Add ULPs plots to Jacobi Theta docs [CI SKIP]

Also add the built HTML files for easy evaluation. A full rebuild is needed for the new docs to appear in the indexes.
boostorg · NAThompson · Aug 15, 2020 · Jul 7, 2020 · Jul 7, 2020 · Jul 7, 2020
commit fb8d3f3527342fad3f6dfd336d5be8afb5ae48f9
diff --git a/doc/html/math_toolkit/jacobi_theta.html b/doc/html/math_toolkit/jacobi_theta.html
@@ -0,0 +1,45 @@
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+<title>Jacobi Theta Functions</title>
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+<a name="math_toolkit.jacobi_theta"></a><a class="link" href="jacobi_theta.html" title="Jacobi Theta Functions">Jacobi Theta Functions</a>
+</h2></div></div></div>
+
+
+
+
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+
+  </div>
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diff --git a/doc/html/math_toolkit/jacobi_theta/jacobi_theta1.html b/doc/html/math_toolkit/jacobi_theta/jacobi_theta1.html
@@ -0,0 +1,158 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+<title>Jacobi Theta Function θ1</title>
+<link rel="stylesheet" href="../../math.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.79.2">
+<link rel="home" href="../../index.html" title="Math Toolkit 2.12.0">
+<link rel="up" href="../jacobi_theta.html" title="Jacobi Theta Functions">
+<link rel="prev" href="jacobi_theta_overview.html" title="Overview of the Jacobi Theta Functions">
+<link rel="next" href="jacobi_theta2.html" title="Jacobi Theta Function θ2">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center"><a href="../../../../../../index.html">Home</a></td>
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+<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_theta_overview.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi_theta.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_theta2.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_theta.jacobi_theta1"></a><a class="link" href="jacobi_theta1.html" title="Jacobi Theta Function θ1">Jacobi Theta
+      Function θ<sub>1</sub></a>
+</h3></div></div></div>
+
+      <h5>
+<a name="math_toolkit.jacobi_theta.jacobi_theta1.h0"></a>
+        <span class="phrase"><a name="math_toolkit.jacobi_theta.jacobi_theta1.synopsis"></a></span><a class="link" href="jacobi_theta1.html#math_toolkit.jacobi_theta.jacobi_theta1.synopsis">Synopsis</a>
+      </h5>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">jacobi_theta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+    <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+    <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">jacobi_theta1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">q</span><span class="special">);</span>
+
+    <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+    <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">jacobi_theta1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+    <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+    <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">jacobi_theta1tau</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">tau</span><span class="special">);</span>
+
+    <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+    <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">jacobi_theta1tau</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">tau</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+<span class="special">}}</span> <span class="comment">// namespaces</span>
+</pre>
+      <h5>
+<a name="math_toolkit.jacobi_theta.jacobi_theta1.h1"></a>
+        <span class="phrase"><a name="math_toolkit.jacobi_theta.jacobi_theta1.description"></a></span><a class="link" href="jacobi_theta1.html#math_toolkit.jacobi_theta.jacobi_theta1.description">Description</a>
+      </h5>
+      <p>
+        The functions calculate the value of first <a class="link" href="jacobi_theta_overview.html" title="Overview of the Jacobi Theta Functions">Jacobi
+        Theta function</a>, parameterized either in terms of the nome <span class="emphasis"><em>q</em></span>:
+      </p>
+      <div class="blockquote"><blockquote class="blockquote">
+        <p>
+          <span class="inlinemediaobject"><img src="../../../equations/jacobi_theta1.svg"></span>
+
+        </p>
+      </blockquote></div>
+      <p>
+        Or in terms of an imaginary τ:
+      </p>
+      <div class="blockquote"><blockquote class="blockquote">
+        <p>
+          <span class="inlinemediaobject"><img src="../../../equations/jacobi_theta1tau.svg"></span>
+
+        </p>
+      </blockquote></div>
+      <p>
+        The nome <span class="emphasis"><em>q</em></span> is restricted to the domain (0, 1), returning
+        the result of <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
+        otherwise. The following graph shows the theta function at various values
+        of <span class="emphasis"><em>q</em></span>:
+      </p>
+      <div class="blockquote"><blockquote class="blockquote">
+        <p>
+          <span class="inlinemediaobject"><img src="../../../graphs/jacobi_theta1.svg" align="middle"></span>
+
+        </p>
+      </blockquote></div>
+      <p>
+        The final <a class="link" href="../../policy.html" title="Chapter 21. 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 21. Policies: Controlling Precision, Error Handling etc">policy
+        documentation for more details</a>.
+      </p>
+      <h5>
+<a name="math_toolkit.jacobi_theta.jacobi_theta1.h2"></a>
+        <span class="phrase"><a name="math_toolkit.jacobi_theta.jacobi_theta1.accuracy"></a></span><a class="link" href="jacobi_theta1.html#math_toolkit.jacobi_theta.jacobi_theta1.accuracy">Accuracy</a>
+      </h5>
+      <p>
+        The following <a class="link" href="../ulps_plots.html" title="ULPs Plots">ULPs plot</a> is
+        representative, fixing <span class="emphasis"><em>q</em></span>=0.5 and varying <span class="emphasis"><em>x</em></span>
+        from 0 to 2π:
+      </p>
+      <div class="blockquote"><blockquote class="blockquote">
+        <p>
+          <span class="inlinemediaobject"><img src="../../../graphs/jacobi_theta1_float.svg" align="middle"></span>
+
+        </p>
+      </blockquote></div>
+      <p>
+        The envelope represents the function's <a class="link" href="../cond.html" title="Condition Numbers">condition
+        number</a>. Note that relative accuracy degenerates periodically near
+        θ<sub>1</sub>=0.
+      </p>
+      <p>
+        Fixing <span class="emphasis"><em>x</em></span>=5 and varying <span class="emphasis"><em>q</em></span>, the ULPs
+        plot looks like:
+      </p>
+      <div class="blockquote"><blockquote class="blockquote">
+        <p>
+          <span class="inlinemediaobject"><img src="../../../graphs/jacobi_theta1q_float.svg" align="middle"></span>
+
+        </p>
+      </blockquote></div>
+      <p>
+        Accuracy tends to degenerate near <span class="emphasis"><em>q</em></span>=1 (small τ).
+      </p>
+      <h5>
+<a name="math_toolkit.jacobi_theta.jacobi_theta1.h3"></a>
+        <span class="phrase"><a name="math_toolkit.jacobi_theta.jacobi_theta1.implementation"></a></span><a class="link" href="jacobi_theta1.html#math_toolkit.jacobi_theta.jacobi_theta1.implementation">Implementation</a>
+      </h5>
+      <p>
+        The <span class="emphasis"><em>q</em></span> parameterization is implemented using the τ parameterization,
+        where τ=-log(<span class="emphasis"><em>q</em></span>)/π.
+      </p>
+      <p>
+        If τ is greater than or equal to 1, the summation above is used as-is. However
+        if τ &lt; 1, the following identity <a class="ulink" href="https://dlmf.nist.gov/20.7#viii" target="_top">DLMF
+        20.7.30</a> is used, defining τ'=-1/τ:
+      </p>
+      <div class="blockquote"><blockquote class="blockquote">
+        <p>
+          <span class="inlinemediaobject"><img src="../../../equations/jacobi_theta1_imaginary.svg"></span>
+
+        </p>
+      </blockquote></div>
+      <p>
+        This transformation of variables ensures that the function will always converge
+        in a small number of iterations.
+      </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"></div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="jacobi_theta_overview.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../jacobi_theta.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_theta2.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>