libs/math/doc/html/math_toolkit/sf_beta/beta_derivative.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   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 2.11.0">
   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">&lt;</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">&gt;</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">&lt;</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">&gt;</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">&lt;</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&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</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&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</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&#160;20.&#160;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&#160;20.&#160;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 &#169; 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       R&#229;de, 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>