1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Derivative of the Incomplete Beta Function</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="../sf_beta.html" title="Beta Functions"> 9<link rel="prev" href="ibeta_inv_function.html" title="The Incomplete Beta Function Inverses"> 10<link rel="next" href="../sf_erf.html" title="Error Functions"> 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="ibeta_inv_function.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_beta.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="../sf_erf.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="math_toolkit.sf_beta.beta_derivative"></a><a class="link" href="beta_derivative.html" title="Derivative of the Incomplete Beta Function">Derivative of the 28 Incomplete Beta Function</a> 29</h3></div></div></div> 30<h5> 31<a name="math_toolkit.sf_beta.beta_derivative.h0"></a> 32 <span class="phrase"><a name="math_toolkit.sf_beta.beta_derivative.synopsis"></a></span><a class="link" href="beta_derivative.html#math_toolkit.sf_beta.beta_derivative.synopsis">Synopsis</a> 33 </h5> 34<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 35</pre> 36<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 37 38<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">></span> 39<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_derivative</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span> 40 41<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span> 42<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_derivative</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span> 43 44<span class="special">}}</span> <span class="comment">// namespaces</span> 45</pre> 46<h5> 47<a name="math_toolkit.sf_beta.beta_derivative.h1"></a> 48 <span class="phrase"><a name="math_toolkit.sf_beta.beta_derivative.description"></a></span><a class="link" href="beta_derivative.html#math_toolkit.sf_beta.beta_derivative.description">Description</a> 49 </h5> 50<p> 51 This function finds some uses in statistical distributions: it computes the 52 partial derivative with respect to <span class="emphasis"><em>x</em></span> of the incomplete 53 beta function <a class="link" href="ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>. 54 </p> 55<div class="blockquote"><blockquote class="blockquote"><p> 56 <span class="inlinemediaobject"><img src="../../../equations/derivative2.svg"></span> 57 58 </p></blockquote></div> 59<p> 60 The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result 61 type calculation rules</em></span></a> when T1, T2 and T3 are different 62 types. 63 </p> 64<p> 65 The final <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can 66 be used to control the behaviour of the function: how it handles errors, 67 what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">policy 68 documentation for more details</a>. 69 </p> 70<h5> 71<a name="math_toolkit.sf_beta.beta_derivative.h2"></a> 72 <span class="phrase"><a name="math_toolkit.sf_beta.beta_derivative.accuracy"></a></span><a class="link" href="beta_derivative.html#math_toolkit.sf_beta.beta_derivative.accuracy">Accuracy</a> 73 </h5> 74<p> 75 Almost identical to the incomplete beta function <a class="link" href="ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>. 76 </p> 77<h5> 78<a name="math_toolkit.sf_beta.beta_derivative.h3"></a> 79 <span class="phrase"><a name="math_toolkit.sf_beta.beta_derivative.implementation"></a></span><a class="link" href="beta_derivative.html#math_toolkit.sf_beta.beta_derivative.implementation">Implementation</a> 80 </h5> 81<p> 82 This function just expose some of the internals of the incomplete beta function 83 <a class="link" href="ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>: refer to 84 the documentation for that function for more information. 85 </p> 86</div> 87<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 88<td align="left"></td> 89<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 90 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 91 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 92 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 93 Daryle Walker and Xiaogang Zhang<p> 94 Distributed under the Boost Software License, Version 1.0. (See accompanying 95 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>) 96 </p> 97</div></td> 98</tr></table> 99<hr> 100<div class="spirit-nav"> 101<a accesskey="p" href="ibeta_inv_function.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_beta.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="../sf_erf.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 102</div> 103</body> 104</html> 105
