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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<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/math/randomnumbers/sobolrsg.hpp></code>
<p>
<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 in <a class="el" href="namespace_quant_lib.html">QuantLib</a>. Jckel has calculated 8 129 334 polynomials: if you need that many dimensions you can replace the primitivepolynomials.c file included in <a class="el" href="namespace_quant_lib.html">QuantLib</a> with the one provided in the CD of the "Monte Carlo Methods in Finance" book.<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Bratley and Fox published coefficients of the free direction integers up to dimension 40, crediting unpublished work of Sobol' and Levitan.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 <a class="el" href="namespace_quant_lib.html">QuantLib</a> 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>
The Joe--Kuo numbers and the Kuo numbers are due to Stephen Joe and Frances Kuo.<p>
S. Joe and F. Y. Kuo, Constructing Sobol sequences with better two-dimensional projections, preprint Nov 22 2007<p>
See <a href="http://web.maths.unsw.edu.au/~fkuo/sobol/">http://web.maths.unsw.edu.au/~fkuo/sobol/</a> for more information.<p>
Note that the Kuo numbers were generated to work with a different ordering of primitive polynomials for the first 40 or so dimensions which is why we have the Alternative Primitive Polynomials.<p>
<dl compact><dt><b><a class="el" href="test.html#_test000050">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> { <br>
<b>Unit</b>,
<b>Jaeckel</b>,
<b>SobolLevitan</b>,
<b>SobolLevitanLemieux</b>,
<br>
<b>JoeKuoD5</b>,
<b>JoeKuoD6</b>,
<b>JoeKuoD7</b>,
<b>Kuo</b>,
<br>
<b>Kuo2</b>,
<b>Kuo3</b>
<br>
}</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f3b59a3dd56521693efc68c221a2bf38"></a><!-- doxytag: member="QuantLib::SobolRsg::sample_type" ref="f3b59a3dd56521693efc68c221a2bf38" args="" -->
typedef <a class="el" href="struct_quant_lib_1_1_sample.html">Sample</a>< std::vector<br>
< <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</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> (<a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a> 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="12298c913deb1e1134ac23f669b1b294"></a><!-- doxytag: member="QuantLib::SobolRsg::nextInt32Sequence" ref="12298c913deb1e1134ac23f669b1b294" 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="24eb8d9ace7d89bd65c3767bdc1edf57"></a><!-- doxytag: member="QuantLib::SobolRsg::nextSequence" ref="24eb8d9ace7d89bd65c3767bdc1edf57" 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="8d216498c4107b3bca19b47a929407fc"></a><!-- doxytag: member="QuantLib::SobolRsg::lastSequence" ref="8d216498c4107b3bca19b47a929407fc" 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="d089a89a18aa50ad2c64712cf5fb5e3d"></a><!-- doxytag: member="QuantLib::SobolRsg::dimension" ref="d089a89a18aa50ad2c64712cf5fb5e3d" args="() const " -->
<a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a> </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"><a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a> </td>
<td class="paramname"> <em>dimensionality</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned long </td>
<td class="paramname"> <em>seed</em> = <code>0</code>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">DirectionIntegers </td>
<td class="paramname"> <em>directionIntegers</em> = <code>Jaeckel</code></td><td> </td>
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<td>)</td>
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<p>
<dl class="pre" compact><dt><b>Precondition:</b></dt><dd>dimensionality must be <= PPMT_MAX_DIM </dd></dl>
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<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="aa2d30eb47ba0545410f2a87ebbacf1a"></a><!-- doxytag: member="QuantLib::SobolRsg::skipTo" ref="aa2d30eb47ba0545410f2a87ebbacf1a" args="(unsigned long n)" -->
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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>
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<p>
skip to the n-th sample in the low-discrepancy sequence
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