1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 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 V1.79.1"> 7<link rel="home" href="../../../index.html" title="Math Toolkit 2.12.0"> 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">&</span><span class="identifier">plek</span><span class="special">,</span> <span class="special">&</span><span class="identifier">pgtk</span><span class="special">,</span> <span class="special">&</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"><<</span> <span class="identifier">my_dist</span><span class="special">.</span><span class="identifier">trials</span><span class="special">()</span> <span class="special"><<</span> <span class="string">" "</span> <span class="comment">// Echo the NAG input n = 4 trials.</span> 75 <span class="special"><<</span> <span class="identifier">my_dist</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span> <span class="special"><<</span> <span class="string">" "</span> <span class="comment">// Echo the NAG input p = 0.5</span> 76 <span class="special"><<</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"><<</span> <span class="string">" "</span> <span class="comment">// NAG plek with k = 2</span> 77 <span class="special"><<</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"><<</span> <span class="string">" "</span> <span class="comment">// NAG pgtk with k = 2</span> 78 <span class="special"><<</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"><<</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 <= 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 > 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 © 2006-2019 Nikhar 103 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 104 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 105 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 106 Daryle Walker and Xiaogang Zhang<p> 107 Distributed under the Boost Software License, Version 1.0. (See accompanying 108 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>) 109 </p> 110</div></td> 111</tr></table> 112<hr> 113<div class="spirit-nav"> 114<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> 115</div> 116</body> 117</html> 118
