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ublas/doc/matrix_proxy.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">
Matrix Proxies</h1>
<h2><a name="matrix_row"></a> Matrix Row</h2>
<h4>Description</h4>
<p>The templated class <code>matrix_row&lt;M&gt;</code> allows
addressing a row of a matrix.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix&lt;double&gt; m (3, 3);<br>
for (unsigned i = 0; i &lt; m.size1 (); ++ i) {<br>
matrix_row&lt;matrix&lt;double&gt; &gt; mr (m, i);<br>
for (unsigned j = 0; j &lt; mr.size (); ++ j)<br>
mr (j) = 3 * i + j;<br>
std::cout &lt;&lt; mr &lt;&lt; std::endl;<br>
}<br>
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code> </td>
<td>The type of matrix referenced.</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression.htm#vector_expression">Vector Expression</a>
.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression.htm#vector_expression">Vector Expression</a> .</p>
<h4>Public base classes</h4>
<p><code>vector_expression&lt;matrix_row&lt;M&gt; &gt;</code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix_row (matrix_type &amp;data, size_type
i)</code></td>
<td>Constructs a sub vector.</td>
</tr>
<tr>
<td><code>size_type size () const</code></td>
<td>Returns the size of the sub vector.</td>
</tr>
<tr>
<td><code>const_reference operator () (size_type i)
const</code></td>
<td>Returns the value of the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>reference operator () (size_type i)</code></td>
<td>Returns a reference of the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>matrix_row &amp;operator = (const matrix_row
&amp;mr)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>matrix_row &amp;assign_temporary (matrix_row
&amp;mr)</code></td>
<td>Assigns a temporary. May change the matrix row <code>mr</code>
.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_row &amp;operator = (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_row &amp;assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a vector expression to the sub vector. Left and right
hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_row &amp;operator += (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Adds the vector expression to
the sub vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_row &amp;plus_assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Adds a vector expression to the sub vector. Left and right hand
side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_row &amp;operator -= (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the vector expression
from the sub vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_row &amp;minus_assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Subtracts a vector expression from the sub vector. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_row &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the sub vector with
a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_row &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the sub vector through
a scalar.</td>
</tr>
<tr>
<td><code>void swap (matrix_row &amp;mr)</code></td>
<td>Swaps the contents of the sub vectors.</td>
</tr>
<tr>
<td><code>const_iterator begin () const</code></td>
<td>Returns a <code>const_iterator</code> pointing to the beginning
of the <code>matrix_row</code>.</td>
</tr>
<tr>
<td><code>const_iterator end () const</code></td>
<td>Returns a <code>const_iterator</code> pointing to the end of
the <code>matrix_row</code>.</td>
</tr>
<tr>
<td><code>iterator begin ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the beginning of
the <code>matrix_row</code>.</td>
</tr>
<tr>
<td><code>iterator end ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the end of the
<code>matrix_row</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator rbegin () const</code></td>
<td>Returns a <code>const_reverse_iterator</code> pointing to the
beginning of the reversed <code>matrix_row</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator rend () const</code></td>
<td>Returns a <code>const_reverse_iterator</code> pointing to the
end of the reversed <code>matrix_row</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator rbegin ()</code> </td>
<td>Returns a <code>reverse_iterator</code> pointing to the
beginning of the reversed <code>matrix_row</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator rend ()</code> </td>
<td>Returns a <code>reverse_iterator</code> pointing to the end of
the reversed <code>matrix_row</code>.</td>
</tr>
</tbody>
</table>
<h4>Interface</h4>
<pre>
<code>// Matrix based row vector class<br>
template&lt;class M&gt;<br>
class matrix_row:<br>
public vector_expression&lt;matrix_row&lt;M&gt; &gt; {<br>
public:<br>
typedef const M const_matrix_type;<br>
typedef M matrix_type;<br>
typedef typename M::size_type size_type;<br>
typedef typename M::difference_type difference_type;<br>
typedef typename M::value_type value_type;<br>
typedef typename M::const_reference const_reference;<br>
typedef typename M::reference reference;<br>
typedef typename M::const_pointer const_pointer;<br>
typedef typename M::pointer pointer;<br>
typedef const vector_const_reference&lt;const matrix_row&lt;matrix_type&gt; &gt; const_closure_type;<br>
typedef vector_reference&lt;matrix_row&lt;matrix_type&gt; &gt; closure_type;<br>
typedef typename M::const_iterator2 const_iterator_type;<br>
typedef typename M::iterator2 iterator_type;<br>
typedef typename storage_restrict_traits&lt;typename M::storage_category,<br>
dense_proxy_tag&gt;::storage_category storage_category;<br>
<br>
// Construction and destruction<br>
matrix_row ();<br>
matrix_row (matrix_type &amp;data, size_type i);<br>
<br>
// Accessors<br>
size_type size () const;<br>
const_matrix_type &amp;data () const;<br>
matrix_type &amp;data ();<br>
<br>
<br>
// Element access<br>
const_reference operator () (size_type j) const;<br>
reference operator () (size_type j);<br>
<br>
const_reference operator [] (size_type j) const;<br>
reference operator [] (size_type j);<br>
<br>
// Assignment<br>
matrix_row &amp;operator = (const matrix_row &amp;mr);<br>
matrix_row &amp;assign_temporary (matrix_row &amp;mr);<br>
template&lt;class AE&gt;<br>
matrix_row &amp;operator = (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_row &amp;assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_row &amp;operator += (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_row &amp;plus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_row &amp;operator -= (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_row &amp;minus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AT&gt;<br>
matrix_row &amp;operator *= (const AT &amp;at);<br>
template&lt;class AT&gt;<br>
matrix_row &amp;operator /= (const AT &amp;at);<br>
<br>
// Swapping<br>
void swap (matrix_row &amp;mr);<br>
friend void swap (matrix_row &amp;mr1, matrix_row &amp;mr2);<br>
<br>
class const_iterator;<br>
class iterator;<br>
<br>
// Element lookup<br>
const_iterator find_first (size_type j) const;<br>
iterator find_first (size_type j);<br>
const_iterator find_last (size_type j) const;<br>
iterator find_last (size_type j);<br>
<br>
// Iterators simply are pointers.<br>
<br>
class const_iterator:<br>
public container_const_reference&lt;matrix_row&gt;,<br>
public random_access_iterator_base&lt;const_iterator, value_type&gt; {<br>
public:<br>
typedef typename const_iterator_type::iterator_category iterator_category;<br>
typedef typename const_iterator_type::difference_type difference_type;<br>
typedef typename const_iterator_type::value_type value_type;<br>
typedef typename const_iterator_type::reference reference;<br>
typedef typename const_iterator_type::pointer pointer;<br>
<br>
// Construction and destruction<br>
const_iterator ();<br>
const_iterator (const matrix_row &amp;mr, const const_iterator_type &amp;it);<br>
const_iterator (const iterator &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator &amp;operator ++ ();<br>
const_iterator &amp;operator -- ();<br>
const_iterator &amp;operator += (difference_type n);<br>
const_iterator &amp;operator -= (difference_type n);<br>
difference_type operator - (const const_iterator &amp;it) const;<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
const_iterator &amp;operator = (const const_iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const const_iterator &amp;it) const;<br>
bool operator &lt;(const const_iterator &amp;it) const;<br>
};<br>
<br>
const_iterator begin () const;<br>
const_iterator end () const;<br>
<br>
class iterator:<br>
public container_reference&lt;matrix_row&gt;,<br>
public random_access_iterator_base&lt;iterator, value_type&gt; {<br>
public:<br>
typedef typename iterator_type::iterator_category iterator_category;<br>
typedef typename iterator_type::difference_type difference_type;<br>
typedef typename iterator_type::value_type value_type;<br>
typedef typename iterator_type::reference reference;<br>
typedef typename iterator_type::pointer pointer;<br>
<br>
// Construction and destruction<br>
iterator ();<br>
iterator (matrix_row &amp;mr, const iterator_type &amp;it);<br>
<br>
// Arithmetic<br>
iterator &amp;operator ++ ();<br>
iterator &amp;operator -- ();<br>
iterator &amp;operator += (difference_type n);<br>
iterator &amp;operator -= (difference_type n);<br>
difference_type operator - (const iterator &amp;it) const;<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
iterator &amp;operator = (const iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const iterator &amp;it) const;<br>
bool operator &lt;(const iterator &amp;it) const;<br>
};<br>
<br>
iterator begin ();<br>
iterator end ();<br>
<br>
// Reverse iterator<br>
<br>
typedef reverse_iterator_base&lt;const_iterator&gt; const_reverse_iterator;<br>
<br>
const_reverse_iterator rbegin () const;<br>
const_reverse_iterator rend () const;<br>
<br>
typedef reverse_iterator_base&lt;iterator&gt; reverse_iterator;<br>
<br>
reverse_iterator rbegin ();<br>
reverse_iterator rend ();<br>
};</code>
</pre>
<h3>Projections</h3>
<h4>Prototypes</h4>
<pre>
<code>template&lt;class M&gt;<br>
matrix_row&lt;M&gt; row (M &amp;data, std::size_t i);<br>
template&lt;class M&gt;<br>
const matrix_row&lt;const M&gt; row (const M &amp;data, std::size_t i);</code>
</pre>
<h4>Description</h4>
<p>The free <code>row</code> functions support the construction of
matrix rows.</p>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Type requirements</h4>
<ul>
<li><code>M</code> is a model of <a href=
"expression.htm#matrix_expression">Matrix Expression</a> .</li>
</ul>
<h4>Preconditions</h4>
<ul type="Disc">
<li><code>i &lt; data.size1 ()</code></li>
</ul>
<h4>Complexity</h4>
<p>Linear depending from the size of the row.</p>
<h4>Examples</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix&lt;double&gt; m (3, 3);<br>
for (unsigned i = 0; i &lt; m.size1 (); ++ i) {<br>
for (unsigned j = 0; j &lt; m.size2 (); ++ j)<br>
row (m, i) (j) = 3 * i + j;<br>
std::cout &lt;&lt; row (m, i) &lt;&lt; std::endl;<br>
}<br>
}<br>
</pre>
<h2><a name="matrix_column"></a> Matrix Column</h2>
<h4>Description</h4>
<p>The templated class <code>matrix_column&lt;M&gt;</code> allows
addressing a column of a matrix.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix&lt;double&gt; m (3, 3);<br>
for (unsigned j = 0; j &lt; m.size2 (); ++ j) {<br>
matrix_column&lt;matrix&lt;double&gt; &gt; mc (m, j);<br>
for (unsigned i = 0; i &lt; mc.size (); ++ i)<br>
mc (i) = 3 * i + j;<br>
std::cout &lt;&lt; mc &lt;&lt; std::endl;<br>
}<br>
}<br>
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code> </td>
<td>The type of matrix referenced.</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression.htm#vector_expression">Vector Expression</a>
.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression.htm#vector_expression">Vector Expression</a> .</p>
<h4>Public base classes</h4>
<p><code>vector_expression&lt;matrix_column&lt;M&gt;
&gt;</code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix_column (matrix_type &amp;data, size_type
j)</code></td>
<td>Constructs a sub vector.</td>
</tr>
<tr>
<td><code>size_type size () const</code></td>
<td>Returns the size of the sub vector.</td>
</tr>
<tr>
<td><code>const_reference operator () (size_type i)
const</code></td>
<td>Returns the value of the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>reference operator () (size_type i)</code></td>
<td>Returns a reference of the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>matrix_column &amp;operator = (const matrix_column
&amp;mc)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>matrix_column &amp;assign_temporary (matrix_column
&amp;mc)</code></td>
<td>Assigns a temporary. May change the matrix column
<code>mc</code> .</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_column &amp;operator = (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_column &amp;assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a vector expression to the sub vector. Left and right
hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_column &amp;operator += (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Adds the vector expression to
the sub vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_column &amp;plus_assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Adds a vector expression to the sub vector. Left and right hand
side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_column &amp;operator -= (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the vector expression
from the sub vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_column &amp;minus_assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Subtracts a vector expression from the sub vector. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_column &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the sub vector with
a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_column &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the sub vector through
a scalar.</td>
</tr>
<tr>
<td><code>void swap (matrix_column &amp;mc)</code></td>
<td>Swaps the contents of the sub vectors.</td>
</tr>
<tr>
<td><code>const_iterator begin () const</code></td>
<td>Returns a <code>const_iterator</code> pointing to the beginning
of the <code>matrix_column</code>.</td>
</tr>
<tr>
<td><code>const_iterator end () const</code></td>
<td>Returns a <code>const_iterator</code> pointing to the end of
the <code>matrix_column</code>.</td>
</tr>
<tr>
<td><code>iterator begin ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the beginning of
the <code>matrix_column</code>.</td>
</tr>
<tr>
<td><code>iterator end ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the end of the
<code>matrix_column</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator rbegin () const</code></td>
<td>Returns a <code>const_reverse_iterator</code> pointing to the
beginning of the reversed <code>matrix_column</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator rend () const</code></td>
<td>Returns a <code>const_reverse_iterator</code> pointing to the
end of the reversed <code>matrix_column</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator rbegin ()</code> </td>
<td>Returns a <code>reverse_iterator</code> pointing to the
beginning of the reversed <code>matrix_column</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator rend ()</code> </td>
<td>Returns a <code>reverse_iterator</code> pointing to the end of
the reversed <code>matrix_column</code>.</td>
</tr>
</tbody>
</table>
<h4>Interface</h4>
<pre>
<code>// Matrix based column vector class<br>
template&lt;class M&gt;<br>
class matrix_column:<br>
public vector_expression&lt;matrix_column&lt;M&gt; &gt; {<br>
public: <br>
typedef const M const_matrix_type;<br>
typedef M matrix_type;<br>
typedef typename M::size_type size_type;<br>
typedef typename M::difference_type difference_type;<br>
typedef typename M::value_type value_type;<br>
typedef typename M::const_reference const_reference;<br>
typedef typename M::reference reference;<br>
typedef typename M::const_pointer const_pointer;<br>
typedef typename M::pointer pointer;<br>
typedef const vector_const_reference&lt;const matrix_column&lt;matrix_type&gt; &gt; const_closure_type;<br>
typedef vector_reference&lt;matrix_column&lt;matrix_type&gt; &gt; closure_type;<br>
typedef typename M::const_iterator1 const_iterator_type;<br>
typedef typename M::iterator1 iterator_type;<br>
typedef typename storage_restrict_traits&lt;typename M::storage_category,<br>
dense_proxy_tag&gt;::storage_category storage_category;<br>
<br>
// Construction and destruction<br>
matrix_column ();<br>
matrix_column (matrix_type &amp;data, size_type j);<br>
<br>
// Accessors<br>
size_type size () const;<br>
const_matrix_type &amp;data () const;<br>
matrix_type &amp;data ();<br>
<br>
<br>
// Element access<br>
const_reference operator () (size_type i) const;<br>
reference operator () (size_type i);<br>
<br>
const_reference operator [] (size_type i) const;<br>
reference operator [] (size_type i);<br>
<br>
// Assignment<br>
matrix_column &amp;operator = (const matrix_column &amp;mc);<br>
matrix_column &amp;assign_temporary (matrix_column &amp;mc);<br>
template&lt;class AE&gt;<br>
matrix_column &amp;operator = (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_column &amp;assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_column &amp;operator += (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_column &amp;plus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_column &amp;operator -= (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_column &amp;minus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AT&gt;<br>
matrix_column &amp;operator *= (const AT &amp;at);<br>
template&lt;class AT&gt;<br>
matrix_column &amp;operator /= (const AT &amp;at);<br>
<br>
// Swapping<br>
void swap (matrix_column &amp;mc);<br>
friend void swap (matrix_column &amp;mc1, matrix_column &amp;mc2);<br>
<br>
class const_iterator;<br>
class iterator;<br>
<br>
// Element lookup<br>
const_iterator find_first (size_type i) const;<br>
iterator find_first (size_type i);<br>
const_iterator find_last (size_type i) const;<br>
iterator find_last (size_type i);<br>
<br>
// Iterators simply are pointers.<br>
<br>
class const_iterator:<br>
public container_const_reference&lt;matrix_column&gt;,<br>
public random_access_iterator_base&lt;const_iterator, value_type&gt; {<br>
public:<br>
typedef typename const_iterator_type::iterator_category iterator_category;<br>
typedef typename const_iterator_type::difference_type difference_type;<br>
typedef typename const_iterator_type::value_type value_type;<br>
typedef typename const_iterator_type::reference reference;<br>
typedef typename const_iterator_type::pointer pointer;<br>
<br>
// Construction and destruction<br>
const_iterator ();<br>
const_iterator (const matrix_column &amp;mc, const const_iterator_type &amp;it);<br>
const_iterator (const iterator &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator &amp;operator ++ ();<br>
const_iterator &amp;operator -- ();<br>
const_iterator &amp;operator += (difference_type n);<br>
const_iterator &amp;operator -= (difference_type n);<br>
difference_type operator - (const const_iterator &amp;it) const;<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
const_iterator &amp;operator = (const const_iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const const_iterator &amp;it) const;<br>
bool operator &lt;(const const_iterator &amp;it) const;<br>
};<br>
<br>
const_iterator begin () const;<br>
const_iterator end () const;<br>
<br>
class iterator:<br>
public container_reference&lt;matrix_column&gt;,<br>
public random_access_iterator_base&lt;iterator, value_type&gt; {<br>
public:<br>
typedef typename iterator_type::iterator_category iterator_category;<br>
typedef typename iterator_type::difference_type difference_type;<br>
typedef typename iterator_type::value_type value_type;<br>
typedef typename iterator_type::reference reference;<br>
typedef typename iterator_type::pointer pointer;<br>
<br>
// Construction and destruction<br>
iterator ();<br>
iterator (matrix_column &amp;mc, const iterator_type &amp;it);<br>
<br>
// Arithmetic<br>
iterator &amp;operator ++ ();<br>
iterator &amp;operator -- ();<br>
iterator &amp;operator += (difference_type n);<br>
iterator &amp;operator -= (difference_type n);<br>
difference_type operator - (const iterator &amp;it) const;<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
iterator &amp;operator = (const iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const iterator &amp;it) const;<br>
bool operator &lt;(const iterator &amp;it) const;<br>
};<br>
<br>
iterator begin ();<br>
iterator end ();<br>
<br>
// Reverse iterator<br>
<br>
typedef reverse_iterator_base&lt;const_iterator&gt; const_reverse_iterator;<br>
<br>
const_reverse_iterator rbegin () const;<br>
const_reverse_iterator rend () const;<br>
<br>
typedef reverse_iterator_base&lt;iterator&gt; reverse_iterator;<br>
<br>
reverse_iterator rbegin ();<br>
reverse_iterator rend ();<br>
};</code>
</pre>
<h3>Projections</h3>
<h4>Prototypes</h4>
<pre>
<code>template&lt;class M&gt;<br>
matrix_column&lt;M&gt; column (M &amp;data, std::size_t j);<br>
template&lt;class M&gt;<br>
const matrix_column&lt;const M&gt; column (const M &amp;data, std::size_t j);</code>
</pre>
<h4>Description</h4>
<p>The free <code>column</code> functions support the construction
of matrix columns.</p>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Type requirements</h4>
<ul>
<li><code>M</code> is a model of <a href=
"expression.htm#matrix_expression">Matrix Expression</a> .</li>
</ul>
<h4>Preconditions</h4>
<ul type="Disc">
<li><code>j &lt; data.size2 ()</code></li>
</ul>
<h4>Complexity</h4>
<p>Linear depending from the size of the column.</p>
<h4>Examples</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix&lt;double&gt; m (3, 3);<br>
for (unsigned j = 0; j &lt; m.size2 (); ++ j) {<br>
for (unsigned i = 0; i &lt; m.size1 (); ++ i)<br>
column (m, j) (i) = 3 * i + j;<br>
std::cout &lt;&lt; column (m, j) &lt;&lt; std::endl;<br>
}<br>
}<br>
</pre>
<h2><a name="vector_range"></a> Vector Range</h2>
<h4>Description</h4>
<p>The templated class <code>matrix_vector_range&lt;M&gt;</code>
allows addressing a sub vector of a matrix.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix&lt;double&gt; m (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>
<br>
matrix_vector_range&lt;matrix&lt;double&gt; &gt; mvr (m, range (0, 3), range (0, 3));<br>
std::cout &lt;&lt; mvr &lt;&lt; std::endl;<br>
}<br>
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code> </td>
<td>The type of matrix referenced.</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression.htm#vector_expression">Vector Expression</a>
.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression.htm#vector_expression">Vector Expression</a> .</p>
<h4>Public base classes</h4>
<p><code>vector_expression&lt;matrix_vector_range&lt;M&gt;
&gt;</code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix_vector_range (matrix_type &amp;data,<br>
&nbsp;const range &amp;r1, const range &amp;r2)</code></td>
<td>Constructs a sub vector.</td>
</tr>
<tr>
<td><code>size_type size () const</code></td>
<td>Returns the size of the sub vector.</td>
</tr>
<tr>
<td><code>const_reference operator () (size_type i)
const</code></td>
<td>Returns the value of the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>reference operator () (size_type i)</code></td>
<td>Returns a reference of the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>matrix_vector_range &amp;operator = (const
matrix_vector_range &amp;mvr)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>matrix_vector_range &amp;assign_temporary
(matrix_vector_range &amp;mvr)</code></td>
<td>Assigns a temporary. May change the matrix vector range
<code>mvr</code>.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_range &amp;operator = (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_range &amp;assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a vector expression to the sub vector. Left and right
hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_range &amp;operator += (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Adds the vector expression to
the sub vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_range &amp;plus_assign (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Adds a vector expression to the sub vector. Left and right hand
side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_range &amp;operator -= (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the vector expression
from the sub vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_range &amp;minus_assign (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Subtracts a vector expression from the sub vector. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_vector_range &amp;operator *= (const AT
&amp;at)</code></td>
<td>A computed assignment operator. Multiplies the sub vector with
a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_vector_range &amp;operator /= (const AT
&amp;at)</code></td>
<td>A computed assignment operator. Divides the sub vector through
a scalar.</td>
</tr>
<tr>
<td><code>void swap (matrix_vector_range &amp;mvr)</code></td>
<td>Swaps the contents of the sub vectors.</td>
</tr>
<tr>
<td><code>const_iterator begin () const</code></td>
<td>Returns a <code>const_iterator</code> pointing to the beginning
of the <code>matrix_vector_range</code>.</td>
</tr>
<tr>
<td><code>const_iterator end () const</code></td>
<td>Returns a <code>const_iterator</code> pointing to the end of
the <code>matrix_vector_range</code>.</td>
</tr>
<tr>
<td><code>iterator begin ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the beginning of
the <code>matrix_vector_range</code>.</td>
</tr>
<tr>
<td><code>iterator end ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the end of the
<code>matrix_vector_range</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator rbegin () const</code></td>
<td>Returns a <code>const_reverse_iterator</code> pointing to the
beginning of the <code>matrix_vector_range</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator rend () const</code></td>
<td>Returns a <code>const_reverse_iterator</code> pointing to the
end of the reversed <code>matrix_vector_range</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator rbegin ()</code> </td>
<td>Returns a <code>reverse_iterator</code> pointing to the
beginning of the reversed <code>matrix_vector_range</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator rend ()</code> </td>
<td>Returns a <code>reverse_iterator</code> pointing to the end of
the reversed <code>matrix_vector_range</code>.</td>
</tr>
</tbody>
</table>
<h4>Interface</h4>
<pre>
<code>// Matrix based vector range class<br>
template&lt;class M&gt;<br>
class matrix_vector_range:<br>
public vector_expression&lt;matrix_vector_range&lt;M&gt; &gt; {<br>
public: <br>
typedef const M const_matrix_type;<br>
typedef M matrix_type;<br>
typedef typename M::size_type size_type;<br>
typedef typename M::difference_type difference_type;<br>
typedef typename M::value_type value_type;<br>
typedef typename M::const_reference const_reference;<br>
typedef typename M::reference reference;<br>
typedef typename M::const_pointer const_pointer;<br>
typedef typename M::pointer pointer;<br>
typedef const vector_const_reference&lt;const matrix_vector_range&lt;matrix_type&gt; &gt; const_closure_type;<br>
typedef vector_reference&lt;matrix_vector_range&lt;matrix_type&gt; &gt; closure_type;<br>
typedef range::const_iterator const_iterator1_type;<br>
typedef range::const_iterator iterator1_type;<br>
typedef range::const_iterator const_iterator2_type;<br>
typedef range::const_iterator iterator2_type;<br>
typedef typename storage_restrict_traits&lt;typename M::storage_category,<br>
dense_proxy_tag&gt;::storage_category storage_category;<br>
<br>
// Construction and destruction<br>
matrix_vector_range ();<br>
matrix_vector_range (matrix_type &amp;data, const range &amp;r1, const range &amp;r2);<br>
<br>
// Accessors<br>
size_type size () const;<br>
const_matrix_type &amp;data () const;<br>
matrix_type &amp;data ();<br>
<br>
<br>
// Element access<br>
const_reference operator () (size_type i) const;<br>
reference operator () (size_type i);<br>
<br>
const_reference operator [] (size_type i) const;<br>
reference operator [] (size_type i);<br>
<br>
// Assignment<br>
matrix_vector_range &amp;operator = (const matrix_vector_range &amp;mvr);<br>
matrix_vector_range &amp;assign_temporary (matrix_vector_range &amp;mvr);<br>
template&lt;class AE&gt;<br>
matrix_vector_range &amp;operator = (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_vector_range &amp;assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_vector_range &amp;operator += (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_vector_range &amp;plus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_vector_range &amp;operator -= (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_vector_range &amp;minus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AT&gt;<br>
matrix_vector_range &amp;operator *= (const AT &amp;at);<br>
template&lt;class AT&gt;<br>
matrix_vector_range &amp;operator /= (const AT &amp;at);<br>
<br>
// Swapping<br>
void swap (matrix_vector_range &amp;mvr);<br>
friend void swap (matrix_vector_range &amp;mvr1, matrix_vector_range &amp;mvr2);<br>
<br>
class const_iterator;<br>
class iterator;<br>
<br>
// Element lookup<br>
const_iterator find_first (size_type i) const;<br>
iterator find_first (size_type i);<br>
const_iterator find_last (size_type i) const;<br>
iterator find_last (size_type i);<br>
<br>
// Iterators simply are indices.<br>
<br>
class const_iterator:<br>
public container_const_reference&lt;matrix_vector_range&gt;,<br>
public random_access_iterator_base&lt;const_iterator, value_type&gt; {<br>
public:<br>
typedef typename restrict_traits&lt;typename M::const_iterator1::iterator_category,<br>
typename M::const_iterator2::iterator_category&gt;::iterator_category iterator_category;<br>
typedef typename matrix_vector_range::difference_type difference_type;<br>
typedef typename matrix_vector_range::value_type value_type;<br>
typedef typename matrix_vector_range::const_reference reference;<br>
typedef typename matrix_vector_range::const_pointer pointer;<br>
<br>
// Construction and destruction<br>
const_iterator ();<br>
const_iterator (const matrix_vector_range &amp;mvr, const const_iterator1_type &amp;it1, const const_iterator2_type &amp;it2);<br>
const_iterator (const iterator &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator &amp;operator ++ ();<br>
const_iterator &amp;operator -- ();<br>
const_iterator &amp;operator += (difference_type n);<br>
const_iterator &amp;operator -= (difference_type n);<br>
difference_type operator - (const const_iterator &amp;it) const;<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
const_iterator &amp;operator = (const const_iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const const_iterator &amp;it) const;<br>
bool operator &lt;(const const_iterator &amp;it) const;<br>
};<br>
<br>
const_iterator begin () const;<br>
const_iterator end () const;<br>
<br>
class iterator:<br>
public container_reference&lt;matrix_vector_range&gt;,<br>
public random_access_iterator_base&lt;iterator, value_type&gt; {<br>
public:<br>
typedef typename restrict_traits&lt;typename M::iterator1::iterator_category,<br>
typename M::iterator2::iterator_category&gt;::iterator_category iterator_category;<br>
typedef typename matrix_vector_range::difference_type difference_type;<br>
typedef typename matrix_vector_range::value_type value_type;<br>
typedef typename matrix_vector_range::reference reference;<br>
typedef typename matrix_vector_range::pointer pointer;<br>
<br>
// Construction and destruction<br>
iterator ();<br>
iterator (matrix_vector_range &amp;mvr, const iterator1_type &amp;it1, const iterator2_type &amp;it2);<br>
<br>
// Arithmetic<br>
iterator &amp;operator ++ ();<br>
iterator &amp;operator -- ();<br>
iterator &amp;operator += (difference_type n);<br>
iterator &amp;operator -= (difference_type n);<br>
difference_type operator - (const iterator &amp;it) const;<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
iterator &amp;operator = (const iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const iterator &amp;it) const;<br>
bool operator &lt;(const iterator &amp;it) const;<br>
};<br>
<br>
iterator begin ();<br>
iterator end ();<br>
<br>
// Reverse iterator<br>
<br>
typedef reverse_iterator_base&lt;const_iterator&gt; const_reverse_iterator;<br>
<br>
const_reverse_iterator rbegin () const;<br>
const_reverse_iterator rend () const;<br>
<br>
typedef reverse_iterator_base&lt;iterator&gt; reverse_iterator;<br>
<br>
reverse_iterator rbegin ();<br>
reverse_iterator rend ();<br>
};</code>
</pre>
<h2><a name="vector_slice"></a> Vector Slice</h2>
<h4>Description</h4>
<p>The templated class <code>matrix_vector_slice&lt;M&gt;</code>
allows addressing a sliced sub vector of a matrix.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix&lt;double&gt; m (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>
<br>
matrix_vector_slice&lt;matrix&lt;double&gt; &gt; mvs (m, slice (0, 1, 3), slice (0, 1, 3));<br>
std::cout &lt;&lt; mvs &lt;&lt; std::endl;<br>
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code> </td>
<td>The type of matrix referenced.</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression.htm#vector_expression">Vector Expression</a>
.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression.htm#vector_expression">Vector Expression</a> .</p>
<h4>Public base classes</h4>
<p><code>vector_expression&lt;matrix_vector_slice&lt;M&gt;
&gt;</code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix_vector_slice (matrix_type &amp;data,<br>
&nbsp;const slice &amp;s1, const slice &amp;s2)</code></td>
<td>Constructs a sub vector.</td>
</tr>
<tr>
<td><code>size_type size () const</code></td>
<td>Returns the size of the sub vector.</td>
</tr>
<tr>
<td><code>const_reference operator () (size_type i)
const</code></td>
<td>Returns the value of the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>reference operator () (size_type i)</code></td>
<td>Returns a reference of the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>matrix_vector_slice &amp;operator = (const
matrix_vector_slice &amp;mvs)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>matrix_vector_slice &amp;assign_temporary
(matrix_vector_slice &amp;mvs)</code></td>
<td>Assigns a temporary. May change the matrix vector slice
<code>vs</code>.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_slice &amp;operator = (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_slice &amp;assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a vector expression to the sub vector. Left and right
hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_slice &amp;operator += (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Adds the vector expression to
the sub vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_slice &amp;plus_assign (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Adds a vector expression to the sub vector. Left and right hand
side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_slice &amp;operator -= (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the vector expression
from the sub vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_vector_slice &amp;minus_assign (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Subtracts a vector expression from the sub vector. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_vector_slice &amp;operator *= (const AT
&amp;at)</code></td>
<td>A computed assignment operator. Multiplies the sub vector with
a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_vector_slice &amp;operator /= (const AT
&amp;at)</code></td>
<td>A computed assignment operator. Divides the sub vector through
a scalar.</td>
</tr>
<tr>
<td><code>void swap (matrix_vector_slice &amp;mvs)</code></td>
<td>Swaps the contents of the sub vectors.</td>
</tr>
<tr>
<td><code>const_iterator begin () const</code></td>
<td>Returns a <code>const_iterator</code> pointing to the beginning
of the <code>matrix_vector_slice</code>.</td>
</tr>
<tr>
<td><code>const_iterator end () const</code></td>
<td>Returns a <code>const_iterator</code> pointing to the end of
the <code>matrix_vector_slice</code>.</td>
</tr>
<tr>
<td><code>iterator begin ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the beginning of
the <code>matrix_vector_slice</code>.</td>
</tr>
<tr>
<td><code>iterator end ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the end of the
<code>matrix_vector_slice</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator rbegin () const</code></td>
<td>Returns a <code>const_reverse_iterator</code> pointing to the
beginning of the reversed <code>matrix_vector_slice</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator rend () const</code></td>
<td>Returns a <code>const_reverse_iterator</code> pointing to the
end of the reversed <code>matrix_vector_slice</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator rbegin ()</code> </td>
<td>Returns a <code>reverse_iterator</code> pointing to the
beginning of the reversed <code>matrix_vector_slice</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator rend ()</code> </td>
<td>Returns a <code>reverse_iterator</code> pointing to the end of
the reversed <code>matrix_vector_slice</code>.</td>
</tr>
</tbody>
</table>
<h4>Interface</h4>
<pre>
<code>// Matrix based vector slice class<br>
template&lt;class M&gt;<br>
class matrix_vector_slice:<br>
public vector_expression&lt;matrix_vector_slice&lt;M&gt; &gt; {<br>
public: <br>
typedef const M const_matrix_type;<br>
typedef M matrix_type;<br>
typedef typename M::size_type size_type;<br>
typedef typename M::difference_type difference_type;<br>
typedef typename M::value_type value_type;<br>
typedef typename M::const_reference const_reference;<br>
typedef typename M::reference reference;<br>
typedef typename M::const_pointer const_pointer;<br>
typedef typename M::pointer pointer;<br>
typedef const vector_const_reference&lt;const matrix_vector_slice&lt;matrix_type&gt; &gt; const_closure_type;<br>
typedef vector_reference&lt;matrix_vector_slice&lt;matrix_type&gt; &gt; closure_type;<br>
typedef slice::const_iterator const_iterator1_type;<br>
typedef slice::const_iterator iterator1_type;<br>
typedef slice::const_iterator const_iterator2_type;<br>
typedef slice::const_iterator iterator2_type;<br>
typedef typename storage_restrict_traits&lt;typename M::storage_category,<br>
dense_proxy_tag&gt;::storage_category storage_category;<br>
<br>
// Construction and destruction<br>
matrix_vector_slice ();<br>
matrix_vector_slice (matrix_type &amp;data, const slice &amp;s1, const slice &amp;s2);<br>
<br>
// Accessors<br>
size_type size () const;<br>
const_matrix_type &amp;data () const;<br>
matrix_type &amp;data ();<br>
<br>
<br>
// Element access<br>
const_reference operator () (size_type i) const;<br>
reference operator () (size_type i);<br>
<br>
const_reference operator [] (size_type i) const;<br>
reference operator [] (size_type i);<br>
<br>
// Assignment<br>
matrix_vector_slice &amp;operator = (const matrix_vector_slice &amp;mvs);<br>
matrix_vector_slice &amp;assign_temporary (matrix_vector_slice &amp;mvs);<br>
template&lt;class AE&gt;<br>
matrix_vector_slice &amp;operator = (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_vector_slice &amp;assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_vector_slice &amp;operator += (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_vector_slice &amp;plus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_vector_slice &amp;operator -= (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_vector_slice &amp;minus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AT&gt;<br>
matrix_vector_slice &amp;operator *= (const AT &amp;at);<br>
template&lt;class AT&gt;<br>
matrix_vector_slice &amp;operator /= (const AT &amp;at);<br>
<br>
// Swapping<br>
void swap (matrix_vector_slice &amp;mvs);<br>
friend void swap (matrix_vector_slice &amp;mvs1, matrix_vector_slice &amp;mvs2);<br>
<br>
class const_iterator;<br>
class iterator;<br>
<br>
// Element lookup<br>
const_iterator find_first (size_type i) const;<br>
iterator find_first (size_type i);<br>
const_iterator find_last (size_type i) const;<br>
iterator find_last (size_type i);<br>
<br>
// Iterators simply are indices.<br>
<br>
class const_iterator:<br>
public container_const_reference&lt;matrix_vector_slice&gt;,<br>
public random_access_iterator_base&lt;const_iterator, value_type&gt; {<br>
public:<br>
typedef typename restrict_traits&lt;typename M::const_iterator1::iterator_category,<br>
typename M::const_iterator2::iterator_category&gt;::iterator_category iterator_category;<br>
typedef typename matrix_vector_slice::difference_type difference_type;<br>
typedef typename matrix_vector_slice::value_type value_type;<br>
typedef typename matrix_vector_slice::const_reference reference;<br>
typedef typename matrix_vector_slice::const_pointer pointer;<br>
<br>
// Construction and destruction<br>
const_iterator ();<br>
const_iterator (const matrix_vector_slice &amp;mvs, const const_iterator1_type &amp;it1, const const_iterator2_type &amp;it2);<br>
const_iterator (const iterator &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator &amp;operator ++ ();<br>
const_iterator &amp;operator -- ();<br>
const_iterator &amp;operator += (difference_type n);<br>
const_iterator &amp;operator -= (difference_type n);<br>
difference_type operator - (const const_iterator &amp;it) const;<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
const_iterator &amp;operator = (const const_iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const const_iterator &amp;it) const;<br>
bool operator &lt;(const const_iterator &amp;it) const;<br>
};<br>
<br>
const_iterator begin () const;<br>
const_iterator end () const;<br>
<br>
class iterator:<br>
public container_reference&lt;matrix_vector_slice&gt;,<br>
public random_access_iterator_base&lt;iterator, value_type&gt; {<br>
public:<br>
typedef typename restrict_traits&lt;typename M::iterator1::iterator_category,<br>
typename M::iterator2::iterator_category&gt;::iterator_category iterator_category;<br>
typedef typename matrix_vector_slice::difference_type difference_type;<br>
typedef typename matrix_vector_slice::value_type value_type;<br>
typedef typename matrix_vector_slice::reference reference;<br>
typedef typename matrix_vector_slice::pointer pointer;<br>
<br>
// Construction and destruction<br>
iterator ();<br>
iterator (matrix_vector_slice &amp;mvs, const iterator1_type &amp;it1, const iterator2_type &amp;it2);<br>
<br>
// Arithmetic<br>
iterator &amp;operator ++ ();<br>
iterator &amp;operator -- ();<br>
iterator &amp;operator += (difference_type n);<br>
iterator &amp;operator -= (difference_type n);<br>
difference_type operator - (const iterator &amp;it) const;<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
iterator &amp;operator = (const iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const iterator &amp;it) const;<br>
bool operator &lt;(const iterator &amp;it) const;<br>
};<br>
<br>
iterator begin ();<br>
iterator end ();<br>
<br>
// Reverse iterator<br>
<br>
typedef reverse_iterator_base&lt;const_iterator&gt; const_reverse_iterator;<br>
<br>
const_reverse_iterator rbegin () const;<br>
const_reverse_iterator rend () const;<br>
<br>
typedef reverse_iterator_base&lt;iterator&gt; reverse_iterator;<br>
<br>
reverse_iterator rbegin ();<br>
reverse_iterator rend ();<br>
};</code>
</pre>
<h2><a name="matrix_range"></a> Matrix Range</h2>
<h4>Description</h4>
<p>The templated class <code>matrix_range&lt;M&gt;</code> allows
addressing a sub matrix of a matrix.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix&lt;double&gt; m (3, 3);<br>
matrix_range&lt;matrix&lt;double&gt; &gt; mr (m, range (0, 3), range (0, 3));<br>
for (unsigned i = 0; i &lt; mr.size1 (); ++ i)<br>
for (unsigned j = 0; j &lt; mr.size2 (); ++ j)<br>
mr (i, j) = 3 * i + j;<br>
std::cout &lt;&lt; mr &lt;&lt; std::endl;<br>
}<br>
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code> </td>
<td>The type of matrix referenced.</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression.htm#matrix_expression">Matrix Expression</a>
.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression.htm#matrix_expression">Matrix Expression</a> .</p>
<h4>Public base classes</h4>
<p><code>matrix_expression&lt;matrix_range&lt;M&gt; &gt;</code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix_range (matrix_type &amp;data,<br>
&nbsp;const range &amp;r1, const range &amp;r2)</code></td>
<td>Constructs a sub matrix.</td>
</tr>
<tr>
<td><code>size_type start1 () const</code></td>
<td>Returns the index of the first row.</td>
</tr>
<tr>
<td><code>size_type size1 () const</code></td>
<td>Returns the number of rows.</td>
</tr>
<tr>
<td><code>size_type start2 () const</code></td>
<td>Returns the index of the first column.</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>matrix_range &amp;operator = (const matrix_range
&amp;mr)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>matrix_range &amp;assign_temporary (matrix_range
&amp;mr)</code></td>
<td>Assigns a temporary. May change the matrix range
<code>mr</code> .</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_range &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>
matrix_range &amp;assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a matrix expression to the sub matrix. Left and right
hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_range &amp;operator += (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression to
the sub matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_range &amp;plus_assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Adds a matrix expression to the sub matrix. Left and right hand
side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_range &amp;operator -= (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix expression
from the sub matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_range &amp;minus_assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Subtracts a matrix expression from the sub matrix. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_range &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the sub matrix with
a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_range &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the sub matrix through
a scalar.</td>
</tr>
<tr>
<td><code>void swap (matrix_range &amp;mr)</code></td>
<td>Swaps the contents of the sub matrices.</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>matrix_range</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>matrix_range</code>.</td>
</tr>
<tr>
<td><code>iterator1 begin1 ()</code> </td>
<td>Returns a <code>iterator1</code> pointing to the beginning of
the <code>matrix_range</code>.</td>
</tr>
<tr>
<td><code>iterator1 end1 ()</code> </td>
<td>Returns a <code>iterator1</code> pointing to the end of the
<code>matrix_range</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>matrix_range</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>matrix_range</code>.</td>
</tr>
<tr>
<td><code>iterator2 begin2 ()</code> </td>
<td>Returns a <code>iterator2</code> pointing to the beginning of
the <code>matrix_range</code>.</td>
</tr>
<tr>
<td><code>iterator2 end2 ()</code> </td>
<td>Returns a <code>iterator2</code> pointing to the end of the
<code>matrix_range</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>matrix_range</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>matrix_range</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>matrix_range</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>matrix_range</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>matrix_range</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>matrix_range</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>matrix_range</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator2 rend2 ()</code> </td>
<td>Returns a <code>reverse_iterator2</code> pointing to the end of
reversed the <code>matrix_range</code>.</td>
</tr>
</tbody>
</table>
<h4>Interface</h4>
<pre>
<code>// Matrix based range class<br>
template&lt;class M&gt;<br>
class matrix_range:<br>
public matrix_expression&lt;matrix_range&lt;M&gt; &gt; {<br>
public: <br>
typedef const M const_matrix_type;<br>
typedef M matrix_type;<br>
typedef typename M::size_type size_type;<br>
typedef typename M::difference_type difference_type;<br>
typedef typename M::value_type value_type;<br>
typedef typename M::const_reference const_reference;<br>
typedef typename M::reference reference;<br>
typedef typename M::const_pointer const_pointer;<br>
typedef typename M::pointer pointer;<br>
typedef const matrix_const_reference&lt;const matrix_range&lt;matrix_type&gt; &gt; const_closure_type;<br>
typedef matrix_reference&lt;matrix_range&lt;matrix_type&gt; &gt; closure_type;<br>
typedef typename M::const_iterator1 const_iterator1_type;<br>
typedef typename M::iterator1 iterator1_type;<br>
typedef typename M::const_iterator2 const_iterator2_type;<br>
typedef typename M::iterator2 iterator2_type;<br>
typedef typename storage_restrict_traits&lt;typename M::storage_category,<br>
dense_proxy_tag&gt;::storage_category storage_category;<br>
typedef typename M::orientation_category orientation_category;<br>
<br>
// Construction and destruction<br>
matrix_range ();<br>
matrix_range (matrix_type &amp;data, const range &amp;r1, const range &amp;r2);<br>
<br>
// Accessors<br>
size_type start1 () const;<br>
size_type size1 () const;<br>
size_type start2() const;<br>
size_type size2 () const;<br>
const_matrix_type &amp;data () const;<br>
matrix_type &amp;data ();<br>
<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>
matrix_range&lt;matrix_type&gt; project (const range &amp;r1, const range &amp;r2) const;<br>
<br>
// Assignment<br>
matrix_range &amp;operator = (const matrix_range &amp;mr);<br>
matrix_range &amp;assign_temporary (matrix_range &amp;mr);<br>
template&lt;class AE&gt;<br>
matrix_range &amp;operator = (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_range &amp;assign (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_range&amp; operator += (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_range &amp;plus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_range&amp; operator -= (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_range &amp;minus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AT&gt;<br>
matrix_range&amp; operator *= (const AT &amp;at);<br>
template&lt;class AT&gt;<br>
matrix_range&amp; operator /= (const AT &amp;at);<br>
<br>
// Swapping<br>
void swap (matrix_range &amp;mr);<br>
friend void swap (matrix_range &amp;mr1, matrix_range &amp;mr2);<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 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;matrix_range&gt;,<br>
public random_access_iterator_base&lt;const_iterator1, value_type&gt; {<br>
public:<br>
typedef typename const_iterator1_type::iterator_category iterator_category;<br>
typedef typename const_iterator1_type::difference_type difference_type;<br>
typedef typename const_iterator1_type::value_type value_type;<br>
typedef typename const_iterator1_type::reference reference;<br>
typedef typename const_iterator1_type::pointer pointer;<br>
typedef const_iterator2 dual_iterator_type;<br>
typedef const_reverse_iterator2 dual_reverse_iterator_type;<br>
<br>
// Construction and destruction<br>
const_iterator1 ();<br>
const_iterator1 (const matrix_range &amp;mr, const const_iterator1_type &amp;it);<br>
const_iterator1 (const iterator1 &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator1 &amp;operator ++ ();<br>
const_iterator1 &amp;operator -- ();<br>
const_iterator1 &amp;operator += (difference_type n);<br>
const_iterator1 &amp;operator -= (difference_type n);<br>
difference_type operator - (const const_iterator1 &amp;it) const;<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>
bool operator &lt;(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;matrix_range&gt;,<br>
public random_access_iterator_base&lt;iterator1, value_type&gt; {<br>
public:<br>
typedef typename iterator1_type::iterator_category iterator_category;<br>
typedef typename iterator1_type::difference_type difference_type;<br>
typedef typename iterator1_type::value_type value_type;<br>
typedef typename iterator1_type::reference reference;<br>
typedef typename iterator1_type::pointer pointer;<br>
typedef iterator2 dual_iterator_type;<br>
typedef reverse_iterator2 dual_reverse_iterator_type;<br>
<br>
// Construction and destruction<br>
iterator1 ();<br>
iterator1 (matrix_range &amp;mr, const iterator1_type &amp;it);<br>
<br>
// Arithmetic<br>
iterator1 &amp;operator ++ ();<br>
iterator1 &amp;operator -- ();<br>
iterator1 &amp;operator += (difference_type n);<br>
iterator1 &amp;operator -= (difference_type n);<br>
difference_type operator - (const iterator1 &amp;it) const;<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>
bool operator &lt;(const iterator1 &amp;it) const;<br>
};<br>
<br>
iterator1 begin1 ();<br>
iterator1 end1 ();<br>
<br>
class const_iterator2:<br>
public container_const_reference&lt;matrix_range&gt;,<br>
public random_access_iterator_base&lt;const_iterator2, value_type&gt; {<br>
public:<br>
typedef typename const_iterator2_type::iterator_category iterator_category;<br>
typedef typename const_iterator2_type::difference_type difference_type;<br>
typedef typename const_iterator2_type::value_type value_type;<br>
typedef typename const_iterator2_type::reference reference;<br>
typedef typename const_iterator2_type::pointer pointer;<br>
typedef const_iterator1 dual_iterator_type;<br>
typedef const_reverse_iterator1 dual_reverse_iterator_type;<br>
<br>
// Construction and destruction<br>
const_iterator2 ();<br>
const_iterator2 (const matrix_range &amp;mr, const const_iterator2_type &amp;it);<br>
const_iterator2 (const iterator2 &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator2 &amp;operator ++ ();<br>
const_iterator2 &amp;operator -- ();<br>
const_iterator2 &amp;operator += (difference_type n);<br>
const_iterator2 &amp;operator -= (difference_type n);<br>
difference_type operator - (const const_iterator2 &amp;it) const;<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>
bool operator &lt;(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;matrix_range&gt;,<br>
public random_access_iterator_base&lt;iterator2, value_type&gt; {<br>
public:<br>
typedef typename iterator2_type::iterator_category iterator_category;<br>
typedef typename iterator2_type::difference_type difference_type;<br>
typedef typename iterator2_type::value_type value_type;<br>
typedef typename iterator2_type::reference reference;<br>
typedef typename iterator2_type::pointer pointer;<br>
typedef iterator1 dual_iterator_type;<br>
typedef reverse_iterator1 dual_reverse_iterator_type;<br>
<br>
// Construction and destruction<br>
iterator2 ();<br>
iterator2 (matrix_range &amp;mr, const iterator2_type &amp;it);<br>
<br>
// Arithmetic<br>
iterator2 &amp;operator ++ ();<br>
iterator2 &amp;operator -- ();<br>
iterator2 &amp;operator += (difference_type n);<br>
iterator2 &amp;operator -= (difference_type n);<br>
difference_type operator - (const iterator2 &amp;it) const;<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>
bool operator &lt;(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>
<h3>Projections</h3>
<h4>Prototypes</h4>
<pre>
<code>template&lt;class M&gt;<br>
matrix_range&lt;M&gt; project (M &amp;data, const range &amp;r1, const range &amp;r2);<br>
template&lt;class M&gt;<br>
const matrix_range&lt;const M&gt; project (const M &amp;data, const range &amp;r1, const range &amp;r2);<br>
template&lt;class M&gt;<br>
matrix_range&lt;M&gt; project (const matrix_range&lt;M&gt; &amp;data, const range &amp;r1, const range &amp;r2);</code>
</pre>
<h4>Description</h4>
<p>The free <code>project</code> functions support the construction
of matrix ranges.</p>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Type requirements</h4>
<ul>
<li><code>M</code> is a model of <a href=
"expression.htm#matrix_expression">Matrix Expression</a> .</li>
</ul>
<h4>Preconditions</h4>
<ul type="Disc">
<li><code>r1.start () + r1.size () &lt;= data.size1 ()</code></li>
<li><code>r2.start () + r2.size () &lt;= data.size2 ()</code></li>
</ul>
<h4>Complexity</h4>
<p>Quadratic depending from the size of the ranges.</p>
<h4>Examples</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix&lt;double&gt; m (3, 3);<br>
for (unsigned i = 0; i &lt; m.size1 (); ++ i)<br>
for (unsigned j = 0; j &lt; m.size2 (); ++ j)<br>
project (m, range (0, 3), range (0, 3)) (i, j) = 3 * i + j;<br>
std::cout &lt;&lt; project (m, range (0, 3), range (0, 3)) &lt;&lt; std::endl;<br>
}<br>
</pre>
<h2><a name="matrix_slice"></a> Matrix Slice</h2>
<h4>Description</h4>
<p>The templated class <code>matrix_slice&lt;M&gt;</code> allows
addressing a sliced sub matrix of a matrix.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix&lt;double&gt; m (3, 3);<br>
matrix_slice&lt;matrix&lt;double&gt; &gt; ms (m, slice (0, 1, 3), slice (0, 1, 3));<br>
for (unsigned i = 0; i &lt; ms.size1 (); ++ i)<br>
for (unsigned j = 0; j &lt; ms.size2 (); ++ j)<br>
ms (i, j) = 3 * i + j;<br>
std::cout &lt;&lt; ms &lt;&lt; std::endl;<br>
}<br>
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code> </td>
<td>The type of matrix referenced.</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression.htm#matrix_expression">Matrix Expression</a>
.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression.htm#matrix_expression">Matrix Expression</a> .</p>
<h4>Public base classes</h4>
<p><code>matrix_expression&lt;matrix_slice&lt;M&gt; &gt;</code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix_slice (matrix_type &amp;data,<br>
&nbsp;const slice &amp;s1, const slice &amp;s2)</code></td>
<td>Constructs a sub matrix.</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>matrix_slice &amp;operator = (const matrix_slice
&amp;ms)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>matrix_slice &amp;assign_temporary (matrix_slice
&amp;ms)</code></td>
<td>Assigns a temporary. May change the matrix slice
<code>ms</code> .</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_slice &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>
matrix_slice &amp;assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a matrix expression to the sub matrix. Left and right
hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_slice &amp;operator += (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression to
the sub matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_slice &amp;plus_assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Adds a matrix expression to the sub matrix. Left and right hand
side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_slice &amp;operator -= (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix expression
from the sub matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix_slice &amp;minus_assign (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Subtracts a matrix expression from the sub matrix. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_slice &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the sub matrix with
a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix_slice &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the sub matrix
through a scalar.</td>
</tr>
<tr>
<td><code>void swap (matrix_slice &amp;ms)</code></td>
<td>Swaps the contents of the sub matrices.</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>matrix_slice</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>matrix_slice</code>.</td>
</tr>
<tr>
<td><code>iterator1 begin1 ()</code> </td>
<td>Returns a <code>iterator1</code> pointing to the beginning of
the <code>matrix_slice</code>.</td>
</tr>
<tr>
<td><code>iterator1 end1 ()</code> </td>
<td>Returns a <code>iterator1</code> pointing to the end of the
<code>matrix_slice</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>matrix_slice</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>matrix_slice</code>.</td>
</tr>
<tr>
<td><code>iterator2 begin2 ()</code> </td>
<td>Returns a <code>iterator2</code> pointing to the beginning of
the <code>matrix_slice</code>.</td>
</tr>
<tr>
<td><code>iterator2 end2 ()</code> </td>
<td>Returns a <code>iterator2</code> pointing to the end of the
<code>matrix_slice</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>matrix_slice</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>matrix_slice</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>matrix_slice</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>matrix_slice</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>matrix_slice</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>matrix_slice</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>matrix_slice</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>matrix_slice</code>.</td>
</tr>
</tbody>
</table>
<h4>Interface</h4>
<pre>
<code>// Matrix based slice class<br>
template&lt;class M&gt;<br>
class matrix_slice:<br>
public matrix_expression&lt;matrix_slice&lt;M&gt; &gt; {<br>
public: <br>
typedef const M const_matrix_type;<br>
typedef M matrix_type;<br>
typedef typename M::size_type size_type;<br>
typedef typename M::difference_type difference_type;<br>
typedef typename M::value_type value_type;<br>
typedef typename M::const_reference const_reference;<br>
typedef typename M::reference reference;<br>
typedef typename M::const_pointer const_pointer;<br>
typedef typename M::pointer pointer;<br>
typedef const matrix_const_reference&lt;const matrix_slice&lt;matrix_type&gt; &gt; const_closure_type;<br>
typedef matrix_reference&lt;matrix_slice&lt;matrix_type&gt; &gt; closure_type;<br>
typedef slice::const_iterator const_iterator1_type;<br>
typedef slice::const_iterator iterator1_type;<br>
typedef slice::const_iterator const_iterator2_type;<br>
typedef slice::const_iterator iterator2_type;<br>
typedef typename storage_restrict_traits&lt;typename M::storage_category,<br>
dense_proxy_tag&gt;::storage_category storage_category;<br>
typedef typename M::orientation_category orientation_category;<br>
<br>
// Construction and destruction<br>
matrix_slice ();<br>
matrix_slice (matrix_type &amp;data, const slice &amp;s1, const slice &amp;s2);<br>
<br>
// Accessors<br>
size_type size1 () const;<br>
size_type size2 () const;<br>
const_matrix_type &amp;data () const;<br>
matrix_type &amp;data ();<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>
matrix_slice&lt;matrix_type&gt; project (const range &amp;r1, const range &amp;r2) const;<br>
matrix_slice&lt;matrix_type&gt; project (const slice &amp;s1, const slice &amp;s2) const;<br>
<br>
// Assignment<br>
matrix_slice &amp;operator = (const matrix_slice &amp;ms);<br>
matrix_slice &amp;assign_temporary (matrix_slice &amp;ms);<br>
template&lt;class AE&gt;<br>
matrix_slice &amp;operator = (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_slice &amp;assign (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_slice&amp; operator += (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_slice &amp;plus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_slice&amp; operator -= (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix_slice &amp;minus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AT&gt;<br>
matrix_slice&amp; operator *= (const AT &amp;at);<br>
template&lt;class AT&gt;<br>
matrix_slice&amp; operator /= (const AT &amp;at);<br>
<br>
// Swapping<br>
void swap (matrix_slice &amp;ms);<br>
friend void swap (matrix_slice &amp;ms1, matrix_slice &amp;ms2);<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 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 indices.<br>
<br>
class const_iterator1:<br>
public container_const_reference&lt;matrix_slice&gt;,<br>
public random_access_iterator_base&lt;const_iterator1, value_type&gt; {<br>
public:<br>
typedef typename M::const_iterator1::iterator_category iterator_category;<br>
typedef typename M::const_iterator1::difference_type difference_type;<br>
typedef typename M::const_iterator1::value_type value_type;<br>
typedef typename M::const_iterator1::reference reference;<br>
typedef typename M::const_iterator1::pointer pointer;<br>
typedef const_iterator2 dual_iterator_type;<br>
typedef const_reverse_iterator2 dual_reverse_iterator_type;<br>
<br>
// Construction and destruction<br>
const_iterator1 ();<br>
const_iterator1 (const matrix_slice &amp;ms, const const_iterator1_type &amp;it1, const const_iterator2_type &amp;it2);<br>
const_iterator1 (const iterator1 &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator1 &amp;operator ++ ();<br>
const_iterator1 &amp;operator -- ();<br>
const_iterator1 &amp;operator += (difference_type n);<br>
const_iterator1 &amp;operator -= (difference_type n);<br>
difference_type operator - (const const_iterator1 &amp;it) const;<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>
bool operator &lt;(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;matrix_slice&gt;,<br>
public random_access_iterator_base&lt;iterator1, value_type&gt; {<br>
public:<br>
typedef typename M::iterator1::iterator_category iterator_category;<br>
typedef typename M::iterator1::difference_type difference_type;<br>
typedef typename M::iterator1::value_type value_type;<br>
typedef typename M::iterator1::reference reference;<br>
typedef typename M::iterator1::pointer pointer;<br>
typedef iterator2 dual_iterator_type;<br>
typedef reverse_iterator2 dual_reverse_iterator_type;<br>
<br>
// Construction and destruction<br>
iterator1 ();<br>
iterator1 (matrix_slice &amp;ms, const iterator1_type &amp;it1, const iterator2_type &amp;it2);<br>
<br>
// Arithmetic<br>
iterator1 &amp;operator ++ ();<br>
iterator1 &amp;operator -- ();<br>
iterator1 &amp;operator += (difference_type n);<br>
iterator1 &amp;operator -= (difference_type n);<br>
difference_type operator - (const iterator1 &amp;it) const;<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>
bool operator &lt;(const iterator1 &amp;it) const;<br>
};<br>
<br>
iterator1 begin1 ();<br>
iterator1 end1 ();<br>
<br>
class const_iterator2:<br>
public container_const_reference&lt;matrix_slice&gt;,<br>
public random_access_iterator_base&lt;const_iterator2, value_type&gt; {<br>
public:<br>
typedef typename M::const_iterator2::iterator_category iterator_category;<br>
typedef typename M::const_iterator2::difference_type difference_type;<br>
typedef typename M::const_iterator2::value_type value_type;<br>
typedef typename M::const_iterator2::reference reference;<br>
typedef typename M::const_iterator2::pointer pointer;<br>
typedef const_iterator1 dual_iterator_type;<br>
typedef const_reverse_iterator1 dual_reverse_iterator_type;<br>
<br>
// Construction and destruction<br>
const_iterator2 ();<br>
const_iterator2 (const matrix_slice &amp;ms, const const_iterator1_type &amp;it1, const const_iterator2_type &amp;it2);<br>
const_iterator2 (const iterator2 &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator2 &amp;operator ++ ();<br>
const_iterator2 &amp;operator -- ();<br>
const_iterator2 &amp;operator += (difference_type n);<br>
const_iterator2 &amp;operator -= (difference_type n);<br>
difference_type operator - (const const_iterator2 &amp;it) const;<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>
bool operator &lt;(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;matrix_slice&gt;,<br>
public random_access_iterator_base&lt;iterator2, value_type&gt; {<br>
public:<br>
typedef typename M::iterator2::iterator_category iterator_category;<br>
typedef typename M::iterator2::difference_type difference_type;<br>
typedef typename M::iterator2::value_type value_type;<br>
typedef typename M::iterator2::reference reference;<br>
typedef typename M::iterator2::pointer pointer;<br>
typedef iterator1 dual_iterator_type;<br>
typedef reverse_iterator1 dual_reverse_iterator_type;<br>
<br>
// Construction and destruction<br>
iterator2 ();<br>
iterator2 (matrix_slice &amp;ms, const iterator1_type &amp;it1, const iterator2_type &amp;it2);<br>
<br>
// Arithmetic<br>
iterator2 &amp;operator ++ ();<br>
iterator2 &amp;operator -- ();<br>
iterator2 &amp;operator += (difference_type n);<br>
iterator2 &amp;operator -= (difference_type n);<br>
difference_type operator - (const iterator2 &amp;it) const;<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>
bool operator &lt;(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>
<h3>Projections</h3>
<h4>Prototypes</h4>
<pre>
<code>template&lt;class M&gt;<br>
matrix_slice&lt;M&gt; project (const matrix_slice&lt;M&gt; &amp;data, const range &amp;r1, const range &amp;r2);<br>
template&lt;class M&gt;<br>
matrix_slice&lt;M&gt; project (M &amp;data, const slice &amp;s1, const slice &amp;s2);<br>
template&lt;class M&gt;<br>
const matrix_slice&lt;const M&gt; project (const M &amp;data, const slice &amp;s1, const slice &amp;s2);<br>
template&lt;class M&gt;<br>
matrix_slice&lt;M&gt; project (const matrix_slice&lt;M&gt; &amp;data, const slice &amp;s1, const slice &amp;s2);</code>
</pre>
<h4>Description</h4>
<p>The free <code>project</code> functions support the construction
of matrix slices.</p>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Type requirements</h4>
<ul>
<li><code>M</code> is a model of <a href=
"expression.htm#matrix_expression">Matrix Expression</a> .</li>
</ul>
<h4>Preconditions</h4>
<ul type="Disc">
<li><code>s1.start () + s1.stride () * s1.size () &lt;= data.size1
()</code></li>
<li><code>s2.start () + s2.stride () * s2.size () &lt;= data.size2
()</code></li>
</ul>
<h4>Complexity</h4>
<p>Quadratic depending from the size of the slices.</p>
<h4>Examples</h4>
<pre>
#include &lt;boost/numeric/ublas/matrix.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix&lt;double&gt; m (3, 3);<br>
for (unsigned i = 0; i &lt; m.size1 (); ++ i)<br>
for (unsigned j = 0; j &lt; m.size2 (); ++ j)<br>
project (m, slice (0, 1, 3), slice (0, 1, 3)) (i, j) = 3 * i + j;<br>
std::cout &lt;&lt; project (m, slice (0, 1, 3), slice (0, 1, 3)) &lt;&lt; std::endl;<br>
}<br>
</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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