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<h1><img src="../../../../boost.png" align="middle" />Matrix Proxies</h1>
<div class="toc" id="toc"></div>
<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;
#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;double&gt; m (3, 3);
    for (unsigned i = 0; i &lt; m.size1 (); ++ i) {
        matrix_row&lt;matrix&lt;double&gt; &gt; mr (m, i);
        for (unsigned j = 0; j &lt; mr.size (); ++ j)
            mr (j) = 3 * i + j;
        std::cout &lt;&lt; mr &lt;&lt; std::endl;
    }
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code></td>
<td>The type of matrix referenced.</td>
<td></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
.</p>
<p>If the specified row falls outside that of the row index range
of the matrix, then the <code>matrix_row</code> is not a well
formed Vector Expression. That is, access to an element which is
outside of the matrix is <i>undefined</i>.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression_concept.html#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" summary="members">
<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>
<h3>Projections</h3>
<h4>Description</h4>
<p>The free <code>row</code> functions support the construction of
matrix rows.</p>
<h4>Prototypes</h4>
<pre><code>
    template&lt;class M&gt;
    matrix_row&lt;M&gt; row (M &amp;data, std::size_t i);
    template&lt;class M&gt;
    const matrix_row&lt;const M&gt; row (const M &amp;data, std::size_t i);
</code></pre>
<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_concept.html#matrix_expression">Matrix Expression</a> .</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;
#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;double&gt; m (3, 3);
    for (unsigned i = 0; i &lt; m.size1 (); ++ i) {
        for (unsigned j = 0; j &lt; m.size2 (); ++ j)
            row (m, i) (j) = 3 * i + j;
        std::cout &lt;&lt; row (m, i) &lt;&lt; std::endl;
    }
}
</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;
#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;double&gt; m (3, 3);
    for (unsigned j = 0; j &lt; m.size2 (); ++ j) {
        matrix_column&lt;matrix&lt;double&gt; &gt; mc (m, j);
        for (unsigned i = 0; i &lt; mc.size (); ++ i)
            mc (i) = 3 * i + j;
        std::cout &lt;&lt; mc &lt;&lt; std::endl;
    }
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code></td>
<td>The type of matrix referenced.</td>
<td></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
.</p>
<p>If the specified column falls outside that of the column index
range of the matrix, then the <code>matrix_column</code> is not a
well formed Vector Expression. That is, access to an element which
is outside of the matrix is <i>undefined</i>.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression_concept.html#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" summary="members">
<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>
<h3>Projections</h3>
<h4>Description</h4>
<p>The free <code>column</code> functions support the construction
of matrix columns.</p>
<h4>Prototypes</h4>
<pre><code>
    template&lt;class M&gt;
    matrix_column&lt;M&gt; column (M &amp;data, std::size_t j);
    template&lt;class M&gt;
    const matrix_column&lt;const M&gt; column (const M &amp;data, std::size_t j);
</code></pre>
<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_concept.html#matrix_expression">Matrix Expression</a> .</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;
#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;double&gt; m (3, 3);
    for (unsigned j = 0; j &lt; m.size2 (); ++ j) {
        for (unsigned i = 0; i &lt; m.size1 (); ++ i)
            column (m, j) (i) = 3 * i + j;
        std::cout &lt;&lt; column (m, j) &lt;&lt; std::endl;
    }
}
</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;
#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;double&gt; m (3, 3);
    for (unsigned i = 0; i &lt; m.size1 (); ++ i)
        for (unsigned j = 0; j &lt; m.size2 (); ++ j)
            m (i, j) = 3 * i + j;

    matrix_vector_range&lt;matrix&lt;double&gt; &gt; mvr (m, range (0, 3), range (0, 3));
    std::cout &lt;&lt; mvr &lt;&lt; std::endl;
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code></td>
<td>The type of matrix referenced.</td>
<td></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
.</p>
<p>If the specified ranges fall outside that of the index range of
the matrix, then the <code>matrix_vector_range</code> is not a well
formed Vector Expression. That is, access to an element which is
outside of the matrix is <i>undefined</i>.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression_concept.html#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" summary="members">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix_vector_range (matrix_type &amp;data,<br />
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>
<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;
#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;double&gt; m (3, 3);
    for (unsigned i = 0; i &lt; m.size1 (); ++ i)
        for (unsigned j = 0; j &lt; m.size2 (); ++ j)
            m (i, j) = 3 * i + j;

    matrix_vector_slice&lt;matrix&lt;double&gt; &gt; mvs (m, slice (0, 1, 3), slice (0, 1, 3));
    std::cout &lt;&lt; mvs &lt;&lt; std::endl;
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code></td>
<td>The type of matrix referenced.</td>
<td></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression_concept.html#vector_expression">Vector Expression</a>
.</p>
<p>If the specified slices fall outside that of the index range of
the matrix, then the <code>matrix_vector_slice</code> is not a well
formed Vector Expression. That is, access to an element which is
outside of the matrix is <i>undefined</i>.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression_concept.html#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" summary="members">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix_vector_slice (matrix_type &amp;data,<br />
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>
<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;
#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;double&gt; m (3, 3);
    matrix_range&lt;matrix&lt;double&gt; &gt; mr (m, range (0, 3), range (0, 3));
    for (unsigned i = 0; i &lt; mr.size1 (); ++ i)
        for (unsigned j = 0; j &lt; mr.size2 (); ++ j)
            mr (i, j) = 3 * i + j;
    std::cout &lt;&lt; mr &lt;&lt; std::endl;
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code></td>
<td>The type of matrix referenced.</td>
<td></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
.</p>
<p>If the specified ranges fall outside that of the index range of
the matrix, then the <code>matrix_range</code> is not a well formed
Matrix Expression. That is, access to an element which is outside
of the matrix is <i>undefined</i>.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression_concept.html#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" summary="members">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix_range (matrix_type &amp;data,<br />
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>
<h3>Simple Projections</h3>
<h4>Description</h4>
<p>The free <code>subrange</code> functions support the construction
of matrix ranges.</p>
<h4>Prototypes</h4>
<pre><code>
    template&lt;class M&gt;
    matrix_range&lt;M&gt; subrange (M &amp;data,
       M::size_type start1, M::size_type stop1, M::size_type start2, M::size_type, stop2);
    template&lt;class M&gt;
    const matrix_range&lt;const M&gt; subrange (const M &amp;data,
       M::size_type start1, M::size_type stop1, M::size_type start2, M::size_type, stop2);
</code></pre>
<h3>Generic Projections</h3>
<h4>Description</h4>
<p>The free <code>project</code> functions support the construction
of matrix ranges. Existing <code>matrix_range</code>'s can be composed with further ranges. The resulting ranges are computed using this existing ranges' <code>compose</code> function.</p>
<h4>Prototypes</h4>
<pre><code>
    template&lt;class M&gt;
    matrix_range&lt;M&gt; project (M &amp;data, const range &amp;r1, const range &amp;r2);
    template&lt;class M&gt;
    const matrix_range&lt;const M&gt; project (const M &amp;data, const range &amp;r1, const range &amp;r2);
    template&lt;class M&gt;
    matrix_range&lt;M&gt; project (matrix_range&lt;M&gt; &amp;data, const range &amp;r1, const range &amp;r2);
    template&lt;class M&gt;
    const 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>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_concept.html#matrix_expression">Matrix Expression</a> .</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;
#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;double&gt; m (3, 3);
    for (unsigned i = 0; i &lt; m.size1 (); ++ i)
        for (unsigned j = 0; j &lt; m.size2 (); ++ j)
            project (m, range (0, 3), range (0, 3)) (i, j) = 3 * i + j;
    std::cout &lt;&lt; project (m, range (0, 3), range (0, 3)) &lt;&lt; std::endl;
}
</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;
#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;double&gt; m (3, 3);
    matrix_slice&lt;matrix&lt;double&gt; &gt; ms (m, slice (0, 1, 3), slice (0, 1, 3));
    for (unsigned i = 0; i &lt; ms.size1 (); ++ i)
        for (unsigned j = 0; j &lt; ms.size2 (); ++ j)
            ms (i, j) = 3 * i + j;
    std::cout &lt;&lt; ms &lt;&lt; std::endl;
}
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix_proxy.hpp.</p>
<h4>Template parameters</h4>
<table border="1" summary="parameters">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>M</code></td>
<td>The type of matrix referenced.</td>
<td></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="expression_concept.html#matrix_expression">Matrix Expression</a>
.</p>
<p>If the specified slices fall outside that of the index range of
the matrix, then the <code>matrix_slice</code> is not a well formed
Matrix Expression. That is, access to an element which is outside
of the matrix is <i>undefined</i>.</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"expression_concept.html#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" summary="members">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix_slice (matrix_type &amp;data,<br />
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>
<h3>Simple Projections</h3>
<h4>Description</h4>
<p>The free <code>subslice</code> functions support the construction
of matrix slices.</p>
<h4>Prototypes</h4>
<pre><code>
    template&lt;class M&gt;
    matrix_slice&lt;M&gt; subslice (M &amp;data,
       M::size_type start1, M::difference_type stride1, M::size_type size1,
       M::size_type start2, M::difference_type stride2, M::size_type size2);
    template&lt;class M&gt;
    const matrix_slice&lt;const M&gt; subslice (const M &amp;data,
       M::size_type start1, M::difference_type stride1, M::size_type size1,
       M::size_type start2, M::difference_type stride2, M::size_type size2);
</code></pre>
<h3>Generic Projections</h3>
<h4>Description</h4>
<p>The free <code>project</code> functions support the construction
of matrix slices. Existing <code>matrix_slice</code>'s can be composed with further ranges or slices. The resulting slices are computed using this existing slices' <code>compose</code> function.</p>
<h4>Prototypes</h4>
<pre><code>
    template&lt;class M&gt;
    matrix_slice&lt;M&gt; project (M &amp;data, const slice &amp;s1, const slice &amp;s2);
    template&lt;class M&gt;
    const matrix_slice&lt;const M&gt; project (const M &amp;data, const slice &amp;s1, const slice &amp;s2);
    template&lt;class M&gt;
    matrix_slice&lt;M&gt; project (matrix_slice&lt;M&gt; &amp;data, const range &amp;r1, const range &amp;r2);
    template&lt;class M&gt;
    const matrix_slice&lt;M&gt; project (const matrix_slice&lt;M&gt; &amp;data, const range &amp;r1, const range &amp;r2);
    template&lt;class M&gt;
    matrix_slice&lt;M&gt; project (matrix_slice&lt;M&gt; &amp;data, const slice &amp;s1, const slice &amp;s2);
    template&lt;class M&gt;
    const 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>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_concept.html#matrix_expression">Matrix Expression</a> .</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;
#include &lt;boost/numeric/ublas/matrix_proxy.hpp&gt;
#include &lt;boost/numeric/ublas/io.hpp&gt;

int main () {
    using namespace boost::numeric::ublas;
    matrix&lt;double&gt; m (3, 3);
    for (unsigned i = 0; i &lt; m.size1 (); ++ i)
        for (unsigned j = 0; j &lt; m.size2 (); ++ j)
            project (m, slice (0, 1, 3), slice (0, 1, 3)) (i, j) = 3 * i + j;
    std::cout &lt;&lt; project (m, slice (0, 1, 3), slice (0, 1, 3)) &lt;&lt; std::endl;
}
</pre>
<hr />
<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br />
   Use, modification and distribution are subject to the
   Boost Software License, Version 1.0.
   (See accompanying file LICENSE_1_0.txt
   or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
      http://www.boost.org/LICENSE_1_0.txt
   </a>).
</p>
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