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4 | <title>Derivative of the Incomplete Gamma Function</title> | |
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24 | </div> | |
25 | <div class="section"> | |
26 | <div class="titlepage"><div><div><h3 class="title"> | |
27 | <a name="math_toolkit.sf_gamma.gamma_derivatives"></a><a class="link" href="gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">Derivative of | |
28 | the Incomplete Gamma Function</a> | |
29 | </h3></div></div></div> | |
30 | <h5> | |
31 | <a name="math_toolkit.sf_gamma.gamma_derivatives.h0"></a> | |
32 | <span class="phrase"><a name="math_toolkit.sf_gamma.gamma_derivatives.synopsis"></a></span><a class="link" href="gamma_derivatives.html#math_toolkit.sf_gamma.gamma_derivatives.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">gamma</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> | |
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">gamma_p_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">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> <a class="link" href="../../policy.html" title="Chapter 15. 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">gamma_p_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">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 15. 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_gamma.gamma_derivatives.h1"></a> | |
48 | <span class="phrase"><a name="math_toolkit.sf_gamma.gamma_derivatives.description"></a></span><a class="link" href="gamma_derivatives.html#math_toolkit.sf_gamma.gamma_derivatives.description">Description</a> | |
49 | </h5> | |
50 | <p> | |
51 | This function find some uses in statistical distributions: it implements | |
52 | the partial derivative with respect to <span class="emphasis"><em>x</em></span> of the incomplete | |
53 | gamma function. | |
54 | </p> | |
55 | <p> | |
56 | <span class="inlinemediaobject"><img src="../../../equations/derivative1.svg"></span> | |
57 | </p> | |
58 | <p> | |
59 | The final <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can | |
60 | be used to control the behaviour of the function: how it handles errors, | |
61 | what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 15. Policies: Controlling Precision, Error Handling etc">policy | |
62 | documentation for more details</a>. | |
63 | </p> | |
64 | <p> | |
65 | Note that the derivative of the function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_q</a> | |
66 | can be obtained by negating the result of this function. | |
67 | </p> | |
68 | <p> | |
69 | 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 | |
70 | type calculation rules</em></span></a> when T1 and T2 are different types, | |
71 | otherwise the return type is simply T1. | |
72 | </p> | |
73 | <h5> | |
74 | <a name="math_toolkit.sf_gamma.gamma_derivatives.h2"></a> | |
75 | <span class="phrase"><a name="math_toolkit.sf_gamma.gamma_derivatives.accuracy"></a></span><a class="link" href="gamma_derivatives.html#math_toolkit.sf_gamma.gamma_derivatives.accuracy">Accuracy</a> | |
76 | </h5> | |
77 | <p> | |
78 | Almost identical to the incomplete gamma function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>: | |
79 | refer to the documentation for that function for more information. | |
80 | </p> | |
81 | <h5> | |
82 | <a name="math_toolkit.sf_gamma.gamma_derivatives.h3"></a> | |
83 | <span class="phrase"><a name="math_toolkit.sf_gamma.gamma_derivatives.implementation"></a></span><a class="link" href="gamma_derivatives.html#math_toolkit.sf_gamma.gamma_derivatives.implementation">Implementation</a> | |
84 | </h5> | |
85 | <p> | |
86 | This function just expose some of the internals of the incomplete gamma function | |
87 | <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>: refer to the | |
88 | documentation for that function for more information. | |
89 | </p> | |
90 | </div> | |
91 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
92 | <td align="left"></td> | |
93 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
94 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
95 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
96 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
97 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
98 | 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>) | |
99 | </p> | |
100 | </div></td> | |
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