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<html>
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<title>Sparse Vector</title>
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<h1><img src="c++boost.gif" alt="c++boost.gif" align="center"
width="277" height="86">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>every non-zero
element <em>v</em><sub><em>i</em></sub> is mapped to the <em>i-</em>th
element of the container.</p>
<h4>Example</h4>
<pre>int main () {
using namespace boost::numeric::ublas;
sparse_vector&lt;double&gt; v (3, 3);
for (int i = 0; i &lt; v.size (); ++ i)
v (i) = i;
std::cout &lt;&lt; v &lt;&lt; std::endl;
}</pre>
<h4>Definition</h4>
<p>Defined in the header vector_sparse.hpp.</p>
<h4>Template parameters</h4>
<table border="1">
<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>F</code></td>
<td>Functor describing the storage organization.</td>
<td><code>forward</code></td>
</tr>
<tr>
<td><code>A</code></td>
<td>The type of the adapted array.</td>
<td><code>map_array&lt;std::size_t, T&gt;</code></td>
</tr>
</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">
<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>
</table>
<h4>Interface</h4>
<pre><code> // Array based sparse vector class
template&lt;class T, class A&gt;
class sparse_vector:
public vector_expression&lt;sparse_vector&lt;T, A&gt; &gt; {
public:
typedef std::size_t size_type;
typedef std::ptrdiff_t difference_type;
typedef T value_type;
typedef const T &amp;const_reference;
typedef T &amp;reference;
typedef const T *const_pointer;
typedef T *pointer;
typedef F functor_type;
typedef A array_type;
typedef const A const_array_type;
typedef const sparse_vector&lt;T, A&gt; const_self_type;
typedef sparse_vector&lt;T, A&gt; self_type;
typedef const vector_const_reference&lt;const_self_type&gt; const_closure_type;
typedef vector_reference&lt;self_type&gt; closure_type;
typedef typename A::const_iterator const_iterator_type;
typedef typename A::iterator iterator_type;
typedef sparse_tag storage_category;
// Construction and destruction
sparse_vector ();
sparse_vector (size_type size, size_type non_zeros = 0);
sparse_vector (const sparse_vector &amp;v);
template&lt;class AE&gt;
sparse_vector (const vector_expression&lt;AE&gt; &amp;ae, size_type non_zeros = 0);
// Accessors
size_type size () const;
size_type non_zeros () const;
const_array_type &amp;data () const;
array_type &amp;data ();
// Resizing
void resize (size_type size, size_type non_zeros = 0);
// Element access
const_reference operator () (size_type i) const;
reference operator () (size_type i);
const_reference operator [] (size_type i) const;
reference operator [] (size_type i);
// Assignment
sparse_vector &amp;operator = (const sparse_vector &amp;v);
sparse_vector &amp;assign_temporary (sparse_vector &amp;v);
template&lt;class AE&gt;
sparse_vector &amp;operator = (const vector_expression&lt;AE&gt; &amp;ae);
template&lt;class AE&gt;
sparse_vector &amp;reset (const vector_expression&lt;AE&gt; &amp;ae);
template&lt;class AE&gt;
sparse_vector &amp;assign (const vector_expression&lt;AE&gt; &amp;ae);
template&lt;class AE&gt;
sparse_vector &amp;operator += (const vector_expression&lt;AE&gt; &amp;ae);
template&lt;class AE&gt;
sparse_vector &amp;plus_assign (const vector_expression&lt;AE&gt; &amp;ae);
template&lt;class AE&gt;
sparse_vector &amp;operator -= (const vector_expression&lt;AE&gt; &amp;ae);
template&lt;class AE&gt;
sparse_vector &amp;minus_assign (const vector_expression&lt;AE&gt; &amp;ae);
template&lt;class AT&gt;
sparse_vector &amp;operator *= (const AT &amp;at);
template&lt;class AT&gt;
sparse_vector &amp;operator /= (const AT &amp;at);
// Swapping
void swap (sparse_vector &amp;v);
friend void swap (sparse_vector &amp;v1, sparse_vector &amp;v2);
// Element insertion and erasure
void insert (size_type i, const_reference t);
void erase (size_type i);
void clear ();
class const_iterator;
class iterator;
// Element lookup
const_iterator find (size_type i) const;
iterator find (size_type i);
const_iterator find_first (size_type i) const;
iterator find_first (size_type i);
const_iterator find_last (size_type i) const;
iterator find_last (size_type i);
// Iterators simply are pointers.
class const_iterator:
public container_const_reference&lt;sparse_vector&gt;,
public bidirectional_iterator_base&lt;const_iterator, value_type&gt; {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename sparse_vector::difference_type difference_type;
typedef typename sparse_vector::value_type value_type;
typedef typename sparse_vector::const_reference reference;
typedef typename sparse_vector::const_pointer pointer;
// Construction and destruction
const_iterator ();
const_iterator (const sparse_vector &amp;v, const const_iterator_type &amp;it);
const_iterator (const iterator &amp;it);
// Arithmetic
const_iterator &amp;operator ++ ();
const_iterator &amp;operator -- ();
// Dereference
reference operator * () const;
// Index
size_type index () const;
// Assignment
const_iterator &amp;operator = (const const_iterator &amp;it);
// Comparison
bool operator == (const const_iterator &amp;it) const;
};
const_iterator begin () const;
const_iterator end () const;
class iterator:
public container_reference&lt;sparse_vector&gt;,
public bidirectional_iterator_base&lt;iterator, value_type&gt; {
public:
typedef sparse_bidirectional_iterator_tag iterator_category;
typedef typename sparse_vector::difference_type difference_type;
typedef typename sparse_vector::value_type value_type;
typedef typename sparse_vector::reference reference;
typedef typename sparse_vector::pointer pointer;
// Construction and destruction
iterator ();
iterator (sparse_vector &amp;v, const iterator_type &amp;it);
// Arithmetic
iterator &amp;operator ++ ();
iterator &amp;operator -- ();
// Dereference
reference operator * () const;
// Index
size_type index () const;
// Assignment
iterator &amp;operator = (const iterator &amp;it);
// Comparison
bool operator == (const iterator &amp;it) const;
};
iterator begin ();
iterator end ();
// Reverse iterator
typedef reverse_iterator_base&lt;const_iterator&gt; const_reverse_iterator;
const_reverse_iterator rbegin () const;
const_reverse_iterator rend () const;
typedef reverse_iterator_base&lt;iterator&gt; reverse_iterator;
reverse_iterator rbegin ();
reverse_iterator rend ();
};</code></pre>
<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: 8/3/2002</p>
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