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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_sobol_rsg.html">SobolRsg</a></div>
<h1>SobolRsg Class Reference</h1><!-- doxytag: class="QuantLib::SobolRsg" --><code>#include <ql/RandomNumbers/sobolrsg.hpp></code>
<p>
<a href="class_quant_lib_1_1_sobol_rsg-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Sobol low-discrepancy sequence generator.
<p>
A Gray code counter and bitwise operations are used for very fast sequence generation.<p>
The implementation relies on primitive polynomials modulo two from the book "Monte Carlo Methods in Finance" by Peter Jckel.<p>
21 200 primitive polynomials modulo two are provided by default in QuantLib. Jckel has calculated 8 129 334 polynomials, also available in a different file that can be downloaded from <a href="http://quantlib.org.">http://quantlib.org.</a> If you need that many dimensions you must replace the default version of the primitivepolynomials.c file with the extended one.<p>
The choice of initialization numbers (also know as free direction integers) is crucial for the homogeneity properties of the sequence. Sobol defines two homogeneity properties: Property A and Property A'.<p>
The unit initialization numbers suggested in "Numerical Recipes in C", 2nd edition, by Press, Teukolsky, Vetterling, and Flannery (section 7.7) fail the test for Property A even for low dimensions.<p>
Bratley and Fox published coefficients of the free direction integers up to dimension 40, crediting unpublished work of Sobol' and Levitan. See Bratley, P., Fox, B.L. (1988) "Algorithm 659: Implementing Sobol's quasirandom sequence generator," ACM Transactions on Mathematical Software 14:88-100. These values satisfy Property A for d<=20 and d = 23, 31, 33, 34, 37; Property A' holds for d<=6.<p>
Jckel provides in his book (section 8.3) initialization numbers up to dimension 32. Coefficients for d<=8 are the same as in Bradley-Fox, so Property A' holds for d<=6 but Property A holds for d<=32.<p>
The implementation of Lemieux, Cieslak, and Luttmer includes coefficients of the free direction integers up to dimension 360. Coefficients for d<=40 are the same as in Bradley-Fox. For dimension 40<d<=360 the coefficients have been calculated as optimal values based on the "resolution" criterion. See "RandQMC user's guide - A package for randomized quasi-Monte Carlo methods in C," by C. Lemieux, M. Cieslak, and K. Luttmer, version January 13 2004, and references cited there (<a href="http://www.math.ucalgary.ca/~lemieux/randqmc.html">http://www.math.ucalgary.ca/~lemieux/randqmc.html</a>). The values up to d<=360 has been provided to the QuantLib team by Christiane Lemieux, private communication, September 2004.<p>
For more info on Sobol' sequences see also "Monte Carlo Methods in Financial Engineering," by P. Glasserman, 2004, Springer, section 5.2.3<p>
<dl compact><dt><b><a class="el" href="test.html#_test000112">Tests:</a></b></dt><dd><ul>
<li>the correctness of the returned values is tested by reproducing known good values.</li><li>the correctness of the returned values is tested by checking their discrepancy against known good values. </li></ul>
</dd></dl>
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<tr><td colspan="2"><br><h2>Public Types</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">enum </td><td class="memItemRight" valign="bottom"><b>DirectionIntegers</b> { <b>Unit</b>,
<b>Jaeckel</b>,
<b>SobolLevitan</b>,
<b>SobolLevitanLemieux</b>
}</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c10175ab8a401908363648e5f3dad08d"></a><!-- doxytag: member="QuantLib::SobolRsg::sample_type" ref="c10175ab8a401908363648e5f3dad08d" args="" -->
typedef <a class="el" href="struct_quant_lib_1_1_sample.html">Sample</a>< <a class="el" href="class_quant_lib_1_1_array.html">Array</a> > </td><td class="memItemRight" valign="bottom"><b>sample_type</b></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_sobol_rsg.html#517494ec668ecd36efffc01912e484c0">SobolRsg</a> (Size dimensionality, unsigned long seed=0, DirectionIntegers directionIntegers=Jaeckel)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_sobol_rsg.html#aa2d30eb47ba0545410f2a87ebbacf1a">skipTo</a> (unsigned long n)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1d53ad1d2488bf01773158e9e10dce96"></a><!-- doxytag: member="QuantLib::SobolRsg::nextInt32Sequence" ref="1d53ad1d2488bf01773158e9e10dce96" args="() const" -->
const std::vector< unsigned <br>
long > & </td><td class="memItemRight" valign="bottom"><b>nextInt32Sequence</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f099844672ae163c458ad6f0aafba9ae"></a><!-- doxytag: member="QuantLib::SobolRsg::nextSequence" ref="f099844672ae163c458ad6f0aafba9ae" args="() const" -->
const <a class="el" href="struct_quant_lib_1_1_sample.html">SobolRsg::sample_type</a> & </td><td class="memItemRight" valign="bottom"><b>nextSequence</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="21fb9bff0e8370796df2b4a9d16b372b"></a><!-- doxytag: member="QuantLib::SobolRsg::lastSequence" ref="21fb9bff0e8370796df2b4a9d16b372b" args="() const" -->
const <a class="el" href="struct_quant_lib_1_1_sample.html">sample_type</a> & </td><td class="memItemRight" valign="bottom"><b>lastSequence</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6d909a81181d49375588c96fd1494043"></a><!-- doxytag: member="QuantLib::SobolRsg::dimension" ref="6d909a81181d49375588c96fd1494043" args="() const" -->
Size </td><td class="memItemRight" valign="bottom"><b>dimension</b> () const</td></tr>
</table>
<hr><h2>Constructor & Destructor Documentation</h2>
<a class="anchor" name="517494ec668ecd36efffc01912e484c0"></a><!-- doxytag: member="QuantLib::SobolRsg::SobolRsg" ref="517494ec668ecd36efffc01912e484c0" args="(Size dimensionality, unsigned long seed=0, DirectionIntegers directionIntegers=Jaeckel)" -->
<div class="memitem">
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<td class="memname"><a class="el" href="class_quant_lib_1_1_sobol_rsg.html">SobolRsg</a> </td>
<td>(</td>
<td class="paramtype">Size </td>
<td class="paramname"> <em>dimensionality</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned long </td>
<td class="paramname"> <em>seed</em> = <code>0</code>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">DirectionIntegers </td>
<td class="paramname"> <em>directionIntegers</em> = <code>Jaeckel</code></td><td> </td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"></td>
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<div class="memdoc">
<p>
<dl class="pre" compact><dt><b>Precondition:</b></dt><dd>dimensionality must be <= PPMT_MAX_DIM </dd></dl>
</div>
</div><p>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="aa2d30eb47ba0545410f2a87ebbacf1a"></a><!-- doxytag: member="QuantLib::SobolRsg::skipTo" ref="aa2d30eb47ba0545410f2a87ebbacf1a" args="(unsigned long n)" -->
<div class="memitem">
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<td class="memname">void skipTo </td>
<td>(</td>
<td class="paramtype">unsigned long </td>
<td class="paramname"> <em>n</em> </td>
<td> ) </td>
<td width="100%"></td>
</tr>
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<p>
skip to the n-th sample in the low-discrepancy sequence
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