ceph/src/boost/libs/math/doc/html/math_toolkit/stat_tut/weg/nag_library.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   4 <title>Comparison with C, R, FORTRAN-style Free Functions</title>
   5 <link rel="stylesheet" href="../../../math.css" type="text/css">
   6 <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
   7 <link rel="home" href="../../../index.html" title="Math Toolkit 2.5.1">
   8 <link rel="up" href="../weg.html" title="Worked Examples">
   9 <link rel="prev" href="find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">
  10 <link rel="next" href="c_sharp.html" title="Using the Distributions from Within C#">
  11 </head>
  12 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
  13 <table cellpadding="2" width="100%"><tr>
  14 <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
  15 <td align="center"><a href="../../../../../../../index.html">Home</a></td>
  16 <td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
  17 <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
  18 <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
  19 <td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
  20 </tr></table>
  21 <hr>
  22 <div class="spirit-nav">
  23 <a accesskey="p" href="find_eg/find_mean_and_sd_eg.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../weg.html"><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="c_sharp.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
  24 </div>
  25 <div class="section">
  26 <div class="titlepage"><div><div><h4 class="title">
  27 <a name="math_toolkit.stat_tut.weg.nag_library"></a><a class="link" href="nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">Comparison with
  28         C, R, FORTRAN-style Free Functions</a>
  29 </h4></div></div></div>
  30 <p>
  31           You are probably familiar with a statistics library that has free functions,
  32           for example the classic <a href="http://nag.com/numeric/CL/CLdescription.asp" target="_top">NAG
  33           C library</a> and matching <a href="http://nag.com/numeric/FL/FLdescription.asp" target="_top">NAG
  34           FORTRAN Library</a>, <a href="http://office.microsoft.com/en-us/excel/HP052090051033.aspx" target="_top">Microsoft
  35           Excel BINOMDIST(number_s,trials,probability_s,cumulative)</a>, <a href="http://www.r-project.org/" target="_top">R</a>, <a href="http://www.ptc.com/products/mathcad/mathcad14/mathcad_func_chart.htm" target="_top">MathCAD
  36           pbinom</a> and many others.
  37         </p>
  38 <p>
  39           If so, you may find 'Distributions as Objects' unfamiliar, if not alien.
  40         </p>
  41 <p>
  42           However, <span class="bold"><strong>do not panic</strong></span>, both definition
  43           and usage are not really very different.
  44         </p>
  45 <p>
  46           A very simple example of generating the same values as the <a href="http://nag.com/numeric/CL/CLdescription.asp" target="_top">NAG
  47           C library</a> for the binomial distribution follows. (If you find slightly
  48           different values, the Boost C++ version, using double or better, is very
  49           likely to be the more accurate. Of course, accuracy is not usually a concern
  50           for most applications of this function).
  51         </p>
  52 <p>
  53           The <a href="http://www.nag.co.uk/numeric/cl/manual/pdf/G01/g01bjc.pdf" target="_top">NAG
  54           function specification</a> is
  55         </p>
  56 <pre class="programlisting"><span class="keyword">void</span> <span class="identifier">nag_binomial_dist</span><span class="special">(</span><span class="identifier">Integer</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">Integer</span> <span class="identifier">k</span><span class="special">,</span>
  57 <span class="keyword">double</span> <span class="special">*</span><span class="identifier">plek</span><span class="special">,</span> <span class="keyword">double</span> <span class="special">*</span><span class="identifier">pgtk</span><span class="special">,</span> <span class="keyword">double</span> <span class="special">*</span><span class="identifier">peqk</span><span class="special">,</span> <span class="identifier">NagError</span> <span class="special">*</span><span class="identifier">fail</span><span class="special">)</span>
  58 </pre>
  59 <p>
  60           and is called
  61         </p>
  62 <pre class="programlisting"><span class="identifier">g01bjc</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">k</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">plek</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">pgtk</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">peqk</span><span class="special">,</span> <span class="identifier">NAGERR_DEFAULT</span><span class="special">);</span>
  63 </pre>
  64 <p>
  65           The equivalent using this Boost C++ library is:
  66         </p>
  67 <pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>  <span class="comment">// Using declaration avoids very long names.</span>
  68 <span class="identifier">binomial</span> <span class="identifier">my_dist</span><span class="special">(</span><span class="number">4</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// c.f. NAG n = 4, p = 0.5</span>
  69 </pre>
  70 <p>
  71           and values can be output thus:
  72         </p>
  73 <pre class="programlisting"><span class="identifier">cout</span>
  74   <span class="special">&lt;&lt;</span> <span class="identifier">my_dist</span><span class="special">.</span><span class="identifier">trials</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" "</span>             <span class="comment">// Echo the NAG input n = 4 trials.</span>
  75   <span class="special">&lt;&lt;</span> <span class="identifier">my_dist</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" "</span>   <span class="comment">// Echo the NAG input p = 0.5</span>
  76   <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">"  "</span>             <span class="comment">// NAG plek with k = 2</span>
  77   <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="number">2</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="string">"  "</span> <span class="comment">// NAG pgtk with k = 2</span>
  78   <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>            <span class="comment">// NAG peqk with k = 2</span>
  79 </pre>
  80 <p>
  81           <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">k</span><span class="special">)</span></code> is
  82           equivalent to NAG library <code class="computeroutput"><span class="identifier">plek</span></code>,
  83           lower tail probability of &lt;= k
  84         </p>
  85 <p>
  86           <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">k</span><span class="special">))</span></code> is
  87           equivalent to NAG library <code class="computeroutput"><span class="identifier">pgtk</span></code>,
  88           upper tail probability of &gt; k
  89         </p>
  90 <p>
  91           <code class="computeroutput"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">k</span><span class="special">)</span></code> is
  92           equivalent to NAG library <code class="computeroutput"><span class="identifier">peqk</span></code>,
  93           point probability of == k
  94         </p>
  95 <p>
  96           See <a href="../../../../../example/binomial_example_nag.cpp" target="_top">binomial_example_nag.cpp</a>
  97           for details.
  98         </p>
  99 </div>
 100 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 101 <td align="left"></td>
 102 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 103       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 104       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 105       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 106         Distributed under the Boost Software License, Version 1.0. (See accompanying
 107         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>)
 108       </p>
 109 </div></td>
 110 </tr></table>
 111 <hr>
 112 <div class="spirit-nav">
 113 <a accesskey="p" href="find_eg/find_mean_and_sd_eg.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../weg.html"><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="c_sharp.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
 114 </div>
 115 </body>
 116 </html>