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Jörg Walter bbca4f92fa A couple of fixes and improvements
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<h1><img src="c++boost.gif" alt="c++boost.gif" align="Center">
Sparse Vector</h1>
<h2><a name="sparse_vector"></a> Sparse Vector</h2>
<h4>Description</h4>
<p>The templated class <code>sparse_vector&lt;T, A&gt;</code> is
the base container adaptor for sparse vectors. For a
<em>n</em>-dimensional sparse vector and <em>0 &lt;= i &lt; n</em>
the non-zero elements <em>v</em><sub><em>i</em></sub> are mapped to
consecutive elements of the associative container, i.e. for
elements <em>k</em> =
<em>v</em><sub><em>i</em></sub><sub><sub><em>1</em></sub></sub><sub>
<em></em></sub>and <em>k + 1 =
v</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
</em></sub>of the container holds <em>i</em><sub><em>1</em></sub>
<em>&lt; i</em><sub><em>2</em></sub>.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/vector_sparse.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
sparse_vector&lt;double&gt; v (3, 3);<br>
for (unsigned i = 0; i &lt; v.size (); ++ i)<br>
v (i) = i;<br>
std::cout &lt;&lt; v &lt;&lt; std::endl;<br>
}<br>
</pre>
<h4>Definition</h4>
<p>Defined in the header vector_sparse.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>T</code> </td>
<td>The type of object stored in the sparse vector.</td>
<td>&nbsp;</td>
</tr>
<tr>
<td><code>A</code></td>
<td>The type of the adapted array. <a href=
"#sparse_vector_1">[1]</a> </td>
<td><code>map_array&lt;std::size_t, T&gt;</code></td>
</tr>
</tbody>
</table>
<h4>Model of</h4>
<p><a href="container.htm#vector">Vector</a> .</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"container.htm#vector">Vector</a> .</p>
<h4>Public base classes</h4>
<p><code>vector_expression&lt;sparse_vector&lt;T, A&gt;
&gt;</code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>sparse_vector ()</code> </td>
<td>Allocates a <code>sparse_vector</code> that holds zero
elements.</td>
</tr>
<tr>
<td><code>sparse_vector (size_type size, size_type
non_zeros)</code></td>
<td>Allocates a <code>sparse_vector</code> that holds at most
<code>size</code> elements.</td>
</tr>
<tr>
<td><code>sparse_vector (const sparse_vector &amp;v)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_vector (size_type non_zeros, const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended copy constructor.</td>
</tr>
<tr>
<td><code>void resize (size_type size, size_type
non_zeros)</code></td>
<td>Reallocates a <code>sparse_vector</code> to hold at most
<code>size</code> elements. The content of the
<code>sparse_vector</code> is preserved.</td>
</tr>
<tr>
<td><code>size_type size () const</code></td>
<td>Returns the size of the <code>sparse_vector</code>.</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>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>sparse_vector &amp;operator = (const sparse_vector
&amp;v)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>sparse_vector &amp;assign_temporary (sparse_vector
&amp;v)</code></td>
<td>Assigns a temporary. May change the sparse vector
<code>v</code> .</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_vector &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>
sparse_vector &amp;assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a vector expression to the sparse vector. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_vector &amp;operator += (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Adds the vector expression to
the sparse vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_vector &amp;plus_assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Adds a vector expression to the sparse vector. Left and right
hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_vector &amp;operator -= (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the vector expression
from the sparse vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
sparse_vector &amp;minus_assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Subtracts a vector expression from the sparse vector. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
sparse_vector &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the sparse vector
with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
sparse_vector &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the sparse vector
through a scalar.</td>
</tr>
<tr>
<td><code>void swap (sparse_vector &amp;v)</code></td>
<td>Swaps the contents of the sparse vectors.</td>
</tr>
<tr>
<td><code>void insert (size_type i, const_reference t)</code></td>
<td>Inserts the value <code>t</code> at the <code>i</code>-th
element.</td>
</tr>
<tr>
<td><code>void erase (size_type i)</code></td>
<td>Erases the value at the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>void clear ()</code></td>
<td>Clears the sparse vector.</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>sparse_vector</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>sparse_vector</code>.</td>
</tr>
<tr>
<td><code>iterator begin ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the beginning of
the <code>sparse_vector</code>.</td>
</tr>
<tr>
<td><code>iterator end ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the end of the
<code>sparse_vector</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>sparse_vector</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>sparse_vector</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>sparse_vector</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>sparse_vector</code>.</td>
</tr>
</tbody>
</table>
<h4>Notes</h4>
<p><a name="#sparse_vector_1">[1]</a> Supported parameters for the
adapted array are <code>map_array&lt;std::size_t, T&gt;</code> and
<code>std::map&lt;std::size_t, T&gt;</code>.</p>
<h4>Interface</h4>
<pre>
<code>// Array based sparse vector class<br>
template&lt;class T, class A&gt;<br>
class sparse_vector:<br>
public vector_expression&lt;sparse_vector&lt;T, 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 A array_type;<br>
typedef const A const_array_type;<br>
typedef const sparse_vector&lt;T, A&gt; const_self_type;<br>
typedef sparse_vector&lt;T, A&gt; self_type;<br>
typedef const vector_const_reference&lt;const_self_type&gt; const_closure_type;<br>
typedef vector_reference&lt;self_type&gt; closure_type;<br>
typedef typename A::const_iterator const_iterator_type;<br>
typedef typename A::iterator iterator_type;<br>
typedef sparse_tag storage_category;<br>
<br>
// Construction and destruction<br>
sparse_vector ();<br>
sparse_vector (size_type size, size_type non_zeros = 0);<br>
sparse_vector (const sparse_vector &amp;v);<br>
template&lt;class AE&gt;<br>
sparse_vector (const vector_expression&lt;AE&gt; &amp;ae, size_type non_zeros = 0);<br>
<br>
// Accessors<br>
size_type size () const;<br>
size_type non_zeros () const;<br>
const_array_type &amp;data () const;<br>
array_type &amp;data ();<br>
<br>
// Resizing<br>
void resize (size_type size, size_type non_zeros = 0);<br>
<br>
// Element access<br>
const_reference operator () (size_type i) const;<br>
reference operator () (size_type i);<br>
<br>
const_reference operator [] (size_type i) const;<br>
reference operator [] (size_type i);<br>
<br>
// Assignment<br>
sparse_vector &amp;operator = (const sparse_vector &amp;v);<br>
sparse_vector &amp;assign_temporary (sparse_vector &amp;v);<br>
template&lt;class AE&gt;<br>
sparse_vector &amp;operator = (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
sparse_vector &amp;reset (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
sparse_vector &amp;assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
sparse_vector &amp;operator += (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
sparse_vector &amp;plus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
sparse_vector &amp;operator -= (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
sparse_vector &amp;minus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AT&gt;<br>
sparse_vector &amp;operator *= (const AT &amp;at);<br>
template&lt;class AT&gt;<br>
sparse_vector &amp;operator /= (const AT &amp;at);<br>
<br>
// Swapping<br>
void swap (sparse_vector &amp;v);<br>
friend void swap (sparse_vector &amp;v1, sparse_vector &amp;v2);<br>
<br>
// Element insertion and erasure<br>
void insert (size_type i, const_reference t);<br>
void erase (size_type i);<br>
void clear ();<br>
<br>
class const_iterator;<br>
class iterator;<br>
<br>
// Element lookup<br>
const_iterator find (size_type i) const;<br>
iterator find (size_type i);<br>
const_iterator find_first (size_type i) const;<br>
iterator find_first (size_type i);<br>
const_iterator find_last (size_type i) const;<br>
iterator find_last (size_type i);<br>
<br>
// Iterators simply are pointers.<br>
<br>
class const_iterator:<br>
public container_const_reference&lt;sparse_vector&gt;,<br>
public bidirectional_iterator_base&lt;const_iterator, value_type&gt; {<br>
public:<br>
typedef sparse_bidirectional_iterator_tag iterator_category;<br>
typedef typename sparse_vector::difference_type difference_type;<br>
typedef typename sparse_vector::value_type value_type;<br>
typedef typename sparse_vector::const_reference reference;<br>
typedef typename sparse_vector::const_pointer pointer;<br>
<br>
// Construction and destruction<br>
const_iterator ();<br>
const_iterator (const sparse_vector &amp;v, const const_iterator_type &amp;it);<br>
const_iterator (const iterator &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator &amp;operator ++ ();<br>
const_iterator &amp;operator -- ();<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
const_iterator &amp;operator = (const const_iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const const_iterator &amp;it) const;<br>
};<br>
<br>
const_iterator begin () const;<br>
const_iterator end () const;<br>
<br>
class iterator:<br>
public container_reference&lt;sparse_vector&gt;,<br>
public bidirectional_iterator_base&lt;iterator, value_type&gt; {<br>
public:<br>
typedef sparse_bidirectional_iterator_tag iterator_category;<br>
typedef typename sparse_vector::difference_type difference_type;<br>
typedef typename sparse_vector::value_type value_type;<br>
typedef typename sparse_vector::reference reference;<br>
typedef typename sparse_vector::pointer pointer;<br>
<br>
// Construction and destruction<br>
iterator ();<br>
iterator (sparse_vector &amp;v, const iterator_type &amp;it);<br>
<br>
// Arithmetic<br>
iterator &amp;operator ++ ();<br>
iterator &amp;operator -- ();<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
iterator &amp;operator = (const iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const iterator &amp;it) const;<br>
};<br>
<br>
iterator begin ();<br>
iterator end ();<br>
<br>
// Reverse iterator<br>
<br>
typedef reverse_iterator_base&lt;const_iterator&gt; const_reverse_iterator;<br>
<br>
const_reverse_iterator rbegin () const;<br>
const_reverse_iterator rend () const;<br>
<br>
typedef reverse_iterator_base&lt;iterator&gt; reverse_iterator;<br>
<br>
reverse_iterator rbegin ();<br>
reverse_iterator rend ();<br>
};</code>
</pre>
<h2><a name="compressed_vector"></a> Compressed Vector</h2>
<h4>Description</h4>
<p>The templated class <code>compressed_vector&lt;T, IB, IA,
TA&gt;</code> is the base container adaptor for compressed vectors.
For a <em>n</em>-dimensional compressed vector and <em>0 &lt;= i
&lt; n</em> the non-zero elements <em>v</em><sub><em>i</em></sub>
are mapped to consecutive elements of the index and value
container, i.e. for elements <em>k</em> =
<em>v</em><sub><em>i</em></sub><sub><sub><em>1</em></sub></sub><sub>
<em></em></sub>and <em>k + 1 =
v</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
</em></sub>of these containers holds
<em>i</em><sub><em>1</em></sub> <em>&lt;
i</em><sub><em>2</em></sub>.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/vector_sparse.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
compressed_vector&lt;double&gt; v (3, 3);<br>
for (unsigned i = 0; i &lt; v.size (); ++ i)<br>
v (i) = i;<br>
std::cout &lt;&lt; v &lt;&lt; std::endl;<br>
}
</pre>
<h4>Definition</h4>
<p>Defined in the header vector_sparse.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>T</code> </td>
<td>The type of object stored in the compressed vector.</td>
<td>&nbsp;</td>
</tr>
<tr>
<td><code>IB</code></td>
<td>The index base of the compressed vector. <a href=
"#compressed_vector_1">[1]</a> </td>
<td><code>0</code></td>
</tr>
<tr>
<td><code>IA</code></td>
<td>The type of the adapted array for indices. <a href=
"#compressed_vector_2">[2]</a> </td>
<td><code>unbounded_array&lt;std::size_t&gt;</code></td>
</tr>
<tr>
<td><code>TA</code></td>
<td>The type of the adapted array for values. <a href=
"#compressed_vector_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#vector">Vector</a> .</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"container.htm#vector">Vector</a> .</p>
<h4>Public base classes</h4>
<p><code>vector_expression&lt;compressed_vector&lt;T, IB, IA,
TA&gt; &gt;</code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>compressed_vector ()</code> </td>
<td>Allocates a <code>compressed_vector</code> that holds zero
elements.</td>
</tr>
<tr>
<td><code>compressed_vector (size_type size, size_type
non_zeros)</code></td>
<td>Allocates a <code>compressed_vector</code> that holds at most
<code>size</code> elements.</td>
</tr>
<tr>
<td><code>compressed_vector (const compressed_vector
&amp;v)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_vector (size_type non_zeros, const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended copy constructor.</td>
</tr>
<tr>
<td><code>void resize (size_type size, size_type
non_zeros)</code></td>
<td>Reallocates a <code>compressed_vector</code> to hold at most
<code>size</code> elements. The content of the
<code>compressed_vector</code> is preserved.</td>
</tr>
<tr>
<td><code>size_type size () const</code></td>
<td>Returns the size of the <code>compressed_vector</code>.</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>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>compressed_vector &amp;operator = (const
compressed_vector &amp;v)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>compressed_vector &amp;assign_temporary
(compressed_vector &amp;v)</code></td>
<td>Assigns a temporary. May change the compressed vector
<code>v</code>.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_vector &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>
compressed_vector &amp;assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a vector expression to the compressed vector. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_vector &amp;operator += (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Adds the vector expression to
the compressed vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_vector &amp;plus_assign (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Adds a vector expression to the compressed vector. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_vector &amp;operator -= (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the vector expression
from the compressed vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
compressed_vector &amp;minus_assign (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Subtracts a vector expression from the compressed vector. Left
and right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
compressed_vector &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the compressed
vector with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
compressed_vector &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the compressed vector
through a scalar.</td>
</tr>
<tr>
<td><code>void swap (compressed_vector &amp;v)</code></td>
<td>Swaps the contents of the compressed vectors.</td>
</tr>
<tr>
<td><code>void insert (size_type i, const_reference t)</code></td>
<td>Inserts the value <code>t</code> at the <code>i</code>-th
element.</td>
</tr>
<tr>
<td><code>void erase (size_type i)</code></td>
<td>Erases the value at the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>void clear ()</code></td>
<td>Clears the compressed vector.</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>compressed_vector</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>compressed_vector</code>.</td>
</tr>
<tr>
<td><code>iterator begin ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the beginning of
the <code>compressed_vector</code>.</td>
</tr>
<tr>
<td><code>iterator end ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the end of the
<code>compressed_vector</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>compressed_vector</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>compressed_vector</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>compressed_vector</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>compressed_vector</code>.</td>
</tr>
</tbody>
</table>
<h4>Notes</h4>
<p><a name="#compressed_vector_1">[1]</a> Supported parameters for
the index base are <code>0</code> and <code>1</code> at least.</p>
<p><a name="#compressed_vector_2">[2]</a> Supported parameters for
the adapted array are <code>unbounded_array&lt;&gt;</code> ,
<code>bounded_array&lt;&gt;</code> and
<code>std::vector&lt;&gt;</code> .</p>
<h4>Interface</h4>
<pre>
<code>// Array based sparse vector class<br>
template&lt;class T, std::size_t IB, class IA, class TA&gt;<br>
class compressed_vector:<br>
public vector_expression&lt;compressed_vector&lt;T, IB, IA, TA&gt; &gt; {<br>
public:<br>
typedef std::size_t size_type;<br>
typedef std::ptrdiff_t difference_type;<br>
typedef T value_type;<br>
typedef const T &amp;const_reference;<br>
typedef T &amp;reference;<br>
typedef const T *const_pointer;<br>
typedef T *pointer;<br>
typedef IA index_array_type;<br>
typedef TA value_array_type;<br>
typedef const compressed_vector&lt;T, IB, IA, TA&gt; const_self_type;<br>
typedef compressed_vector&lt;T, IB, IA, TA&gt; self_type;<br>
typedef const vector_const_reference&lt;const_self_type&gt; const_closure_type;<br>
typedef vector_reference&lt;self_type&gt; closure_type;<br>
typedef typename IA::const_iterator const_iterator_type;<br>
typedef typename IA::iterator iterator_type;<br>
typedef sparse_tag storage_category;<br>
<br>
// Construction and destruction<br>
compressed_vector ();<br>
compressed_vector (size_type size, size_type non_zeros = 0);<br>
compressed_vector (const compressed_vector &amp;v);<br>
template&lt;class AE&gt;<br>
compressed_vector (const vector_expression&lt;AE&gt; &amp;ae, size_type non_zeros = 0);<br>
<br>
// Accessors<br>
size_type size () const;<br>
size_type non_zeros () const;<br>
static size_type index_base ();<br>
const index_array_type &amp;index_data () const;<br>
index_array_type &amp;index_data ();<br>
const value_array_type &amp;value_data () const;<br>
value_array_type &amp;value_data ();<br>
<br>
// Resizing<br>
void resize (size_type size, size_type non_zeros = 0);<br>
<br>
// Element access<br>
const_reference operator () (size_type i) const;<br>
reference operator () (size_type i);<br>
<br>
const_reference operator [] (size_type i) const;<br>
reference operator [] (size_type i);<br>
<br>
// Assignment<br>
compressed_vector &amp;operator = (const compressed_vector &amp;v);<br>
compressed_vector &amp;assign_temporary (compressed_vector &amp;v);<br>
template&lt;class AE&gt;<br>
compressed_vector &amp;operator = (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
compressed_vector &amp;reset (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
compressed_vector &amp;assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
compressed_vector &amp;operator += (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
compressed_vector &amp;plus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
compressed_vector &amp;operator -= (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
compressed_vector &amp;minus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AT&gt;<br>
compressed_vector &amp;operator *= (const AT &amp;at);<br>
template&lt;class AT&gt;<br>
compressed_vector &amp;operator /= (const AT &amp;at);<br>
<br>
// Swapping<br>
void swap (compressed_vector &amp;v);<br>
friend void swap (compressed_vector &amp;v1, compressed_vector &amp;v2);<br>
<br>
// Element insertion and erasure<br>
void insert (size_type i, const_reference t);<br>
void erase (size_type i);<br>
void clear ();<br>
<br>
class const_iterator;<br>
class iterator;<br>
<br>
// Element lookup<br>
const_iterator find (size_type i) const;<br>
iterator find (size_type i);<br>
const_iterator find_first (size_type i) const;<br>
iterator find_first (size_type i);<br>
const_iterator find_last (size_type i) const;<br>
iterator find_last (size_type i);<br>
<br>
// Iterators simply are pointers.<br>
<br>
class const_iterator:<br>
public container_const_reference&lt;compressed_vector&gt;,<br>
public bidirectional_iterator_base&lt;const_iterator, value_type&gt; {<br>
public:<br>
typedef sparse_bidirectional_iterator_tag iterator_category;<br>
typedef typename compressed_vector::difference_type difference_type;<br>
typedef typename compressed_vector::value_type value_type;<br>
typedef typename compressed_vector::const_reference reference;<br>
typedef typename compressed_vector::const_pointer pointer;<br>
<br>
// Construction and destruction<br>
const_iterator ();<br>
const_iterator (const compressed_vector &amp;v, const const_iterator_type &amp;it);<br>
const_iterator (const iterator &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator &amp;operator ++ ();<br>
const_iterator &amp;operator -- ();<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
const_iterator &amp;operator = (const const_iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const const_iterator &amp;it) const;<br>
};<br>
<br>
const_iterator begin () const;<br>
const_iterator end () const;<br>
<br>
class iterator:<br>
public container_reference&lt;compressed_vector&gt;,<br>
public bidirectional_iterator_base&lt;iterator, value_type&gt; {<br>
public:<br>
typedef sparse_bidirectional_iterator_tag iterator_category;<br>
typedef typename compressed_vector::difference_type difference_type;<br>
typedef typename compressed_vector::value_type value_type;<br>
typedef typename compressed_vector::reference reference;<br>
typedef typename compressed_vector::pointer pointer;<br>
<br>
// Construction and destruction<br>
iterator ();<br>
iterator (compressed_vector &amp;v, const iterator_type &amp;it);<br>
<br>
// Arithmetic<br>
iterator &amp;operator ++ ();<br>
iterator &amp;operator -- ();<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
iterator &amp;operator = (const iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const iterator &amp;it) const;<br>
};<br>
<br>
iterator begin ();<br>
iterator end ();<br>
<br>
// Reverse iterator<br>
<br>
typedef reverse_iterator_base&lt;const_iterator&gt; const_reverse_iterator;<br>
<br>
const_reverse_iterator rbegin () const;<br>
const_reverse_iterator rend () const;<br>
<br>
typedef reverse_iterator_base&lt;iterator&gt; reverse_iterator;<br>
<br>
reverse_iterator rbegin ();<br>
reverse_iterator rend ();<br>
};</code>
</pre>
<h2><a name="coordinate_vector"></a> Coordinate Vector</h2>
<h4>Description</h4>
<p>The templated class <code>coordinate_vector&lt;T, IB, IA,
TA&gt;</code> is the base container adaptor for compressed vectors.
For a <em>n</em>-dimensional sorted coordinate vector and <em>0
&lt;= i &lt; n</em> the non-zero elements
<em>v</em><sub><em>i</em></sub> are mapped to consecutive elements
of the index and value container, i.e. for elements <em>k</em> =
<em>v</em><sub><em>i</em></sub><sub><sub><em>1</em></sub></sub><sub>
<em></em></sub>and <em>k + 1 =
v</em><sub><em>i</em></sub><sub><sub><em>2</em></sub></sub><sub><em>
</em></sub>of these containers holds
<em>i</em><sub><em>1</em></sub> <em>&lt;
i</em><sub><em>2</em></sub>.</p>
<h4>Example</h4>
<pre>
#include &lt;boost/numeric/ublas/vector_sparse.hpp&gt;<br>
#include &lt;boost/numeric/ublas/io.hpp&gt;<br>
<br>
int main () {<br>
using namespace boost::numeric::ublas;<br>
coordinate_vector&lt;double&gt; v (3, 3);<br>
for (unsigned i = 0; i &lt; v.size (); ++ i)<br>
v (i) = i;<br>
std::cout &lt;&lt; v &lt;&lt; std::endl;<br>
}<br>
</pre>
<h4>Definition</h4>
<p>Defined in the header vector_sparse.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<tbody>
<tr>
<th>Parameter</th>
<th>Description</th>
<th>Default</th>
</tr>
<tr>
<td><code>T</code> </td>
<td>The type of object stored in the coordinate vector.</td>
<td>&nbsp;</td>
</tr>
<tr>
<td><code>IB</code></td>
<td>The index base of the coordinate vector. <a href=
"#coordinate_vector_1">[1]</a> </td>
<td><code>0</code></td>
</tr>
<tr>
<td><code>IA</code></td>
<td>The type of the adapted array for indices. <a href=
"#coordinate_vector_2">[2]</a> </td>
<td><code>unbounded_array&lt;std::size_t&gt;</code></td>
</tr>
<tr>
<td><code>TA</code></td>
<td>The type of the adapted array for values. <a href=
"#coordinate_vector_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#vector">Vector</a> .</p>
<h4>Type requirements</h4>
<p>None, except for those imposed by the requirements of <a href=
"container.htm#vector">Vector</a> .</p>
<h4>Public base classes</h4>
<p><code>vector_expression&lt;coordinate_vector&lt;T, IB, IA,
TA&gt; &gt;</code></p>
<h4>Members</h4>
<table border="1">
<tbody>
<tr>
<th>Member</th>
<th>Description</th>
</tr>
<tr>
<td><code>coordinate_vector ()</code> </td>
<td>Allocates a <code>coordinate_vector</code> that holds zero
elements.</td>
</tr>
<tr>
<td><code>coordinate_vector (size_type size, size_type
non_zeros)</code></td>
<td>Allocates a <code>coordinate_vector</code> that holds at most
<code>size</code> elements.</td>
</tr>
<tr>
<td><code>coordinate_vector (const coordinate_vector
&amp;v)</code></td>
<td>The copy constructor.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_vector (size_type non_zeros, const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>The extended copy constructor.</td>
</tr>
<tr>
<td><code>void resize (size_type size, size_type
non_zeros)</code></td>
<td>Reallocates a <code>coordinate_vector</code> to hold at most
<code>size</code> elements. The content of the
<code>coordinate_vector</code> is preserved.</td>
</tr>
<tr>
<td><code>size_type size () const</code></td>
<td>Returns the size of the <code>coordinate_vector</code>.</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>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>coordinate_vector &amp;operator = (const
coordinate_vector &amp;v)</code></td>
<td>The assignment operator.</td>
</tr>
<tr>
<td><code>coordinate_vector &amp;assign_temporary
(coordinate_vector &amp;v)</code></td>
<td>Assigns a temporary. May change the coordinate vector
<code>v</code>.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_vector &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>
coordinate_vector &amp;assign (const vector_expression&lt;AE&gt;
&amp;ae)</code></td>
<td>Assigns a vector expression to the coordinate vector. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_vector &amp;operator += (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Adds the vector expression to
the coordinate vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_vector &amp;plus_assign (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Adds a vector expression to the coordinate vector. Left and
right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_vector &amp;operator -= (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>A computed assignment operator. Subtracts the vector expression
from the coordinate vector.</td>
</tr>
<tr>
<td><code>template&lt;class AE&gt;<br>
coordinate_vector &amp;minus_assign (const
vector_expression&lt;AE&gt; &amp;ae)</code></td>
<td>Subtracts a vector expression from the coordinate vector. Left
and right hand side of the assignment should be independent.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
coordinate_vector &amp;operator *= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Multiplies the coordinate
vector with a scalar.</td>
</tr>
<tr>
<td><code>template&lt;class AT&gt;<br>
coordinate_vector &amp;operator /= (const AT &amp;at)</code></td>
<td>A computed assignment operator. Divides the coordinate vector
through a scalar.</td>
</tr>
<tr>
<td><code>void swap (coordinate_vector &amp;v)</code></td>
<td>Swaps the contents of the coordinate vectors.</td>
</tr>
<tr>
<td><code>void insert (size_type i, const_reference t)</code></td>
<td>Inserts the value <code>t</code> at the <code>i</code>-th
element.</td>
</tr>
<tr>
<td><code>void erase (size_type i)</code></td>
<td>Erases the value at the <code>i</code>-th element.</td>
</tr>
<tr>
<td><code>void clear ()</code></td>
<td>Clears the coordinate vector.</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>coordinate_vector</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>coordinate_vector</code>.</td>
</tr>
<tr>
<td><code>iterator begin ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the beginning of
the <code>coordinate_vector</code>.</td>
</tr>
<tr>
<td><code>iterator end ()</code> </td>
<td>Returns a <code>iterator</code> pointing to the end of the
<code>coordinate_vector</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>coordinate_vector</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>coordinate_vector</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>coordinate_vector</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>coordinate_vector</code>.</td>
</tr>
</tbody>
</table>
<h4>Notes</h4>
<p><a name="#coordinate_vector_1">[1]</a> Supported parameters for
the index base are <code>0</code> and <code>1</code> at least.</p>
<p><a name="#coordinate_vector_2">[2]</a> Supported parameters for
the adapted array are <code>unbounded_array&lt;&gt;</code> ,
<code>bounded_array&lt;&gt;</code> and
<code>std::vector&lt;&gt;</code> .</p>
<h4>Interface</h4>
<pre>
<code>// Array based sparse vector class<br>
template&lt;class T, std::size_t IB, class IA, class TA&gt;<br>
class coordinate_vector:<br>
public vector_expression&lt;coordinate_vector&lt;T, IB, IA, TA&gt; &gt; {<br>
public:<br>
typedef std::size_t size_type;<br>
typedef std::ptrdiff_t difference_type;<br>
typedef T value_type;<br>
typedef const T &amp;const_reference;<br>
typedef T &amp;reference;<br>
typedef const T *const_pointer;<br>
typedef T *pointer;<br>
typedef IA index_array_type;<br>
typedef TA value_array_type;<br>
typedef const coordinate_vector&lt;T, IB, IA, TA&gt; const_self_type;<br>
typedef coordinate_vector&lt;T, IB, IA, TA&gt; self_type;<br>
typedef const vector_const_reference&lt;const_self_type&gt; const_closure_type;<br>
typedef vector_reference&lt;self_type&gt; closure_type;<br>
typedef typename IA::const_iterator const_iterator_type;<br>
typedef typename IA::iterator iterator_type;<br>
typedef sparse_tag storage_category;<br>
<br>
// Construction and destruction<br>
coordinate_vector ();<br>
coordinate_vector (size_type size, size_type non_zeros = 0);<br>
coordinate_vector (const coordinate_vector &amp;v);<br>
template&lt;class AE&gt;<br>
coordinate_vector (const vector_expression&lt;AE&gt; &amp;ae, size_type non_zeros = 0);<br>
<br>
// Accessors<br>
size_type size () const;<br>
size_type non_zeros () const;<br>
static size_type index_base ();<br>
const index_array_type &amp;index_data () const;<br>
index_array_type &amp;index_data ();<br>
const value_array_type &amp;value_data () const;<br>
value_array_type &amp;value_data ();<br>
<br>
// Resizing<br>
void resize (size_type size, size_type non_zeros = 0);<br>
<br>
// Element access<br>
const_reference operator () (size_type i) const;<br>
reference operator () (size_type i);<br>
<br>
const_reference operator [] (size_type i) const;<br>
reference operator [] (size_type i);<br>
<br>
// Assignment<br>
coordinate_vector &amp;operator = (const coordinate_vector &amp;v);<br>
coordinate_vector &amp;assign_temporary (coordinate_vector &amp;v);<br>
template&lt;class AE&gt;<br>
coordinate_vector &amp;operator = (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
coordinate_vector &amp;reset (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
coordinate_vector &amp;assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
coordinate_vector &amp;operator += (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
coordinate_vector &amp;plus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
coordinate_vector &amp;operator -= (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AE&gt;<br>
coordinate_vector &amp;minus_assign (const vector_expression&lt;AE&gt; &amp;ae);<br>
template&lt;class AT&gt;<br>
coordinate_vector &amp;operator *= (const AT &amp;at);<br>
template&lt;class AT&gt;<br>
coordinate_vector &amp;operator /= (const AT &amp;at);<br>
<br>
// Swapping<br>
void swap (coordinate_vector &amp;v);<br>
friend void swap (coordinate_vector &amp;v1, coordinate_vector &amp;v2);<br>
<br>
// Element insertion and erasure<br>
void insert (size_type i, const_reference t);<br>
void erase (size_type i);<br>
void clear ();<br>
<br>
class const_iterator;<br>
class iterator;<br>
<br>
// Element lookup<br>
const_iterator find (size_type i) const;<br>
iterator find (size_type i);<br>
const_iterator find_first (size_type i) const;<br>
iterator find_first (size_type i);<br>
const_iterator find_last (size_type i) const;<br>
iterator find_last (size_type i);<br>
<br>
// Iterators simply are pointers.<br>
<br>
class const_iterator:<br>
public container_const_reference&lt;coordinate_vector&gt;,<br>
public bidirectional_iterator_base&lt;const_iterator, value_type&gt; {<br>
public:<br>
typedef sparse_bidirectional_iterator_tag iterator_category;<br>
typedef typename coordinate_vector::difference_type difference_type;<br>
typedef typename coordinate_vector::value_type value_type;<br>
typedef typename coordinate_vector::const_reference reference;<br>
typedef typename coordinate_vector::const_pointer pointer;<br>
<br>
// Construction and destruction<br>
const_iterator ();<br>
const_iterator (const coordinate_vector &amp;v, const const_iterator_type &amp;it);<br>
const_iterator (const iterator &amp;it);<br>
<br>
// Arithmetic<br>
const_iterator &amp;operator ++ ();<br>
const_iterator &amp;operator -- ();<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
const_iterator &amp;operator = (const const_iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const const_iterator &amp;it) const;<br>
};<br>
<br>
const_iterator begin () const;<br>
const_iterator end () const;<br>
<br>
class iterator:<br>
public container_reference&lt;coordinate_vector&gt;,<br>
public bidirectional_iterator_base&lt;iterator, value_type&gt; {<br>
public:<br>
typedef sparse_bidirectional_iterator_tag iterator_category;<br>
typedef typename coordinate_vector::difference_type difference_type;<br>
typedef typename coordinate_vector::value_type value_type;<br>
typedef typename coordinate_vector::reference reference;<br>
typedef typename coordinate_vector::pointer pointer;<br>
<br>
// Construction and destruction<br>
iterator ();<br>
iterator (coordinate_vector &amp;v, const iterator_type &amp;it);<br>
<br>
// Arithmetic<br>
iterator &amp;operator ++ ();<br>
iterator &amp;operator -- ();<br>
<br>
// Dereference<br>
reference operator * () const;<br>
<br>
// Index<br>
size_type index () const;<br>
<br>
// Assignment<br>
iterator &amp;operator = (const iterator &amp;it);<br>
<br>
// Comparison<br>
bool operator == (const iterator &amp;it) const;<br>
};<br>
<br>
iterator begin ();<br>
iterator end ();<br>
<br>
// Reverse iterator<br>
<br>
typedef reverse_iterator_base&lt;const_iterator&gt; const_reverse_iterator;<br>
<br>
const_reverse_iterator rbegin () const;<br>
const_reverse_iterator rend () const;<br>
<br>
typedef reverse_iterator_base&lt;iterator&gt; reverse_iterator;<br>
<br>
reverse_iterator rbegin ();<br>
reverse_iterator rend ();<br>
};</code>
</pre>
<hr>
<p>Copyright (&copy;) 2000-2002 Joerg Walter, Mathias Koch<br>
Permission to copy, use, modify, sell and distribute this document
is granted provided this copyright notice appears in all copies.
This document is provided ``as is'' without express or implied
warranty, and with no claim as to its suitability for any
purpose.</p>
<p>Last revised: 1/15/2003</p>
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