1<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> 2<html> 3<head> 4<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 5<title>Class template sobol_engine</title> 6<link rel="stylesheet" href="../../../../doc/src/boostbook.css" type="text/css"> 7<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 8<link rel="home" href="../../index.html" title="The Boost C++ Libraries BoostBook Documentation Subset"> 9<link rel="up" href="../../boost_random/reference.html#header.boost.random.sobol_hpp" title="Header <boost/random/sobol.hpp>"> 10<link rel="prev" href="knuth_b.html" title="Type definition knuth_b"> 11<link rel="next" href="sobol.html" title="Type definition sobol"> 12</head> 13<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 14<table cellpadding="2" width="100%"><tr> 15<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" 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class="titlepage"></div> 28<div class="refnamediv"> 29<h2><span class="refentrytitle">Class template sobol_engine</span></h2> 30<p>boost::random::sobol_engine</p> 31</div> 32<h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2> 33<div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: <<a class="link" href="../../boost_random/reference.html#header.boost.random.sobol_hpp" title="Header <boost/random/sobol.hpp>">boost/random/sobol.hpp</a>> 34 35</span><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> UIntType<span class="special">,</span> <span class="keyword">unsigned</span> w<span class="special">,</span> 36 <span class="keyword">typename</span> SobolTables <span class="special">=</span> <span class="identifier">default_sobol_table</span><span class="special">></span> 37<span class="keyword">class</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">{</span> 38<span class="keyword">public</span><span class="special">:</span> 39 <span class="comment">// types</span> 40 <span class="keyword">typedef</span> <span class="identifier">UIntType</span> <a name="boost.random.sobol_engine.result_type"></a><span class="identifier">result_type</span><span class="special">;</span> 41 42 <span class="comment">// <a class="link" href="sobol_engine.html#boost.random.sobol_engineconstruct-copy-destruct">construct/copy/destruct</a></span> 43 <span class="keyword">explicit</span> <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_5-bb"><span class="identifier">sobol_engine</span></a><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span><span class="special">)</span><span class="special">;</span> 44 45 <span class="comment">// <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_4-bb">public member functions</a></span> 46 <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_4_1-bb"><span class="identifier">dimension</span></a><span class="special">(</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> 47 <span class="keyword">void</span> <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_4_2-bb"><span class="identifier">seed</span></a><span class="special">(</span><span class="special">)</span><span class="special">;</span> 48 <span class="keyword">void</span> <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_4_3-bb"><span class="identifier">seed</span></a><span class="special">(</span><span class="identifier">UIntType</span><span class="special">)</span><span class="special">;</span> 49 <span class="identifier">result_type</span> <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_4_4-bb"><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span></a><span class="special">(</span><span class="special">)</span><span class="special">;</span> 50 <span class="keyword">void</span> <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_4_5-bb"><span class="identifier">discard</span></a><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">)</span><span class="special">;</span> 51 52 <span class="comment">// <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_6-bb">public static functions</a></span> 53 <span class="keyword">static</span> <span class="keyword">constexpr</span> <span class="identifier">result_type</span> <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_6_1-bb"><span class="identifier">min</span></a><span class="special">(</span><span class="special">)</span><span class="special">;</span> 54 <span class="keyword">static</span> <span class="keyword">constexpr</span> <span class="identifier">result_type</span> <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_6_2-bb"><span class="identifier">max</span></a><span class="special">(</span><span class="special">)</span><span class="special">;</span> 55 56 <span class="comment">// <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_7-bb">friend functions</a></span> 57 <span class="keyword">friend</span> <span class="keyword">bool</span> <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_7_1-bb"><span class="keyword">operator</span><span class="special">==</span></a><span class="special">(</span><span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span><span class="special">)</span><span class="special">;</span> 58 <span class="keyword">friend</span> <span class="keyword">bool</span> <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_7_2-bb"><span class="keyword">operator</span><span class="special">!=</span></a><span class="special">(</span><span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span><span class="special">)</span><span class="special">;</span> 59 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> CharT<span class="special">,</span> <span class="keyword">typename</span> Traits<span class="special">></span> 60 <span class="keyword">friend</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">></span> <span class="special">&</span> 61 <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_7_3-bb"><span class="keyword">operator</span><span class="special"><<</span></a><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">></span> <span class="special">&</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span><span class="special">)</span><span class="special">;</span> 62 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> CharT<span class="special">,</span> <span class="keyword">typename</span> Traits<span class="special">></span> 63 <span class="keyword">friend</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">></span> <span class="special">&</span> 64 <a class="link" href="sobol_engine.html#id-1_3_34_5_6_39_1_1_1_7_4-bb"><span class="keyword">operator</span><span class="special">>></span></a><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">></span> <span class="special">&</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span><span class="special">)</span><span class="special">;</span> 65<span class="special">}</span><span class="special">;</span></pre></div> 66<div class="refsect1"> 67<a name="id-1.3.34.5.6.38.3.4"></a><h2>Description</h2> 68<p>Instantiations of class template <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> model a <a class="link" href="../../boost_random/reference.html#boost_random.reference.concepts.quasi_random_number_generator" title="Quasi-Random Number Generator">quasi-random number generator</a> . The <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> uses the algorithm described in </p> 69<div class="blockquote"><blockquote class="blockquote"><p> [Bratley+Fox, TOMS 14, 88 (1988)] and [Antonov+Saleev, USSR Comput. Maths. Math. Phys. 19, 252 (1980)] </p></blockquote></div> 70<p> </p> 71<div class="note"><table border="0" summary="Note"> 72<tr> 73<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../doc/src/images/note.png"></td> 74<th align="left">Note</th> 75</tr> 76<tr><td align="left" valign="top"> 77<p><a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> skips trivial zeroes at the start of the sequence. For example, the beginning of the 2-dimensional Sobol sequence in <code class="computeroutput"><a class="link" href="uniform_01.html" title="Class template uniform_01">uniform_01</a></code> distribution will look like this: </p> 78<pre class="programlisting"><span class="number">0</span><span class="special">.</span><span class="number">5</span><span class="special">,</span> <span class="number">0</span><span class="special">.</span><span class="number">5</span><span class="special">,</span> 79<span class="number">0</span><span class="special">.</span><span class="number">75</span><span class="special">,</span> <span class="number">0</span><span class="special">.</span><span class="number">25</span><span class="special">,</span> 80<span class="number">0</span><span class="special">.</span><span class="number">25</span><span class="special">,</span> <span class="number">0</span><span class="special">.</span><span class="number">75</span><span class="special">,</span> 81<span class="number">0</span><span class="special">.</span><span class="number">375</span><span class="special">,</span> <span class="number">0</span><span class="special">.</span><span class="number">375</span><span class="special">,</span> 82<span class="number">0</span><span class="special">.</span><span class="number">875</span><span class="special">,</span> <span class="number">0</span><span class="special">.</span><span class="number">875</span><span class="special">,</span> 83<span class="special">...</span> 84</pre> 85</td></tr> 86</table></div> 87<p> 88In the following documentation <code class="computeroutput">X</code> denotes the concrete class of the template <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> returning objects of type <code class="computeroutput">UIntType</code>, u and v are the values of <code class="computeroutput">X</code>.</p> 89<p>Some member functions may throw exceptions of type <code class="computeroutput">std::range_error</code>. This happens when the quasi-random domain is exhausted and the generator cannot produce any more values. The length of the low discrepancy sequence is given by <span class="inlinemediaobject"><img src="../../images/random//form_31.png"></span>. </p> 90<div class="refsect2"> 91<a name="id-1.3.34.5.6.38.3.4.5"></a><h3> 92<a name="boost.random.sobol_engineconstruct-copy-destruct"></a><code class="computeroutput">sobol_engine</code> 93 public 94 construct/copy/destruct</h3> 95<div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"> 96<pre class="literallayout"><span class="keyword">explicit</span> <a name="id-1_3_34_5_6_39_1_1_1_5-bb"></a><span class="identifier">sobol_engine</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> s<span class="special">)</span><span class="special">;</span></pre> 97<p>Effects: Constructs the default <code class="computeroutput">s</code>-dimensional Sobol quasi-random number generator.</p> 98<p>Throws: bad_alloc, invalid_argument, range_error. </p> 99</li></ol></div> 100</div> 101<div class="refsect2"> 102<a name="id-1.3.34.5.6.38.3.4.6"></a><h3> 103<a name="id-1_3_34_5_6_39_1_1_1_4-bb"></a><code class="computeroutput">sobol_engine</code> public member functions</h3> 104<div class="orderedlist"><ol class="orderedlist" type="1"> 105<li class="listitem"> 106<pre class="literallayout"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <a name="id-1_3_34_5_6_39_1_1_1_4_1-bb"></a><span class="identifier">dimension</span><span class="special">(</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre> 107<p>Returns: The dimension of of the quasi-random domain.</p> 108<p>Throws: nothing. </p> 109</li> 110<li class="listitem"> 111<pre class="literallayout"><span class="keyword">void</span> <a name="id-1_3_34_5_6_39_1_1_1_4_2-bb"></a><span class="identifier">seed</span><span class="special">(</span><span class="special">)</span><span class="special">;</span></pre>Throws: nothing. <p>Effects: Resets the quasi-random number generator state to the one given by the default construction. Equivalent to u.seed(0). </p> 112</li> 113<li class="listitem"> 114<pre class="literallayout"><span class="keyword">void</span> <a name="id-1_3_34_5_6_39_1_1_1_4_3-bb"></a><span class="identifier">seed</span><span class="special">(</span><span class="identifier">UIntType</span> init<span class="special">)</span><span class="special">;</span></pre>Throws: range_error. <p>Effects: Effectively sets the quasi-random number generator state to the <code class="computeroutput">init</code>-th vector in the <code class="computeroutput">s</code>-dimensional quasi-random domain, where <code class="computeroutput">s</code> == X::dimension(). </p> 115<pre class="programlisting"><span class="identifier">X</span> <span class="identifier">u</span><span class="special">,</span> <span class="identifier">v</span><span class="special">;</span> 116<span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">N</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> 117 <span class="keyword">for</span><span class="special">(</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">j</span> <span class="special"><</span> <span class="identifier">u</span><span class="special">.</span><span class="identifier">dimension</span><span class="special">(</span><span class="special">)</span><span class="special">;</span> <span class="special">++</span><span class="identifier">j</span> <span class="special">)</span> 118 <span class="identifier">u</span><span class="special">(</span><span class="special">)</span><span class="special">;</span> 119<span class="identifier">v</span><span class="special">.</span><span class="identifier">seed</span><span class="special">(</span><span class="identifier">N</span><span class="special">)</span><span class="special">;</span> 120<span class="identifier">assert</span><span class="special">(</span><span class="identifier">u</span><span class="special">(</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">v</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span> 121</pre> 122<p> </p> 123</li> 124<li class="listitem"> 125<pre class="literallayout"><span class="identifier">result_type</span> <a name="id-1_3_34_5_6_39_1_1_1_4_4-bb"></a><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span><span class="special">(</span><span class="special">)</span><span class="special">;</span></pre> 126<p>Returns: Returns a successive element of an <code class="computeroutput">s</code>-dimensional (s = X::dimension()) vector at each invocation. When all elements are exhausted, X::operator() begins anew with the starting element of a subsequent <code class="computeroutput">s</code>-dimensional vector.</p> 127<p>Throws: range_error. </p> 128</li> 129<li class="listitem"> 130<pre class="literallayout"><span class="keyword">void</span> <a name="id-1_3_34_5_6_39_1_1_1_4_5-bb"></a><span class="identifier">discard</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span> z<span class="special">)</span><span class="special">;</span></pre> 131<p>Effects: Advances *this state as if <code class="computeroutput">z</code> consecutive X::operator() invocations were executed. </p> 132<pre class="programlisting"><span class="identifier">X</span> <span class="identifier">u</span> <span class="special">=</span> <span class="identifier">v</span><span class="special">;</span> 133<span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">N</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> 134 <span class="identifier">u</span><span class="special">(</span><span class="special">)</span><span class="special">;</span> 135<span class="identifier">v</span><span class="special">.</span><span class="identifier">discard</span><span class="special">(</span><span class="identifier">N</span><span class="special">)</span><span class="special">;</span> 136<span class="identifier">assert</span><span class="special">(</span><span class="identifier">u</span><span class="special">(</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">v</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span> 137</pre> 138<p>Throws: range_error. </p> 139</li> 140</ol></div> 141</div> 142<div class="refsect2"> 143<a name="id-1.3.34.5.6.38.3.4.7"></a><h3> 144<a name="id-1_3_34_5_6_39_1_1_1_6-bb"></a><code class="computeroutput">sobol_engine</code> public static functions</h3> 145<div class="orderedlist"><ol class="orderedlist" type="1"> 146<li class="listitem"> 147<pre class="literallayout"><span class="keyword">static</span> <span class="keyword">constexpr</span> <span class="identifier">result_type</span> <a name="id-1_3_34_5_6_39_1_1_1_6_1-bb"></a><span class="identifier">min</span><span class="special">(</span><span class="special">)</span><span class="special">;</span></pre> 148<p>Returns: Tight lower bound on the set of values returned by operator().</p> 149<p>Throws: nothing. </p> 150</li> 151<li class="listitem"> 152<pre class="literallayout"><span class="keyword">static</span> <span class="keyword">constexpr</span> <span class="identifier">result_type</span> <a name="id-1_3_34_5_6_39_1_1_1_6_2-bb"></a><span class="identifier">max</span><span class="special">(</span><span class="special">)</span><span class="special">;</span></pre> 153<p>Returns: Tight upper bound on the set of values returned by operator().</p> 154<p>Throws: nothing. </p> 155</li> 156</ol></div> 157</div> 158<div class="refsect2"> 159<a name="id-1.3.34.5.6.38.3.4.8"></a><h3> 160<a name="id-1_3_34_5_6_39_1_1_1_7-bb"></a><code class="computeroutput">sobol_engine</code> friend functions</h3> 161<div class="orderedlist"><ol class="orderedlist" type="1"> 162<li class="listitem"> 163<pre class="literallayout"><span class="keyword">friend</span> <span class="keyword">bool</span> <a name="id-1_3_34_5_6_39_1_1_1_7_1-bb"></a><span class="keyword">operator</span><span class="special">==</span><span class="special">(</span><span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span> x<span class="special">,</span> <span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span> y<span class="special">)</span><span class="special">;</span></pre> 164<p>Returns true if the two generators will produce identical sequences of outputs. </p> 165</li> 166<li class="listitem"> 167<pre class="literallayout"><span class="keyword">friend</span> <span class="keyword">bool</span> <a name="id-1_3_34_5_6_39_1_1_1_7_2-bb"></a><span class="keyword">operator</span><span class="special">!=</span><span class="special">(</span><span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span> lhs<span class="special">,</span> <span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span> rhs<span class="special">)</span><span class="special">;</span></pre> 168<p>Returns true if the two generators will produce different sequences of outputs. </p> 169</li> 170<li class="listitem"> 171<pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> CharT<span class="special">,</span> <span class="keyword">typename</span> Traits<span class="special">></span> 172 <span class="keyword">friend</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">></span> <span class="special">&</span> 173 <a name="id-1_3_34_5_6_39_1_1_1_7_3-bb"></a><span class="keyword">operator</span><span class="special"><<</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">></span> <span class="special">&</span> os<span class="special">,</span> <span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span> s<span class="special">)</span><span class="special">;</span></pre> 174<p>Writes the textual representation of the generator to a <code class="computeroutput">std::ostream</code>. </p> 175</li> 176<li class="listitem"> 177<pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> CharT<span class="special">,</span> <span class="keyword">typename</span> Traits<span class="special">></span> 178 <span class="keyword">friend</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">></span> <span class="special">&</span> 179 <a name="id-1_3_34_5_6_39_1_1_1_7_4-bb"></a><span class="keyword">operator</span><span class="special">>></span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">></span> <span class="special">&</span> is<span class="special">,</span> <span class="keyword">const</span> <a class="link" href="sobol_engine.html" title="Class template sobol_engine">sobol_engine</a> <span class="special">&</span> s<span class="special">)</span><span class="special">;</span></pre> 180<p>Reads the textual representation of the generator from a <code class="computeroutput">std::istream</code>. </p> 181</li> 182</ol></div> 183</div> 184</div> 185</div> 186<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 187<td align="left"></td> 188<td align="right"><div class="copyright-footer">Copyright © 2000-2005 Jens Maurer<br>Copyright © 2009, 2010 Steven Watanabe<p> 189 Distributed under the Boost Software License, Version 1.0. (See accompanying 190 file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) 191 </p> 192</div></td> 193</tr></table> 194<hr> 195<div class="spirit-nav"> 196<a accesskey="p" href="knuth_b.html"><img src="../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../boost_random/reference.html#header.boost.random.sobol_hpp"><img src="../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="sobol.html"><img src="../../../../doc/src/images/next.png" alt="Next"></a> 197</div> 198</body> 199</html> 200
