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ublas/doc/matrix.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</h1>
<h2><a name="matrix"></a> Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>matrix&lt;T, F, A&gt;</code> is the
base container adaptor for dense matrices. For a <em>(m x
n</em>)-dimensional matrix and <em>0 &lt;= i &lt; m</em>, <em>0
&lt;= j &lt; 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 &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>
std::cout &lt;&lt; m &lt;&lt; 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>&nbsp;</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&lt;T&gt;</code></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="container.htm#matrix">Matrix</a> .</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"container.htm#matrix">Matrix</a> .</p>
<h4>Public base classes</h4>
<p><code>matrix_expression&lt;matrix&lt;T, F, A&gt; &gt;</code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>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 &amp;m)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix (const matrix_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended copy constructor.</td>
</tr>
<tr>
<td><code>void resize (size_type size1, size_type
size2)</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 &amp;operator = (const matrix &amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>matrix &amp;assign_temporary (matrix &amp;m)</code></td>
<td>Assigns a temporary. May change the matrix <code>m</code>.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix &amp;operator = (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>The extended assignment operator.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix &amp;assign (const matrix_expression&lt;AE&gt;
&amp;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&lt;class AE&gt;<br>
matrix &amp;operator += (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Adds the matrix expression to
the matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix &amp;plus_assign (const matrix_expression&lt;AE&gt;
&amp;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&lt;class AE&gt;<br>
matrix &amp;operator -= (const matrix_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the matrix expression
from the matrix.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
matrix &amp;minus_assign (const matrix_expression&lt;AE&gt;
&amp;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&lt;class AT&gt;<br>
matrix &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the matrix with a
scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
matrix &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the matrix through a
scalar.</td>
</tr>
<tr>
<td><code>void swap (matrix &amp;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&lt;T&gt;</code> ,
<code>bounded_array&lt;T&gt;</code> and
<code>std::vector&lt;T&gt;</code> .</p>
<h4>Interface</h4>
<pre>
<code>// Array based matrix class<br>
template&lt;class T, class F, class A&gt;<br>
class matrix:<br>
public matrix_expression&lt;matrix&lt;T, F, A&gt; &gt; {<br>
public:<br>
typedef std::size_t size_type;<br>
typedef std::ptrdiff_t difference_type;<br>
typedef T value_type;<br>
typedef const T &amp;const_reference;<br>
typedef T &amp;reference;<br>
typedef const T *const_pointer;<br>
typedef T *pointer;<br>
typedef F functor_type;<br>
typedef A array_type;<br>
typedef const A const_array_type;<br>
typedef const matrix&lt;T, F, A&gt; const_self_type;<br>
typedef matrix&lt;T, F, A&gt; self_type;<br>
typedef const matrix_const_reference&lt;const_self_type&gt; const_closure_type;<br>
typedef matrix_reference&lt;self_type&gt; closure_type;<br>
typedef typename A::const_iterator const_iterator_type;<br>
typedef typename A::iterator iterator_type;<br>
typedef dense_tag storage_category;<br>
typedef typename F::orientation_category orientation_category;<br>
<br>
// Construction and destruction<br>
matrix ();<br>
matrix (size_type size1, size_type size2);<br>
matrix (const matrix &amp;m);<br>
template&lt;class AE&gt;<br>
matrix (const matrix_expression&lt;AE&gt; &amp;ae);<br>
<br>
// Accessors<br>
size_type size1 () const;<br>
size_type size2 () const;<br>
const_array_type &amp;data () const;<br>
array_type &amp;data ();<br>
<br>
// Resizing<br>
void resize (size_type size1, size_type size2);<br>
<br>
// Element access<br>
const_reference operator () (size_type i, size_type j) const;<br>
reference operator () (size_type i, size_type j);<br>
<br>
// Assignment<br>
matrix &amp;operator = (const matrix &amp;m);<br>
matrix &amp;assign_temporary (matrix &amp;m);<br>
template&lt;class AE&gt;<br>
matrix &amp;operator = (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix &amp;reset (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix &amp;assign (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix&amp; operator += (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix &amp;plus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix&amp; operator -= (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
matrix &amp;minus_assign (const matrix_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AT&gt;<br>
matrix&amp; operator *= (const AT &amp;at);<br>
template&lt;class AT&gt;<br>
matrix&amp; operator /= (const AT &amp;at);<br>
<br>
// Swapping<br>
void swap (matrix &amp;m);<br>
friend void swap (matrix &amp;m1, matrix &amp;m2);<br>
<br>
// Element insertion and erasure<br>
void insert (size_type i, size_type j, const_reference t);<br>
void erase (size_type i, size_type j);<br>
void clear ();<br>
<br>
class const_iterator1;<br>
class iterator1;<br>
class const_iterator2;<br>
class iterator2;<br>
typedef reverse_iterator_base1&lt;const_iterator1&gt; const_reverse_iterator1;<br>
typedef reverse_iterator_base1&lt;iterator1&gt; reverse_iterator1;<br>
typedef reverse_iterator_base2&lt;const_iterator2&gt; const_reverse_iterator2;<br>
typedef reverse_iterator_base2&lt;iterator2&gt; reverse_iterator2;<br>
<br>
// Element lookup<br>
const_iterator1 find1 (int rank, size_type i, size_type j) const;<br>
iterator1 find1 (int rank, size_type i, size_type j);<br>
const_iterator2 find2 (int rank, size_type i, size_type j) const;<br>
iterator2 find2 (int rank, size_type i, size_type j);<br>
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;<br>
iterator1 find_first1 (int rank, size_type i, size_type j);<br>
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;<br>
iterator1 find_last1 (int rank, size_type i, size_type j);<br>
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;<br>
iterator2 find_first2 (int rank, size_type i, size_type j);<br>
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;<br>
iterator2 find_last2 (int rank, size_type i, size_type j);<br>
<br>
// Iterators simply are pointers.<br>
<br>
class const_iterator1:<br>
public container_const_reference&lt;matrix&gt;,<br>
public random_access_iterator_base&lt;const_iterator1, value_type&gt; {<br>
public:<br>
typedef dense_random_access_iterator_tag iterator_category;<br>
typedef typename matrix::difference_type difference_type;<br>
typedef typename matrix::value_type value_type;<br>
typedef typename matrix::const_reference reference;<br>
typedef typename matrix::const_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 &amp;m, const const_iterator_type &amp;it);<br>
const_iterator1 (const iterator1 &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator1 &amp;operator ++ ();<br>
const_iterator1 &amp;operator -- ();<br>
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&gt;,<br>
public random_access_iterator_base&lt;iterator1, value_type&gt; {<br>
public:<br>
typedef dense_random_access_iterator_tag iterator_category;<br>
typedef typename matrix::difference_type difference_type;<br>
typedef typename matrix::value_type value_type;<br>
typedef typename matrix::reference reference;<br>
typedef typename matrix::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 &amp;m, const iterator_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&gt;,<br>
public random_access_iterator_base&lt;const_iterator2, value_type&gt; {<br>
public:<br>
typedef dense_random_access_iterator_tag iterator_category;<br>
typedef typename matrix::difference_type difference_type;<br>
typedef typename matrix::value_type value_type;<br>
typedef typename matrix::const_reference reference;<br>
typedef typename matrix::const_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 &amp;m, const const_iterator_type &amp;it);<br>
const_iterator2 (const iterator2 &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator2 &amp;operator ++ ();<br>
const_iterator2 &amp;operator -- ();<br>
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&gt;,<br>
public random_access_iterator_base&lt;iterator2, value_type&gt; {<br>
public:<br>
typedef dense_random_access_iterator_tag iterator_category;<br>
typedef typename matrix::difference_type difference_type;<br>
typedef typename matrix::value_type value_type;<br>
typedef typename matrix::reference reference;<br>
typedef typename matrix::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 &amp;m, const iterator_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>
<h2><a name="identity_matrix"></a> Identity Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>identity_matrix&lt;T&gt;</code>
represents identity matrices. For a <em>(m x n</em>)-dimensional
identity matrix and <em>0 &lt;= i &lt; m</em>, <em>0 &lt;= j &lt;
n</em> holds <em>id</em><sub><em>i, j</em></sub> <em>= 0</em>, if
<em>i &lt;&gt; j</em>, and <em>id</em><sub><em>i, i</em></sub><em>=
1</em>.</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>
identity_matrix&lt;double&gt; m (3);<br>
std::cout &lt;&lt; m &lt;&lt; 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>&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;identity_matrix&lt;T&gt;
&gt;</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
&amp;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 &amp;operator = (const identity_matrix
&amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>identity_matrix &amp;assign_temporary (identity_matrix
&amp;m)</code></td>
<td>Assigns a temporary. May change the identity matrix
<code>m</code> .</td>
</tr>
<tr>
<td><code>void swap (identity_matrix &amp;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>
<h4>Interface</h4>
<pre>
<code>// Identity matrix class<br>
template&lt;class T&gt;<br>
class identity_matrix:<br>
public matrix_expression&lt;identity_matrix&lt;T&gt; &gt; {<br>
public:<br>
typedef std::size_t size_type;<br>
typedef std::ptrdiff_t difference_type;<br>
typedef T value_type;<br>
typedef const T &amp;const_reference;<br>
typedef T &amp;reference;<br>
typedef const T *const_pointer;<br>
typedef T *pointer;<br>
typedef const identity_matrix&lt;T&gt; const_self_type;<br>
typedef identity_matrix&lt;T&gt; self_type;<br>
typedef const matrix_const_reference&lt;const_self_type&gt; const_closure_type;<br>
typedef size_type const_iterator_type;<br>
typedef packed_tag storage_category;<br>
typedef unknown_orientation_tag orientation_category;<br>
<br>
// Construction and destruction<br>
identity_matrix ();<br>
identity_matrix (size_type size);<br>
identity_matrix (size_type size1, size_type size2);<br>
identity_matrix (const identity_matrix &amp;m);<br>
<br>
// Accessors<br>
size_type size1 () const;<br>
size_type size2 () const;<br>
<br>
// Resizing<br>
void resize (size_type size);<br>
void resize (size_type size1, size_type size2);<br>
<br>
// Element access<br>
const_reference operator () (size_type i, size_type j) const;<br>
<br>
// Assignment<br>
identity_matrix &amp;operator = (const identity_matrix &amp;m);<br>
identity_matrix &amp;assign_temporary (identity_matrix &amp;m);<br>
<br>
// Swapping<br>
void swap (identity_matrix &amp;m);<br>
friend void swap (identity_matrix &amp;m1, identity_matrix &amp;m2);<br>
<br>
class const_iterator1;<br>
class const_iterator2;<br>
typedef reverse_iterator_base1&lt;const_iterator1&gt; const_reverse_iterator1;<br>
typedef reverse_iterator_base2&lt;const_iterator2&gt; const_reverse_iterator2;<br>
<br>
// Element lookup<br>
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;<br>
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;<br>
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;<br>
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;<br>
<br>
// Iterators simply are indices.<br>
<br>
class const_iterator1:<br>
public container_const_reference&lt;identity_matrix&gt;,<br>
public random_access_iterator_base&lt;const_iterator1, value_type&gt; {<br>
public:<br>
typedef packed_random_access_iterator_tag iterator_category;<br>
typedef typename identity_matrix::difference_type difference_type;<br>
typedef typename identity_matrix::value_type value_type;<br>
typedef typename identity_matrix::const_reference reference;<br>
typedef typename identity_matrix::const_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 identity_matrix &amp;m, const const_iterator_type &amp;it1, const const_iterator_type &amp;it2);<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>
typedef const_iterator1 iterator1;<br>
<br>
const_iterator1 begin1 () const;<br>
const_iterator1 end1 () const;<br>
<br>
class const_iterator2:<br>
public container_const_reference&lt;identity_matrix&gt;,<br>
public random_access_iterator_base&lt;const_iterator2, value_type&gt; {<br>
public:<br>
typedef packed_random_access_iterator_tag iterator_category;<br>
typedef typename identity_matrix::difference_type difference_type;<br>
typedef typename identity_matrix::value_type value_type;<br>
typedef typename identity_matrix::const_reference reference;<br>
typedef typename identity_matrix::const_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 identity_matrix &amp;m, const const_iterator_type &amp;it1, const const_iterator_type &amp;it2);<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>
typedef const_iterator2 iterator2;<br>
<br>
const_iterator2 begin2 () const;<br>
const_iterator2 end2 () const;<br>
<br>
// Reverse iterators<br>
<br>
const_reverse_iterator1 rbegin1 () const;<br>
const_reverse_iterator1 rend1 () const;<br>
<br>
const_reverse_iterator2 rbegin2 () const;<br>
const_reverse_iterator2 rend2 () const;<br>
};</code>
</pre>
<h2><a name="zero_matrix"></a> Zero Matrix</h2>
<h4>Description</h4>
<p>The templated class <code>zero_matrix&lt;T&gt;</code> represents
zero matrices. For a <em>(m x n</em>)-dimensional zero matrix and
<em>0 &lt;= i &lt; m</em>, <em>0 &lt;= j &lt; n</em> holds
<em>z</em><sub><em>i, j</em></sub> <em>= 0</em>.</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>
zero_matrix&lt;double&gt; m (3, 3);<br>
std::cout &lt;&lt; m &lt;&lt; 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>&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;zero_matrix&lt;T&gt; &gt;</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 &amp;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 &amp;operator = (const zero_matrix
&amp;m)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>zero_matrix &amp;assign_temporary (zero_matrix
&amp;m)</code></td>
<td>Assigns a temporary. May change the zero matrix <code>m</code>
.</td>
</tr>
<tr>
<td><code>void swap (zero_matrix &amp;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>
<h4>Interface</h4>
<pre>
<code>// Zero matrix class<br>
template&lt;class T&gt;<br>
class zero_matrix:<br>
public matrix_expression&lt;zero_matrix&lt;T&gt; &gt; {<br>
public:<br>
typedef std::size_t size_type;<br>
typedef std::ptrdiff_t difference_type;<br>
typedef T value_type;<br>
typedef const T &amp;const_reference;<br>
typedef T &amp;reference;<br>
typedef const T *const_pointer;<br>
typedef T *pointer;<br>
typedef const zero_matrix&lt;T&gt; const_self_type;<br>
typedef zero_matrix&lt;T&gt; self_type;<br>
typedef const matrix_const_reference&lt;const_self_type&gt; const_closure_type;<br>
typedef size_type const_iterator_type;<br>
typedef sparse_tag storage_category;<br>
typedef unknown_orientation_tag orientation_category;<br>
<br>
// Construction and destruction<br>
zero_matrix ();<br>
zero_matrix (size_type size1, size_type size2);<br>
zero_matrix (const zero_matrix &amp;m);<br>
<br>
// Accessors<br>
size_type size1 () const;<br>
size_type size2 () const;<br>
<br>
// Resizing<br>
void resize (size_type size1, size_type size2);<br>
<br>
// Element access<br>
const_reference operator () (size_type i, size_type j) const;<br>
<br>
// Assignment<br>
zero_matrix &amp;operator = (const zero_matrix &amp;m);<br>
zero_matrix &amp;assign_temporary (zero_matrix &amp;m);<br>
<br>
// Swapping<br>
void swap (zero_matrix &amp;m);<br>
friend void swap (zero_matrix &amp;m1, zero_matrix &amp;m2);<br>
<br>
class const_iterator1;<br>
class const_iterator2;<br>
typedef reverse_iterator_base1&lt;const_iterator1&gt; const_reverse_iterator1;<br>
typedef reverse_iterator_base2&lt;const_iterator2&gt; const_reverse_iterator2;<br>
<br>
// Element lookup<br>
const_iterator1 find_first1 (int rank, size_type i, size_type j) const;<br>
const_iterator1 find_last1 (int rank, size_type i, size_type j) const;<br>
const_iterator2 find_first2 (int rank, size_type i, size_type j) const;<br>
const_iterator2 find_last2 (int rank, size_type i, size_type j) const;<br>
<br>
// Iterators simply are indices.<br>
<br>
class const_iterator1:<br>
public container_const_reference&lt;zero_matrix&gt;,<br>
public bidirectional_iterator_base&lt;const_iterator1, value_type&gt; {<br>
public:<br>
typedef sparse_bidirectional_iterator_tag iterator_category;<br>
typedef typename zero_matrix::difference_type difference_type;<br>
typedef typename zero_matrix::value_type value_type;<br>
typedef typename zero_matrix::const_reference reference;<br>
typedef typename zero_matrix::const_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 zero_matrix &amp;m, const const_iterator_type &amp;it1, const const_iterator_type &amp;it2);<br>
<br>
// Arithmetic<br>
const_iterator1 &amp;operator ++ ();<br>
const_iterator1 &amp;operator -- ();<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
const_iterator2 begin () const;<br>
const_iterator2 end () const;<br>
const_reverse_iterator2 rbegin () const;<br>
const_reverse_iterator2 rend () const;<br>
<br>
// Indices<br>
size_type index1 () const;<br>
size_type index2 () const;<br>
<br>
// Assignment<br>
const_iterator1 &amp;operator = (const const_iterator1 &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const const_iterator1 &amp;it) const;<br>
};<br>
<br>
typedef const_iterator1 iterator1;<br>
<br>
const_iterator1 begin1 () const;<br>
const_iterator1 end1 () const;<br>
<br>
class const_iterator2:<br>
public container_const_reference&lt;zero_matrix&gt;,<br>
public bidirectional_iterator_base&lt;const_iterator2, value_type&gt; {<br>
public:<br>
typedef sparse_bidirectional_iterator_tag iterator_category;<br>
typedef typename zero_matrix::difference_type difference_type;<br>
typedef typename zero_matrix::value_type value_type;<br>
typedef typename zero_matrix::const_reference reference;<br>
typedef typename zero_matrix::const_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 zero_matrix &amp;m, const const_iterator_type &amp;it1, const const_iterator_type &amp;it2);<br>
<br>
// Arithmetic<br>
const_iterator2 &amp;operator ++ ();<br>
const_iterator2 &amp;operator -- ();<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
const_iterator1 begin () const;<br>
const_iterator1 end () const;<br>
const_reverse_iterator1 rbegin () const;<br>
const_reverse_iterator1 rend () const;<br>
<br>
// Indices<br>
size_type index1 () const;<br>
size_type index2 () const;<br>
<br>
// Assignment<br>
const_iterator2 &amp;operator = (const const_iterator2 &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const const_iterator2 &amp;it) const;<br>
};<br>
<br>
typedef const_iterator2 iterator2;<br>
<br>
const_iterator2 begin2 () const;<br>
const_iterator2 end2 () const;<br>
<br>
// Reverse iterators<br>
<br>
const_reverse_iterator1 rbegin1 () const;<br>
const_reverse_iterator1 rend1 () const;<br>
<br>
const_reverse_iterator2 rbegin2 () const;<br>
const_reverse_iterator2 rend2 () const;<br>
};</code>
</pre>
<hr>
<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br>
Permission to copy, use, modify, sell and distribute this document
is granted provided this copyright notice appears in all copies.
This document is provided ``as is'' without express or implied
warranty, and with no claim as to its suitability for any
purpose.</p>
<p>Last revised: 1/15/2003</p>
</body>
</html>