator ++ ();<br> iterator2 &amp;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 &amp;operator = (const iterator2 &amp;it);<br><br> // Comparison<br> bool operator == (const iterator2 &amp;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>
<hr>
<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch <br>
Permission to copy, use, modify, sell and distribute this document is granted
provided this copyright notice appears in all copies. This document is provided
``as is'' without express or implied warranty, and with no claim as to its
suitability for any purpose.</p>
<p>Last revised: 1/15/2003</p>
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