[DEV] add v1.66.0

This commit is contained in:
2018-01-12 21:47:58 +01:00
parent 87059bb1af
commit a97e9ae7d4
49032 changed files with 7668950 additions and 0 deletions

View File

@@ -0,0 +1,124 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Overvew of the Jacobi Elliptic Functions</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="next" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../jacobi.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_elliptic.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jac_over"></a><a class="link" href="jac_over.html" title="Overvew of the Jacobi Elliptic Functions">Overvew of the Jacobi Elliptic
Functions</a>
</h3></div></div></div>
<p>
There are twelve Jacobi Elliptic functions, of which the three copolar functions
<span class="emphasis"><em>sn</em></span>, <span class="emphasis"><em>cn</em></span> and <span class="emphasis"><em>dn</em></span>
are the most important as the other nine can be computed from these three
<a href="#ftn.math_toolkit.jacobi.jac_over.f0" class="footnote" name="math_toolkit.jacobi.jac_over.f0"><sup class="footnote">[2]</sup></a> <a href="#ftn.math_toolkit.jacobi.jac_over.f1" class="footnote" name="math_toolkit.jacobi.jac_over.f1"><sup class="footnote">[3]</sup></a> <a href="#ftn.math_toolkit.jacobi.jac_over.f2" class="footnote" name="math_toolkit.jacobi.jac_over.f2"><sup class="footnote">[4]</sup></a>.
</p>
<p>
These functions each take two arguments: a parameter, and a variable as described
below.
</p>
<p>
Like all elliptic functions these can be parameterised in a number of ways:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
In terms of a parameter <span class="emphasis"><em>m</em></span>.
</li>
<li class="listitem">
In terms of the elliptic modulus <span class="emphasis"><em>k</em></span> where <span class="emphasis"><em>m
= k<sup>2</sup></em></span>.
</li>
<li class="listitem">
In terms of the modular angle &#945;, where <span class="emphasis"><em>m = sin<sup>2</sup>&#945;</em></span>.
</li>
</ul></div>
<p>
In our implementation, these functions all take the elliptic modulus <span class="emphasis"><em>k</em></span>
as the parameter.
</p>
<p>
In addition the variable <span class="emphasis"><em>u</em></span> is sometimes expressed as
an amplitude &#966;, in our implementation we always use <span class="emphasis"><em>u</em></span>.
</p>
<p>
Finally note that our functions all take the elliptic modulus as the first
argument - this is for alignment with the Elliptic Integrals.
</p>
<p>
There are twenve functions for computing the twelve individual Jacobi elliptic
functions: <a class="link" href="jacobi_cd.html" title="Jacobi Elliptic Function cd">jacobi_cd</a>,
<a class="link" href="jacobi_cn.html" title="Jacobi Elliptic Function cn">jacobi_cn</a>, <a class="link" href="jacobi_cs.html" title="Jacobi Elliptic Function cs">jacobi_cs</a>,
<a class="link" href="jacobi_dc.html" title="Jacobi Elliptic Function dc">jacobi_dc</a>, <a class="link" href="jacobi_dn.html" title="Jacobi Elliptic Function dn">jacobi_dn</a>,
<a class="link" href="jacobi_ds.html" title="Jacobi Elliptic Function ds">jacobi_ds</a>, <a class="link" href="jacobi_nc.html" title="Jacobi Elliptic Function nc">jacobi_nc</a>,
<a class="link" href="jacobi_nd.html" title="Jacobi Elliptic Function nd">jacobi_nd</a>, <a class="link" href="jacobi_ns.html" title="Jacobi Elliptic Function ns">jacobi_ns</a>,
<a class="link" href="jacobi_sc.html" title="Jacobi Elliptic Function sc">jacobi_sc</a>, <a class="link" href="jacobi_sd.html" title="Jacobi Elliptic Function sd">jacobi_sd</a>
and <a class="link" href="jacobi_sn.html" title="Jacobi Elliptic Function sn">jacobi_sn</a>.
</p>
<p>
They are all called as for example:
</p>
<pre class="programlisting"><span class="identifier">jacobi_cs</span><span class="special">(</span><span class="identifier">k</span><span class="special">,</span> <span class="identifier">u</span><span class="special">);</span>
</pre>
<p>
Note however that these individual functions are all really thin wrappers
around the function <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>
which calculates the three copolar functions <span class="emphasis"><em>sn</em></span>, <span class="emphasis"><em>cn</em></span>
and <span class="emphasis"><em>dn</em></span> in a single function call. Thus if you need more
than one of these functions for a given set of arguments, it's most efficient
to use <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
</p>
<div class="footnotes">
<br><hr style="width:100; text-align:left;margin-left: 0">
<div id="ftn.math_toolkit.jacobi.jac_over.f0" class="footnote"><p><a href="#math_toolkit.jacobi.jac_over.f0" class="para"><sup class="para">[2] </sup></a>
<a href="http://en.wikipedia.org/wiki/Jacobi_elliptic_functions" target="_top">Wikipedia:
Jacobi elliptic functions</a>
</p></div>
<div id="ftn.math_toolkit.jacobi.jac_over.f1" class="footnote"><p><a href="#math_toolkit.jacobi.jac_over.f1" class="para"><sup class="para">[3] </sup></a>
<a href="http://mathworld.wolfram.com/JacobiEllipticFunctions.html" target="_top">Weisstein,
Eric W. "Jacobi Elliptic Functions." From MathWorld - A Wolfram
Web Resource.</a>
</p></div>
<div id="ftn.math_toolkit.jacobi.jac_over.f2" class="footnote"><p><a href="#math_toolkit.jacobi.jac_over.f2" class="para"><sup class="para">[4] </sup></a>
<a href="http://dlmf.nist.gov/22" target="_top">Digital Library of Mathematical Functions:
Jacobian Elliptic Functions</a>
</p></div>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../jacobi.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_elliptic.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,87 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function cd</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">
<link rel="next" href="jacobi_cn.html" title="Jacobi Elliptic Function cn">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_elliptic.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_cn.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_cd"></a><a class="link" href="jacobi_cd.html" title="Jacobi Elliptic Function cd">Jacobi Elliptic Function
cd</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_cd.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_cd.synopsis"></a></span><a class="link" href="jacobi_cd.html#math_toolkit.jacobi.jacobi_cd.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_cd</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_cd</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_cd.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_cd.description"></a></span><a class="link" href="jacobi_cd.html#math_toolkit.jacobi.jacobi_cd.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>cd</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>,
with:
</p>
<p>
<span class="emphasis"><em>cd(u, k) = cn(u, k) / dn(u, k)</em></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_cd.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_elliptic.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_cn.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,83 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function cn</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_cd.html" title="Jacobi Elliptic Function cd">
<link rel="next" href="jacobi_cs.html" title="Jacobi Elliptic Function cs">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_cd.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_cs.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_cn"></a><a class="link" href="jacobi_cn.html" title="Jacobi Elliptic Function cn">Jacobi Elliptic Function
cn</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_cn.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_cn.synopsis"></a></span><a class="link" href="jacobi_cn.html#math_toolkit.jacobi.jacobi_cn.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_cn</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_cn</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_cn.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_cn.description"></a></span><a class="link" href="jacobi_cn.html#math_toolkit.jacobi.jacobi_cn.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>cn</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_cn.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_cd.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_cs.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,87 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function cs</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_cn.html" title="Jacobi Elliptic Function cn">
<link rel="next" href="jacobi_dc.html" title="Jacobi Elliptic Function dc">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_cn.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_dc.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_cs"></a><a class="link" href="jacobi_cs.html" title="Jacobi Elliptic Function cs">Jacobi Elliptic Function
cs</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_cs.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_cs.synopsis"></a></span><a class="link" href="jacobi_cs.html#math_toolkit.jacobi.jacobi_cs.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_cs</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_cs</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_cs.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_cs.description"></a></span><a class="link" href="jacobi_cs.html#math_toolkit.jacobi.jacobi_cs.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>cs</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>,
with:
</p>
<p>
<span class="emphasis"><em>cs(u, k) = cn(u, k) / sn(u, k)</em></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_cs.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_cn.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_dc.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,87 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function dc</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_cs.html" title="Jacobi Elliptic Function cs">
<link rel="next" href="jacobi_dn.html" title="Jacobi Elliptic Function dn">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_cs.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_dn.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_dc"></a><a class="link" href="jacobi_dc.html" title="Jacobi Elliptic Function dc">Jacobi Elliptic Function
dc</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_dc.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_dc.synopsis"></a></span><a class="link" href="jacobi_dc.html#math_toolkit.jacobi.jacobi_dc.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_dc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_dc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_dc.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_dc.description"></a></span><a class="link" href="jacobi_dc.html#math_toolkit.jacobi.jacobi_dc.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>dc</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>,
with:
</p>
<p>
<span class="emphasis"><em>dc(u, k) = dn(u, k) / cn(u, k)</em></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_dc.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_cs.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_dn.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,83 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function dn</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_dc.html" title="Jacobi Elliptic Function dc">
<link rel="next" href="jacobi_ds.html" title="Jacobi Elliptic Function ds">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_dc.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_ds.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_dn"></a><a class="link" href="jacobi_dn.html" title="Jacobi Elliptic Function dn">Jacobi Elliptic Function
dn</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_dn.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_dn.synopsis"></a></span><a class="link" href="jacobi_dn.html#math_toolkit.jacobi.jacobi_dn.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_dn</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_dn</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_dn.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_dn.description"></a></span><a class="link" href="jacobi_dn.html#math_toolkit.jacobi.jacobi_dn.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>dn</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_dn.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_dc.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_ds.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,87 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function ds</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_dn.html" title="Jacobi Elliptic Function dn">
<link rel="next" href="jacobi_nc.html" title="Jacobi Elliptic Function nc">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_dn.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_nc.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_ds"></a><a class="link" href="jacobi_ds.html" title="Jacobi Elliptic Function ds">Jacobi Elliptic Function
ds</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_ds.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_ds.synopsis"></a></span><a class="link" href="jacobi_ds.html#math_toolkit.jacobi.jacobi_ds.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_ds</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_ds</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_ds.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_ds.description"></a></span><a class="link" href="jacobi_ds.html#math_toolkit.jacobi.jacobi_ds.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>ds</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>,
with:
</p>
<p>
<span class="emphasis"><em>ds(u, k) = dn(u, k) / sn(u, k)</em></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_ds.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_dn.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_nc.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,782 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic SN, CN and DN</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jac_over.html" title="Overvew of the Jacobi Elliptic Functions">
<link rel="next" href="jacobi_cd.html" title="Jacobi Elliptic Function cd">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jac_over.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_cd.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_elliptic"></a><a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">Jacobi Elliptic
SN, CN and DN</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_elliptic.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_elliptic.synopsis"></a></span><a class="link" href="jacobi_elliptic.html#math_toolkit.jacobi.jacobi_elliptic.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
<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">jacobi_elliptic</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="identifier">V</span><span class="special">*</span> <span class="identifier">pcn</span><span class="special">,</span> <span class="identifier">V</span><span class="special">*</span> <span class="identifier">pdn</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_elliptic</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="identifier">V</span><span class="special">*</span> <span class="identifier">pcn</span><span class="special">,</span> <span class="identifier">V</span><span class="special">*</span> <span class="identifier">pdn</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_elliptic.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_elliptic.description"></a></span><a class="link" href="jacobi_elliptic.html#math_toolkit.jacobi.jacobi_elliptic.description">Description</a>
</h5>
<p>
The function <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>
calculates the three copolar Jacobi elliptic functions <span class="emphasis"><em>sn(u, k)</em></span>,
<span class="emphasis"><em>cn(u, k)</em></span> and <span class="emphasis"><em>dn(u, k)</em></span>. The returned
value is <span class="emphasis"><em>sn(u, k)</em></span>, and if provided, <span class="emphasis"><em>*pcn</em></span>
is set to <span class="emphasis"><em>cn(u, k)</em></span>, and <span class="emphasis"><em>*pdn</em></span> is
set to <span class="emphasis"><em>dn(u, k)</em></span>.
</p>
<p>
The functions are defined as follows, given:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/jacobi1.svg"></span>
</p>
<p>
The the angle &#966; is called the <span class="emphasis"><em>amplitude</em></span> and:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/jacobi2.svg"></span>
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top">
<p>
<span class="emphasis"><em>&#966;</em></span> is called the amplitude.
</p>
<p>
<span class="emphasis"><em>k</em></span> is called the modulus.
</p>
</td></tr>
</table></div>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../doc/src/images/caution.png"></td>
<th align="left">Caution</th>
</tr>
<tr><td align="left" valign="top">
<p>
Rather like other elliptic functions, the Jacobi functions are expressed
in a variety of different ways. In particular, the parameter <span class="emphasis"><em>k</em></span>
(the modulus) may also be expressed using a modular angle &#945;, or a parameter
<span class="emphasis"><em>m</em></span>. These are related by:
</p>
<p>
k = sin&#945;
</p>
<p>
m = k<sup>2</sup> = sin<sup>2</sup>&#945;
</p>
<p>
So that the function <span class="emphasis"><em>sn</em></span> (for example) may be expressed
as either:
</p>
<p>
sn(u, k)
</p>
<p>
sn(u \ &#945;)
</p>
<p>
sn(u| m)
</p>
<p>
To further complicate matters, some texts refer to the <span class="emphasis"><em>complement
of the parameter m</em></span>, or 1 - m, where:
</p>
<p>
1 - m = 1 - k<sup>2</sup> = cos<sup>2</sup>&#945;
</p>
<p>
This implementation uses <span class="emphasis"><em>k</em></span> throughout, and makes this
the first argument to the functions: this is for alignment with the elliptic
integrals which match the requirements of the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical
Report on C++ Library Extensions</a>. However, you should be extra
careful when using these functions!
</p>
</td></tr>
</table></div>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
The following graphs illustrate how these functions change as <span class="emphasis"><em>k</em></span>
changes: for small <span class="emphasis"><em>k</em></span> these are sine waves, while as
<span class="emphasis"><em>k</em></span> tends to 1 they become hyperbolic functions:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_sn.svg" align="middle"></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_cn.svg" align="middle"></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_dn.svg" align="middle"></span>
</p>
<h5>
<a name="math_toolkit.jacobi.jacobi_elliptic.h2"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_elliptic.accuracy"></a></span><a class="link" href="jacobi_elliptic.html#math_toolkit.jacobi.jacobi_elliptic.accuracy">Accuracy</a>
</h5>
<p>
These functions are computed using only basic arithmetic operations and trigomometric
functions, so there isn't much variation in accuracy over differing platforms.
Typically errors are trivially small for small angles, and as is typical
for cyclic functions, grow as the angle increases. Note that only results
for the widest floating point type on the system are given as narrower types
have <a class="link" href="../relative_error.html#math_toolkit.relative_error.zero_error">effectively zero
error</a>. All values are relative errors in units of epsilon.
</p>
<div class="table">
<a name="math_toolkit.jacobi.jacobi_elliptic.table_jacobi_cn"></a><p class="title"><b>Table&#160;6.70.&#160;Error rates for jacobi_cn</b></p>
<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
<th>
<p>
GNU C++ version 5.1.0<br> linux<br> double
</p>
</th>
<th>
<p>
GNU C++ version 5.1.0<br> linux<br> long double
</p>
</th>
<th>
<p>
Sun compiler version 0x5130<br> Sun Solaris<br> long double
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
Jacobi Elliptic: Mathworld Data
</p>
</td>
<td>
<p>
<span class="blue">Max = 45.8&#949; (Mean = 11.4&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1.16:</em></span> Max = 17.3&#949; (Mean = 4.29&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
other failures.</a>)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 71.6&#949; (Mean = 19.3&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 71.6&#949; (Mean = 19.4&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Random Data
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.83&#949; (Mean = 0.455&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0.816&#949; (Mean = 0.0563&#949;)</span><br>
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.43&#949; (Mean = 0.803&#949;))<br>
(<span class="emphasis"><em>Cephes:</em></span> Max = 1.83&#949; (Mean = 0.437&#949;))
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.68&#949; (Mean = 0.443&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.68&#949; (Mean = 0.454&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Random Small Values
</p>
</td>
<td>
<p>
<span class="blue">Max = 26.2&#949; (Mean = 1.17&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1.16:</em></span> Max = 55.2&#949; (Mean = 1.64&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
other failures.</a>)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 10.4&#949; (Mean = 0.594&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 10.4&#949; (Mean = 0.602&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Modulus near 1
</p>
</td>
<td>
<p>
<span class="blue">Max = 513&#949; (Mean = 126&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0.919&#949; (Mean = 0.127&#949;)</span><br> <br>
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
other failures.</a>)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 675&#949; (Mean = 87.1&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 675&#949; (Mean = 86.8&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Large Phi
</p>
</td>
<td>
<p>
<span class="blue">Max = 3.27e+004&#949; (Mean = 1.93e+003&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 14.2&#949; (Mean = 0.927&#949;)</span><br> <br>
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 5.92e+03&#949; (Mean = 477&#949;))<br>
(<span class="emphasis"><em>Cephes:</em></span> Max = 3.27e+04&#949; (Mean = 1.93e+03&#949;))
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.jacobi.jacobi_elliptic.table_jacobi_dn"></a><p class="title"><b>Table&#160;6.71.&#160;Error rates for jacobi_dn</b></p>
<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
<th>
<p>
GNU C++ version 5.1.0<br> linux<br> double
</p>
</th>
<th>
<p>
GNU C++ version 5.1.0<br> linux<br> long double
</p>
</th>
<th>
<p>
Sun compiler version 0x5130<br> Sun Solaris<br> long double
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
Jacobi Elliptic: Mathworld Data
</p>
</td>
<td>
<p>
<span class="blue">Max = 34.3&#949; (Mean = 8.71&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1.16:</em></span> Max = 2.82&#949; (Mean = 1.18&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
other failures.</a>)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Random Data
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.52&#949; (Mean = 0.466&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1.16:</em></span> Max = 3&#949; (Mean = 0.61&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
Max = 1.49&#949; (Mean = 0.321&#949;))
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.53&#949; (Mean = 0.473&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.53&#949; (Mean = 0.481&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Random Small Values
</p>
</td>
<td>
<p>
<span class="blue">Max = 16.1&#949; (Mean = 0.685&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0.5&#949; (Mean = 0.0122&#949;)</span><br> <br>
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.5&#949; (Mean = 0.391&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
other failures.</a>)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 22.4&#949; (Mean = 0.777&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 22.4&#949; (Mean = 0.763&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Modulus near 1
</p>
</td>
<td>
<p>
<span class="blue">Max = 6.24e+003&#949; (Mean = 482&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.28&#949; (Mean = 0.194&#949;)</span><br> <br>
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
other failures.</a>)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Large Phi
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.67e+004&#949; (Mean = 1e+003&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 14.1&#949; (Mean = 0.897&#949;)</span><br> <br>
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 121&#949; (Mean = 22&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
Max = 196&#949; (Mean = 30.2&#949;))
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.jacobi.jacobi_elliptic.table_jacobi_sn"></a><p class="title"><b>Table&#160;6.72.&#160;Error rates for jacobi_sn</b></p>
<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
<p>
Microsoft Visual C++ version 12.0<br> Win32<br> double
</p>
</th>
<th>
<p>
GNU C++ version 5.1.0<br> linux<br> double
</p>
</th>
<th>
<p>
GNU C++ version 5.1.0<br> linux<br> long double
</p>
</th>
<th>
<p>
Sun compiler version 0x5130<br> Sun Solaris<br> long double
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
Jacobi Elliptic: Mathworld Data
</p>
</td>
<td>
<p>
<span class="blue">Max = 481&#949; (Mean = 113&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1.16:</em></span> Max = 588&#949; (Mean = 146&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
other failures.</a>)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Random Data
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.92&#949; (Mean = 0.567&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1.16:</em></span> Max = 4.02&#949; (Mean = 1.07&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
Max = 1.92&#949; (Mean = 0.567&#949;))
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.01&#949; (Mean = 0.584&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.01&#949; (Mean = 0.593&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Random Small Values
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.11&#949; (Mean = 0.385&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1.16:</em></span> Max = 11.7&#949; (Mean = 1.65&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
other failures.</a>)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Modulus near 1
</p>
</td>
<td>
<p>
<span class="blue">Max = 23.2&#949; (Mean = 1.85&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1.16:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="../logs_and_tables/logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
other failures.</a>)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 109&#949; (Mean = 7.35&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 109&#949; (Mean = 7.38&#949;)</span>
</p>
</td>
</tr>
<tr>
<td>
<p>
Jacobi Elliptic: Large Phi
</p>
</td>
<td>
<p>
<span class="blue">Max = 4.36e+004&#949; (Mean = 2.54e+003&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 12&#949; (Mean = 0.771&#949;)</span><br> <br>
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.54e+04&#949; (Mean = 2.63e+03&#949;))<br>
(<span class="emphasis"><em>Cephes:</em></span> Max = 4.36e+04&#949; (Mean = 2.54e+03&#949;))
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
</p>
</td>
<td>
<p>
<span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><h5>
<a name="math_toolkit.jacobi.jacobi_elliptic.h3"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_elliptic.testing"></a></span><a class="link" href="jacobi_elliptic.html#math_toolkit.jacobi.jacobi_elliptic.testing">Testing</a>
</h5>
<p>
The tests use a mixture of spot test values calculated using the online calculator
at <a href="http://functions.wolfram.com/" target="_top">functions.wolfram.com</a>,
and random test data generated using MPFR at 1000-bit precision and this
implementation.
</p>
<h5>
<a name="math_toolkit.jacobi.jacobi_elliptic.h4"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_elliptic.implementation"></a></span><a class="link" href="jacobi_elliptic.html#math_toolkit.jacobi.jacobi_elliptic.implementation">Implementation</a>
</h5>
<p>
For <span class="emphasis"><em>k &gt; 1</em></span> we apply the relations:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/jacobi3.svg"></span>
</p>
<p>
Then filter off the special cases:
</p>
<p>
<span class="emphasis"><em>sn(0, k) = 0</em></span> and <span class="emphasis"><em>cn(0, k) = dn(0, k) = 1</em></span>.
</p>
<p>
<span class="emphasis"><em>sn(u, 0) = sin(u), cn(u, 0) = cos(u) and dn(u, 0) = 1</em></span>.
</p>
<p>
<span class="emphasis"><em>sn(u, 1) = tanh(u), cn(u, 1) = dn(u, 1) = 1 / cosh(u)</em></span>.
</p>
<p>
And for <span class="emphasis"><em>k<sup>4</sup> &lt; &#949;</em></span> we have:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/jacobi4.svg"></span>
</p>
<p>
Otherwise the values are calculated using the method of <a href="http://dlmf.nist.gov/22.20#SS2" target="_top">arithmetic
geometric means</a>.
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jac_over.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_cd.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,87 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function nc</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_ds.html" title="Jacobi Elliptic Function ds">
<link rel="next" href="jacobi_nd.html" title="Jacobi Elliptic Function nd">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_ds.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_nd.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_nc"></a><a class="link" href="jacobi_nc.html" title="Jacobi Elliptic Function nc">Jacobi Elliptic Function
nc</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_nc.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_nc.synopsis"></a></span><a class="link" href="jacobi_nc.html#math_toolkit.jacobi.jacobi_nc.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_nc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_nc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_nc.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_nc.description"></a></span><a class="link" href="jacobi_nc.html#math_toolkit.jacobi.jacobi_nc.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>nc</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>,
with:
</p>
<p>
<span class="emphasis"><em>nc(u, k) = 1 / cn(u, k)</em></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_nc.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_ds.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_nd.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,87 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function nd</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_nc.html" title="Jacobi Elliptic Function nc">
<link rel="next" href="jacobi_ns.html" title="Jacobi Elliptic Function ns">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_nc.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_ns.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_nd"></a><a class="link" href="jacobi_nd.html" title="Jacobi Elliptic Function nd">Jacobi Elliptic Function
nd</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_nd.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_nd.synopsis"></a></span><a class="link" href="jacobi_nd.html#math_toolkit.jacobi.jacobi_nd.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_nd</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_nd</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_nd.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_nd.description"></a></span><a class="link" href="jacobi_nd.html#math_toolkit.jacobi.jacobi_nd.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>nd</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>,
with:
</p>
<p>
<span class="emphasis"><em>nd(u, k) = 1 / dn(u, k)</em></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_nd.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_nc.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_ns.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,87 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function ns</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_nd.html" title="Jacobi Elliptic Function nd">
<link rel="next" href="jacobi_sc.html" title="Jacobi Elliptic Function sc">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_nd.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_sc.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_ns"></a><a class="link" href="jacobi_ns.html" title="Jacobi Elliptic Function ns">Jacobi Elliptic Function
ns</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_ns.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_ns.synopsis"></a></span><a class="link" href="jacobi_ns.html#math_toolkit.jacobi.jacobi_ns.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_ns</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_ns</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_ns.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_ns.description"></a></span><a class="link" href="jacobi_ns.html#math_toolkit.jacobi.jacobi_ns.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>ns</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>,
with:
</p>
<p>
<span class="emphasis"><em>ns(u, k) = 1 / sn(u, k)</em></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_ns.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_nd.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_sc.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,87 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function sc</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_ns.html" title="Jacobi Elliptic Function ns">
<link rel="next" href="jacobi_sd.html" title="Jacobi Elliptic Function sd">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_ns.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_sd.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_sc"></a><a class="link" href="jacobi_sc.html" title="Jacobi Elliptic Function sc">Jacobi Elliptic Function
sc</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_sc.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_sc.synopsis"></a></span><a class="link" href="jacobi_sc.html#math_toolkit.jacobi.jacobi_sc.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_sc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_sc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_sc.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_sc.description"></a></span><a class="link" href="jacobi_sc.html#math_toolkit.jacobi.jacobi_sc.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>sc</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>,
with:
</p>
<p>
<span class="emphasis"><em>sc(u, k) = sn(u, k) / cn(u, k)</em></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_sc.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_ns.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_sd.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,87 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function sd</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_sc.html" title="Jacobi Elliptic Function sc">
<link rel="next" href="jacobi_sn.html" title="Jacobi Elliptic Function sn">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_sc.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_sn.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_sd"></a><a class="link" href="jacobi_sd.html" title="Jacobi Elliptic Function sd">Jacobi Elliptic Function
sd</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_sd.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_sd.synopsis"></a></span><a class="link" href="jacobi_sd.html#math_toolkit.jacobi.jacobi_sd.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_sd</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_sd</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_sd.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_sd.description"></a></span><a class="link" href="jacobi_sd.html#math_toolkit.jacobi.jacobi_sd.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>sd</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>,
with:
</p>
<p>
<span class="emphasis"><em>sd(u, k) = sn(u, k) / dn(u, k)</em></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_sd.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_sc.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="jacobi_sn.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -0,0 +1,83 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Jacobi Elliptic Function sn</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
<link rel="prev" href="jacobi_sd.html" title="Jacobi Elliptic Function sd">
<link rel="next" href="../zetas.html" title="Zeta Functions">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_sd.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="../zetas.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.jacobi.jacobi_sn"></a><a class="link" href="jacobi_sn.html" title="Jacobi Elliptic Function sn">Jacobi Elliptic Function
sn</a>
</h3></div></div></div>
<h5>
<a name="math_toolkit.jacobi.jacobi_sn.h0"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_sn.synopsis"></a></span><a class="link" href="jacobi_sn.html#math_toolkit.jacobi.jacobi_sn.synopsis">Synopsis</a>
</h5>
<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">jacobi_elliptic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<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>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
<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">jacobi_sn</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<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">jacobi_sn</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.jacobi.jacobi_sn.h1"></a>
<span class="phrase"><a name="math_toolkit.jacobi.jacobi_sn.description"></a></span><a class="link" href="jacobi_sn.html#math_toolkit.jacobi.jacobi_sn.description">Description</a>
</h5>
<p>
This function returns the Jacobi elliptic function <span class="emphasis"><em>sn</em></span>.
</p>
<p>
The final <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
be used to control the behaviour of the function: how it handles errors,
what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">policy
documentation for more details</a>.
</p>
<p>
This function is a trivial wrapper around <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
</p>
<p>
<span class="inlinemediaobject"><img src="../../../graphs/jacobi_sn.svg" align="middle"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="jacobi_sd.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi.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="../zetas.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>