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ublas/doc/matrix_sparse.htm
Jörg Walter bbca4f92fa A couple of fixes and improvements
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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;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;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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