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<title>Sparse Vector</title>
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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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