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<div id="projectbrief">A free/open-source library for quantitative finance</div>
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<li class="navelem"><a class="el" href="namespace_quant_lib.html">QuantLib</a></li><li class="navelem"><a class="el" href="class_quant_lib_1_1_sobol_rsg.html">SobolRsg</a></li> </ul>
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<div class="header">
<div class="summary">
<a href="#pub-types">Public Types</a> |
<a href="#pub-methods">Public Member Functions</a> |
<a href="class_quant_lib_1_1_sobol_rsg-members.html">List of all members</a> </div>
<div class="headertitle">
<div class="title">SobolRsg Class Reference</div> </div>
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<div class="contents">
<p>Sobol low-discrepancy sequence generator.
<a href="class_quant_lib_1_1_sobol_rsg.html#details">More...</a></p>
<p><code>#include <ql/math/randomnumbers/sobolrsg.hpp></code></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr class="memitem:af5254f10d63ffdac50ac07c6df7cc90d"><td class="memItemLeft" align="right" valign="top"><a id="af5254f10d63ffdac50ac07c6df7cc90d"></a>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 class="separator:af5254f10d63ffdac50ac07c6df7cc90d"><td class="memSeparator" colspan="2"> </td></tr>
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typedef <a class="el" href="struct_quant_lib_1_1_sample.html">Sample</a>< std::vector< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > > </td><td class="memItemRight" valign="bottom"><b>sample_type</b></td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a517494ec668ecd36efffc01912e484c0"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_sobol_rsg.html#a517494ec668ecd36efffc01912e484c0">SobolRsg</a> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> dimensionality, unsigned long seed=0, DirectionIntegers directionIntegers=Jaeckel)</td></tr>
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<tr class="memitem:a7b9e11f498dab87a37a3cb75965e94c8"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_sobol_rsg.html#a7b9e11f498dab87a37a3cb75965e94c8">skipTo</a> (boost::uint_least32_t n)</td></tr>
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const std::vector< boost::uint_least32_t > & </td><td class="memItemRight" valign="bottom"><b>nextInt32Sequence</b> () const</td></tr>
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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>
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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>
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<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>dimension</b> () const</td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Sobol low-discrepancy sequence generator. </p>
<p>A Gray code counter and bitwise operations are used for very fast sequence generation.</p>
<p>The implementation relies on primitive polynomials modulo two from the book "Monte Carlo Methods in Finance" by Peter Jäckel.</p>
<p>21 200 primitive polynomials modulo two are provided in <a class="el" href="namespace_quant_lib.html">QuantLib</a>. Jäckel has calculated 8 129 334 polynomials: if you need that many dimensions you can replace the primitivepolynomials.cpp 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>
<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>
<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>
<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>
<p>Jäckel 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>
<p>The implementation of Lemieux, Cieslak, and Luttmer includes coefficients of the free direction integers up to dimension</p><ol type="1">
<li>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.</li>
</ol>
<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>
<p>The Joe–Kuo numbers and the Kuo numbers are due to Stephen Joe and Frances Kuo.</p>
<p>S. Joe and F. Y. Kuo, Constructing Sobol sequences with better two-dimensional projections, preprint Nov 22 2007</p>
<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>
<p>The Joe-Kuo numbers are available under a BSD-style license available at the above link.</p>
<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 class="test"><dt><b><a class="el" href="test.html#_test000067">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>
</div><h2 class="groupheader">Constructor & Destructor Documentation</h2>
<a id="a517494ec668ecd36efffc01912e484c0"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a517494ec668ecd36efffc01912e484c0">◆ </a></span>SobolRsg()</h2>
<div class="memitem">
<div class="memproto">
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<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#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </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>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">explicit</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<dl class="section pre"><dt>Precondition</dt><dd>dimensionality must be <= PPMT_MAX_DIM </dd></dl>
</div>
</div>
<h2 class="groupheader">Member Function Documentation</h2>
<a id="a7b9e11f498dab87a37a3cb75965e94c8"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7b9e11f498dab87a37a3cb75965e94c8">◆ </a></span>skipTo()</h2>
<div class="memitem">
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<td class="memname">void skipTo </td>
<td>(</td>
<td class="paramtype">boost::uint_least32_t </td>
<td class="paramname"><em>n</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>skip to the n-th sample in the low-discrepancy sequence </p>
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