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<title>Overvew of the Jacobi Elliptic Functions</title>
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<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>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<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
|
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Functions</a>
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</h3></div></div></div>
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<p>
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There are twelve Jacobi Elliptic functions, of which the three copolar functions
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<span class="emphasis"><em>sn</em></span>, <span class="emphasis"><em>cn</em></span> and <span class="emphasis"><em>dn</em></span>
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are the most important as the other nine can be computed from these three
|
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<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>.
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</p>
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<p>
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These functions each take two arguments: a parameter, and a variable as described
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below.
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</p>
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<p>
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Like all elliptic functions these can be parameterised in a number of ways:
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</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem">
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In terms of a parameter <span class="emphasis"><em>m</em></span>.
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</li>
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<li class="listitem">
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In terms of the elliptic modulus <span class="emphasis"><em>k</em></span> where <span class="emphasis"><em>m
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= k<sup>2</sup></em></span>.
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</li>
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<li class="listitem">
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In terms of the modular angle α, where <span class="emphasis"><em>m = sin<sup>2</sup>α</em></span>.
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</li>
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</ul></div>
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<p>
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In our implementation, these functions all take the elliptic modulus <span class="emphasis"><em>k</em></span>
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as the parameter.
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</p>
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<p>
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In addition the variable <span class="emphasis"><em>u</em></span> is sometimes expressed as
|
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an amplitude φ, in our implementation we always use <span class="emphasis"><em>u</em></span>.
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</p>
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<p>
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Finally note that our functions all take the elliptic modulus as the first
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argument - this is for alignment with the Elliptic Integrals.
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</p>
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<p>
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There are twenve functions for computing the twelve individual Jacobi elliptic
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functions: <a class="link" href="jacobi_cd.html" title="Jacobi Elliptic Function cd">jacobi_cd</a>,
|
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<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>,
|
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<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>,
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<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>,
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<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>,
|
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<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>
|
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and <a class="link" href="jacobi_sn.html" title="Jacobi Elliptic Function sn">jacobi_sn</a>.
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</p>
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<p>
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They are all called as for example:
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</p>
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<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>
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</pre>
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<p>
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Note however that these individual functions are all really thin wrappers
|
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around the function <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>
|
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which calculates the three copolar functions <span class="emphasis"><em>sn</em></span>, <span class="emphasis"><em>cn</em></span>
|
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and <span class="emphasis"><em>dn</em></span> in a single function call. Thus if you need more
|
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than one of these functions for a given set of arguments, it's most efficient
|
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to use <a class="link" href="jacobi_elliptic.html" title="Jacobi Elliptic SN, CN and DN">jacobi_elliptic</a>.
|
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</p>
|
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<div class="footnotes">
|
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<br><hr style="width:100; text-align:left;margin-left: 0">
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<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>
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<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>
|
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<td align="left"></td>
|
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<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>)
|
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</p>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.jacobi.jacobi_cd"></a><a class="link" href="jacobi_cd.html" title="Jacobi Elliptic Function cd">Jacobi Elliptic Function
|
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cd</a>
|
||||
</h3></div></div></div>
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<h5>
|
||||
<a name="math_toolkit.jacobi.jacobi_cd.h0"></a>
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||||
<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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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>
|
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<td align="left"></td>
|
||||
<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>)
|
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</p>
|
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</div></td>
|
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|
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<div class="spirit-nav">
|
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</div>
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<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
|
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cn</a>
|
||||
</h3></div></div></div>
|
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<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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>
|
||||
@@ -0,0 +1,86 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
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|
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|
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
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|
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<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
|
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<link rel="prev" href="jacobi_cn.html" title="Jacobi Elliptic Function cn">
|
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|
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|
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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|
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|
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|
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|
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<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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>
|
||||
@@ -0,0 +1,86 @@
|
||||
<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 2.5.1">
|
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<link rel="up" href="../jacobi.html" title="Jacobi Elliptic Functions">
|
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|
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|
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|
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
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<table cellpadding="2" width="100%"><tr>
|
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|
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<td align="center"><a href="../../../../../../index.html">Home</a></td>
|
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<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
|
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<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
|
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<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
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<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
|
||||
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|
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|
||||
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|
||||
<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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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">
|
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<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>
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|
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|
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|
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@@ -0,0 +1,82 @@
|
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<html>
|
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<head>
|
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|
||||
<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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>
|
||||
@@ -0,0 +1,86 @@
|
||||
<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 2.5.1">
|
||||
<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">
|
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|
||||
<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>
|
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<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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>
|
||||
@@ -0,0 +1,781 @@
|
||||
<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 2.5.1">
|
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<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>
|
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<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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&);</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 φ 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>φ</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 α, or a parameter
|
||||
<span class="emphasis"><em>m</em></span>. These are related by:
|
||||
</p>
|
||||
<p>
|
||||
k = sinα
|
||||
</p>
|
||||
<p>
|
||||
m = k<sup>2</sup> = sin<sup>2</sup>α
|
||||
</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 \ α)
|
||||
</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>α
|
||||
</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 15. 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 15. 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 6.70. 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 = 45.8ε (Mean = 11.4ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
||||
1.16:</em></span> Max = 17.3ε (Mean = 4.29ε) <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 = +INFε (Mean = +INFε) <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 = 71.6ε (Mean = 19.3ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 71.6ε (Mean = 19.4ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Random Data
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 1.83ε (Mean = 0.455ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br>
|
||||
<br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.43ε (Mean = 0.803ε))<br>
|
||||
(<span class="emphasis"><em>Cephes:</em></span> Max = 1.83ε (Mean = 0.437ε))
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 1.68ε (Mean = 0.443ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 1.68ε (Mean = 0.454ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Random Small Values
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 26.2ε (Mean = 1.17ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
||||
1.16:</em></span> Max = 55.2ε (Mean = 1.64ε) <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 = +INFε (Mean = +INFε) <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 = 10.4ε (Mean = 0.594ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 10.4ε (Mean = 0.602ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Modulus near 1
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 513ε (Mean = 126ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br>
|
||||
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0ε (Mean = 0ε) <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 = +INFε (Mean = +INFε) <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 = 675ε (Mean = 87.1ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 675ε (Mean = 86.8ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Large Phi
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 3.27e+004ε (Mean = 1.93e+003ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br>
|
||||
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 5.92e+03ε (Mean = 477ε))<br>
|
||||
(<span class="emphasis"><em>Cephes:</em></span> Max = 3.27e+04ε (Mean = 1.93e+03ε))
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</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 6.71. 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 = 34.3ε (Mean = 8.71ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
||||
1.16:</em></span> Max = 2.82ε (Mean = 1.18ε) <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 = +INFε (Mean = +INFε) <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 = 49ε (Mean = 14ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 49ε (Mean = 14ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Random Data
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 1.52ε (Mean = 0.466ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
||||
1.16:</em></span> Max = 3ε (Mean = 0.61ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
||||
Max = 1.49ε (Mean = 0.321ε))
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 1.53ε (Mean = 0.473ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 1.53ε (Mean = 0.481ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Random Small Values
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 16.1ε (Mean = 0.685ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br>
|
||||
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.5ε (Mean = 0.391ε) <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 = +INFε (Mean = +INFε) <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 = 22.4ε (Mean = 0.777ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 22.4ε (Mean = 0.763ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Modulus near 1
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 6.24e+003ε (Mean = 482ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br>
|
||||
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0ε (Mean = 0ε) <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 = +INFε (Mean = +INFε) <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+03ε (Mean = 293ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Large Phi
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 1.67e+004ε (Mean = 1e+003ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br>
|
||||
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 121ε (Mean = 22ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
||||
Max = 196ε (Mean = 30.2ε))
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</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 6.72. 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 = 481ε (Mean = 113ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
||||
1.16:</em></span> Max = 588ε (Mean = 146ε) <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 = +INFε (Mean = +INFε) <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 = 341ε (Mean = 80.7ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 341ε (Mean = 80.7ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Random Data
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 1.92ε (Mean = 0.567ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
||||
1.16:</em></span> Max = 4.02ε (Mean = 1.07ε))<br> (<span class="emphasis"><em>Cephes:</em></span>
|
||||
Max = 1.92ε (Mean = 0.567ε))
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 2.01ε (Mean = 0.584ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 2.01ε (Mean = 0.593ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Random Small Values
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 2.11ε (Mean = 0.385ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
||||
1.16:</em></span> Max = 11.7ε (Mean = 1.65ε) <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 = +INFε (Mean = +INFε) <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 = 1.99ε (Mean = 0.347ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Modulus near 1
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 23.2ε (Mean = 1.85ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
|
||||
1.16:</em></span> Max = 0ε (Mean = 0ε) <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 = +INFε (Mean = +INFε) <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 = 109ε (Mean = 7.35ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 109ε (Mean = 7.38ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Jacobi Elliptic: Large Phi
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 4.36e+004ε (Mean = 2.54e+003ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br>
|
||||
(<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε))<br>
|
||||
(<span class="emphasis"><em>Cephes:</em></span> Max = 4.36e+04ε (Mean = 2.54e+03ε))
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</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 > 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> < ε</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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>
|
||||
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|
||||
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|
||||
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|
||||
@@ -0,0 +1,86 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
||||
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|
||||
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|
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<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>
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||||
</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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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">
|
||||
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nd</a>
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</h3></div></div></div>
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<h5>
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<a name="math_toolkit.jacobi.jacobi_nd.h0"></a>
|
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<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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>
|
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<div class="spirit-nav">
|
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|
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|
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@@ -0,0 +1,86 @@
|
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<html>
|
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<head>
|
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|
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<div class="section">
|
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<div class="titlepage"><div><div><h3 class="title">
|
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<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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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">
|
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<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>
|
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|
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|
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</html>
|
||||
@@ -0,0 +1,86 @@
|
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<html>
|
||||
<head>
|
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<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>
|
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</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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>
|
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<div class="spirit-nav">
|
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>
|
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|
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|
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</html>
|
||||
@@ -0,0 +1,82 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
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|
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|
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
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|
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|
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|
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|
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|
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|
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<table cellpadding="2" width="100%"><tr>
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<td align="center"><a href="../../../../../../index.html">Home</a></td>
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|
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|
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|
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|
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<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>
|
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</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"><</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">></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"><</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>
|
||||
<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"><</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">></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">&</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 15. 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 15. 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
|
||||
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
|
||||
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
|
||||
Benjamin Sobotta, 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>
|
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<div class="spirit-nav">
|
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<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>
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Block a user