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<h1><img src="c++boost.gif" alt="c++boost.gif" align="Center">
Matrix</h1>
<h2><a name="matrix"></a> Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>matrix<T, F, A></code> is the
base container adaptor for dense matrices. For a <em>(m x
n</em>)-dimensional matrix and <em>0 <= i < m</em>, <em>0
<= j < n</em> every element <em>m</em><sub><em>i,
j</em></sub> is mapped to the <em>(i x n + j)-</em>th element of
the container for row major orientation or the <em>(i + j x
m)-</em>th element of the container for column major
orientation.</p>
<h4>Example</h4>
<pre>
#include <boost/numeric/ublas/matrix.hpp><br>
#include <boost/numeric/ublas/io.hpp><br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
matrix<double> m (3, 3);<br>
for (unsigned i = 0; i < m.size1 (); ++ i)<br>
for (unsigned j = 0; j < m.size2 (); ++ j)<br>
m (i, j) = 3 * i + j;<br>
std::cout << m << std::endl;<br>
}<br>
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>T</code> </td>
<td>The type of object stored in the matrix.</td>
<td> </td>
</tr>
<tr>
<td><code>F</code></td>
<td>Functor describing the storage organization. <a href=
"#matrix_1">[1]</a> </td>
<td><code>row_major</code></td>
</tr>
<tr>
<td><code>A</code></td>
<td>The type of the adapted array. <a href="#matrix_2">[2]</a>
</td>
<td><code>unbounded_array<T></code></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="container.htm#matrix">Matrix</a> .</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"container.htm#matrix">Matrix</a> .</p>
<h4>Public base classes</h4>
<p><code>matrix_expression<matrix<T, F, A> ></code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>matrix ()</code> </td>
<td>Allocates an uninitialized <code>matrix</code> that holds zero
rows of zero elements.</td>
</tr>
<tr>
<td><code>matrix (size_type size1, size_type size2)</code></td>
<td>Allocates an uninitialized <code>matrix</code> that holds
<code>size1</code> rows of <code>size2</code> elements.</td>
</tr>
<tr>
<td><code>matrix (const matrix &m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template<class AE><br>
matrix (const matrix_expression<AE> &ae)</code></td>
<td>The extended copy constructor.</td>
</tr>
<tr>
<td><code>void resize (size_type size1, size_type
size2)</code></td>
<td>Reallocates a <code>matrix</code> to hold <code>size1</code>
rows of <code>size2</code> elements. The content of the
<code>matrix</code> is not preserved.</td>
</tr>
<tr>
<td><code>size_type size1 () const</code></td>
<td>Returns the number of rows.</td>
</tr>
<tr>
<td><code>size_type size2 () const</code></td>
<td>Returns the number of columns.</td>
</tr>
<tr>
<td><code>const_reference operator () (size_type i, size_type j)
const</code></td>
<td>Returns a <code>const</code> reference 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 &operator = (const matrix &m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>matrix &assign_temporary (matrix &m)</code></td>
<td>Assigns a temporary. May change the matrix <code>m</code>.</td>
</tr>
<tr>
<td><code>template<class AE><br>
matrix &operator = (const matrix_expression<AE>
&ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template<class AE><br>
matrix &assign (const matrix_expression<AE>
&ae)</code></td>
<td>Assigns a matrix expression to the matrix. Left and right hand
side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template<class AE><br>
matrix &operator += (const matrix_expression<AE>
&ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression to
the matrix.</td>
</tr>
<tr>
<td><code>template<class AE><br>
matrix &plus_assign (const matrix_expression<AE>
&ae)</code></td>
<td>Adds a matrix expression to the matrix. Left and right hand
side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template<class AE><br>
matrix &operator -= (const matrix_expression<AE>
&ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix expression
from the matrix.</td>
</tr>
<tr>
<td><code>template<class AE><br>
matrix &minus_assign (const matrix_expression<AE>
&ae)</code></td>
<td>Subtracts a matrix expression from the matrix. Left and right
hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template<class AT><br>
matrix &operator *= (const AT &at)</code></td>
<td>A computed assignment operator. Multiplies the matrix with a
scalar.</td>
</tr>
<tr>
<td><code>template<class AT><br>
matrix &operator /= (const AT &at)</code></td>
<td>A computed assignment operator. Divides the matrix through a
scalar.</td>
</tr>
<tr>
<td><code>void swap (matrix &m)</code></td>
<td>Swaps the contents of the matrices.</td>
</tr>
<tr>
<td><code>void insert (size_type i, size_type j, const_reference
t)</code></td>
<td>Inserts the value <code>t</code> at the <code>j</code>-th
element of the <code>i</code>-th row.</td>
</tr>
<tr>
<td><code>void erase (size_type i, size_type j)</code></td>
<td>Erases the value at the <code>j</code>-th element of the
<code>i</code>-th row.</td>
</tr>
<tr>
<td><code>void clear ()</code></td>
<td>Clears the matrix.</td>
</tr>
<tr>
<td><code>const_iterator1 begin1 () const</code></td>
<td>Returns a <code>const_iterator1</code> pointing to the
beginning of the <code>matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator1 end1 () const</code></td>
<td>Returns a <code>const_iterator1</code> pointing to the end of
the <code>matrix</code>.</td>
</tr>
<tr>
<td><code>iterator1 begin1 ()</code> </td>
<td>Returns a <code>iterator1</code> pointing to the beginning of
the <code>matrix</code>.</td>
</tr>
<tr>
<td><code>iterator1 end1 ()</code> </td>
<td>Returns a <code>iterator1</code> pointing to the end of the
<code>matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 begin2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the
beginning of the <code>matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 end2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the end of
the <code>matrix</code>.</td>
</tr>
<tr>
<td><code>iterator2 begin2 ()</code> </td>
<td>Returns a <code>iterator2</code> pointing to the beginning of
the <code>matrix</code>.</td>
</tr>
<tr>
<td><code>iterator2 end2 ()</code> </td>
<td>Returns a <code>iterator2</code> pointing to the end of the
<code>matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
beginning of the reversed <code>matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rend1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
end of the reversed <code>matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator1 rbegin1 ()</code> </td>
<td>Returns a <code>reverse_iterator1</code> pointing to the
beginning of the reversed <code>matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator1 rend1 ()</code> </td>
<td>Returns a <code>reverse_iterator1</code> pointing to the end of
the reversed <code>matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
beginning of the reversed <code>matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rend2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
end of the reversed <code>matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator2 rbegin2 ()</code> </td>
<td>Returns a <code>reverse_iterator2</code> pointing to the
beginning of the reversed <code>matrix</code>.</td>
</tr>
<tr>
<td><code>reverse_iterator2 rend2 ()</code> </td>
<td>Returns a <code>reverse_iterator2</code> pointing to the end of
the reversed <code>matrix</code>.</td>
</tr>
</tbody>
</table>
<h4>Notes</h4>
<p><a name="#matrix_1">[1]</a> Supported parameters for the storage
organization are <code>row_major</code> and
<code>column_major</code>.</p>
<p><a name="#matrix_2">[2]</a> Supported parameters for the adapted
array are <code>unbounded_array<T></code> ,
<code>bounded_array<T></code> and
<code>std::vector<T></code> .</p>
<h2><a name="identity_matrix"></a> Identity Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>identity_matrix<T></code>
represents identity matrices. For a <em>(m x n</em>)-dimensional
identity matrix and <em>0 <= i < m</em>, <em>0 <= j <
n</em> holds <em>id</em><sub><em>i, j</em></sub> <em>= 0</em>, if
<em>i <> j</em>, and <em>id</em><sub><em>i, i</em></sub><em>=
1</em>.</p>
<h4>Example</h4>
<pre>
#include <boost/numeric/ublas/matrix.hpp><br>
#include <boost/numeric/ublas/io.hpp><br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
identity_matrix<double> m (3);<br>
std::cout << m << std::endl;<br>
}<br>
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>T</code> </td>
<td>The type of object stored in the matrix.</td>
<td> </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<identity_matrix<T>
></code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>identity_matrix ()</code> </td>
<td>Constructs an <code>identity_matrix</code> that holds zero rows
of zero elements.</td>
</tr>
<tr>
<td><code>identity_matrix (size_type size)</code></td>
<td>Constructs an <code>identity_matrix</code> that holds
<code>size</code> rows of <code>size</code> elements.</td>
</tr>
<tr>
<td><code>identity_matrix (const identity_matrix
&m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>void resize (size_type size)</code></td>
<td>Resizes a <code>identity_matrix</code> to hold
<code>size</code> rows of <code>size</code> elements.</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>identity_matrix &operator = (const identity_matrix
&m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>identity_matrix &assign_temporary (identity_matrix
&m)</code></td>
<td>Assigns a temporary. May change the identity matrix
<code>m</code> .</td>
</tr>
<tr>
<td><code>void swap (identity_matrix &m)</code></td>
<td>Swaps the contents of the identity 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>identity_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator1 end1 () const</code></td>
<td>Returns a <code>const_iterator1</code> pointing to the end of
the <code>identity_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 begin2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the
beginning of the <code>identity_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 end2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the end of
the <code>identity_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
beginning of the reversed <code>identity_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rend1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
end of the reversed <code>identity_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
beginning of the reversed <code>identity_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rend2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
end of the reversed <code>identity_matrix</code>.</td>
</tr>
</tbody>
</table>
<h2><a name="zero_matrix"></a> Zero Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>zero_matrix<T></code> represents
zero matrices. For a <em>(m x n</em>)-dimensional zero matrix and
<em>0 <= i < m</em>, <em>0 <= j < n</em> holds
<em>z</em><sub><em>i, j</em></sub> <em>= 0</em>.</p>
<h4>Example</h4>
<pre>
#include <boost/numeric/ublas/matrix.hpp><br>
#include <boost/numeric/ublas/io.hpp><br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
zero_matrix<double> m (3, 3);<br>
std::cout << m << std::endl;<br>
}<br>
</pre>
<h4>Definition</h4>
<p>Defined in the header matrix.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>T</code> </td>
<td>The type of object stored in the matrix.</td>
<td> </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<zero_matrix<T> ></code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>zero_matrix ()</code> </td>
<td>Constructs a <code>zero_matrix</code> that holds zero rows of
zero elements.</td>
</tr>
<tr>
<td><code>zero_matrix (size_type size1, size_type
size2)</code></td>
<td>Constructs a <code>zero_matrix</code> that holds
<code>size1</code> rows of <code>size2</code> elements.</td>
</tr>
<tr>
<td><code>zero_matrix (const zero_matrix &m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>void resize (size_type size1, size_type
size2)</code></td>
<td>Resizes a <code>zero_matrix</code> to hold <code>size1</code>
rows of <code>size2</code> elements.</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>zero_matrix &operator = (const zero_matrix
&m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>zero_matrix &assign_temporary (zero_matrix
&m)</code></td>
<td>Assigns a temporary. May change the zero matrix <code>m</code>
.</td>
</tr>
<tr>
<td><code>void swap (zero_matrix &m)</code></td>
<td>Swaps the contents of the zero 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>zero_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator1 end1 () const</code></td>
<td>Returns a <code>const_iterator1</code> pointing to the end of
the <code>zero_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 begin2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the
beginning of the <code>zero_matrix</code>.</td>
</tr>
<tr>
<td><code>const_iterator2 end2 () const</code></td>
<td>Returns a <code>const_iterator2</code> pointing to the end of
the <code>zero_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rbegin1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
beginning of the reversed <code>zero_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator1 rend1 () const</code></td>
<td>Returns a <code>const_reverse_iterator1</code> pointing to the
end of the reversed <code>zero_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rbegin2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
beginning of the reversed <code>zero_matrix</code>.</td>
</tr>
<tr>
<td><code>const_reverse_iterator2 rend2 () const</code></td>
<td>Returns a <code>const_reverse_iterator2</code> pointing to the
end of the reversed <code>zero_matrix</code>.</td>
</tr>
</tbody>
</table>
<hr>
<p>Copyright (©) 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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